CLASS XII SUBJECT- ENGLISH CORE WORK SHEET 1 ADVANCED...

1

CLASS XII

SUBJECT- ENGLISH CORE

WORK SHEET 1 ADVANCED WRITING SKILLS

LETTER WRITING

1 Write a letter to the Municipal Chairman of New Town North Arcot District about the

dilapidated condition of a public monument requesting him to take urgent steps for the

preservation of this valuable heritage Your are ANarkaliAkbar 10 Pudupet New Town

2 You are RohitYashmin a resident of 10 Civil lines Saharanpur During your college life

you participated in various curricular and co-curricular activities with meritorious

performance Write a letter to the Principal of your college ie Gurunanak College

Ambala requesting him to issue you a testimonial including the details of your

performance

3 As Cultural Secretary of GDBirla School Jamshedpur you are organizing an inter school

poster making competition in connection with the Diamond Jubilee Celebration of your

school Draft a circular letter to be sent to various schools in your city requesting their

participation Invent details

4 Write a letter to the Dean DPI School of Management Mumbai requesting him to apprise

you of the details such as eligibility criteria fees hostel facitlity prospects of placement

etc for admission to PGDiploma in HRM You are RamRomala of 21 Civil Lines

Bareily

2

SPEECH WRITING

PRACTICE QUESTIONS

1 You are RamRama Head BoyGirl of ABC School Write a speech in 150-200 words

that you would deliver in the prayer assembly on the need for students to inculcate in

themselves virtues like truthfulness punctuality etc so that they may not only succeed in

their own life but also prove role models for others

2 You are RajRani the Head BodyHead Girls of ABC Public School Patna You have to

deliver a speech in your school assembly on the lsquoWorld Peace Dayrsquo on the topic lsquoLetrsquos

Practise Non-Violencersquo Write the speech in 150-200 words pointing out the recent acts of

terrorism that claimed innocent lives and highlighting the value of non-violence which is

the need of the hour

3 Regular practice of yoga can help in maintaining good health and even in the prevention

of so many ailments Write a speech in 150-200 words to be delivered in the morning

assembly on the usefulness of yoga

ARTICLE WRITING

1ldquoWhat people read is what people believerdquo You are concerned about the ongoing controversy

regarding mediarsquos role in sensationalizing news moulding public opinion and moral policing

Write an article emphasizing the responsibility of media You are Nayna BatraNaresh Sharma

(word limit 150-200)

2The number of women in police force seems insufficient specially when we see the increasing

involvement of women in terrorist activities Write an article in 150-200 words for lsquoHindustan

Timesrsquo on need of having more women in the police force

3Every activity that man indulges in creates waste of some kind Some of the waste can be

recycled or reused In fact the need of the hour is to conserve the earthrsquos resources in all possible

ways Write an article on the topic ldquoConservation Need of the Hourrdquo in 150-200 words You are

KamalKamla a keen environmentalist

4Today the 24 hour television news channels give us instant news from every nook and corner

of the world But the fact remains that the importance of the newspaper remains intact Write an

3

article in 150-200 words expressing your view on lsquoThe Relevance of Newspapersrsquo You are

SunilSunita

DEBATE WRITING

PRACTICE QUESTIONS

1 You are required to speak in favour of the topic ldquoStudents should be allowed to use cell

phones in schoolsrdquo for the Inter Class Debate Competition Draft the debate in about 120

words

2 Draft a debate against the topic ldquoGadgets make people dependent and lazy You are Saumya

Head Girl of DPS Meerut The debate should be about 120 words

3 Your school is organizing an Inter School Debate on the topic ldquoCricket should be our

National Sportsrdquo Draft a debate either for or against the motion in about 120 words

4 You have to participate in a debate on the motion ldquoGandhian Philosophy is irrelevant

in todayrsquos worldrdquo Draft the debate either in favour of or against the motion in not more than

120 words

4

FLAMINGO WORK SHEET ndash(I)

POEM 1 lsquoMY MOTHER AT 66rsquo

1Read the extract and answer the questions that follow

------------- She

Looked but soon

Put that thought awayand

Looked out at young

Trees sprinting the merry children spilling

Out of their homes

Questions ndash

a) What did the poet realize How did she feel

b) What did she do then

c) What did she notice in the world outside

d) Find the words from the passage which mean the following

1) Running fast 2)happy 3) moving out

2 Driving from my parentrsquos

home to Cochin last Friday

morning I saw my mother

beside me

doze open mouthed her face

ashen like that

of a corpse and realized with pain

that she was as old as she looked but soon

put that thought away

Questions ndash

a)Where was the poet driving to Who sitting beside her

5

b)What did the poet notice about her mother

c)Why her motherrsquos face looked like that of a corpse


1sleep slightly 2deadbody 3 felt

3What was the poetrsquos childhood fear

4What is the poetrsquos familiar ache and why does it return

5How does the poet try to put away the thoughts of her ageing mother

6 Why does the poet smile and what does she say while bidding good bye to her mother

7 Mention the comparisons and the contrast used in the poem

AN ELEMENTARY SCHOOL CLASSROOM IN A SLUM

1 What does the poet wish for the children of the slums

2 Why is Shakespeare ldquowickedrdquo and map ldquoa bad examplerdquo

1 Why are the children referred as ldquorootless weedsrdquo

2 lsquoThe children of slum are destined to a life trapped in ldquonarrow streetrdquo and ldquosealed with lead

skyrdquo Comment

3 The slum children seem to be resigned to their fate What are the examples in the poem that

suggest this

4 Extract from the poem

a)ldquoFar far from gusty waves these childrenrsquos faces

Like rootless weeds their hair torn round their pallor

The tall girl with her weighed- down head The paper-

Seeming boy with ratrsquos eyesrdquo

Answer the questions that follow-

aName the poem and the poet (1)

b What is peculiar about the faces of these children(1)

c Explain lsquo like rootless weedsrsquo(1)

d What is the poetic device used in the expression lsquothe paper seeming boy with ratrsquos

eyesrsquo(1)

b)rdquoOn sour cream walls donations Shakespearersquos head

Cloudless at dawn civilized dome riding all cities

Belled flowery Tyrolese valley Open ndashhanded map

Awarding the world its world And yet for these

Children these windows not this map their worldrdquo

6


a How do the ldquo sour cream wallsrdquo reflect the mood of the classroom(1)

b The images on the wall are antithetical to the life of the slum dwellersExplain(1)

c Why is the world of these children like a window(1)

d What does ldquoShakespearersquos headrdquo symbolize

7

कारय परपतर ndash 1 (सतर 2018-19)

ककषा ndash 12 (ह िदी)

आरो - पदय खिड ndash 1 ररविशरार बचचन

(1 आतमपररचर 2 ददन जलदी-जलदी ढलता )

परशन ndash 1 lsquoननज उर क उदगार व उप ारrsquo स कनव का करा तातपरय

परशन ndash 2 कनव जग का धरान करो न ी करता

परशन ndash 3 कनव सिसार को अपरय करो क ता

परशन ndash 4 कनव सन -सरा का पान कस करता

परशन ndash 5 थका हआ पिथी दकस कारर जलदी-जलदी चलता

परशन ndash 6 lsquoबचच परतराशा म ोग नीड़ो स झािक र ोगrsquo स करा आशर

परशन ndash 7 lsquoददन जलदी-जलदी ढलता rsquo म परम की अनिवयनि हई नसदध कीनजए

परशन ndash 8 lsquoआतमपररचरrsquo कनवता क कनव की सिसार क बार म करा रार समझाइए

परशन ndash 9 lsquo ररविशरार बचचनrsquo की कनवता का नशलप सौनदरय नलनखए

रचनातमक लखन

परशन ndash 10 श रो का दमघोटि वातावरर पर एक आलख नलनखए

8



पदय खिड ndash 2 आलोक धनवा (पतिग)

परशन ndash 1 शरद ऋत म वातावरर कसा ो जाता

परशन ndash 2 पथवी बचचो क बचन परो क पास दकस परकार घमती हई आती

परशन ndash 3 कौन जो पतिगो क स ार उड़ र और कस उड़ र

परशन ndash 4 छतो क खतरनाक दकनारो स बचच कस बच जात

परशन ndash 5 पतिग क बार म कनव न करा क ा

परशन ndash 6 नततनलरो की नाजक दननरा स करा आशर

परशन ndash 7 नगरकर बचन पर बचचो पर करा परिाव पड़ता

परशन ndash 8 lsquoपतिगrsquo कनवता का कावय सौनदरय नवसतार स नलनखए


परशन ndash 9 lsquoइककीसवी सदी म िारत क समकष चनौनतरोrsquo पर एक आलख नलनखए

परशन ndash 10 माननसक तनावो स नघरा रवावगय नवषर पर एक ननबिध नलनखए

9



पदय खिड ndash 3 कि वर नारारर (1 कनवता क ब ान 2 बात सीधी थी पर)

परशन ndash 1 lsquoनचनड़रा कनवता की उड़ान करा जानrsquo क माधरम स कनव करा क ना चा ता

परशन ndash 2 नबना मरझाए म कन क मान ndash का िाव सपषट कीनजए

परशन ndash 3 lsquoकनवता क ब ान कनवताrsquo का परनतपादयकथर अपन शबदो म नलनखए

परशन ndash 4 lsquoजोर जबरदसती स बात की चड़ी मर गईrsquo का िाव सपषट कीनजए

परशन ndash 5 िाषा को सहनलरत स बरतन स करा आशर

परशन ndash 6 lsquoबात सीधी थी परrsquo कनवता का कावय सौदरय नलनखए

परशन ndash 7 बात को कील की तर ठोकन का करा आशर

परशन ndash 8 कनवता रचन और फल नखलन म करा समानता


परशन ndash 9 lsquoपरीकषा की तरारीrsquo नवषर पर एक आलख नलनखए

परशन ndash 10 lsquoधमयननरपकषता और िारतrsquo नवषर पर एक ननबिध नलनखए

10



गदय खिड ndash 11 िनिन (म ादवी वमाय)

परशन ndash 1 िनिन रसोई म घसन स प ल कौन-स कमय दकरा करती थी

परशन ndash 2 िनिन नचतरकारी म म ादवी की दकस परकार स ारता करती थी

परशन ndash 3 रदध क ददनो म िनिन न अपन गााव जाना सवीकार करो न ी दकरा

परशन ndash 4 िनिन कारागार स करो डरती

परशन ndash 5 lsquoिनिन सचची सवानम-िनिन rsquo नसदध कीनजए

परशन ndash 6 िारतीर गरामीर समाज लड़क-लडदकरो म दकर जान वाल िद-िाव का उललख

िनिन पाठ क आधार पर कीनजए

परशन ndash 7 िनिन का दिायगर दकसस अनधक ठी था और करो

परशन ndash 8 िनिन अपना वासतनवक नाम लोगो स करो छपाती थी िनिन को र नाम दकसन

और करो ददरा ोगा


परशन ndash 9 lsquoवजञाननक परगनत और मानव जीवनrsquo नवषर पर एक ननबिध नलनखए

परशन ndash 10 lsquoखानndashपान और र नndashस न की बदलती शलीrsquo पर एक आलख नलनखए

11



गदय खिड ndash 12 बाज़ार दशयन (जननर कमार)

परशन ndash 1 पस को पावर क न का करा आशर

परशन ndash 2 बाज़ार का चौक दकनको कामना स नवकल बना दता

परशन ndash 3 बाज़ार क जाद को lsquoरप का जादrsquo करो क ा गरा

परशन ndash 4 मन खाली ोन और बिद ोन का अितर सपषट कीनजए

परशन ndash 5 िगत जी को ऐसा करा परापत जो बड़-बड़ नवदवानो को परापत न ी

परशन ndash 6 lsquoबाजारपनrsquo स करा तातपरय दकस परकार क वयनि बाज़ार को साथयकता परदान

करत अथवा बाज़ार की साथयकता दकसम

परशन ndash 7 लखक न दकस बाज़ार को मानवता क नलए नवडिबना क ा और करो

परशन ndash 8 सिी पर बाज़ार का जाद करो न ी चल सकता िगत जी का उदा रर दकर इस

कथन की पनषट कीनजए


परशन ndash 9 lsquoलोकतितर म मीनडरा का दानरतवrsquo नवषर पर एक ननबिध नलनखए

परशन ndash 10 lsquoदकसानो की आतम तरा की परवनतrsquo नवषर पर एक आलख नलनखए

12



नवतान ndash 1 नसलवर वहडिग (मनो र शराम जोशी)

परशन ndash 1 रशोधर दकशनदा क मानस पतर - नसदध कीनजए

परशन ndash 2 रशोधर की पतनी अपन पनत स करो नाराज़ र ती

परशन ndash 3 करा रशोधर बाब परातनपिथी चररतर - सतकय उततर दीनजए

परशन ndash 4 lsquoनसलवर वहडिगrsquo क कथानारक रशोधर बाब एक आदशय वयनितव और नई पीढ़ी दवारा

उनक नवचारो को अपनाना ी उनचत ndash इस कथन क पकष रा नवपकष म तकय दीनजए

परशन ndash 5 करा पीढ़ी क अनतराल को lsquoनसलवर वहडिगrsquo क ानी की मल सिवदना क ा जा सकता

तकय सन त उततर दीनजए

परशन ndash 6 दकशनदा न रशोधर बाब को न कवल स ारा ददरा अनपत जीन का ढिग िी

नसखारा- कस

परशन ndash 7 रशोधर बाब सरल और सादगीपरय जीवन क समथयक - नसदध कीनजए

परशन ndash 8 lsquoनसलवर वहडिगrsquo पाठ क रशोधर बाब समर क साथ ढल सकन म असफल र त

ऐसा करो


परशन ndash 9 lsquoनडगरी परापत रवावगय और बरोजगारीrsquo अथवा lsquoराषटरमिडल खल ndash 2018 म िारतrsquo नवषर

पर एक ननबिध नलनखए

परशन ndash 10 lsquoिारत सरकार क समाटय नसटी परोजकटrsquo नवषर पर एक आलख नलनखए

13



नवतान ndash 2 जझ (आनिद रादव)

परशन ndash 1 पाठशाला पहिचकर लखक को दकन परशाननरो का सामना करना पड़ा

परशन ndash 2 कनवता क परनत लगाव स प ल और उसक बाद अकलपन क परनत लखक की धाररा म

करा बदलाव आरा

परशन ndash 3 सवरि कनवता कर लन का आतमनवशवास लखक म कस पदा हआ

परशन ndash 4 जझ आतमकथातमक उपनरास क मखर पातर क सविाव की चार नवशषताओ का

उललख कीनजए

परशन ndash 5 लखक की माा क बार म पाठ क अनसार रटपपरी कीनजए

परशन ndash 6 lsquoलखक परनतिाशाली और बनदधमान बालक rsquo- नसदध कीनजए

परशन ndash 7 मितरी नामक अधरापक की नवशषता बतात हए दक उन ोन लखक को दकस परकार बढ़ावा

ददरा

परशन ndash 8 वसित पाटील कौन था उसकी लखक स दोसती करो और कस बनी


परशन ndash 9 lsquoसफलता का दसरा नाम पररशरमrsquo नवषर पर एक ननबिध नलनखए

परशन ndash 10 lsquoसािपरदानरक सदभावनाrsquo नवषर पर एक आलख नलनखए

14



जनसिचार की नवधाओ आधाररत परशनोततर

परशन ndash 1 lsquoहपरिट मीनडराrsquo दकस क त

परशन ndash 2 पतरकाररता स आप करा समझत

परशन ndash 3 जनसिचार सवा आप करा समझत

परशन ndash 4 नडकोहडिग स आप करा समझत

परशन ndash 5 आज़ादी क दौरान और बाद म पतरकाररता का लकषर करा र ा

परशन ndash 6 सतिि-लखन स करा तातपरय

परशन ndash 7 समाचार लखन म छः ककारो स करा अनिपरार

परशन ndash 8 उलटा नपरानमड शली करा ोती समझाइए

परशन ndash 9 lsquoएिकर बाइटrsquo स करा अनिपरार

परशन ndash 10 इनटरनट पतरकाररता स करा आशर

परशन ndash 11 समपादकीर लखन करा ोता

परशन ndash 12 फोन-इन स करा आशर

परशन ndash 13 lsquoफ़लशrsquo रा lsquoबरककि ग नरज़rsquo स करा आशर

परशन ndash 14 lsquoडडलाइनrsquo स करा अनिपरार

परशन ndash 15 lsquoसमपादकीरrsquo क साथ सिपादक-लखक का नाम करो न ी ददरा जाता

15

WORK SHEET ON CONTINUITY ampDIFFERENTIABILITY

CLASS XII

VERY SHORT ANSWER SHORT ANSWER TYPE

1 Examine the continuity of the function 119891(119909) = 1199092 + 5 at 119909 = minus1

2 Give an example of a function which is continuous at x= 1 but not differentiable at x=1

3 Show that the function f given by f(x)=1199093 + 3 119894119891 119909 ne 0

1 119894119891 119909 = 0 is continuous at x=0

4 For what value of k is the function defined by

119891(119909) = sin 119909+119909 cos 119909

119909

119896 119894119891 119909 = 0 119894119891 119909 ne 0continuous at x=0

5 If y = 119890119909 + 119890minus119909 prove that y ldquo

LONG ANSWER TYPE

6 For what value of k is the function 119890119909+119890minus119909minus2

1199092

4119896 119894119891 119909 = 0 119894119891 119909 ne 0 is continuous at x = 0

7 Examine the differentiability of the function 119909[119909] 119894119891 0 le 119909 lt 2

(119909 minus 1)119909 119894119891 2 le 119909 lt 3 at x=2

8 Differentiate tanminus1 (119886 cos 119909minus119887 sin 119909

119887 cos 119909+119886 sin 119909)minus

120587

2 lt 119909 lt

120587

2 and

119886

119887tan 119909 gt minus1 wrto x

9 If x16y9= (x2+ y)17 prove that 119889119910

119889119909=

2119910

119909

10 Differentiate y = (119909 +1

119909)

119909

+ 119909(119909+1

119909) with respect to x

11 Find 119889119910

119889119909 if y =

1199094radic119909+6

(3119909+5)2

12 If y= 31198902119909 + 21198903119909 prove that 1198892119910

1198891199092 - 5

119889119910

119889119909 +6y = 0

13 If y= sinminus1 119909

radic1minus1199092 show that (1 minus 1199092)

1198892119910

1198891199092 minus 3119909119889119910

119889119909minus 119910 = 0

14 Verify the Rollersquos theorem for the function 119891(119909) = log(1199092 + 2) minus log 3 in[-11]

15 Verify Mean Value Theorem for the function 119891(119909) = sin 119909 minus sin 2119909 in [0120587]

16

WORK SHEET

MATRIX AND DETERMINANTS

CLASS-XII

VSA TYPE(1 marks)

1 The sale figure of three car dealers during march 2015 showed that dealer A sold 6 deluxe 4

premium and 5 standard cars dealer B sold 8 deluxe 3 premium and 4 standard cars dealer C

sold 4 deluxe 2 premium and 3 standard cars Write 3 x 3 order matrices summarizing sales data

for March

2 If a matrix has 14 elements then what are the possible orders it can have What if it has 17

elements

3 If 119860 = [2 4 15 minus6 22 1 5

] then find trace of A

4 Construct a 2 times 3 matrix A=[119886119894119895] whose elements are given by

(i) aij=1

2(119894 minus 2119895)2 (ii) aij=

1

2|4119894 + 119895| (iii) aij=

119894 minus 119895 119894119891 119894 ge 119895119894 + 119895 119894119891 119894 lt 119895

(iv)119886119894119895 = 119894minus119895

119894+119895

5 If A is a square matrix such that 1198602 = 119868 then find the simplest value of (119860 minus 119868)3 + (119860 + 119868)3 minus

7119860

6 Write the number of all possible matrices of order 2 x 2 with each entry 12 or 3

7 If [2 1 3] (minus1 0 minus1minus1 1 00 1 1

) (10

minus1) = 119860 the write the order of matrix A

8 If 2 [3 45 119909

] + [1 1199100 1

] = [7 0

10 5] then find (x-y)

9 Solve the following matrix equation for x (119909 1) [1 0

minus2 0]=O

10 If matrix A=[1 minus1

minus1 1] 119886119899119889 1198602 = 119896119860 119905ℎ119890119899 119908119903119894119905119890 119905ℎ119890 119905ℎ119890 119907119886119897119906119890 119900119891 119896

11 In the interval 120587

2lt 119909 lt 120587 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119909 119891119900119903 119908ℎ119894119888ℎ 119905ℎ119890 119898119886119905119903119894119909 [

2 sin 119909 31 2 sin 119909

] is

singular matrix

12 If |119909 + 1 119909 minus 1119909 minus 3 119909 + 2

| = |4 minus11 3

| then find the value of x

13 If ∆= |5 3 82 0 11 5 minus7

| the write the value of 11988632 11986032

14 For what value of x A=[2(119909 + 1) 2119909

119909 119909 minus 2] 119894119904 119886 119904119894119899119892119906119897119886119903 119898119886119905119903119894119909

15 What is the value of |4 119886 119887 + 1198884 119887 119888 + 1198864 119888 119886 + 119887

|

16 Write the value of |119886 minus 119887 119887 minus 119888 119888 minus 119886119887 minus 119888 119888 minus 119886 119886 minus 119887119888 minus 119886 119886 minus 119887 119887 minus 119888

|

17

17 For what value of k the system of linear equations

119909 + 119910 + 119911 = 2 2119909 + 119910 minus 119911 = 3 3119909 + 2119910 + 119896119911 = 4 Has a unique solution

18 If A is a square matrix of order 3 such that |119886119889119895119860| = 64 find the |119860|

Short Answer (2 marks)

19 If |119909 sin 120579 cos 120579

minus sin 120579 minus119909 1cos 120579 1 119909

| = 8 119905ℎ119890119899 write the value of x

20 From the following matrix equation find the value of x [1 34 5

] [1199092

] = [56

]

21 Write the value of (x-y+z) from the following matrix [

119909 + 119910 + 119911119909 + 119911119910 + 119911

] = [957

]

22 If 2119883 + 3119884 = [2 34 0

] 119886119899119889 3119883 + 2119884 = [minus2 21 minus5

] find X and Y

23 If 119860 = [3 5] 119861 = [7 3] 119905ℎ119890119899 119891119894119899119889 119898119886119905119903119894119909 119862 119904119906119888ℎ 119905ℎ119886119905 119860119862 = 119861119862

24 If A=[0 05 0

] 119891119894119899119889 11986016

25 If A=[119888119900119904120572 119878119894119899120572

minus119904119894119899120572 119888119900119904120572] find 120572 119904119886119905119894119904119891119910119894119899119892 0 lt 120572 lt

120587

2 119908ℎ119890119899 119860 + 119860119879 = radic21198682 where 119860119879 is

transpose of A

26 If A and B are square matrix of same order and A is skew-symmetric prove that 119861primeAB is also

skew-symmetric

27 if A=[1 24 2

] then find the value of k if |2119860| = 119896|119860|

28 If A=[120783 120782 120784120782 120784 120783120784 120782 120785

] find A(adj A)

29 Show that [2 minus1 3

minus5 3 1minus3 2 3

] 119894119904 119894119899119907119890119903119904119890 119900119891 119905ℎ119890 119898119886119905119903119894119909 [minus7 minus9 10

minus12 minus15 171 1 minus1

]

Long Answer type type I (4 marks)

30 If 119860 = [1 minus3 10 2 minus12 1 3

] 119861 = [minus1 0 15 4 62 1 1

] 119886119899119889 119862 = [minus1 minus2 11 minus2 22 minus1 1

] 119907119890119903119894119891119910 119905ℎ119886119905

(i) A(119861119862) = (119860119861)119862 (ii) (A+B)C=AC+BC

31 If A=[0 3

minus7 5] 119868 = [

1 00 1

] 119891119894119899119889 119896 119904119906119888ℎ 119905ℎ119886119905 1198961198602 = 5119860 minus 21119868

32 Find the matrix A such that [2 minus11 0

minus3 4] 119860 = [

minus1 minus8 minus101 minus2 minus59 22 15

]

33 Let A=[1 minus2 30 4 7

] 119886119899119889 119861 = [0 4 22 minus2 1

] verify that (i)(119860 + 119861)119905 = 119860119905 + 119861119905(ii)(2A)t=2At

34 The co-operative store of a particular school has 10 dozen physics books 8 dozen chemistry

books and 5 dozen mathematics books Their selling prices are Rs 45 40 and 30 each

respectively Find the total amount the store will receive by selling all books

35 If A=[119886 1198870 1

] and 119886 ne 1prove by PMI that 119860119899 = [119886119899 119887(119886119899minus1)

119886minus1

0 1] for all natural number

18

36 If A=[352

] 119886119899119889 119861 = [1 0 4] 119907119890119903119894119891119910 119905ℎ119886119905 (119860119861)prime = 119861prime119860prime

37 Express [2 4 minus13 5 81 minus2 1

] as the sum of a symmetric and a skew-symmetric matrix

38 If A=[1 2 22 1 22 2 1

] 119901119903119900119907119890 119905ℎ119886119905 1198602 minus 4119860 minus 5119868 = 119874 ℎ119890119899119888119890 119891119894119899119889 119860minus1

39 Using elementary row transformation find the inverse of each of the following matrices

(i)[1 23 7

](ii) [2 17 4

]

40 Using properties of determinant prove that |

119909 minus 119910 minus 119911 2119909 21199092119910 119910 minus 119911 minus 119909 21199102119911 2119911 119911 minus 119909 minus 119910

| = (119909 + 119910 + 119911)3


119909 119909 + 119910 119909 + 2119910119909 + 2119910 119909 119909 + 119910119909 + 119910 119909 + 2119910 119909

| = 91199102(119909 + 119910)

42 If 119891(119909) = |119886 minus1 0

119886119909 119886 minus11198861199092 119886119909 119886

| 119906119904119894119899119892 119901119903119900119901119890119903119905119894119890119904 119900119891 119889119890119905119890119903119898119894119899119886119899119905119904 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119891(2119909) minus

119891(119909)

43 Let f(t)=|119888119900119904119905 119905 1

2119904119894119899119905 119905 2119905119904119894119899119905 119905 119905

| 119905ℎ119890119899 119891119894119899119889 lim119905rarr0

119891(119905)

1199052

44 Find the area of triangle whose vertices are 119860(11988611990512 21198861199051) 119861(1198861199052

2 21198861199052) 119886119899119889 119862(11988611990532 21198861199053)

45 Find the equation of line containing points (12)(38)

46 Show that points (a+5a-4)(a-2a+3) and (aa) do not lie on a straight line for any value of a

47 If 119860 = [2 31 4

] 119886119899119889119861 = [1 23 4

] 119907119890119903119894119891119910 119905ℎ119886119905 119886119889119895(119860119861) = (119886119889119895119861)(119886119889119895 119860)

48 Find the adjoint of matrix 119860 = [4 minus6 1

minus1 minus1 1minus4 11 minus1

] 119886119899119889 119907119890119903119894119891119910 119905ℎ119886119905 119860(119886119889119895119860) = (119886119889119895119860)119860 = |119860|1198683

49 Let 119860 = [3 72 5

] 119886119899119889119861 = [6 87 9

] 119907119890119903119894119891119910 119905ℎ119886119905 (119860119861)minus1 = 119861minus1119860minus1

50 Find the inverse of A=[2 1 34 minus1 0

minus7 2 1] 119886119899119889 119907119890119903119894119891119910 119905ℎ119886119905 119860minus1119860 = 119860119860minus1 = 1198683

51 For the matrix A=[3 minus3 42 minus3 40 minus1 1

] 119904ℎ119900119908 119905ℎ119886119905 1198603 = 119860minus1

52 Find the minor and cofactor of each entry of the first column of the matrix A and hence find the

value of determinant in each case

(i)A=[5 200 1

] (ii)A=[1 minus3 24 minus1 23 5 2

]

53 Find the matrix X satisfying the matrix equation [1 22 3

] 119883 [4 73 5

] = [1 00 1

]

54 Find the value of k if area of a triangle is 4 sq unit when its vertices are (k 0) (4 0)(02)

19

55 Solve the equation |119909 minus 2 2119909 minus 3 3119909 minus 4119909 minus 4 2119909 minus 9 3119909 minus 16119909 minus 8 2119909 minus 27 3119909 minus 64

| = 0

56 Prove that the product of matrix (in any order) [ 1198881199001199042120579 119888119900119904120579119904119894119899120579119888119900119904120579119904119894119899120579 1199041198941198992120579

] and

[1198881199001199042empty 119888119900119904empty119904119894119899empty

119888119900119904empty119904119894119899empty 1199041198941198992empty]

is a null matrix where 120579 119886119899119889 empty 119889119894119891119891119890119903 119887119910 119886119899 119900119889119889 119898119906119897119905119894119901119897119890 119900119891 120587

2

57 If A=[1 0 20 2 12 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896

58 A coaching institute of mathematics (subjects) conducts classes in two batches I and II and fees

for rich and poor children are different In batch I it has 20 poor and 5 rich children and total

monthly collection is Rs9000 whereas in batch II it has 5 poor and 25 rich children and total

monthly collection is Rs 26000 Using matrix method find monthly fees paid by each child of

two types

Long Answer type II (6 marks)

59 A total amount of Rs7000 is deposited in three different saving bank accounts with annual

interest rates 5 8 and 81

2 respectively The total annual interest from these three accounts

is Rs550 Equal amounts have been deposited in the 5 and 8 savings accounts Find the

amount deposited in each of the three accounts with the helps of matrices

60 Given that 119860 = [minus4 4 4minus7 1 35 minus3 minus1

] 119886119899119889 119861 = [1 minus1 11 minus2 minus22 1 3

] find AB Use this result to solve the

following system of linear equations x-2y+z=4 x-2y-2z=9 2x+y+3z=1

61 Find A-1 if 119860 = [minus1 2 52 minus3 1

minus1 1 1] and hence solve the system of linear equations

-x+2y+5z=2 2x-3y+z=15 -x +y +z=-3


(i)[2 3 minus3


](ii) [2 0 minus15 1 00 1 3

]

63 Using properties of determinants prove that|

(119887 + 119888)2 119887119886 119888119886

119886119887 (119888 + 119886)2 119888119887

119886119888 119887119888 (119886 + 119887)2

| =

2119886119887119888(119886 + 119887 + 119888)3

64 In a ∆119860119861119862 if |1 1 1

1 + 119904119894119899 119860 1 + 119904119894119899 119861 1 + 119904119894119899 119888119904119894119899 119860 + sin2 119860 119904119894119899 119861 + sin2 119861 119904119894119899 119861 + sin2 119861

|=0 then prove that ∆119860119861119862 is an

isosceles triangle

65 If |119901 119887 119888119886 119902 119888119886 119887 119903

| = 0 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119901

119901minus119886+

119902

119902minus119887+

119903

119903minus119888 119901 ne 119886 119902 ne 119887 119903 ne 119888

66 Solve the following system of equations using matrix method 120783

119961minus

120783

119962+

120783

119963= 120787

120784

119961+

120785

119962minus

120786

119963= minus120789

120784

119961+

120783

119962minus

120784

119963= minus120785

20

67 In a survey of 20 richest persons of three residential society A B C it is found that in society A5

believe in honesty 10 in hard work 5 in unfair means while in B 5 in honesty 8 in hard work 7

in unfair means and in C 6 in honesty 8 in hard work 6 in unfair means If the per day income of

20 richest persons of society A B C are Rs32500 30500Rs31000 respectively then find the

per day income of each type of people by matrix method

a Which type of people has more per day income


(2119909 + 2minus119909)2 (2119909 minus 2minus119909)2 1



| = 0

69 The management committee of a residential colony decided to award some of its members (say x)

for honesty some (say y) for helping others and some others (say z) for supervising the workers

to keep the colony neat and clean The sum of all awardees is 12 Three times the sum of

awardees for cooperation and supervision added to two times the number of awardees for honesty

is 33 If the sum of the number of awardees for honesty and supervision is twice the number of

awardees for helping others using matrix method find the number of awardees of each category

Apart from these values namely honesty cooperation and supervision suggest one more value

which the management of the colony must include for awards

70 Prove that |

119910119911 minus 1199092 119911119909 minus 1199102 119909119910 minus 1199112



|is divisible by (x+y+z) and hence find the quotient

71 Using properties of determinants prove that |

(119886 + 1)(119886 + 2) 119886 + 2 1

(119886 + 3)(119886 + 2) 119886 + 3 1

(119886 + 3)(119886 + 4) 119886 + 4 1| = minus2

If A=[1 0 2

0 2 1

2 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896

21

WORK SHEET I

CLASS XII

MATHEMATICS

RELATION AND FUNCTION

CHAPTER I RELATIONS AND FUNCTIONS

1 MARK QUESTIONS

1 Check whether the relation R in the set 1 2 3 given by R = (13)(31) is transitive

2 Find the number of all onto functions from the set 1 2 3n to itself

3 If f(x) = x+7 and g(x) = x-7 xisin 119877find fog(7)

4 Let S= a b c find the total number of binary operation on S

5 If the binary operation on the set of integers Z is defined by ab = a+3b2 then find the

value of 24

6 If f R rarr R defined by f(x)= 3x+2 defined f[f(x)]

2 MARK QUESTIONS

7 Let A be the set of all students of a boys school Show that the relation R in A given by R =

(ab) a is sister of b is the empty relation and 119877prime = (ab) the difference between heights of a

and b is less than 3 meters is the universal relation

8 Show that the relation R in the set Z of integers given by R = (a b) 2 divides a ndash b is an

equivalence relation Find the equivalence class [0]

9 Show that the number of equivalence relations in the set 1 2 3 containing ( 1 2 ) and ( 2

1 ) is two

10 Show that the relation lsquo is a factor of lsquo on the set N of all natural numbers is reflexive and

transitive but not symmetric

11 Let fg R rarr R be defined as f(x) = x and g(x) = [x] where [x] denotes the greatest

integer function less than or equals to x Find fog ( 5

2 ) and gof ( - radic2 )

22

12 If f A rarr B and g B rarr C are onto functions then show that gof A rarr C is also onto

13 If f(x) = 119909minus1

119909+1 (119909 ne 1 minus1) show that f o 119891minus1 is an identity function

14 Show that the function f R rarr R defined as f(x) = 5 ndash 7x is an invertible function Also find

its inverse

( Ans 119891minus1(119909) = 5minus119909

7 )

15 Let S= 1234 and be an operation on S defines by ab = r where r is the least non negative

remainder when product is divided by 5 Prove that is a binary operation on S

4 MARK QUESTIONS

16 If 1198771 119886119899119889 1198772 are equivalence relations in a set A show that 1198771 cap 1198772 is also an equivalence

relation

17 Let R be the relation on set A of ordered pairs of positive integers defined by ( x y ) R (( u

v ) if and only if xv = yu Show that R is an equivalence relation

18 Let A = 1 2 3 Then show that the number of relations containing (1 2) and (2 3) which

are reflexive and transitive but not symmetric is four

19 Consider a function f [ 0 120587

2 ] rarr 119877 given by f(x) = sinx and g [ 0

120587

2 ] rarr 119877 given by g(x) =

cosx Show that f and g are one one but f o g is not one one

20 Show that the relation R defined by (a b) R (c d) rArr a + d = b + c on the set N is an

equivalence relation

21 If the function f R rarr R is given by f(x) = 119909 + 3

2 and g R rarr R is given by g(x) = 2x ndash 3

find fog and gof Is f -1 = g

22 Let Y = 1198992 ∶ 119899 isin 119873 sub 119873 Consider f N rarr Y given by f(n) = 1198992 Show that f is invertible

Find the inverse of f

23 Given the functions f(x) = sinx and g(x) = cosx are one-one in [ 0 120587

2 ] Prove that f + g is not

one-one in [0 120587

2]

23

WORKSHEET 12 IP

Q1 Table SchoolBus

Rtno Area_covered Capacity Noofstudents Distance Transporter Charges

1 Vasant kunj 100 120 10 Shivam travels 100000

2 Hauz Khas 80 80 10 Anand travels 85000

3 Pitampura 60 55 30 Anand travels 60000

4 Rohini 100 90 35 Anand travels 100000

5 Yamuna Vihar 50 60 20 Bhalla Co 55000

6 Krishna Nagar 70 80 30 Yadav Co 80000

7 Vasundhara 100 110 20 Yadav Co 100000

8 Paschim Vihar 40 40 20 Speed travels 55000

9 Saket 120 120 10 Speed travels 100000

10 Janak Puri 100 100 20 Kisan Tours 95000

(a) To show all information of students where capacity is more than the no of student in

order of rtno

(b) To show area_covered for buses more than 20 km but charges less than 80000

(c) To show the area covered by Bhalla Co and kisan tours

(d) To show the names of all the transporters without repeating their names

(e) To show all the bus routes number where the distance is less than 30

(f) To show the area whose names end with lsquorrsquo in decreasing order of the area covered

(g) To show rtno area_covered and average cost per student for all routes where average

cost per student is - chargesnoofstudents

(h) To show the number of areas covered by all the bus routes

(i) To show the number of area covered by each transporter

(j) To show the maximum capacity of a bus

24

(k) To show transporter wise total number of students traveling

(l) Add new record with data (11 ldquo Moti baghrdquo353210rdquo kisan tours ldquo 35000)

(m) Give the output considering the original relation as given

(i) select sum(distance) from schoolbus where transporter= ldquo Yadav Cordquo

(ii) select min (noofstudents) from schoolbus

(iii) select avg(charges) from schoolbus where transporter= ldquoAnand travelsrdquo

(iv) select distinct transporter from schoolbus

(v) select count(distinct transporter) from schoolbus

(vi) select count() from schoolbus

(vii) select transporter count() from schoolbus group by transporter

(viii) select transporter max(charges) from schoolbus group by transporter

Table CLUB

C_Id CoachName Age Sports DateofApp Pay Sex No_Players

1 KUKREJA 35 KARATE 2012-03-

27 1000 M

20

25

2 RAVINA 34 KARATE 2008-01-

20 1200 F

15

3 KARAN 34 SQUASH 2009-02-

19 2000 M

2

4 TARUN 33 BASKETBALL 2012-01-

01 1500 M

16

5 ZUBIN 36 SWIMMING 2008-01-

12 700 M

10

6 KETAKI 36 SWIMMING 2012-02-

24 800 F

10

7 ANKITA 39 SQUASH 2013-02-

20 2200 F

5

8 ZAREEN 37 KARATE 2010-02-

22 1100 M

18

9 KUSH 41 SWIMMING 2008-01-

13 900 M

17

10 SHAILYA 37 BASKETBALL 2008-02-

19 1700 M

17

Q2 Create the above table AND DO THE FOLLOWING

(a) To show all information about the swimming coaches in the club

(b) To show all information of the CLUB which coach name start with ldquoKrdquo

(c) To show the names of coaches in sorted order of the name

(d) To list the names of all coaches with their date of appointment (DateofApp) in descending order

(e) To display coach name age and sex from CLUB which sex is Male (M)

(f) To show all information which age more than 35 and Pay between 1500 and 2000

(g) To display a report showing coach name pay age and bonus (15 of Pay) for all the coaches

(h) To show distinct names of the games available in club

(i) To count the total number of coaches in the club

(j) To count and display total coaches in each game

(k) To display Sports wise sum of pay from club table

(l) To display highest age of coach lowest pay of coach form table club

(m) Give the output of the following SQL command

(i) Select COUNT( Distinct SPORTS) from CLUB

(ii) Select MIN(Age) From CLUB Where Sex = ldquoFrdquo

(iii) Select AVG(Pay) From CLUB Where Sports = ldquoKARATErdquo

(iv) Select SUM(Pay) From CLUB Where DateofApp gt ldquo2008-01-31rdquo

26

(v) Select Sports From CLUB where Pay Between 700 and 1000

(vi) Select Sports From CLUB where Pay IN ( 700 10002000)

(vii) SELECT Sport SUM(pay) FROM CLUB GROUP BY Sport Having Sex=rsquoMrsquo

(o) To delete record of coaches whose salary is less than 1000

(p) To delete record of coaches whose name ends with lsquoNrsquo and has five characters

(q) To increase the salary of all coaches by 20

Q3 Consider the table student given below Find out the output of

(i) the following queries

(ii) A) SELECT COUNT() FROM STUDENT

B) SELECT COUNT(FEES) FROM STUDENT

C) SELECT AVG(FEES) FROM STUDENT

D) SELECT FEES + 100 FROM STUDENT

Rno Fees

1 4000

2 4300

3 5000

4 Null

Q1 Design a GUI application to read Price per dozen ( TextField) and Price per dozen ( Text field) and

calculate total payable amount( price dozens) in a TextField on the click event of calculate Button Also

place two more buttons ldquoClear Text Boxrdquo and ldquoExitrdquo Write code to clear text fields on the click event of

ldquoClear Text Boxrdquo and close application on the click event of ldquoExit Buttonrdquo

27

Q2 Design a GUI application to enter two numbers (both Text Fields) and place 5 buttons to add

subtract multiply divide and to find out reminder Display the result of above operation in another text

Field

Q3 Design a GUI application to read day number in a text field Place a command button ldquoCalculate Day

Namerdquo Display equivalent day name on the click event of ldquoCalculate Day namerdquo in a text field

Q4 Design a GUI application to read price of a pizza (Textfield) and total order quantity ( TextField) And

two radio button 1- 5 discount 2- 90 discount and 3 command button on the frame 1- Calculate Bill

2- Clear Text 3 Close App Calculate Total payable amount on the click event of ldquoCalculate Billrdquo Clear all

the text fields on the click event of ldquoClear Textrdquo and close application on the click event of ldquoClose apprdquo

28

Q5 Design a GUI application to join your first name( TextField) and second name ( Text Field) Join

these names on the click event of button ldquoJoin Namesrdquo and display them in a third Text Field (Disable)

Q6 Design a GUI application in netbeans to calculate the amount payable by the customer as per the

following GUI The rate of extra toppings are given in the brackets and any applicable discount You are

required to write the code on the click event of ldquocalculate billrdquo

29

Q7 Design a GUI application to read Roll Number name of student and marks obtained in five subject

in text Fields Calculate Total marks and grade on the click event of ldquoCalculaterdquo and display them on the

text Fields The criteria to calculate grade is as follows

marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C

The GUI should be like this

Q8 Design a GUI application to read three numbers ( in TextFields) from the keyboard and calculate the

largest number among them Display the result in Text Field

Q9 Design a GUI Application(Append) to read your name( Textfield) roll Number ( TextField) Class (

TextField) marks obtained in English ( TextField) Accounts ( TextField) Business Studies (TextField)

30

Economics ( Textfield) and informatics Practics( TextField) Using JTextArearsquos Append methods display

all the inputed information in TextArea on the click event of ldquoAdd Informationrdquo button

Q10 Design a GUI application to read starting number( TextField) and end number (Text Field)

Generate all the number between these two numbers and display them in a TextArea on the click event

of ldquogenerate seriesrdquo button

Q11 Create a table school in mysql with the following structure

Field Name Data Type Size Constraint

Admno Char 10 Primary key

Name Varchar 30 Not null

Class Char 15

Section Char 1

Fees Char 10

Design a GUI in netbeans to insert record in this newly created table school

31

Q12 Create a table student in mysql with the following structure




Class Char 15

Section Char 1

Fees Char 15

Insert 5 record in this newly created table of student Design a GUI in netbeans to show all the records

of this table in netbeans in table format

32

Q13 Design a GUI in netbeans to search a record in the above generated table student If the record

exist then delete that record from the table


exist then UPDATE that record from the table ( Screenshot is for reference purpose) otherwise display a

33

popup message ldquorecord does not existrdquo Modify button only enable if the record exist in the database

otherwise it remains disable

Q15 ABN Corporation impose charges on customer for different products The shipping company costs

for an order in two forms 1- Wholeseller 2- retailer The cost is calculated on unit basis as follows

Units Price per unit(wholeseller) Price per unit ( Retailer)

1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35

Special customers ( checkbox ) are given 10 extra discount The following is the screenshot used to

calculate cost for order

Jpanel container is used for customer type as two radio buttons are hosted on this container Wholesale

and Retailer

You are required to calculate ldquoDiscountrdquo and total cost on the click event of ldquoCalculaterdquo button and also

display discount and total cost in textfields

34

Q16 Mr XYZ visited mahagun mega mall His family purchased some products form mahagun metro

mall The mall have some attractive discount for credit cards holders You are requested to calculate the

discount on total amount ( enter in text field) and calculate discount as per the criteria table given below

Card Company Name discount offered

HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18

Please referrer the following image for more details

35

Q17 Ms Vidhyarthi is Working in DAV Centenary Public School Chander Nagar as a programmer She

was asked to develop a GUI in netbeans to develop an application The school offers two streams ndash 1

Medical 2- Non Medical with the following grading criteria

Stream Percentage Grade

Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C

The school also offers special incentive to NCC cadets in the form of 3 increment in percentage for all

the NCC cadets

36

37

WORKSHEET 1 CLASS- 12 ACCOUNTS TOPIC -FINANCIAL STATEMENT OF A COMPANY ANSWER THE FOLLOWING QUESTION 1 List any five items that are shown under Reserves and surplus 2 Name the items that are shown under Long-term borrowings 3 Calculate cost of material consumed from the followings opening inventory material Rs 500000 purchase of material Rs 2500000 and closing inventory of material Rs 400000 4From the following information calculate change in inventory of finished goods opening inventory and closing inventory of finished goods Rs 200000 and Rs 175000 respectively 5From the following information calculate change in inventory of stock -in - trade opening and closing stock in trade Rs 500000 and Rs 400000 respectively 6 From the following information compute the amount to be shown in note to accounts on employees benefit expenses wages Rs 540000 salaries Rs 720000 bonus Rs 105000 staff welfare expenses Rs 60000 and business promotion expenses Rs 50000 7 From the following information prepare note to accounts on finance costs interest paid to bank Rs 75000 interest on debenture Rs 58000 loss on issue of debenture written off Rs 27500 and commitment charges Rs 15000 8 From the following information of best marketing ltd for the year ended 31st march 2018 prepare note to accounts on depreciation and amortisationn expenses Depreciation on building Rs 15500 plant and machinery Rs 25000 computers Rs 60000 goodwill written off Rs 7500 patents written off Rs 12500 9What are the major heads in the equity and liabilities part of the balance sheet as per schedule III 10How is change in inventories calculated and shown in the statement of profit and loss

38

WORKSHEET -2 CLASS- 12 COMMERCE TOPIC- FINANCIAL STATEMENT ANALYSIS AMSWER THE FOLLOWING QUESTION 1 What is meant by financial statement analysis 2 What is cross- sectional analysis 3 What is a time series analysis 4 What is Horizontal analysis of financial statement 5 Why are investors interested in analysing financial statement 6 List ant three objectives of analysing the financial statement 7 Differentiate between intra firm and inter firm analysis 8 Discuss the advantages of financial statement analysis 9 Why is analysis of financial statement is important to creditors 10 How is analysis of financial statement important to government authority

39

PHYSICAL EDUCATION WORK SHEET

FOR CLASS XII

Practical-1 Modified AAHPER administration for all items

Practical-2 Conduct Barrow 3 Item Test on 10 students

Practical-3 Procedure for Asanas Benefits amp Contraindication for any two Asanas for each

lifestyle disease

Practical-4 Procedure for administering Senior Citizen Fitness Test for 5 elderly family members

Practical-5 Any one game of your choice out of the list below

Games Basketball Football Volleyball

1 Neat amp clean diagram of field amp equipment

2 Rules amp Regulation of the game

3 Terminologies of the game

4 Skills of the game

40

WORK SHEET

CLASS 12th BSt

1 Sahni garments produce 20000 shirts a month at a cost of 170 per shirt Due to a sudden

rise in the labour cost due to Diwali season the cost of production went up to 190 per

shirt The production manager had the option of making less than the target to save cost

but he decided to meet the target at the higher cost because they didnrsquot want to loose

sales Which concept of management has the manager followed and which has he

ignored

2 In an organisation sales department wants to increase the sale by 20 so sales department

planned to offer extra discounts to customers Finance department raised objection on it

as they say it will result in loss of revenue and company may face liquidity problem

What quality of management is lacking in the above case

3 X Ltd a tyre manufacturing concern has been established for more than ten years Having

made good profits in the past company wanted to expand further and hence did not

declare bonus for the previous year With this decision the workers got agitated but

management promised that the bonus will be declared once the projects achieves a stable

position State relevant management principle of Fayol used by management

4 Which level of managers are responsible for coordination

5 Alia Enterprises a company was initially producing grinders and mixers Now with the

changing scenario and emerging trends of working women there is a greater demand for a

product which is more efficient and a multi-tasker On analyzing the situation the

company decided to penetrate into the market for producing Food Processor

a Which feature of management is highlighted here

b Which level of management will take this decision

6 Successful organisations do not achieve their goals by chance but by following a process

Name the process

7 The aim of this study is to eliminate unnecessary movement so as to ensure timely

completion of workrdquo Which study is emphasized in above statement

8 What changes were made in the industrial policy in the recent past

9 Soni Traders is a chain of retail stores engaged in buying and selling of electronic gadgets

in India Due to increased competition dynamic technology ever-changing tastes and

preferences of customers and of course turbulent political and legal environment the

survival of business is at stake Discuss what the managers of Sony Traders should do in

response to such dynamic business environment

10 Why is it said that knowledge of principles of management are essential for the success

of an organization

41

11 It is common now to see CD-ROMrsquos computerized information kiosks and Internet

World Wide Web multimedia pages highlighting the virtues of products Identify

dimension of business environment related to following situations and explain

12 Kolkata rice foods ltd is a big rice manufacturing firm From the beginning of the year its

sales are falling Being worried about the situation the MD appointed a research

committee to find the reasons They submitted the following report after the survey

a Due to increase in export duty by the government the foreign demand has gone

down

b Due to substitutes available the attention of people has shifted from rice

c Some other rice manufacturing firms have imported machines which are

producing better quality rice

d Also the relations of their country have turned bitter with one main importing

country

Identify the dimensions of business environment identified above by quoting the relevant

lines

Which importance of business environment has the manager missed out

13 Simmi Ltd manufactures fashionable and designer clothes Recently it finds that the

demand for its products has been declining After market research it was discovered that

fashion and tastes of the consumers is changing at a fast pace Customers demand is

increasing New competitors have entered the market with new designs It is very

difficult for the company to predict future happenings Also it is difficult to know the

extent of the relative impact of the social economic political technological or legal

factors on decrease in demand of its products in the market

A meeting was held in which managers from different functional levels heading

Production Marketing Finance etc eg CEO CFO VP (Marketing) were present to

discuss how to deal with the situation After a long discussion it was decided that they

would study and analyse the market first to identify customer tastes and fashion and then

manufacture garments accordingly It was also decided to increase expenditure on

advertising after- sales services etc

a Identify any two features of business environment by quoting the lines from the

above case

b Identify any two impacts of government policy changes on business quoting lines

from the above case

c State the importance of understanding of environment by business managers in

the light of the above para

14 (a)One of technique given by FW Taylor is extension of principle given by Henry

Fayol Identify that and explain

(b) Mohan always comes 1 hour late in the office and leave half an hour before the

scheduled time No penal action is taken against him Other employees also started

coming late in the office Management is very disturbed with this and has started scolding

42

the employees

(1) Which management principle is being violated in the given case

(2) Explain the principle

(3) Mention one probable adverse consequence of violation of the given principle

15 (a)Explain the principle of management which advocated paternalistic style of

management

(b)Suresh is working under supervisor Ramesh Suresh always give useful ideas which

have resulted in gains for organisation but Suresh never acknowledges him and he also

use to take credit for suggestions given by Ramesh Which Principle of management is

being violated and what values are ignored by Ramesh and what will be the

consequences

16 M Ltd was manufacturing water heaters In the first year of its operations the revenue

earned by the company was barely sufficient to meet its costs The firm had also taken

no steps to ensure proper arrangement of things ie materials tools etc and also did not

have a fixed place for every employee This led to a fall in productivity and efficiency

and wastage of time and cost To increase the revenue the company analysed the reasons

for less revenue After this analysis the company decided to

labour was available at a low rate

heaters slowly This will not only help in covering risks but will also help in meeting

materials tools etc and a fixed place for every employee to increase productivity and

efficiency and minimization of wastage of time and cost

a Identify and explain the objectives of management discussed above giving 3 examples

of each b Identify the principle of Fayol that has not been followed in M Ltd What are

the benefits of following this principle and the adverse effects of not following this

principle

43

CLASS XII

SUB ECONOMICS CH 1( central problem and PPC )

Q1 What is meant by economy

Q2 What are the important function of an economy

Q3 What is meant by resources

Q4What is meant by and economic problem

Q5 Why does an economic problem arise

Q6 Define production possibility curve what does a point below PPC indicate and what does a point on

PPCindicate

Q7 Why is PPC downward sloping from left to right

Q8 Why is PPC concave to origin

Q9 What is marginal rate of transformation

Q9 State central problem of an economy why does the problem of what to produce arise Explain

Q10 Explain the central problem for whom to produce

Q11 Explain the problem of how to produce

Q12 State reasons why does an economic problem arise

Q13 Massive unemployment shift the PPC to the left defend or refute

Q14 An economy always produces on but not inside production possibility curve defend or refute

Q15 Government has started promoting foreign capital what is its economic value in the context of

PPC

Q16 Large number of Technical training institutions have been started by the government state its

economic value in the context of PPC

Q17 Can there be an economy without any economic problem

Q18 Why does technological advancement for growth of resources shift the PPC to the right

Q19 Name the economic value achieved through spread of education in the context of PPC

Q20 Explain the concept of MOC with the help of numerical example

44

CLASS XII

SUB ECONOMICS CH 2 (CONSUMER EQUILIBRIUM)

Q1 Define total utility and marginal utility

Q2 State the law of diminishing marginal utility

Q3 State the conditions of consumers equilibrium through utility approach

Q4 What is meant by marginal rate of substitution why is MRS always diminishing

Q5 When does a consumer attain equilibrium according to indifference curve approach

Q6 What do you mean by the budget set of a consumer

Q7 What is a budget line explain why the budget line is downward sloping

Q8 What do you mean by monotonic preference

Q9 Explain why an indifference curve is convex to the origin

Q10 A consumer consumes two goods X and Y what will happen if the consumer is not in equilibrium

Q11 A consumer consumes only two goods explain the conditions that need to be satisfied for the

consumer to be in equilibrium under indifference curve analysis

Q12 Explain the three properties of indifference curve

Q13 Explain the concept of marginal rate of substitution with the help of a numerical example also

explain its behaviour along an indifference curve

Q14 Assuming that a consumer consumes only two goods Explain the conditions of consumers

equilibrium with the help of utility analysis

Q15 Explain the difference between Cardinal and ordinal utility approach

Q16 What happens to the budget set if both the prices as well as income double

Q17 If a consumer has monotonic preference can he be indifferent between the bundles with (8-4) and

(8-6)

Q18 What happens if MRS is greater or lesser than ratio of price of two goods

Q19 Derive the law of demand from single commodity equilibrium condition ndash Marginal utility = price

Q20 Define a budget line When can it shift to the right

45

CLASS XII

SUB ECONOMICS CH 3 (THEORY OF DEMAND) Q1 Define demand and demand schedule

Q2 What is a demand functionExplain

Q3 What is law of demand

Q4 What is extension of demand and contraction of demand

Q5 Define increase in demand and decrease in demand

Q6 What is meant by one good being complementary to another

Q7 What is meant by one good being a substitute to another

Q8 What is an inferior good How is it different within normal goods

Q9 How is the price elasticity of demand of a commodity affected by the change in price of its a

substitute

Q10 Define price elasticity of demand when is the demand for a good is said to be perfectly inelastic

and perfectly elastic

Q11 How does change in price of a substitute good affect the demand of the given good explain with the

help of example

Q12 What is the effect of increase in income of a consumer on the demand for inferior commodity

Q13 Why demand for salt is inelastic

Q14 What is the elasticity of demand for a particular brand of lipstick

Q15 If the price of a product increases the expenditure of a family on that product is bound to increase

defend or refute

Q16 When does a consumer purchase more at the same price give 3 points

Q17 When does a consumer purchase more at high price give 3 points

Q18 In order to encourage tourism in North East States Air India reduces the airfare how will it affect

market demand curve for air travel to North East

Q19 A good is an inferior good for one and at the same time normal good for another consumer Do you

agree

46

Q20 Explain with the help of an example price elasticity of demand of two goods a and b is minus 3 and

minus 4 respectively which of the two goods has higher elasticity and why

Note - Numericals based on price elasticity of demand

47

CLASS XII

SUB ECONOMICS CH 4 (PRODUCTION FUNCTION)

1 DEFINE PRODUCTION FUNCTION

2 DEFINE MPP

3 WHAT IS MEANT BY RETURNS TO FACTOR

4 EXPLAIN LAW OF VARIABLE PROPORTION IN TERMS OF TP AND MP USE DIAGRAM

5 EXPLAIN REASONS BEHIND LAW OF VARIABLE PROPORTION

6 WHAT IS LAW OF DIMINISHING RETURNS

7 EXPLAIN MEANING OF INCREASING RETURNS WITH THE HELP OF TP SCHEDULE AND

DIAGRAM

8 EXPLAIN RELATIONSHIP BETWEEN TP ANDMP

9 GIVE REASON

A IN SHORT RUN PRODUCTION IS DONE ONLY BY USING VARIABLE FACTORS

B INCREASING RETURN OCCUR BECAUSE FIXED FACTORS ARE EXCESSIVELY USED

C WHEN MP DECLINES TP MUST ALSO DECLINE

D AP CAN RISE EVEN WHEN MP IS FALLING

E IT IS MORE PROFITABLE FOR THE PRODUCER TO BE IN THE STAGE OF INCREASING

RETURN THAN IN INCREASING RETURN

F WHEN MP FALLS AP WILL ALSO FALL

G IN CASE OF DIMINISHING RETURN MP AND TP BOTH WILL DECREASE

10 WHY SHOULD TP BE MAX WHEN MP=0

11 DO THE TERM DIMINISHING OR CONSTANT MEAN THAT THE OUTPUT DECREASES OR

REMAIN CONSTANT IN CONTEXT OF LAW OF VARIABLE PROPORTION

12 WHEN LAW OF DIMINISHING RETURN IS UNIVERSAL LAW WHY IS AP FOUND TO BE

MUCH HIGHER IN DEVELOPED COUNTRIES LIKE USA THAN IN LESS DEVELOPED

COUNTRIES LIKE INDIA

13 DRAW SHAPE OF MP AND FIND OUT TP FROM IT

14 WHAT IS MEANT BY DIVISION OF LABOUR

48

15 WHAT IS KNOWN AS VOLUME DISCOUNT

16 EFFECT ON TP OR MP WHEN ONLY ONE VARIABLE FACTOR IS INCREASING

17 NUMERICAL PROBLEMS BASED ON PRODUCTION

49

CLASS XII

SUB ECONOMICS ch 5 (cost)

1 DISTINGUISH BETWEEN EXPLICIT AND IMPLICIT COST

2 DISTINGUISH BETWEEN FIXED AND VARIABLE COST WITH THE HELP OF EXAMPLE

3 HOW DOES AFC BEHAVE AS OUTPUT IS INCREASED

4 DEFINE TCACMC

5 RELATIONSHIP BETWEEN AC AND MC WITH THE HELP OF SCHEDULE AND DIAGRAM

6 RELATIONSHIP BETWEEN AVC AND MC

7 RELATIONSHIP BETWEEN TC AND MC

8 WHY DOES DIFFERENCE BETWEEN ATC AND AVC DECREASE WITH INCREASE IN

OUTPUT

9 WHY AC IS GREATER THANAVC

10 WHY IS MC U SHAPED

11 DRAW TCTVC AND TFC IN SINGLE DIAGRAM

12 DIFFERENCE BETWEEN TC AND TVC FALLS WITH INCREASE IN OUTPUT

13BEHAVIOUR OF AFC AND TVC AS OUTPUT INCREASES

14 AN INDIVIDUAL IS BOTH THE OWNER AND MANAGER OF A SHOP TAKEN ON RENT

IDENTIFY EXPLICIT AND IMPLICIT COST EXPLAIN

15 DOES TC ALWAYS SHOOT FROM Y AXIS

16 MARGINAL COST INCLUDES BOTH FIXED AND VARIABLE COST

17 WHY SHOULD TVC INCREASE AT DECREASING RATE IN INITIAL STAGE OF

PRODUCTION

18 ATC MUST FALL BECAUSE AFC FALLS

19 A PRODUCER STARTS HIS BUSINESS BY INVESTING HIS SAVINGS AND HIRING

LABOUR

IDENTIFY EXPLICIT AND IMPLICIT COST FROM THIS INFORMATION

20 AS AN OWNER OF A FIRM YOU FIND THAT YOUR OVERHEAD COST PER UNIT OF

OUTPUT IS CONTINUOUSLY FALLING AS OUTPUT IS INCREASINGDOES IT MEAN A

SITUATION OF EVER RISING PROFIT OF YOUR FIRM

50

21 ELECTRICITY TARIFF IS INCREASED FOR THE COMMERCIAL USE WOULD IT AFFECT

FIXED COST OR VARIABLE COST OF THE INDUSTRY EXPLAIN

22NUMERICAL PROBLEMS BASED ON COST

8

51

CLASS XII

SUB ECONOMICS CH 6 ( REVENUE)

WHAT IS MEANT BY REVENUE

TR CURVE UNDER PERFECT COMPETITION IS A STRAIGHT LINE SLOPING UPWARD FROM THE

ORIGIN

UNDER MONOPOLY TR CURVE INCREASES ONLY AT A DIMINISHING RATE

UNDER PERFECT COMPETITION RATE OF TR NEVER DECLINES BUT UNDER MONOPOLY AND MONOPOLISTIC COMPETITION IT CAN

AR = 0 WHEN TR IS MAXIMUM

MR TENDS TO FALL EVEN WHEN AR IS CONSTANT

UNDER PERFECT COMPETITION BOTH AR AND MR ARE INDICATED BY THE SAME HORIZONTAL STRAIGHT LINE BECAUSE --------------------------------------------------------------------------------------------------------____________________________________________________________________________________ AR CURVE IS ABOVE MR CURVE UNDER MONOPOLY BECAUSE

__________________________________________

MR IS THE RATE OF ___________________________

WHEN TR IS INCREASING AT A DECREASING RATE MR SHOULD BE

______________________________________

WHEN TR IS INCREASING AT A CONSTANT RATE MR SHOULD BE

________________________________________

WHEN PRICE IS CONSTANT TR INCREASES AT A

_____________________________________________________

WHEN MR IS NEGATIVE TR _________________________

TR ALWAYS SHOOTS FROM ORIGIN

GREATER REVENUE ALWAYS IMPLIES GREATER PROFIT

SHAPE OF REVENUE CURVEDEMAND CURVE IN DIFFERENT MARKET

AR=0 WHEN TR IS MAX

MR CAN NEVER BE NEGATIVE AS IT IMPLIES A SITUATION OF ZERO PROFIT

MR IS THE SLOPE OF TR

WHEN PRICE REDUCESAS OUTPUT INCREASESAR=MR

52

UNDER PERFECT COMPETITIONAR AND MR CURVES TENDS TO SLOPE DOWN

WHEN TR IS MAX MR IS ALSO MAX

WHEN MR IS POSITIVE AND CONSTANT AR AND TR BOTH INCREASE AT CONSTANT RATE

A FARMERS ENTIRE PRODUCE OF POTATOES IS DESTROYED BYWILD ANIMALS WHAT IMPACT

WOULD IT CAUSE ON THE AR CURVE OF FARMER ASSUME PERFECT COMPETITION

53

CLASS XII

SUB ECONOMICS CH 7 (PRODUCER EQUI)

1 WHAT IS MEANT BY PRODUCER EQUI

2 WHAT IS THE CONDITION OF PRODUCER EQUI

3 WHAT IS THE RELATION BETWEEN PRICE LINE AND TOTAL REVENUE

4 IS CONDITION OF MR=MC SUFFICIENT FOR PROFIT MAX

5 WHAT IS BREAK EVEN POINT

6 IF MCgtMR WHAT SHOULD A PRODUCER DO TO MAX HIS PROFIT

7 IS CONDITION OF P=MC FOR FIRM EQUI IN PERFECT COMPETITION DIFFERENT FROM

CONDITION OF MR=MC

8 IS A PRODUCER IN EQUI WHEN MRgtMC OR MRltMC EXPLAIN

9 EXPLAIN MEANING ampCONDITION OF PRODUCER EQUI WITH THE HELP OF SCHEDULE AND

DIAGRAM

10 NORMAL PROFIT IS A PART OF TOTAL COST

11 WHAT IS SHUT DOWN POINT

12 IS A PRODUCER AT EQUI UNDER THE FOLLOWING CONDITION

(A) WHEN MARGINAL REVENUE IS GREATER THAN MARGINAL COST

(B) WHEN MARGINAL REVENUE IS EQUAL TO MARGINAL COST

GIVE REASON FOR YOUR ANSWER

54

CLASS XII

SUB ECONOMICS CH 8 (THEORY OF SUPPLY)

1 DEFINE SUPPLY AND MARKET SUPPLY FOR A PRODUCER

2 WHAT DOES THE UPWARD SLOPING SUPPLY CURVE INDICATE

3 HOW CAN YOU FIND MARKET SUPPLY SCHEDULE FROM INDIVIDUAL SUPPLY SCHEDULE

4 EXPLAIN HOW INPUT PRICE AND TECHNOLOGICAL PROGRESS ARE THE DETERMINANT OF SUPPLY OF A

GOOD BY A FIRM

5 DEVELOPING COUNTRIES HAVE SUPPLY CONSTRAINTSDO YOU AGREE

6 USING DIAGRAM AND SCHEDULE EXPLAIN LAW OF SUPPLY

7 GIVE REASONS FOR INCREASE AND DECREASE IN SUPPLY

8 WHAT IS MEANT BY INCREASE AND DECREASE IN SUPPLY

9 WHAT DOES AN UPWARD OR DOWNWARD MOVEMENT ALONG SUPPLY CURVE INDICATE

10 IF A FARMER GROWSRISE AND WHEAT HOW WILL AN INCREASE IN PRICE OF WHEAT AFFECT THE

SUPPLY CURVE OF RICE

11 EXPLAIN HOW CHANGES IN PRICES OF OTHER PRODUCTS INFLUENCE THE SUPPLY OF A GIVEN

PRODUCT

12 DEFINE MARKET SUPPLYWHAT IS THE EFFECT ON THE SUPPLY OF A GOOD WHEN GOVT IMPOSES

TAX ON THE PRODUCTION OF THE GOOD`

13 CAN THE SUPPLY OF A GOOD INCREASE EVEN AT SAME PRICE

14 DISTINGUISH BETWEEN CHANGE IN SUPPLY AND CHANGE IN QUANTITY SUPPLIEDWHICH OF THESE

CAUSES A SHIFT OF SUPPLY CURVE

15 IVE MEANING OF PRICE ELASTICITY OF SUPPLYHOW DO WE MEASURE IT

16 A LOSS MAKING FIRM MAY HAVE INELASTIC SUPPLYIF YESWHY

17 MENTION ANY SITUATION OF ELASTICITY OF SUPPLY WHICH IS GENERALLY FOUND IN PRACTICAL

LIFE

18 WHAT IS THE EFFECT OF SHORT TIME PERIOD ON SUPPLY OF A COMMODITY

19 FIRNS SUPPLY CURVE SHOWS SUPPLY FUNCTIONCOMMENT

55

20 WILL THE SELLER ALWAYS READY TO SELL MORE OF A COMMODITY AT HIGH PRICE IN THE MARKET

21 IF THREE UPWARD SLOPING SUPPLY CURVES SHOOTS FROM ORIGIN AND MAKING DIFFERENT

ANGLESWHAT WILL YOU SAY ABOUT THEIR PRICE ELASTICITY

22 AT A POINT OF INTERSECTION OF TWO SUPPLY CURVESWHICH ONE WILL BE MORE ELASTIC

23 WHAT CHANGE IN SUPPLY TAKES PLACE WHEN PRICE REMAINS CONSTANT AT RS 10 PER UNITTHE

SUPPLY INCREASES FROM 25 UNIT TO 40 UNIT

24 EXPLAIN ANY THREE FACTORS AFFECTING PRICE ELASTICITY OF SUPPLY

56

CLASS XII

SUB ECONOMICS CH 9 (MARKET FORMS AND PRICE DETERMINATION)

1 DEFINE MARKET AND ITS VARIOUS FORMS

2 WHAT IS PERFECT AND IMPERFECT OLIGOPOLY

3 UNDER WHICH MARKET FORM A FIRMS MARGINAL REVENUE CURVE IS EQUAL TO PRICE

4 WHEN IS A FIRM CALLED PRICE MAKER

5 WHICH MARKET FORM HAS THE LEAST NUMBER OF PRODUCERS

6 WHAT IS THE EFFECT ON PRICE WHEN A PERFECTLY COMPETITIVE FIRM TRIES TO SELL MORE

7 IN 2001 THE SUPREME COURT OF INDIA BANNED SMOKING IN PUBLIC PLACESWHAT WILL BE ITS LIKELY EFFECT

ON AVERAGE PRICE OF CIGARETTE AND QUANTITY SOLD

8 WHAT IS CARTEL

9 A FIRM UNDER MONOPOLISTIC COMPETITION CANNOT DECIDE PRICEHOWEVER IT HAS PARTIAL CONTROL OVER

ITWHY

10 WHY CAN A FIRM NOT EARN ABNORMAL PROFIT UNDER PERFECT COMPETITION IN THE LONG RUN

11 WHY IS THE DEMAND CURVE OF A FIRM UNDER MONOPOLISTIC COMPETITION MORE ELASTIC THAN UNDER

MONOPOLY

12 EXPLAIN THE IMPLICATIONS OF LARGE NUMBER OF BUYERS IN PERFECTLY COMPETITIVE MARKET

13 WHY THERE ARE ONLY FEW FIRMS IN OLIGOPOLY MARKET

14 IT IS GENERALLY OBSERVED THAT A FIRM UNDER MONOPOLISTIC COMPETITION PRODUCES AN EXCESS

QUANTITYIN YOUR VIEW IS IT A WASTAGE OF SCARCE RESOURCES

15 GIVING REASONSDISTINGUISH BTWEEN THE BEHAVIOUR OF DEMAND CURVES OF FIRMS UNDER DIFFERENT

MARKET COMPETITION

16 FIRMS UNDER MONOPOLISTIC AND OLIGOPOLY SPEND HUGE SUM OF MONEYIN PROMOTIONAL ACTIVITIES IS

IT JUSTIFIED

17 GIVE MEANING OF EQUI PRICEMARKET EQUIAND EQUI QUANTITY

18 WHAT DO YOU MEAN BY PRICE CEILING AND PRICE FLOOR

19 BY THE GIVEN EQUI IN THE MARKET EXPLAIN THE CHAIN OF EFFECTS OF

INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY

SIMULTANEOUS CHANGES IN DEMAND AND SUPPLY

20 DISTINGUISH BETWEEN COLLUSIVE AND NONCOLLUSIVEAND PERFECT AND IMPERFECT OLIGOPOLY

21 AT A GIVEN PRICE OF A GOODTHERE IS EXCESS DEMAND HOW THE EQUI PRICE BE REACHED

2

SPEECH WRITING

PRACTICE QUESTIONS

1 You are RamRama Head BoyGirl of ABC School Write a speech in 150-200 words

that you would deliver in the prayer assembly on the need for students to inculcate in

themselves virtues like truthfulness punctuality etc so that they may not only succeed in

their own life but also prove role models for others

2 You are RajRani the Head BodyHead Girls of ABC Public School Patna You have to

deliver a speech in your school assembly on the lsquoWorld Peace Dayrsquo on the topic lsquoLetrsquos

Practise Non-Violencersquo Write the speech in 150-200 words pointing out the recent acts of

terrorism that claimed innocent lives and highlighting the value of non-violence which is

the need of the hour

3 Regular practice of yoga can help in maintaining good health and even in the prevention

of so many ailments Write a speech in 150-200 words to be delivered in the morning

assembly on the usefulness of yoga

ARTICLE WRITING

1ldquoWhat people read is what people believerdquo You are concerned about the ongoing controversy

regarding mediarsquos role in sensationalizing news moulding public opinion and moral policing

Write an article emphasizing the responsibility of media You are Nayna BatraNaresh Sharma

(word limit 150-200)

2The number of women in police force seems insufficient specially when we see the increasing

involvement of women in terrorist activities Write an article in 150-200 words for lsquoHindustan

Timesrsquo on need of having more women in the police force

3Every activity that man indulges in creates waste of some kind Some of the waste can be

recycled or reused In fact the need of the hour is to conserve the earthrsquos resources in all possible

ways Write an article on the topic ldquoConservation Need of the Hourrdquo in 150-200 words You are

KamalKamla a keen environmentalist

4Today the 24 hour television news channels give us instant news from every nook and corner

of the world But the fact remains that the importance of the newspaper remains intact Write an

3


SunilSunita

DEBATE WRITING

PRACTICE QUESTIONS



words







120 words

4




------------- She

Looked but soon


Looked out at young


Out of their homes

Questions ndash









beside me


ashen like that




Questions ndash


5















skyrdquo Comment


suggest this











eyesrsquo(1)






6






7
















8















9















10

















11

















12















ऐसा करो





13













ददरा





14



















15


CLASS XII







119891(119909) = sin 119909+119909 cos 119909

119909



LONG ANSWER TYPE


1199092



(119909 minus 1)119909 119894119891 2 le 119909 lt 3 at x=2


119887 cos 119909+119886 sin 119909)minus

120587

2 lt 119909 lt

120587

2 and

119886



119889119909=

2119910

119909


119909)

119909

+ 119909(119909+1


11 Find 119889119910

119889119909 if y =

1199094radic119909+6

(3119909+5)2

12 If y= 31198902119909 + 21198903119909 prove that 1198892119910

1198891199092 - 5

119889119910

119889119909 +6y = 0



1198892119910

1198891199092 minus 3119909119889119910

119889119909minus 119910 = 0



16

WORK SHEET


CLASS-XII

VSA TYPE(1 marks)




for March


elements

3 If 119860 = [2 4 15 minus6 22 1 5



(i) aij=1

2(119894 minus 2119895)2 (ii) aij=

1

2|4119894 + 119895| (iii) aij=

119894 minus 119895 119894119891 119894 ge 119895119894 + 119895 119894119891 119894 lt 119895

(iv)119886119894119895 = 119894minus119895

119894+119895


7119860



) (10


8 If 2 [3 45 119909

] + [1 1199100 1

] = [7 0



minus2 0]=O


minus1 1] 119886119899119889 1198602 = 119896119860 119905ℎ119890119899 119908119903119894119905119890 119905ℎ119890 119905ℎ119890 119907119886119897119906119890 119900119891 119896


2lt 119909 lt 120587 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119909 119891119900119903 119908ℎ119894119888ℎ 119905ℎ119890 119898119886119905119903119894119909 [

2 sin 119909 31 2 sin 119909

] is

singular matrix

12 If |119909 + 1 119909 minus 1119909 minus 3 119909 + 2

| = |4 minus11 3


13 If ∆= |5 3 82 0 11 5 minus7



119909 119909 minus 2] 119894119904 119886 119904119894119899119892119906119897119886119903 119898119886119905119903119894119909


|


|

17





19 If |119909 sin 120579 cos 120579




] [1199092

] = [56

]


119909 + 119910 + 119911119909 + 119911119910 + 119911

] = [957

]

22 If 2119883 + 3119884 = [2 34 0

] 119886119899119889 3119883 + 2119884 = [minus2 21 minus5

] find X and Y

23 If 119860 = [3 5] 119861 = [7 3] 119905ℎ119890119899 119891119894119899119889 119898119886119905119903119894119909 119862 119904119906119888ℎ 119905ℎ119886119905 119860119862 = 119861119862

24 If A=[0 05 0

] 119891119894119899119889 11986016

25 If A=[119888119900119904120572 119878119894119899120572

minus119904119894119899120572 119888119900119904120572] find 120572 119904119886119905119894119904119891119910119894119899119892 0 lt 120572 lt

120587

2 119908ℎ119890119899 119860 + 119860119879 = radic21198682 where 119860119879 is

transpose of A


skew-symmetric

27 if A=[1 24 2


28 If A=[120783 120782 120784120782 120784 120783120784 120782 120785

] find A(adj A)



] 119894119904 119894119899119907119890119903119904119890 119900119891 119905ℎ119890 119898119886119905119903119894119909 [minus7 minus9 10


]


30 If 119860 = [1 minus3 10 2 minus12 1 3

] 119861 = [minus1 0 15 4 62 1 1


] 119907119890119903119894119891119910 119905ℎ119886119905

(i) A(119861119862) = (119860119861)119862 (ii) (A+B)C=AC+BC

31 If A=[0 3

minus7 5] 119868 = [

1 00 1

] 119891119894119899119889 119896 119904119906119888ℎ 119905ℎ119886119905 1198961198602 = 5119860 minus 21119868


minus3 4] 119860 = [


]

33 Let A=[1 minus2 30 4 7

] 119886119899119889 119861 = [0 4 22 minus2 1





35 If A=[119886 1198870 1


119886minus1


18

36 If A=[352




38 If A=[1 2 22 1 22 2 1



(i)[1 23 7

](ii) [2 17 4

]



| = (119909 + 119910 + 119911)3


119909 119909 + 119910 119909 + 2119910119909 + 2119910 119909 119909 + 119910119909 + 119910 119909 + 2119910 119909

| = 91199102(119909 + 119910)

42 If 119891(119909) = |119886 minus1 0

119886119909 119886 minus11198861199092 119886119909 119886

| 119906119904119894119899119892 119901119903119900119901119890119903119905119894119890119904 119900119891 119889119890119905119890119903119898119894119899119886119899119905119904 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119891(2119909) minus

119891(119909)

43 Let f(t)=|119888119900119904119905 119905 1

2119904119894119899119905 119905 2119905119904119894119899119905 119905 119905

| 119905ℎ119890119899 119891119894119899119889 lim119905rarr0

119891(119905)

1199052


2 21198861199052) 119886119899119889 119862(11988611990532 21198861199053)



47 If 119860 = [2 31 4

] 119886119899119889119861 = [1 23 4

] 119907119890119903119894119891119910 119905ℎ119886119905 119886119889119895(119860119861) = (119886119889119895119861)(119886119889119895 119860)



] 119886119899119889 119907119890119903119894119891119910 119905ℎ119886119905 119860(119886119889119895119860) = (119886119889119895119860)119860 = |119860|1198683

49 Let 119860 = [3 72 5

] 119886119899119889119861 = [6 87 9





] 119904ℎ119900119908 119905ℎ119886119905 1198603 = 119860minus1



(i)A=[5 200 1

] (ii)A=[1 minus3 24 minus1 23 5 2

]


] 119883 [4 73 5

] = [1 00 1

]


19


| = 0


] and




2

57 If A=[1 0 20 2 12 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896





two types













-x+2y+5z=2 2x-3y+z=15 -x +y +z=-3


(i)[2 3 minus3


](ii) [2 0 minus15 1 00 1 3

]


(119887 + 119888)2 119887119886 119888119886

119886119887 (119888 + 119886)2 119888119887

119886119888 119887119888 (119886 + 119887)2

| =

2119886119887119888(119886 + 119887 + 119888)3

64 In a ∆119860119861119862 if |1 1 1

1 + 119904119894119899 119860 1 + 119904119894119899 119861 1 + 119904119894119899 119888119904119894119899 119860 + sin2 119860 119904119894119899 119861 + sin2 119861 119904119894119899 119861 + sin2 119861


isosceles triangle

65 If |119901 119887 119888119886 119902 119888119886 119887 119903

| = 0 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119901

119901minus119886+

119902

119902minus119887+

119903

119903minus119888 119901 ne 119886 119902 ne 119887 119903 ne 119888


119961minus

120783

119962+

120783

119963= 120787

120784

119961+

120785

119962minus

120786

119963= minus120789

120784

119961+

120783

119962minus

120784

119963= minus120785

20











| = 0









70 Prove that |






(119886 + 1)(119886 + 2) 119886 + 2 1

(119886 + 3)(119886 + 2) 119886 + 3 1

(119886 + 3)(119886 + 4) 119886 + 4 1| = minus2

If A=[1 0 2

0 2 1

2 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896

21

WORK SHEET I

CLASS XII

MATHEMATICS



1 MARK QUESTIONS






value of 24


2 MARK QUESTIONS







1 ) is two






22


13 If f(x) = 119909minus1



its inverse

( Ans 119891minus1(119909) = 5minus119909

7 )



4 MARK QUESTIONS


relation







120587













2]

23

WORKSHEET 12 IP

Q1 Table SchoolBus













order of rtno











24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




3


SunilSunita

DEBATE WRITING

PRACTICE QUESTIONS



words







120 words

4




------------- She

Looked but soon


Looked out at young


Out of their homes

Questions ndash









beside me


ashen like that




Questions ndash


5















skyrdquo Comment


suggest this











eyesrsquo(1)






6






7
















8















9















10

















11

















12















ऐसा करो





13













ददरा





14



















15


CLASS XII







119891(119909) = sin 119909+119909 cos 119909

119909



LONG ANSWER TYPE


1199092



(119909 minus 1)119909 119894119891 2 le 119909 lt 3 at x=2


119887 cos 119909+119886 sin 119909)minus

120587

2 lt 119909 lt

120587

2 and

119886



119889119909=

2119910

119909


119909)

119909

+ 119909(119909+1


11 Find 119889119910

119889119909 if y =

1199094radic119909+6

(3119909+5)2

12 If y= 31198902119909 + 21198903119909 prove that 1198892119910

1198891199092 - 5

119889119910

119889119909 +6y = 0



1198892119910

1198891199092 minus 3119909119889119910

119889119909minus 119910 = 0



16

WORK SHEET


CLASS-XII

VSA TYPE(1 marks)




for March


elements

3 If 119860 = [2 4 15 minus6 22 1 5



(i) aij=1

2(119894 minus 2119895)2 (ii) aij=

1

2|4119894 + 119895| (iii) aij=

119894 minus 119895 119894119891 119894 ge 119895119894 + 119895 119894119891 119894 lt 119895

(iv)119886119894119895 = 119894minus119895

119894+119895


7119860



) (10


8 If 2 [3 45 119909

] + [1 1199100 1

] = [7 0



minus2 0]=O


minus1 1] 119886119899119889 1198602 = 119896119860 119905ℎ119890119899 119908119903119894119905119890 119905ℎ119890 119905ℎ119890 119907119886119897119906119890 119900119891 119896


2lt 119909 lt 120587 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119909 119891119900119903 119908ℎ119894119888ℎ 119905ℎ119890 119898119886119905119903119894119909 [

2 sin 119909 31 2 sin 119909

] is

singular matrix

12 If |119909 + 1 119909 minus 1119909 minus 3 119909 + 2

| = |4 minus11 3


13 If ∆= |5 3 82 0 11 5 minus7



119909 119909 minus 2] 119894119904 119886 119904119894119899119892119906119897119886119903 119898119886119905119903119894119909


|


|

17





19 If |119909 sin 120579 cos 120579




] [1199092

] = [56

]


119909 + 119910 + 119911119909 + 119911119910 + 119911

] = [957

]

22 If 2119883 + 3119884 = [2 34 0

] 119886119899119889 3119883 + 2119884 = [minus2 21 minus5

] find X and Y

23 If 119860 = [3 5] 119861 = [7 3] 119905ℎ119890119899 119891119894119899119889 119898119886119905119903119894119909 119862 119904119906119888ℎ 119905ℎ119886119905 119860119862 = 119861119862

24 If A=[0 05 0

] 119891119894119899119889 11986016

25 If A=[119888119900119904120572 119878119894119899120572

minus119904119894119899120572 119888119900119904120572] find 120572 119904119886119905119894119904119891119910119894119899119892 0 lt 120572 lt

120587

2 119908ℎ119890119899 119860 + 119860119879 = radic21198682 where 119860119879 is

transpose of A


skew-symmetric

27 if A=[1 24 2


28 If A=[120783 120782 120784120782 120784 120783120784 120782 120785

] find A(adj A)



] 119894119904 119894119899119907119890119903119904119890 119900119891 119905ℎ119890 119898119886119905119903119894119909 [minus7 minus9 10


]


30 If 119860 = [1 minus3 10 2 minus12 1 3

] 119861 = [minus1 0 15 4 62 1 1


] 119907119890119903119894119891119910 119905ℎ119886119905

(i) A(119861119862) = (119860119861)119862 (ii) (A+B)C=AC+BC

31 If A=[0 3

minus7 5] 119868 = [

1 00 1

] 119891119894119899119889 119896 119904119906119888ℎ 119905ℎ119886119905 1198961198602 = 5119860 minus 21119868


minus3 4] 119860 = [


]

33 Let A=[1 minus2 30 4 7

] 119886119899119889 119861 = [0 4 22 minus2 1





35 If A=[119886 1198870 1


119886minus1


18

36 If A=[352




38 If A=[1 2 22 1 22 2 1



(i)[1 23 7

](ii) [2 17 4

]



| = (119909 + 119910 + 119911)3


119909 119909 + 119910 119909 + 2119910119909 + 2119910 119909 119909 + 119910119909 + 119910 119909 + 2119910 119909

| = 91199102(119909 + 119910)

42 If 119891(119909) = |119886 minus1 0

119886119909 119886 minus11198861199092 119886119909 119886

| 119906119904119894119899119892 119901119903119900119901119890119903119905119894119890119904 119900119891 119889119890119905119890119903119898119894119899119886119899119905119904 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119891(2119909) minus

119891(119909)

43 Let f(t)=|119888119900119904119905 119905 1

2119904119894119899119905 119905 2119905119904119894119899119905 119905 119905

| 119905ℎ119890119899 119891119894119899119889 lim119905rarr0

119891(119905)

1199052


2 21198861199052) 119886119899119889 119862(11988611990532 21198861199053)



47 If 119860 = [2 31 4

] 119886119899119889119861 = [1 23 4

] 119907119890119903119894119891119910 119905ℎ119886119905 119886119889119895(119860119861) = (119886119889119895119861)(119886119889119895 119860)



] 119886119899119889 119907119890119903119894119891119910 119905ℎ119886119905 119860(119886119889119895119860) = (119886119889119895119860)119860 = |119860|1198683

49 Let 119860 = [3 72 5

] 119886119899119889119861 = [6 87 9





] 119904ℎ119900119908 119905ℎ119886119905 1198603 = 119860minus1



(i)A=[5 200 1

] (ii)A=[1 minus3 24 minus1 23 5 2

]


] 119883 [4 73 5

] = [1 00 1

]


19


| = 0


] and




2

57 If A=[1 0 20 2 12 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896





two types













-x+2y+5z=2 2x-3y+z=15 -x +y +z=-3


(i)[2 3 minus3


](ii) [2 0 minus15 1 00 1 3

]


(119887 + 119888)2 119887119886 119888119886

119886119887 (119888 + 119886)2 119888119887

119886119888 119887119888 (119886 + 119887)2

| =

2119886119887119888(119886 + 119887 + 119888)3

64 In a ∆119860119861119862 if |1 1 1

1 + 119904119894119899 119860 1 + 119904119894119899 119861 1 + 119904119894119899 119888119904119894119899 119860 + sin2 119860 119904119894119899 119861 + sin2 119861 119904119894119899 119861 + sin2 119861


isosceles triangle

65 If |119901 119887 119888119886 119902 119888119886 119887 119903

| = 0 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119901

119901minus119886+

119902

119902minus119887+

119903

119903minus119888 119901 ne 119886 119902 ne 119887 119903 ne 119888


119961minus

120783

119962+

120783

119963= 120787

120784

119961+

120785

119962minus

120786

119963= minus120789

120784

119961+

120783

119962minus

120784

119963= minus120785

20











| = 0









70 Prove that |






(119886 + 1)(119886 + 2) 119886 + 2 1

(119886 + 3)(119886 + 2) 119886 + 3 1

(119886 + 3)(119886 + 4) 119886 + 4 1| = minus2

If A=[1 0 2

0 2 1

2 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896

21

WORK SHEET I

CLASS XII

MATHEMATICS



1 MARK QUESTIONS






value of 24


2 MARK QUESTIONS







1 ) is two






22


13 If f(x) = 119909minus1



its inverse

( Ans 119891minus1(119909) = 5minus119909

7 )



4 MARK QUESTIONS


relation







120587













2]

23

WORKSHEET 12 IP

Q1 Table SchoolBus













order of rtno











24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




4




------------- She

Looked but soon


Looked out at young


Out of their homes

Questions ndash









beside me


ashen like that




Questions ndash


5















skyrdquo Comment


suggest this











eyesrsquo(1)






6






7
















8















9















10

















11

















12















ऐसा करो





13













ददरा





14



















15


CLASS XII







119891(119909) = sin 119909+119909 cos 119909

119909



LONG ANSWER TYPE


1199092



(119909 minus 1)119909 119894119891 2 le 119909 lt 3 at x=2


119887 cos 119909+119886 sin 119909)minus

120587

2 lt 119909 lt

120587

2 and

119886



119889119909=

2119910

119909


119909)

119909

+ 119909(119909+1


11 Find 119889119910

119889119909 if y =

1199094radic119909+6

(3119909+5)2

12 If y= 31198902119909 + 21198903119909 prove that 1198892119910

1198891199092 - 5

119889119910

119889119909 +6y = 0



1198892119910

1198891199092 minus 3119909119889119910

119889119909minus 119910 = 0



16

WORK SHEET


CLASS-XII

VSA TYPE(1 marks)




for March


elements

3 If 119860 = [2 4 15 minus6 22 1 5



(i) aij=1

2(119894 minus 2119895)2 (ii) aij=

1

2|4119894 + 119895| (iii) aij=

119894 minus 119895 119894119891 119894 ge 119895119894 + 119895 119894119891 119894 lt 119895

(iv)119886119894119895 = 119894minus119895

119894+119895


7119860



) (10


8 If 2 [3 45 119909

] + [1 1199100 1

] = [7 0



minus2 0]=O


minus1 1] 119886119899119889 1198602 = 119896119860 119905ℎ119890119899 119908119903119894119905119890 119905ℎ119890 119905ℎ119890 119907119886119897119906119890 119900119891 119896


2lt 119909 lt 120587 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119909 119891119900119903 119908ℎ119894119888ℎ 119905ℎ119890 119898119886119905119903119894119909 [

2 sin 119909 31 2 sin 119909

] is

singular matrix

12 If |119909 + 1 119909 minus 1119909 minus 3 119909 + 2

| = |4 minus11 3


13 If ∆= |5 3 82 0 11 5 minus7



119909 119909 minus 2] 119894119904 119886 119904119894119899119892119906119897119886119903 119898119886119905119903119894119909


|


|

17





19 If |119909 sin 120579 cos 120579




] [1199092

] = [56

]


119909 + 119910 + 119911119909 + 119911119910 + 119911

] = [957

]

22 If 2119883 + 3119884 = [2 34 0

] 119886119899119889 3119883 + 2119884 = [minus2 21 minus5

] find X and Y

23 If 119860 = [3 5] 119861 = [7 3] 119905ℎ119890119899 119891119894119899119889 119898119886119905119903119894119909 119862 119904119906119888ℎ 119905ℎ119886119905 119860119862 = 119861119862

24 If A=[0 05 0

] 119891119894119899119889 11986016

25 If A=[119888119900119904120572 119878119894119899120572

minus119904119894119899120572 119888119900119904120572] find 120572 119904119886119905119894119904119891119910119894119899119892 0 lt 120572 lt

120587

2 119908ℎ119890119899 119860 + 119860119879 = radic21198682 where 119860119879 is

transpose of A


skew-symmetric

27 if A=[1 24 2


28 If A=[120783 120782 120784120782 120784 120783120784 120782 120785

] find A(adj A)



] 119894119904 119894119899119907119890119903119904119890 119900119891 119905ℎ119890 119898119886119905119903119894119909 [minus7 minus9 10


]


30 If 119860 = [1 minus3 10 2 minus12 1 3

] 119861 = [minus1 0 15 4 62 1 1


] 119907119890119903119894119891119910 119905ℎ119886119905

(i) A(119861119862) = (119860119861)119862 (ii) (A+B)C=AC+BC

31 If A=[0 3

minus7 5] 119868 = [

1 00 1

] 119891119894119899119889 119896 119904119906119888ℎ 119905ℎ119886119905 1198961198602 = 5119860 minus 21119868


minus3 4] 119860 = [


]

33 Let A=[1 minus2 30 4 7

] 119886119899119889 119861 = [0 4 22 minus2 1





35 If A=[119886 1198870 1


119886minus1


18

36 If A=[352




38 If A=[1 2 22 1 22 2 1



(i)[1 23 7

](ii) [2 17 4

]



| = (119909 + 119910 + 119911)3


119909 119909 + 119910 119909 + 2119910119909 + 2119910 119909 119909 + 119910119909 + 119910 119909 + 2119910 119909

| = 91199102(119909 + 119910)

42 If 119891(119909) = |119886 minus1 0

119886119909 119886 minus11198861199092 119886119909 119886

| 119906119904119894119899119892 119901119903119900119901119890119903119905119894119890119904 119900119891 119889119890119905119890119903119898119894119899119886119899119905119904 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119891(2119909) minus

119891(119909)

43 Let f(t)=|119888119900119904119905 119905 1

2119904119894119899119905 119905 2119905119904119894119899119905 119905 119905

| 119905ℎ119890119899 119891119894119899119889 lim119905rarr0

119891(119905)

1199052


2 21198861199052) 119886119899119889 119862(11988611990532 21198861199053)



47 If 119860 = [2 31 4

] 119886119899119889119861 = [1 23 4

] 119907119890119903119894119891119910 119905ℎ119886119905 119886119889119895(119860119861) = (119886119889119895119861)(119886119889119895 119860)



] 119886119899119889 119907119890119903119894119891119910 119905ℎ119886119905 119860(119886119889119895119860) = (119886119889119895119860)119860 = |119860|1198683

49 Let 119860 = [3 72 5

] 119886119899119889119861 = [6 87 9





] 119904ℎ119900119908 119905ℎ119886119905 1198603 = 119860minus1



(i)A=[5 200 1

] (ii)A=[1 minus3 24 minus1 23 5 2

]


] 119883 [4 73 5

] = [1 00 1

]


19


| = 0


] and




2

57 If A=[1 0 20 2 12 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896





two types













-x+2y+5z=2 2x-3y+z=15 -x +y +z=-3


(i)[2 3 minus3


](ii) [2 0 minus15 1 00 1 3

]


(119887 + 119888)2 119887119886 119888119886

119886119887 (119888 + 119886)2 119888119887

119886119888 119887119888 (119886 + 119887)2

| =

2119886119887119888(119886 + 119887 + 119888)3

64 In a ∆119860119861119862 if |1 1 1

1 + 119904119894119899 119860 1 + 119904119894119899 119861 1 + 119904119894119899 119888119904119894119899 119860 + sin2 119860 119904119894119899 119861 + sin2 119861 119904119894119899 119861 + sin2 119861


isosceles triangle

65 If |119901 119887 119888119886 119902 119888119886 119887 119903

| = 0 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119901

119901minus119886+

119902

119902minus119887+

119903

119903minus119888 119901 ne 119886 119902 ne 119887 119903 ne 119888


119961minus

120783

119962+

120783

119963= 120787

120784

119961+

120785

119962minus

120786

119963= minus120789

120784

119961+

120783

119962minus

120784

119963= minus120785

20











| = 0









70 Prove that |






(119886 + 1)(119886 + 2) 119886 + 2 1

(119886 + 3)(119886 + 2) 119886 + 3 1

(119886 + 3)(119886 + 4) 119886 + 4 1| = minus2

If A=[1 0 2

0 2 1

2 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896

21

WORK SHEET I

CLASS XII

MATHEMATICS



1 MARK QUESTIONS






value of 24


2 MARK QUESTIONS







1 ) is two






22


13 If f(x) = 119909minus1



its inverse

( Ans 119891minus1(119909) = 5minus119909

7 )



4 MARK QUESTIONS


relation







120587













2]

23

WORKSHEET 12 IP

Q1 Table SchoolBus













order of rtno











24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




5















skyrdquo Comment


suggest this











eyesrsquo(1)






6






7
















8















9















10

















11

















12















ऐसा करो





13













ददरा





14



















15


CLASS XII







119891(119909) = sin 119909+119909 cos 119909

119909



LONG ANSWER TYPE


1199092



(119909 minus 1)119909 119894119891 2 le 119909 lt 3 at x=2


119887 cos 119909+119886 sin 119909)minus

120587

2 lt 119909 lt

120587

2 and

119886



119889119909=

2119910

119909


119909)

119909

+ 119909(119909+1


11 Find 119889119910

119889119909 if y =

1199094radic119909+6

(3119909+5)2

12 If y= 31198902119909 + 21198903119909 prove that 1198892119910

1198891199092 - 5

119889119910

119889119909 +6y = 0



1198892119910

1198891199092 minus 3119909119889119910

119889119909minus 119910 = 0



16

WORK SHEET


CLASS-XII

VSA TYPE(1 marks)




for March


elements

3 If 119860 = [2 4 15 minus6 22 1 5



(i) aij=1

2(119894 minus 2119895)2 (ii) aij=

1

2|4119894 + 119895| (iii) aij=

119894 minus 119895 119894119891 119894 ge 119895119894 + 119895 119894119891 119894 lt 119895

(iv)119886119894119895 = 119894minus119895

119894+119895


7119860



) (10


8 If 2 [3 45 119909

] + [1 1199100 1

] = [7 0



minus2 0]=O


minus1 1] 119886119899119889 1198602 = 119896119860 119905ℎ119890119899 119908119903119894119905119890 119905ℎ119890 119905ℎ119890 119907119886119897119906119890 119900119891 119896


2lt 119909 lt 120587 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119909 119891119900119903 119908ℎ119894119888ℎ 119905ℎ119890 119898119886119905119903119894119909 [

2 sin 119909 31 2 sin 119909

] is

singular matrix

12 If |119909 + 1 119909 minus 1119909 minus 3 119909 + 2

| = |4 minus11 3


13 If ∆= |5 3 82 0 11 5 minus7



119909 119909 minus 2] 119894119904 119886 119904119894119899119892119906119897119886119903 119898119886119905119903119894119909


|


|

17





19 If |119909 sin 120579 cos 120579




] [1199092

] = [56

]


119909 + 119910 + 119911119909 + 119911119910 + 119911

] = [957

]

22 If 2119883 + 3119884 = [2 34 0

] 119886119899119889 3119883 + 2119884 = [minus2 21 minus5

] find X and Y

23 If 119860 = [3 5] 119861 = [7 3] 119905ℎ119890119899 119891119894119899119889 119898119886119905119903119894119909 119862 119904119906119888ℎ 119905ℎ119886119905 119860119862 = 119861119862

24 If A=[0 05 0

] 119891119894119899119889 11986016

25 If A=[119888119900119904120572 119878119894119899120572

minus119904119894119899120572 119888119900119904120572] find 120572 119904119886119905119894119904119891119910119894119899119892 0 lt 120572 lt

120587

2 119908ℎ119890119899 119860 + 119860119879 = radic21198682 where 119860119879 is

transpose of A


skew-symmetric

27 if A=[1 24 2


28 If A=[120783 120782 120784120782 120784 120783120784 120782 120785

] find A(adj A)



] 119894119904 119894119899119907119890119903119904119890 119900119891 119905ℎ119890 119898119886119905119903119894119909 [minus7 minus9 10


]


30 If 119860 = [1 minus3 10 2 minus12 1 3

] 119861 = [minus1 0 15 4 62 1 1


] 119907119890119903119894119891119910 119905ℎ119886119905

(i) A(119861119862) = (119860119861)119862 (ii) (A+B)C=AC+BC

31 If A=[0 3

minus7 5] 119868 = [

1 00 1

] 119891119894119899119889 119896 119904119906119888ℎ 119905ℎ119886119905 1198961198602 = 5119860 minus 21119868


minus3 4] 119860 = [


]

33 Let A=[1 minus2 30 4 7

] 119886119899119889 119861 = [0 4 22 minus2 1





35 If A=[119886 1198870 1


119886minus1


18

36 If A=[352




38 If A=[1 2 22 1 22 2 1



(i)[1 23 7

](ii) [2 17 4

]



| = (119909 + 119910 + 119911)3


119909 119909 + 119910 119909 + 2119910119909 + 2119910 119909 119909 + 119910119909 + 119910 119909 + 2119910 119909

| = 91199102(119909 + 119910)

42 If 119891(119909) = |119886 minus1 0

119886119909 119886 minus11198861199092 119886119909 119886

| 119906119904119894119899119892 119901119903119900119901119890119903119905119894119890119904 119900119891 119889119890119905119890119903119898119894119899119886119899119905119904 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119891(2119909) minus

119891(119909)

43 Let f(t)=|119888119900119904119905 119905 1

2119904119894119899119905 119905 2119905119904119894119899119905 119905 119905

| 119905ℎ119890119899 119891119894119899119889 lim119905rarr0

119891(119905)

1199052


2 21198861199052) 119886119899119889 119862(11988611990532 21198861199053)



47 If 119860 = [2 31 4

] 119886119899119889119861 = [1 23 4

] 119907119890119903119894119891119910 119905ℎ119886119905 119886119889119895(119860119861) = (119886119889119895119861)(119886119889119895 119860)



] 119886119899119889 119907119890119903119894119891119910 119905ℎ119886119905 119860(119886119889119895119860) = (119886119889119895119860)119860 = |119860|1198683

49 Let 119860 = [3 72 5

] 119886119899119889119861 = [6 87 9





] 119904ℎ119900119908 119905ℎ119886119905 1198603 = 119860minus1



(i)A=[5 200 1

] (ii)A=[1 minus3 24 minus1 23 5 2

]


] 119883 [4 73 5

] = [1 00 1

]


19


| = 0


] and




2

57 If A=[1 0 20 2 12 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896





two types













-x+2y+5z=2 2x-3y+z=15 -x +y +z=-3


(i)[2 3 minus3


](ii) [2 0 minus15 1 00 1 3

]


(119887 + 119888)2 119887119886 119888119886

119886119887 (119888 + 119886)2 119888119887

119886119888 119887119888 (119886 + 119887)2

| =

2119886119887119888(119886 + 119887 + 119888)3

64 In a ∆119860119861119862 if |1 1 1

1 + 119904119894119899 119860 1 + 119904119894119899 119861 1 + 119904119894119899 119888119904119894119899 119860 + sin2 119860 119904119894119899 119861 + sin2 119861 119904119894119899 119861 + sin2 119861


isosceles triangle

65 If |119901 119887 119888119886 119902 119888119886 119887 119903

| = 0 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119901

119901minus119886+

119902

119902minus119887+

119903

119903minus119888 119901 ne 119886 119902 ne 119887 119903 ne 119888


119961minus

120783

119962+

120783

119963= 120787

120784

119961+

120785

119962minus

120786

119963= minus120789

120784

119961+

120783

119962minus

120784

119963= minus120785

20











| = 0









70 Prove that |






(119886 + 1)(119886 + 2) 119886 + 2 1

(119886 + 3)(119886 + 2) 119886 + 3 1

(119886 + 3)(119886 + 4) 119886 + 4 1| = minus2

If A=[1 0 2

0 2 1

2 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896

21

WORK SHEET I

CLASS XII

MATHEMATICS



1 MARK QUESTIONS






value of 24


2 MARK QUESTIONS







1 ) is two






22


13 If f(x) = 119909minus1



its inverse

( Ans 119891minus1(119909) = 5minus119909

7 )



4 MARK QUESTIONS


relation







120587













2]

23

WORKSHEET 12 IP

Q1 Table SchoolBus













order of rtno











24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




6






7
















8















9















10

















11

















12















ऐसा करो





13













ददरा





14



















15


CLASS XII







119891(119909) = sin 119909+119909 cos 119909

119909



LONG ANSWER TYPE


1199092



(119909 minus 1)119909 119894119891 2 le 119909 lt 3 at x=2


119887 cos 119909+119886 sin 119909)minus

120587

2 lt 119909 lt

120587

2 and

119886



119889119909=

2119910

119909


119909)

119909

+ 119909(119909+1


11 Find 119889119910

119889119909 if y =

1199094radic119909+6

(3119909+5)2

12 If y= 31198902119909 + 21198903119909 prove that 1198892119910

1198891199092 - 5

119889119910

119889119909 +6y = 0



1198892119910

1198891199092 minus 3119909119889119910

119889119909minus 119910 = 0



16

WORK SHEET


CLASS-XII

VSA TYPE(1 marks)




for March


elements

3 If 119860 = [2 4 15 minus6 22 1 5



(i) aij=1

2(119894 minus 2119895)2 (ii) aij=

1

2|4119894 + 119895| (iii) aij=

119894 minus 119895 119894119891 119894 ge 119895119894 + 119895 119894119891 119894 lt 119895

(iv)119886119894119895 = 119894minus119895

119894+119895


7119860



) (10


8 If 2 [3 45 119909

] + [1 1199100 1

] = [7 0



minus2 0]=O


minus1 1] 119886119899119889 1198602 = 119896119860 119905ℎ119890119899 119908119903119894119905119890 119905ℎ119890 119905ℎ119890 119907119886119897119906119890 119900119891 119896


2lt 119909 lt 120587 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119909 119891119900119903 119908ℎ119894119888ℎ 119905ℎ119890 119898119886119905119903119894119909 [

2 sin 119909 31 2 sin 119909

] is

singular matrix

12 If |119909 + 1 119909 minus 1119909 minus 3 119909 + 2

| = |4 minus11 3


13 If ∆= |5 3 82 0 11 5 minus7



119909 119909 minus 2] 119894119904 119886 119904119894119899119892119906119897119886119903 119898119886119905119903119894119909


|


|

17





19 If |119909 sin 120579 cos 120579




] [1199092

] = [56

]


119909 + 119910 + 119911119909 + 119911119910 + 119911

] = [957

]

22 If 2119883 + 3119884 = [2 34 0

] 119886119899119889 3119883 + 2119884 = [minus2 21 minus5

] find X and Y

23 If 119860 = [3 5] 119861 = [7 3] 119905ℎ119890119899 119891119894119899119889 119898119886119905119903119894119909 119862 119904119906119888ℎ 119905ℎ119886119905 119860119862 = 119861119862

24 If A=[0 05 0

] 119891119894119899119889 11986016

25 If A=[119888119900119904120572 119878119894119899120572

minus119904119894119899120572 119888119900119904120572] find 120572 119904119886119905119894119904119891119910119894119899119892 0 lt 120572 lt

120587

2 119908ℎ119890119899 119860 + 119860119879 = radic21198682 where 119860119879 is

transpose of A


skew-symmetric

27 if A=[1 24 2


28 If A=[120783 120782 120784120782 120784 120783120784 120782 120785

] find A(adj A)



] 119894119904 119894119899119907119890119903119904119890 119900119891 119905ℎ119890 119898119886119905119903119894119909 [minus7 minus9 10


]


30 If 119860 = [1 minus3 10 2 minus12 1 3

] 119861 = [minus1 0 15 4 62 1 1


] 119907119890119903119894119891119910 119905ℎ119886119905

(i) A(119861119862) = (119860119861)119862 (ii) (A+B)C=AC+BC

31 If A=[0 3

minus7 5] 119868 = [

1 00 1

] 119891119894119899119889 119896 119904119906119888ℎ 119905ℎ119886119905 1198961198602 = 5119860 minus 21119868


minus3 4] 119860 = [


]

33 Let A=[1 minus2 30 4 7

] 119886119899119889 119861 = [0 4 22 minus2 1





35 If A=[119886 1198870 1


119886minus1


18

36 If A=[352




38 If A=[1 2 22 1 22 2 1



(i)[1 23 7

](ii) [2 17 4

]



| = (119909 + 119910 + 119911)3


119909 119909 + 119910 119909 + 2119910119909 + 2119910 119909 119909 + 119910119909 + 119910 119909 + 2119910 119909

| = 91199102(119909 + 119910)

42 If 119891(119909) = |119886 minus1 0

119886119909 119886 minus11198861199092 119886119909 119886

| 119906119904119894119899119892 119901119903119900119901119890119903119905119894119890119904 119900119891 119889119890119905119890119903119898119894119899119886119899119905119904 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119891(2119909) minus

119891(119909)

43 Let f(t)=|119888119900119904119905 119905 1

2119904119894119899119905 119905 2119905119904119894119899119905 119905 119905

| 119905ℎ119890119899 119891119894119899119889 lim119905rarr0

119891(119905)

1199052


2 21198861199052) 119886119899119889 119862(11988611990532 21198861199053)



47 If 119860 = [2 31 4

] 119886119899119889119861 = [1 23 4

] 119907119890119903119894119891119910 119905ℎ119886119905 119886119889119895(119860119861) = (119886119889119895119861)(119886119889119895 119860)



] 119886119899119889 119907119890119903119894119891119910 119905ℎ119886119905 119860(119886119889119895119860) = (119886119889119895119860)119860 = |119860|1198683

49 Let 119860 = [3 72 5

] 119886119899119889119861 = [6 87 9





] 119904ℎ119900119908 119905ℎ119886119905 1198603 = 119860minus1



(i)A=[5 200 1

] (ii)A=[1 minus3 24 minus1 23 5 2

]


] 119883 [4 73 5

] = [1 00 1

]


19


| = 0


] and




2

57 If A=[1 0 20 2 12 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896





two types













-x+2y+5z=2 2x-3y+z=15 -x +y +z=-3


(i)[2 3 minus3


](ii) [2 0 minus15 1 00 1 3

]


(119887 + 119888)2 119887119886 119888119886

119886119887 (119888 + 119886)2 119888119887

119886119888 119887119888 (119886 + 119887)2

| =

2119886119887119888(119886 + 119887 + 119888)3

64 In a ∆119860119861119862 if |1 1 1

1 + 119904119894119899 119860 1 + 119904119894119899 119861 1 + 119904119894119899 119888119904119894119899 119860 + sin2 119860 119904119894119899 119861 + sin2 119861 119904119894119899 119861 + sin2 119861


isosceles triangle

65 If |119901 119887 119888119886 119902 119888119886 119887 119903

| = 0 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119901

119901minus119886+

119902

119902minus119887+

119903

119903minus119888 119901 ne 119886 119902 ne 119887 119903 ne 119888


119961minus

120783

119962+

120783

119963= 120787

120784

119961+

120785

119962minus

120786

119963= minus120789

120784

119961+

120783

119962minus

120784

119963= minus120785

20











| = 0









70 Prove that |






(119886 + 1)(119886 + 2) 119886 + 2 1

(119886 + 3)(119886 + 2) 119886 + 3 1

(119886 + 3)(119886 + 4) 119886 + 4 1| = minus2

If A=[1 0 2

0 2 1

2 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896

21

WORK SHEET I

CLASS XII

MATHEMATICS



1 MARK QUESTIONS






value of 24


2 MARK QUESTIONS







1 ) is two






22


13 If f(x) = 119909minus1



its inverse

( Ans 119891minus1(119909) = 5minus119909

7 )



4 MARK QUESTIONS


relation







120587













2]

23

WORKSHEET 12 IP

Q1 Table SchoolBus













order of rtno











24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




7
















8















9















10

















11

















12















ऐसा करो





13













ददरा





14



















15


CLASS XII







119891(119909) = sin 119909+119909 cos 119909

119909



LONG ANSWER TYPE


1199092



(119909 minus 1)119909 119894119891 2 le 119909 lt 3 at x=2


119887 cos 119909+119886 sin 119909)minus

120587

2 lt 119909 lt

120587

2 and

119886



119889119909=

2119910

119909


119909)

119909

+ 119909(119909+1


11 Find 119889119910

119889119909 if y =

1199094radic119909+6

(3119909+5)2

12 If y= 31198902119909 + 21198903119909 prove that 1198892119910

1198891199092 - 5

119889119910

119889119909 +6y = 0



1198892119910

1198891199092 minus 3119909119889119910

119889119909minus 119910 = 0



16

WORK SHEET


CLASS-XII

VSA TYPE(1 marks)




for March


elements

3 If 119860 = [2 4 15 minus6 22 1 5



(i) aij=1

2(119894 minus 2119895)2 (ii) aij=

1

2|4119894 + 119895| (iii) aij=

119894 minus 119895 119894119891 119894 ge 119895119894 + 119895 119894119891 119894 lt 119895

(iv)119886119894119895 = 119894minus119895

119894+119895


7119860



) (10


8 If 2 [3 45 119909

] + [1 1199100 1

] = [7 0



minus2 0]=O


minus1 1] 119886119899119889 1198602 = 119896119860 119905ℎ119890119899 119908119903119894119905119890 119905ℎ119890 119905ℎ119890 119907119886119897119906119890 119900119891 119896


2lt 119909 lt 120587 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119909 119891119900119903 119908ℎ119894119888ℎ 119905ℎ119890 119898119886119905119903119894119909 [

2 sin 119909 31 2 sin 119909

] is

singular matrix

12 If |119909 + 1 119909 minus 1119909 minus 3 119909 + 2

| = |4 minus11 3


13 If ∆= |5 3 82 0 11 5 minus7



119909 119909 minus 2] 119894119904 119886 119904119894119899119892119906119897119886119903 119898119886119905119903119894119909


|


|

17





19 If |119909 sin 120579 cos 120579




] [1199092

] = [56

]


119909 + 119910 + 119911119909 + 119911119910 + 119911

] = [957

]

22 If 2119883 + 3119884 = [2 34 0

] 119886119899119889 3119883 + 2119884 = [minus2 21 minus5

] find X and Y

23 If 119860 = [3 5] 119861 = [7 3] 119905ℎ119890119899 119891119894119899119889 119898119886119905119903119894119909 119862 119904119906119888ℎ 119905ℎ119886119905 119860119862 = 119861119862

24 If A=[0 05 0

] 119891119894119899119889 11986016

25 If A=[119888119900119904120572 119878119894119899120572

minus119904119894119899120572 119888119900119904120572] find 120572 119904119886119905119894119904119891119910119894119899119892 0 lt 120572 lt

120587

2 119908ℎ119890119899 119860 + 119860119879 = radic21198682 where 119860119879 is

transpose of A


skew-symmetric

27 if A=[1 24 2


28 If A=[120783 120782 120784120782 120784 120783120784 120782 120785

] find A(adj A)



] 119894119904 119894119899119907119890119903119904119890 119900119891 119905ℎ119890 119898119886119905119903119894119909 [minus7 minus9 10


]


30 If 119860 = [1 minus3 10 2 minus12 1 3

] 119861 = [minus1 0 15 4 62 1 1


] 119907119890119903119894119891119910 119905ℎ119886119905

(i) A(119861119862) = (119860119861)119862 (ii) (A+B)C=AC+BC

31 If A=[0 3

minus7 5] 119868 = [

1 00 1

] 119891119894119899119889 119896 119904119906119888ℎ 119905ℎ119886119905 1198961198602 = 5119860 minus 21119868


minus3 4] 119860 = [


]

33 Let A=[1 minus2 30 4 7

] 119886119899119889 119861 = [0 4 22 minus2 1





35 If A=[119886 1198870 1


119886minus1


18

36 If A=[352




38 If A=[1 2 22 1 22 2 1



(i)[1 23 7

](ii) [2 17 4

]



| = (119909 + 119910 + 119911)3


119909 119909 + 119910 119909 + 2119910119909 + 2119910 119909 119909 + 119910119909 + 119910 119909 + 2119910 119909

| = 91199102(119909 + 119910)

42 If 119891(119909) = |119886 minus1 0

119886119909 119886 minus11198861199092 119886119909 119886

| 119906119904119894119899119892 119901119903119900119901119890119903119905119894119890119904 119900119891 119889119890119905119890119903119898119894119899119886119899119905119904 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119891(2119909) minus

119891(119909)

43 Let f(t)=|119888119900119904119905 119905 1

2119904119894119899119905 119905 2119905119904119894119899119905 119905 119905

| 119905ℎ119890119899 119891119894119899119889 lim119905rarr0

119891(119905)

1199052


2 21198861199052) 119886119899119889 119862(11988611990532 21198861199053)



47 If 119860 = [2 31 4

] 119886119899119889119861 = [1 23 4

] 119907119890119903119894119891119910 119905ℎ119886119905 119886119889119895(119860119861) = (119886119889119895119861)(119886119889119895 119860)



] 119886119899119889 119907119890119903119894119891119910 119905ℎ119886119905 119860(119886119889119895119860) = (119886119889119895119860)119860 = |119860|1198683

49 Let 119860 = [3 72 5

] 119886119899119889119861 = [6 87 9





] 119904ℎ119900119908 119905ℎ119886119905 1198603 = 119860minus1



(i)A=[5 200 1

] (ii)A=[1 minus3 24 minus1 23 5 2

]


] 119883 [4 73 5

] = [1 00 1

]


19


| = 0


] and




2

57 If A=[1 0 20 2 12 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896





two types













-x+2y+5z=2 2x-3y+z=15 -x +y +z=-3


(i)[2 3 minus3


](ii) [2 0 minus15 1 00 1 3

]


(119887 + 119888)2 119887119886 119888119886

119886119887 (119888 + 119886)2 119888119887

119886119888 119887119888 (119886 + 119887)2

| =

2119886119887119888(119886 + 119887 + 119888)3

64 In a ∆119860119861119862 if |1 1 1

1 + 119904119894119899 119860 1 + 119904119894119899 119861 1 + 119904119894119899 119888119904119894119899 119860 + sin2 119860 119904119894119899 119861 + sin2 119861 119904119894119899 119861 + sin2 119861


isosceles triangle

65 If |119901 119887 119888119886 119902 119888119886 119887 119903

| = 0 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119901

119901minus119886+

119902

119902minus119887+

119903

119903minus119888 119901 ne 119886 119902 ne 119887 119903 ne 119888


119961minus

120783

119962+

120783

119963= 120787

120784

119961+

120785

119962minus

120786

119963= minus120789

120784

119961+

120783

119962minus

120784

119963= minus120785

20











| = 0









70 Prove that |






(119886 + 1)(119886 + 2) 119886 + 2 1

(119886 + 3)(119886 + 2) 119886 + 3 1

(119886 + 3)(119886 + 4) 119886 + 4 1| = minus2

If A=[1 0 2

0 2 1

2 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896

21

WORK SHEET I

CLASS XII

MATHEMATICS



1 MARK QUESTIONS






value of 24


2 MARK QUESTIONS







1 ) is two






22


13 If f(x) = 119909minus1



its inverse

( Ans 119891minus1(119909) = 5minus119909

7 )



4 MARK QUESTIONS


relation







120587













2]

23

WORKSHEET 12 IP

Q1 Table SchoolBus













order of rtno











24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




8















9















10

















11

















12















ऐसा करो





13













ददरा





14



















15


CLASS XII







119891(119909) = sin 119909+119909 cos 119909

119909



LONG ANSWER TYPE


1199092



(119909 minus 1)119909 119894119891 2 le 119909 lt 3 at x=2


119887 cos 119909+119886 sin 119909)minus

120587

2 lt 119909 lt

120587

2 and

119886



119889119909=

2119910

119909


119909)

119909

+ 119909(119909+1


11 Find 119889119910

119889119909 if y =

1199094radic119909+6

(3119909+5)2

12 If y= 31198902119909 + 21198903119909 prove that 1198892119910

1198891199092 - 5

119889119910

119889119909 +6y = 0



1198892119910

1198891199092 minus 3119909119889119910

119889119909minus 119910 = 0



16

WORK SHEET


CLASS-XII

VSA TYPE(1 marks)




for March


elements

3 If 119860 = [2 4 15 minus6 22 1 5



(i) aij=1

2(119894 minus 2119895)2 (ii) aij=

1

2|4119894 + 119895| (iii) aij=

119894 minus 119895 119894119891 119894 ge 119895119894 + 119895 119894119891 119894 lt 119895

(iv)119886119894119895 = 119894minus119895

119894+119895


7119860



) (10


8 If 2 [3 45 119909

] + [1 1199100 1

] = [7 0



minus2 0]=O


minus1 1] 119886119899119889 1198602 = 119896119860 119905ℎ119890119899 119908119903119894119905119890 119905ℎ119890 119905ℎ119890 119907119886119897119906119890 119900119891 119896


2lt 119909 lt 120587 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119909 119891119900119903 119908ℎ119894119888ℎ 119905ℎ119890 119898119886119905119903119894119909 [

2 sin 119909 31 2 sin 119909

] is

singular matrix

12 If |119909 + 1 119909 minus 1119909 minus 3 119909 + 2

| = |4 minus11 3


13 If ∆= |5 3 82 0 11 5 minus7



119909 119909 minus 2] 119894119904 119886 119904119894119899119892119906119897119886119903 119898119886119905119903119894119909


|


|

17





19 If |119909 sin 120579 cos 120579




] [1199092

] = [56

]


119909 + 119910 + 119911119909 + 119911119910 + 119911

] = [957

]

22 If 2119883 + 3119884 = [2 34 0

] 119886119899119889 3119883 + 2119884 = [minus2 21 minus5

] find X and Y

23 If 119860 = [3 5] 119861 = [7 3] 119905ℎ119890119899 119891119894119899119889 119898119886119905119903119894119909 119862 119904119906119888ℎ 119905ℎ119886119905 119860119862 = 119861119862

24 If A=[0 05 0

] 119891119894119899119889 11986016

25 If A=[119888119900119904120572 119878119894119899120572

minus119904119894119899120572 119888119900119904120572] find 120572 119904119886119905119894119904119891119910119894119899119892 0 lt 120572 lt

120587

2 119908ℎ119890119899 119860 + 119860119879 = radic21198682 where 119860119879 is

transpose of A


skew-symmetric

27 if A=[1 24 2


28 If A=[120783 120782 120784120782 120784 120783120784 120782 120785

] find A(adj A)



] 119894119904 119894119899119907119890119903119904119890 119900119891 119905ℎ119890 119898119886119905119903119894119909 [minus7 minus9 10


]


30 If 119860 = [1 minus3 10 2 minus12 1 3

] 119861 = [minus1 0 15 4 62 1 1


] 119907119890119903119894119891119910 119905ℎ119886119905

(i) A(119861119862) = (119860119861)119862 (ii) (A+B)C=AC+BC

31 If A=[0 3

minus7 5] 119868 = [

1 00 1

] 119891119894119899119889 119896 119904119906119888ℎ 119905ℎ119886119905 1198961198602 = 5119860 minus 21119868


minus3 4] 119860 = [


]

33 Let A=[1 minus2 30 4 7

] 119886119899119889 119861 = [0 4 22 minus2 1





35 If A=[119886 1198870 1


119886minus1


18

36 If A=[352




38 If A=[1 2 22 1 22 2 1



(i)[1 23 7

](ii) [2 17 4

]



| = (119909 + 119910 + 119911)3


119909 119909 + 119910 119909 + 2119910119909 + 2119910 119909 119909 + 119910119909 + 119910 119909 + 2119910 119909

| = 91199102(119909 + 119910)

42 If 119891(119909) = |119886 minus1 0

119886119909 119886 minus11198861199092 119886119909 119886

| 119906119904119894119899119892 119901119903119900119901119890119903119905119894119890119904 119900119891 119889119890119905119890119903119898119894119899119886119899119905119904 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119891(2119909) minus

119891(119909)

43 Let f(t)=|119888119900119904119905 119905 1

2119904119894119899119905 119905 2119905119904119894119899119905 119905 119905

| 119905ℎ119890119899 119891119894119899119889 lim119905rarr0

119891(119905)

1199052


2 21198861199052) 119886119899119889 119862(11988611990532 21198861199053)



47 If 119860 = [2 31 4

] 119886119899119889119861 = [1 23 4

] 119907119890119903119894119891119910 119905ℎ119886119905 119886119889119895(119860119861) = (119886119889119895119861)(119886119889119895 119860)



] 119886119899119889 119907119890119903119894119891119910 119905ℎ119886119905 119860(119886119889119895119860) = (119886119889119895119860)119860 = |119860|1198683

49 Let 119860 = [3 72 5

] 119886119899119889119861 = [6 87 9





] 119904ℎ119900119908 119905ℎ119886119905 1198603 = 119860minus1



(i)A=[5 200 1

] (ii)A=[1 minus3 24 minus1 23 5 2

]


] 119883 [4 73 5

] = [1 00 1

]


19


| = 0


] and




2

57 If A=[1 0 20 2 12 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896





two types













-x+2y+5z=2 2x-3y+z=15 -x +y +z=-3


(i)[2 3 minus3


](ii) [2 0 minus15 1 00 1 3

]


(119887 + 119888)2 119887119886 119888119886

119886119887 (119888 + 119886)2 119888119887

119886119888 119887119888 (119886 + 119887)2

| =

2119886119887119888(119886 + 119887 + 119888)3

64 In a ∆119860119861119862 if |1 1 1

1 + 119904119894119899 119860 1 + 119904119894119899 119861 1 + 119904119894119899 119888119904119894119899 119860 + sin2 119860 119904119894119899 119861 + sin2 119861 119904119894119899 119861 + sin2 119861


isosceles triangle

65 If |119901 119887 119888119886 119902 119888119886 119887 119903

| = 0 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119901

119901minus119886+

119902

119902minus119887+

119903

119903minus119888 119901 ne 119886 119902 ne 119887 119903 ne 119888


119961minus

120783

119962+

120783

119963= 120787

120784

119961+

120785

119962minus

120786

119963= minus120789

120784

119961+

120783

119962minus

120784

119963= minus120785

20











| = 0









70 Prove that |






(119886 + 1)(119886 + 2) 119886 + 2 1

(119886 + 3)(119886 + 2) 119886 + 3 1

(119886 + 3)(119886 + 4) 119886 + 4 1| = minus2

If A=[1 0 2

0 2 1

2 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896

21

WORK SHEET I

CLASS XII

MATHEMATICS



1 MARK QUESTIONS






value of 24


2 MARK QUESTIONS







1 ) is two






22


13 If f(x) = 119909minus1



its inverse

( Ans 119891minus1(119909) = 5minus119909

7 )



4 MARK QUESTIONS


relation







120587













2]

23

WORKSHEET 12 IP

Q1 Table SchoolBus













order of rtno











24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




9















10

















11

















12















ऐसा करो





13













ददरा





14



















15


CLASS XII







119891(119909) = sin 119909+119909 cos 119909

119909



LONG ANSWER TYPE


1199092



(119909 minus 1)119909 119894119891 2 le 119909 lt 3 at x=2


119887 cos 119909+119886 sin 119909)minus

120587

2 lt 119909 lt

120587

2 and

119886



119889119909=

2119910

119909


119909)

119909

+ 119909(119909+1


11 Find 119889119910

119889119909 if y =

1199094radic119909+6

(3119909+5)2

12 If y= 31198902119909 + 21198903119909 prove that 1198892119910

1198891199092 - 5

119889119910

119889119909 +6y = 0



1198892119910

1198891199092 minus 3119909119889119910

119889119909minus 119910 = 0



16

WORK SHEET


CLASS-XII

VSA TYPE(1 marks)




for March


elements

3 If 119860 = [2 4 15 minus6 22 1 5



(i) aij=1

2(119894 minus 2119895)2 (ii) aij=

1

2|4119894 + 119895| (iii) aij=

119894 minus 119895 119894119891 119894 ge 119895119894 + 119895 119894119891 119894 lt 119895

(iv)119886119894119895 = 119894minus119895

119894+119895


7119860



) (10


8 If 2 [3 45 119909

] + [1 1199100 1

] = [7 0



minus2 0]=O


minus1 1] 119886119899119889 1198602 = 119896119860 119905ℎ119890119899 119908119903119894119905119890 119905ℎ119890 119905ℎ119890 119907119886119897119906119890 119900119891 119896


2lt 119909 lt 120587 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119909 119891119900119903 119908ℎ119894119888ℎ 119905ℎ119890 119898119886119905119903119894119909 [

2 sin 119909 31 2 sin 119909

] is

singular matrix

12 If |119909 + 1 119909 minus 1119909 minus 3 119909 + 2

| = |4 minus11 3


13 If ∆= |5 3 82 0 11 5 minus7



119909 119909 minus 2] 119894119904 119886 119904119894119899119892119906119897119886119903 119898119886119905119903119894119909


|


|

17





19 If |119909 sin 120579 cos 120579




] [1199092

] = [56

]


119909 + 119910 + 119911119909 + 119911119910 + 119911

] = [957

]

22 If 2119883 + 3119884 = [2 34 0

] 119886119899119889 3119883 + 2119884 = [minus2 21 minus5

] find X and Y

23 If 119860 = [3 5] 119861 = [7 3] 119905ℎ119890119899 119891119894119899119889 119898119886119905119903119894119909 119862 119904119906119888ℎ 119905ℎ119886119905 119860119862 = 119861119862

24 If A=[0 05 0

] 119891119894119899119889 11986016

25 If A=[119888119900119904120572 119878119894119899120572

minus119904119894119899120572 119888119900119904120572] find 120572 119904119886119905119894119904119891119910119894119899119892 0 lt 120572 lt

120587

2 119908ℎ119890119899 119860 + 119860119879 = radic21198682 where 119860119879 is

transpose of A


skew-symmetric

27 if A=[1 24 2


28 If A=[120783 120782 120784120782 120784 120783120784 120782 120785

] find A(adj A)



] 119894119904 119894119899119907119890119903119904119890 119900119891 119905ℎ119890 119898119886119905119903119894119909 [minus7 minus9 10


]


30 If 119860 = [1 minus3 10 2 minus12 1 3

] 119861 = [minus1 0 15 4 62 1 1


] 119907119890119903119894119891119910 119905ℎ119886119905

(i) A(119861119862) = (119860119861)119862 (ii) (A+B)C=AC+BC

31 If A=[0 3

minus7 5] 119868 = [

1 00 1

] 119891119894119899119889 119896 119904119906119888ℎ 119905ℎ119886119905 1198961198602 = 5119860 minus 21119868


minus3 4] 119860 = [


]

33 Let A=[1 minus2 30 4 7

] 119886119899119889 119861 = [0 4 22 minus2 1





35 If A=[119886 1198870 1


119886minus1


18

36 If A=[352




38 If A=[1 2 22 1 22 2 1



(i)[1 23 7

](ii) [2 17 4

]



| = (119909 + 119910 + 119911)3


119909 119909 + 119910 119909 + 2119910119909 + 2119910 119909 119909 + 119910119909 + 119910 119909 + 2119910 119909

| = 91199102(119909 + 119910)

42 If 119891(119909) = |119886 minus1 0

119886119909 119886 minus11198861199092 119886119909 119886

| 119906119904119894119899119892 119901119903119900119901119890119903119905119894119890119904 119900119891 119889119890119905119890119903119898119894119899119886119899119905119904 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119891(2119909) minus

119891(119909)

43 Let f(t)=|119888119900119904119905 119905 1

2119904119894119899119905 119905 2119905119904119894119899119905 119905 119905

| 119905ℎ119890119899 119891119894119899119889 lim119905rarr0

119891(119905)

1199052


2 21198861199052) 119886119899119889 119862(11988611990532 21198861199053)



47 If 119860 = [2 31 4

] 119886119899119889119861 = [1 23 4

] 119907119890119903119894119891119910 119905ℎ119886119905 119886119889119895(119860119861) = (119886119889119895119861)(119886119889119895 119860)



] 119886119899119889 119907119890119903119894119891119910 119905ℎ119886119905 119860(119886119889119895119860) = (119886119889119895119860)119860 = |119860|1198683

49 Let 119860 = [3 72 5

] 119886119899119889119861 = [6 87 9





] 119904ℎ119900119908 119905ℎ119886119905 1198603 = 119860minus1



(i)A=[5 200 1

] (ii)A=[1 minus3 24 minus1 23 5 2

]


] 119883 [4 73 5

] = [1 00 1

]


19


| = 0


] and




2

57 If A=[1 0 20 2 12 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896





two types













-x+2y+5z=2 2x-3y+z=15 -x +y +z=-3


(i)[2 3 minus3


](ii) [2 0 minus15 1 00 1 3

]


(119887 + 119888)2 119887119886 119888119886

119886119887 (119888 + 119886)2 119888119887

119886119888 119887119888 (119886 + 119887)2

| =

2119886119887119888(119886 + 119887 + 119888)3

64 In a ∆119860119861119862 if |1 1 1

1 + 119904119894119899 119860 1 + 119904119894119899 119861 1 + 119904119894119899 119888119904119894119899 119860 + sin2 119860 119904119894119899 119861 + sin2 119861 119904119894119899 119861 + sin2 119861


isosceles triangle

65 If |119901 119887 119888119886 119902 119888119886 119887 119903

| = 0 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119901

119901minus119886+

119902

119902minus119887+

119903

119903minus119888 119901 ne 119886 119902 ne 119887 119903 ne 119888


119961minus

120783

119962+

120783

119963= 120787

120784

119961+

120785

119962minus

120786

119963= minus120789

120784

119961+

120783

119962minus

120784

119963= minus120785

20











| = 0









70 Prove that |






(119886 + 1)(119886 + 2) 119886 + 2 1

(119886 + 3)(119886 + 2) 119886 + 3 1

(119886 + 3)(119886 + 4) 119886 + 4 1| = minus2

If A=[1 0 2

0 2 1

2 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896

21

WORK SHEET I

CLASS XII

MATHEMATICS



1 MARK QUESTIONS






value of 24


2 MARK QUESTIONS







1 ) is two






22


13 If f(x) = 119909minus1



its inverse

( Ans 119891minus1(119909) = 5minus119909

7 )



4 MARK QUESTIONS


relation







120587













2]

23

WORKSHEET 12 IP

Q1 Table SchoolBus













order of rtno











24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




10

















11

















12















ऐसा करो





13













ददरा





14



















15


CLASS XII







119891(119909) = sin 119909+119909 cos 119909

119909



LONG ANSWER TYPE


1199092



(119909 minus 1)119909 119894119891 2 le 119909 lt 3 at x=2


119887 cos 119909+119886 sin 119909)minus

120587

2 lt 119909 lt

120587

2 and

119886



119889119909=

2119910

119909


119909)

119909

+ 119909(119909+1


11 Find 119889119910

119889119909 if y =

1199094radic119909+6

(3119909+5)2

12 If y= 31198902119909 + 21198903119909 prove that 1198892119910

1198891199092 - 5

119889119910

119889119909 +6y = 0



1198892119910

1198891199092 minus 3119909119889119910

119889119909minus 119910 = 0



16

WORK SHEET


CLASS-XII

VSA TYPE(1 marks)




for March


elements

3 If 119860 = [2 4 15 minus6 22 1 5



(i) aij=1

2(119894 minus 2119895)2 (ii) aij=

1

2|4119894 + 119895| (iii) aij=

119894 minus 119895 119894119891 119894 ge 119895119894 + 119895 119894119891 119894 lt 119895

(iv)119886119894119895 = 119894minus119895

119894+119895


7119860



) (10


8 If 2 [3 45 119909

] + [1 1199100 1

] = [7 0



minus2 0]=O


minus1 1] 119886119899119889 1198602 = 119896119860 119905ℎ119890119899 119908119903119894119905119890 119905ℎ119890 119905ℎ119890 119907119886119897119906119890 119900119891 119896


2lt 119909 lt 120587 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119909 119891119900119903 119908ℎ119894119888ℎ 119905ℎ119890 119898119886119905119903119894119909 [

2 sin 119909 31 2 sin 119909

] is

singular matrix

12 If |119909 + 1 119909 minus 1119909 minus 3 119909 + 2

| = |4 minus11 3


13 If ∆= |5 3 82 0 11 5 minus7



119909 119909 minus 2] 119894119904 119886 119904119894119899119892119906119897119886119903 119898119886119905119903119894119909


|


|

17





19 If |119909 sin 120579 cos 120579




] [1199092

] = [56

]


119909 + 119910 + 119911119909 + 119911119910 + 119911

] = [957

]

22 If 2119883 + 3119884 = [2 34 0

] 119886119899119889 3119883 + 2119884 = [minus2 21 minus5

] find X and Y

23 If 119860 = [3 5] 119861 = [7 3] 119905ℎ119890119899 119891119894119899119889 119898119886119905119903119894119909 119862 119904119906119888ℎ 119905ℎ119886119905 119860119862 = 119861119862

24 If A=[0 05 0

] 119891119894119899119889 11986016

25 If A=[119888119900119904120572 119878119894119899120572

minus119904119894119899120572 119888119900119904120572] find 120572 119904119886119905119894119904119891119910119894119899119892 0 lt 120572 lt

120587

2 119908ℎ119890119899 119860 + 119860119879 = radic21198682 where 119860119879 is

transpose of A


skew-symmetric

27 if A=[1 24 2


28 If A=[120783 120782 120784120782 120784 120783120784 120782 120785

] find A(adj A)



] 119894119904 119894119899119907119890119903119904119890 119900119891 119905ℎ119890 119898119886119905119903119894119909 [minus7 minus9 10


]


30 If 119860 = [1 minus3 10 2 minus12 1 3

] 119861 = [minus1 0 15 4 62 1 1


] 119907119890119903119894119891119910 119905ℎ119886119905

(i) A(119861119862) = (119860119861)119862 (ii) (A+B)C=AC+BC

31 If A=[0 3

minus7 5] 119868 = [

1 00 1

] 119891119894119899119889 119896 119904119906119888ℎ 119905ℎ119886119905 1198961198602 = 5119860 minus 21119868


minus3 4] 119860 = [


]

33 Let A=[1 minus2 30 4 7

] 119886119899119889 119861 = [0 4 22 minus2 1





35 If A=[119886 1198870 1


119886minus1


18

36 If A=[352




38 If A=[1 2 22 1 22 2 1



(i)[1 23 7

](ii) [2 17 4

]



| = (119909 + 119910 + 119911)3


119909 119909 + 119910 119909 + 2119910119909 + 2119910 119909 119909 + 119910119909 + 119910 119909 + 2119910 119909

| = 91199102(119909 + 119910)

42 If 119891(119909) = |119886 minus1 0

119886119909 119886 minus11198861199092 119886119909 119886

| 119906119904119894119899119892 119901119903119900119901119890119903119905119894119890119904 119900119891 119889119890119905119890119903119898119894119899119886119899119905119904 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119891(2119909) minus

119891(119909)

43 Let f(t)=|119888119900119904119905 119905 1

2119904119894119899119905 119905 2119905119904119894119899119905 119905 119905

| 119905ℎ119890119899 119891119894119899119889 lim119905rarr0

119891(119905)

1199052


2 21198861199052) 119886119899119889 119862(11988611990532 21198861199053)



47 If 119860 = [2 31 4

] 119886119899119889119861 = [1 23 4

] 119907119890119903119894119891119910 119905ℎ119886119905 119886119889119895(119860119861) = (119886119889119895119861)(119886119889119895 119860)



] 119886119899119889 119907119890119903119894119891119910 119905ℎ119886119905 119860(119886119889119895119860) = (119886119889119895119860)119860 = |119860|1198683

49 Let 119860 = [3 72 5

] 119886119899119889119861 = [6 87 9





] 119904ℎ119900119908 119905ℎ119886119905 1198603 = 119860minus1



(i)A=[5 200 1

] (ii)A=[1 minus3 24 minus1 23 5 2

]


] 119883 [4 73 5

] = [1 00 1

]


19


| = 0


] and




2

57 If A=[1 0 20 2 12 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896





two types













-x+2y+5z=2 2x-3y+z=15 -x +y +z=-3


(i)[2 3 minus3


](ii) [2 0 minus15 1 00 1 3

]


(119887 + 119888)2 119887119886 119888119886

119886119887 (119888 + 119886)2 119888119887

119886119888 119887119888 (119886 + 119887)2

| =

2119886119887119888(119886 + 119887 + 119888)3

64 In a ∆119860119861119862 if |1 1 1

1 + 119904119894119899 119860 1 + 119904119894119899 119861 1 + 119904119894119899 119888119904119894119899 119860 + sin2 119860 119904119894119899 119861 + sin2 119861 119904119894119899 119861 + sin2 119861


isosceles triangle

65 If |119901 119887 119888119886 119902 119888119886 119887 119903

| = 0 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119901

119901minus119886+

119902

119902minus119887+

119903

119903minus119888 119901 ne 119886 119902 ne 119887 119903 ne 119888


119961minus

120783

119962+

120783

119963= 120787

120784

119961+

120785

119962minus

120786

119963= minus120789

120784

119961+

120783

119962minus

120784

119963= minus120785

20











| = 0









70 Prove that |






(119886 + 1)(119886 + 2) 119886 + 2 1

(119886 + 3)(119886 + 2) 119886 + 3 1

(119886 + 3)(119886 + 4) 119886 + 4 1| = minus2

If A=[1 0 2

0 2 1

2 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896

21

WORK SHEET I

CLASS XII

MATHEMATICS



1 MARK QUESTIONS






value of 24


2 MARK QUESTIONS







1 ) is two






22


13 If f(x) = 119909minus1



its inverse

( Ans 119891minus1(119909) = 5minus119909

7 )



4 MARK QUESTIONS


relation







120587













2]

23

WORKSHEET 12 IP

Q1 Table SchoolBus













order of rtno











24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




11

















12















ऐसा करो





13













ददरा





14



















15


CLASS XII







119891(119909) = sin 119909+119909 cos 119909

119909



LONG ANSWER TYPE


1199092



(119909 minus 1)119909 119894119891 2 le 119909 lt 3 at x=2


119887 cos 119909+119886 sin 119909)minus

120587

2 lt 119909 lt

120587

2 and

119886



119889119909=

2119910

119909


119909)

119909

+ 119909(119909+1


11 Find 119889119910

119889119909 if y =

1199094radic119909+6

(3119909+5)2

12 If y= 31198902119909 + 21198903119909 prove that 1198892119910

1198891199092 - 5

119889119910

119889119909 +6y = 0



1198892119910

1198891199092 minus 3119909119889119910

119889119909minus 119910 = 0



16

WORK SHEET


CLASS-XII

VSA TYPE(1 marks)




for March


elements

3 If 119860 = [2 4 15 minus6 22 1 5



(i) aij=1

2(119894 minus 2119895)2 (ii) aij=

1

2|4119894 + 119895| (iii) aij=

119894 minus 119895 119894119891 119894 ge 119895119894 + 119895 119894119891 119894 lt 119895

(iv)119886119894119895 = 119894minus119895

119894+119895


7119860



) (10


8 If 2 [3 45 119909

] + [1 1199100 1

] = [7 0



minus2 0]=O


minus1 1] 119886119899119889 1198602 = 119896119860 119905ℎ119890119899 119908119903119894119905119890 119905ℎ119890 119905ℎ119890 119907119886119897119906119890 119900119891 119896


2lt 119909 lt 120587 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119909 119891119900119903 119908ℎ119894119888ℎ 119905ℎ119890 119898119886119905119903119894119909 [

2 sin 119909 31 2 sin 119909

] is

singular matrix

12 If |119909 + 1 119909 minus 1119909 minus 3 119909 + 2

| = |4 minus11 3


13 If ∆= |5 3 82 0 11 5 minus7



119909 119909 minus 2] 119894119904 119886 119904119894119899119892119906119897119886119903 119898119886119905119903119894119909


|


|

17





19 If |119909 sin 120579 cos 120579




] [1199092

] = [56

]


119909 + 119910 + 119911119909 + 119911119910 + 119911

] = [957

]

22 If 2119883 + 3119884 = [2 34 0

] 119886119899119889 3119883 + 2119884 = [minus2 21 minus5

] find X and Y

23 If 119860 = [3 5] 119861 = [7 3] 119905ℎ119890119899 119891119894119899119889 119898119886119905119903119894119909 119862 119904119906119888ℎ 119905ℎ119886119905 119860119862 = 119861119862

24 If A=[0 05 0

] 119891119894119899119889 11986016

25 If A=[119888119900119904120572 119878119894119899120572

minus119904119894119899120572 119888119900119904120572] find 120572 119904119886119905119894119904119891119910119894119899119892 0 lt 120572 lt

120587

2 119908ℎ119890119899 119860 + 119860119879 = radic21198682 where 119860119879 is

transpose of A


skew-symmetric

27 if A=[1 24 2


28 If A=[120783 120782 120784120782 120784 120783120784 120782 120785

] find A(adj A)



] 119894119904 119894119899119907119890119903119904119890 119900119891 119905ℎ119890 119898119886119905119903119894119909 [minus7 minus9 10


]


30 If 119860 = [1 minus3 10 2 minus12 1 3

] 119861 = [minus1 0 15 4 62 1 1


] 119907119890119903119894119891119910 119905ℎ119886119905

(i) A(119861119862) = (119860119861)119862 (ii) (A+B)C=AC+BC

31 If A=[0 3

minus7 5] 119868 = [

1 00 1

] 119891119894119899119889 119896 119904119906119888ℎ 119905ℎ119886119905 1198961198602 = 5119860 minus 21119868


minus3 4] 119860 = [


]

33 Let A=[1 minus2 30 4 7

] 119886119899119889 119861 = [0 4 22 minus2 1





35 If A=[119886 1198870 1


119886minus1


18

36 If A=[352




38 If A=[1 2 22 1 22 2 1



(i)[1 23 7

](ii) [2 17 4

]



| = (119909 + 119910 + 119911)3


119909 119909 + 119910 119909 + 2119910119909 + 2119910 119909 119909 + 119910119909 + 119910 119909 + 2119910 119909

| = 91199102(119909 + 119910)

42 If 119891(119909) = |119886 minus1 0

119886119909 119886 minus11198861199092 119886119909 119886

| 119906119904119894119899119892 119901119903119900119901119890119903119905119894119890119904 119900119891 119889119890119905119890119903119898119894119899119886119899119905119904 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119891(2119909) minus

119891(119909)

43 Let f(t)=|119888119900119904119905 119905 1

2119904119894119899119905 119905 2119905119904119894119899119905 119905 119905

| 119905ℎ119890119899 119891119894119899119889 lim119905rarr0

119891(119905)

1199052


2 21198861199052) 119886119899119889 119862(11988611990532 21198861199053)



47 If 119860 = [2 31 4

] 119886119899119889119861 = [1 23 4

] 119907119890119903119894119891119910 119905ℎ119886119905 119886119889119895(119860119861) = (119886119889119895119861)(119886119889119895 119860)



] 119886119899119889 119907119890119903119894119891119910 119905ℎ119886119905 119860(119886119889119895119860) = (119886119889119895119860)119860 = |119860|1198683

49 Let 119860 = [3 72 5

] 119886119899119889119861 = [6 87 9





] 119904ℎ119900119908 119905ℎ119886119905 1198603 = 119860minus1



(i)A=[5 200 1

] (ii)A=[1 minus3 24 minus1 23 5 2

]


] 119883 [4 73 5

] = [1 00 1

]


19


| = 0


] and




2

57 If A=[1 0 20 2 12 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896





two types













-x+2y+5z=2 2x-3y+z=15 -x +y +z=-3


(i)[2 3 minus3


](ii) [2 0 minus15 1 00 1 3

]


(119887 + 119888)2 119887119886 119888119886

119886119887 (119888 + 119886)2 119888119887

119886119888 119887119888 (119886 + 119887)2

| =

2119886119887119888(119886 + 119887 + 119888)3

64 In a ∆119860119861119862 if |1 1 1

1 + 119904119894119899 119860 1 + 119904119894119899 119861 1 + 119904119894119899 119888119904119894119899 119860 + sin2 119860 119904119894119899 119861 + sin2 119861 119904119894119899 119861 + sin2 119861


isosceles triangle

65 If |119901 119887 119888119886 119902 119888119886 119887 119903

| = 0 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119901

119901minus119886+

119902

119902minus119887+

119903

119903minus119888 119901 ne 119886 119902 ne 119887 119903 ne 119888


119961minus

120783

119962+

120783

119963= 120787

120784

119961+

120785

119962minus

120786

119963= minus120789

120784

119961+

120783

119962minus

120784

119963= minus120785

20











| = 0









70 Prove that |






(119886 + 1)(119886 + 2) 119886 + 2 1

(119886 + 3)(119886 + 2) 119886 + 3 1

(119886 + 3)(119886 + 4) 119886 + 4 1| = minus2

If A=[1 0 2

0 2 1

2 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896

21

WORK SHEET I

CLASS XII

MATHEMATICS



1 MARK QUESTIONS






value of 24


2 MARK QUESTIONS







1 ) is two






22


13 If f(x) = 119909minus1



its inverse

( Ans 119891minus1(119909) = 5minus119909

7 )



4 MARK QUESTIONS


relation







120587













2]

23

WORKSHEET 12 IP

Q1 Table SchoolBus













order of rtno











24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




12















ऐसा करो





13













ददरा





14



















15


CLASS XII







119891(119909) = sin 119909+119909 cos 119909

119909



LONG ANSWER TYPE


1199092



(119909 minus 1)119909 119894119891 2 le 119909 lt 3 at x=2


119887 cos 119909+119886 sin 119909)minus

120587

2 lt 119909 lt

120587

2 and

119886



119889119909=

2119910

119909


119909)

119909

+ 119909(119909+1


11 Find 119889119910

119889119909 if y =

1199094radic119909+6

(3119909+5)2

12 If y= 31198902119909 + 21198903119909 prove that 1198892119910

1198891199092 - 5

119889119910

119889119909 +6y = 0



1198892119910

1198891199092 minus 3119909119889119910

119889119909minus 119910 = 0



16

WORK SHEET


CLASS-XII

VSA TYPE(1 marks)




for March


elements

3 If 119860 = [2 4 15 minus6 22 1 5



(i) aij=1

2(119894 minus 2119895)2 (ii) aij=

1

2|4119894 + 119895| (iii) aij=

119894 minus 119895 119894119891 119894 ge 119895119894 + 119895 119894119891 119894 lt 119895

(iv)119886119894119895 = 119894minus119895

119894+119895


7119860



) (10


8 If 2 [3 45 119909

] + [1 1199100 1

] = [7 0



minus2 0]=O


minus1 1] 119886119899119889 1198602 = 119896119860 119905ℎ119890119899 119908119903119894119905119890 119905ℎ119890 119905ℎ119890 119907119886119897119906119890 119900119891 119896


2lt 119909 lt 120587 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119909 119891119900119903 119908ℎ119894119888ℎ 119905ℎ119890 119898119886119905119903119894119909 [

2 sin 119909 31 2 sin 119909

] is

singular matrix

12 If |119909 + 1 119909 minus 1119909 minus 3 119909 + 2

| = |4 minus11 3


13 If ∆= |5 3 82 0 11 5 minus7



119909 119909 minus 2] 119894119904 119886 119904119894119899119892119906119897119886119903 119898119886119905119903119894119909


|


|

17





19 If |119909 sin 120579 cos 120579




] [1199092

] = [56

]


119909 + 119910 + 119911119909 + 119911119910 + 119911

] = [957

]

22 If 2119883 + 3119884 = [2 34 0

] 119886119899119889 3119883 + 2119884 = [minus2 21 minus5

] find X and Y

23 If 119860 = [3 5] 119861 = [7 3] 119905ℎ119890119899 119891119894119899119889 119898119886119905119903119894119909 119862 119904119906119888ℎ 119905ℎ119886119905 119860119862 = 119861119862

24 If A=[0 05 0

] 119891119894119899119889 11986016

25 If A=[119888119900119904120572 119878119894119899120572

minus119904119894119899120572 119888119900119904120572] find 120572 119904119886119905119894119904119891119910119894119899119892 0 lt 120572 lt

120587

2 119908ℎ119890119899 119860 + 119860119879 = radic21198682 where 119860119879 is

transpose of A


skew-symmetric

27 if A=[1 24 2


28 If A=[120783 120782 120784120782 120784 120783120784 120782 120785

] find A(adj A)



] 119894119904 119894119899119907119890119903119904119890 119900119891 119905ℎ119890 119898119886119905119903119894119909 [minus7 minus9 10


]


30 If 119860 = [1 minus3 10 2 minus12 1 3

] 119861 = [minus1 0 15 4 62 1 1


] 119907119890119903119894119891119910 119905ℎ119886119905

(i) A(119861119862) = (119860119861)119862 (ii) (A+B)C=AC+BC

31 If A=[0 3

minus7 5] 119868 = [

1 00 1

] 119891119894119899119889 119896 119904119906119888ℎ 119905ℎ119886119905 1198961198602 = 5119860 minus 21119868


minus3 4] 119860 = [


]

33 Let A=[1 minus2 30 4 7

] 119886119899119889 119861 = [0 4 22 minus2 1





35 If A=[119886 1198870 1


119886minus1


18

36 If A=[352




38 If A=[1 2 22 1 22 2 1



(i)[1 23 7

](ii) [2 17 4

]



| = (119909 + 119910 + 119911)3


119909 119909 + 119910 119909 + 2119910119909 + 2119910 119909 119909 + 119910119909 + 119910 119909 + 2119910 119909

| = 91199102(119909 + 119910)

42 If 119891(119909) = |119886 minus1 0

119886119909 119886 minus11198861199092 119886119909 119886

| 119906119904119894119899119892 119901119903119900119901119890119903119905119894119890119904 119900119891 119889119890119905119890119903119898119894119899119886119899119905119904 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119891(2119909) minus

119891(119909)

43 Let f(t)=|119888119900119904119905 119905 1

2119904119894119899119905 119905 2119905119904119894119899119905 119905 119905

| 119905ℎ119890119899 119891119894119899119889 lim119905rarr0

119891(119905)

1199052


2 21198861199052) 119886119899119889 119862(11988611990532 21198861199053)



47 If 119860 = [2 31 4

] 119886119899119889119861 = [1 23 4

] 119907119890119903119894119891119910 119905ℎ119886119905 119886119889119895(119860119861) = (119886119889119895119861)(119886119889119895 119860)



] 119886119899119889 119907119890119903119894119891119910 119905ℎ119886119905 119860(119886119889119895119860) = (119886119889119895119860)119860 = |119860|1198683

49 Let 119860 = [3 72 5

] 119886119899119889119861 = [6 87 9





] 119904ℎ119900119908 119905ℎ119886119905 1198603 = 119860minus1



(i)A=[5 200 1

] (ii)A=[1 minus3 24 minus1 23 5 2

]


] 119883 [4 73 5

] = [1 00 1

]


19


| = 0


] and




2

57 If A=[1 0 20 2 12 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896





two types













-x+2y+5z=2 2x-3y+z=15 -x +y +z=-3


(i)[2 3 minus3


](ii) [2 0 minus15 1 00 1 3

]


(119887 + 119888)2 119887119886 119888119886

119886119887 (119888 + 119886)2 119888119887

119886119888 119887119888 (119886 + 119887)2

| =

2119886119887119888(119886 + 119887 + 119888)3

64 In a ∆119860119861119862 if |1 1 1

1 + 119904119894119899 119860 1 + 119904119894119899 119861 1 + 119904119894119899 119888119904119894119899 119860 + sin2 119860 119904119894119899 119861 + sin2 119861 119904119894119899 119861 + sin2 119861


isosceles triangle

65 If |119901 119887 119888119886 119902 119888119886 119887 119903

| = 0 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119901

119901minus119886+

119902

119902minus119887+

119903

119903minus119888 119901 ne 119886 119902 ne 119887 119903 ne 119888


119961minus

120783

119962+

120783

119963= 120787

120784

119961+

120785

119962minus

120786

119963= minus120789

120784

119961+

120783

119962minus

120784

119963= minus120785

20











| = 0









70 Prove that |






(119886 + 1)(119886 + 2) 119886 + 2 1

(119886 + 3)(119886 + 2) 119886 + 3 1

(119886 + 3)(119886 + 4) 119886 + 4 1| = minus2

If A=[1 0 2

0 2 1

2 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896

21

WORK SHEET I

CLASS XII

MATHEMATICS



1 MARK QUESTIONS






value of 24


2 MARK QUESTIONS







1 ) is two






22


13 If f(x) = 119909minus1



its inverse

( Ans 119891minus1(119909) = 5minus119909

7 )



4 MARK QUESTIONS


relation







120587













2]

23

WORKSHEET 12 IP

Q1 Table SchoolBus













order of rtno











24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




13













ददरा





14



















15


CLASS XII







119891(119909) = sin 119909+119909 cos 119909

119909



LONG ANSWER TYPE


1199092



(119909 minus 1)119909 119894119891 2 le 119909 lt 3 at x=2


119887 cos 119909+119886 sin 119909)minus

120587

2 lt 119909 lt

120587

2 and

119886



119889119909=

2119910

119909


119909)

119909

+ 119909(119909+1


11 Find 119889119910

119889119909 if y =

1199094radic119909+6

(3119909+5)2

12 If y= 31198902119909 + 21198903119909 prove that 1198892119910

1198891199092 - 5

119889119910

119889119909 +6y = 0



1198892119910

1198891199092 minus 3119909119889119910

119889119909minus 119910 = 0



16

WORK SHEET


CLASS-XII

VSA TYPE(1 marks)




for March


elements

3 If 119860 = [2 4 15 minus6 22 1 5



(i) aij=1

2(119894 minus 2119895)2 (ii) aij=

1

2|4119894 + 119895| (iii) aij=

119894 minus 119895 119894119891 119894 ge 119895119894 + 119895 119894119891 119894 lt 119895

(iv)119886119894119895 = 119894minus119895

119894+119895


7119860



) (10


8 If 2 [3 45 119909

] + [1 1199100 1

] = [7 0



minus2 0]=O


minus1 1] 119886119899119889 1198602 = 119896119860 119905ℎ119890119899 119908119903119894119905119890 119905ℎ119890 119905ℎ119890 119907119886119897119906119890 119900119891 119896


2lt 119909 lt 120587 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119909 119891119900119903 119908ℎ119894119888ℎ 119905ℎ119890 119898119886119905119903119894119909 [

2 sin 119909 31 2 sin 119909

] is

singular matrix

12 If |119909 + 1 119909 minus 1119909 minus 3 119909 + 2

| = |4 minus11 3


13 If ∆= |5 3 82 0 11 5 minus7



119909 119909 minus 2] 119894119904 119886 119904119894119899119892119906119897119886119903 119898119886119905119903119894119909


|


|

17





19 If |119909 sin 120579 cos 120579




] [1199092

] = [56

]


119909 + 119910 + 119911119909 + 119911119910 + 119911

] = [957

]

22 If 2119883 + 3119884 = [2 34 0

] 119886119899119889 3119883 + 2119884 = [minus2 21 minus5

] find X and Y

23 If 119860 = [3 5] 119861 = [7 3] 119905ℎ119890119899 119891119894119899119889 119898119886119905119903119894119909 119862 119904119906119888ℎ 119905ℎ119886119905 119860119862 = 119861119862

24 If A=[0 05 0

] 119891119894119899119889 11986016

25 If A=[119888119900119904120572 119878119894119899120572

minus119904119894119899120572 119888119900119904120572] find 120572 119904119886119905119894119904119891119910119894119899119892 0 lt 120572 lt

120587

2 119908ℎ119890119899 119860 + 119860119879 = radic21198682 where 119860119879 is

transpose of A


skew-symmetric

27 if A=[1 24 2


28 If A=[120783 120782 120784120782 120784 120783120784 120782 120785

] find A(adj A)



] 119894119904 119894119899119907119890119903119904119890 119900119891 119905ℎ119890 119898119886119905119903119894119909 [minus7 minus9 10


]


30 If 119860 = [1 minus3 10 2 minus12 1 3

] 119861 = [minus1 0 15 4 62 1 1


] 119907119890119903119894119891119910 119905ℎ119886119905

(i) A(119861119862) = (119860119861)119862 (ii) (A+B)C=AC+BC

31 If A=[0 3

minus7 5] 119868 = [

1 00 1

] 119891119894119899119889 119896 119904119906119888ℎ 119905ℎ119886119905 1198961198602 = 5119860 minus 21119868


minus3 4] 119860 = [


]

33 Let A=[1 minus2 30 4 7

] 119886119899119889 119861 = [0 4 22 minus2 1





35 If A=[119886 1198870 1


119886minus1


18

36 If A=[352




38 If A=[1 2 22 1 22 2 1



(i)[1 23 7

](ii) [2 17 4

]



| = (119909 + 119910 + 119911)3


119909 119909 + 119910 119909 + 2119910119909 + 2119910 119909 119909 + 119910119909 + 119910 119909 + 2119910 119909

| = 91199102(119909 + 119910)

42 If 119891(119909) = |119886 minus1 0

119886119909 119886 minus11198861199092 119886119909 119886

| 119906119904119894119899119892 119901119903119900119901119890119903119905119894119890119904 119900119891 119889119890119905119890119903119898119894119899119886119899119905119904 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119891(2119909) minus

119891(119909)

43 Let f(t)=|119888119900119904119905 119905 1

2119904119894119899119905 119905 2119905119904119894119899119905 119905 119905

| 119905ℎ119890119899 119891119894119899119889 lim119905rarr0

119891(119905)

1199052


2 21198861199052) 119886119899119889 119862(11988611990532 21198861199053)



47 If 119860 = [2 31 4

] 119886119899119889119861 = [1 23 4

] 119907119890119903119894119891119910 119905ℎ119886119905 119886119889119895(119860119861) = (119886119889119895119861)(119886119889119895 119860)



] 119886119899119889 119907119890119903119894119891119910 119905ℎ119886119905 119860(119886119889119895119860) = (119886119889119895119860)119860 = |119860|1198683

49 Let 119860 = [3 72 5

] 119886119899119889119861 = [6 87 9





] 119904ℎ119900119908 119905ℎ119886119905 1198603 = 119860minus1



(i)A=[5 200 1

] (ii)A=[1 minus3 24 minus1 23 5 2

]


] 119883 [4 73 5

] = [1 00 1

]


19


| = 0


] and




2

57 If A=[1 0 20 2 12 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896





two types













-x+2y+5z=2 2x-3y+z=15 -x +y +z=-3


(i)[2 3 minus3


](ii) [2 0 minus15 1 00 1 3

]


(119887 + 119888)2 119887119886 119888119886

119886119887 (119888 + 119886)2 119888119887

119886119888 119887119888 (119886 + 119887)2

| =

2119886119887119888(119886 + 119887 + 119888)3

64 In a ∆119860119861119862 if |1 1 1

1 + 119904119894119899 119860 1 + 119904119894119899 119861 1 + 119904119894119899 119888119904119894119899 119860 + sin2 119860 119904119894119899 119861 + sin2 119861 119904119894119899 119861 + sin2 119861


isosceles triangle

65 If |119901 119887 119888119886 119902 119888119886 119887 119903

| = 0 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119901

119901minus119886+

119902

119902minus119887+

119903

119903minus119888 119901 ne 119886 119902 ne 119887 119903 ne 119888


119961minus

120783

119962+

120783

119963= 120787

120784

119961+

120785

119962minus

120786

119963= minus120789

120784

119961+

120783

119962minus

120784

119963= minus120785

20











| = 0









70 Prove that |






(119886 + 1)(119886 + 2) 119886 + 2 1

(119886 + 3)(119886 + 2) 119886 + 3 1

(119886 + 3)(119886 + 4) 119886 + 4 1| = minus2

If A=[1 0 2

0 2 1

2 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896

21

WORK SHEET I

CLASS XII

MATHEMATICS



1 MARK QUESTIONS






value of 24


2 MARK QUESTIONS







1 ) is two






22


13 If f(x) = 119909minus1



its inverse

( Ans 119891minus1(119909) = 5minus119909

7 )



4 MARK QUESTIONS


relation







120587













2]

23

WORKSHEET 12 IP

Q1 Table SchoolBus













order of rtno











24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




14



















15


CLASS XII







119891(119909) = sin 119909+119909 cos 119909

119909



LONG ANSWER TYPE


1199092



(119909 minus 1)119909 119894119891 2 le 119909 lt 3 at x=2


119887 cos 119909+119886 sin 119909)minus

120587

2 lt 119909 lt

120587

2 and

119886



119889119909=

2119910

119909


119909)

119909

+ 119909(119909+1


11 Find 119889119910

119889119909 if y =

1199094radic119909+6

(3119909+5)2

12 If y= 31198902119909 + 21198903119909 prove that 1198892119910

1198891199092 - 5

119889119910

119889119909 +6y = 0



1198892119910

1198891199092 minus 3119909119889119910

119889119909minus 119910 = 0



16

WORK SHEET


CLASS-XII

VSA TYPE(1 marks)




for March


elements

3 If 119860 = [2 4 15 minus6 22 1 5



(i) aij=1

2(119894 minus 2119895)2 (ii) aij=

1

2|4119894 + 119895| (iii) aij=

119894 minus 119895 119894119891 119894 ge 119895119894 + 119895 119894119891 119894 lt 119895

(iv)119886119894119895 = 119894minus119895

119894+119895


7119860



) (10


8 If 2 [3 45 119909

] + [1 1199100 1

] = [7 0



minus2 0]=O


minus1 1] 119886119899119889 1198602 = 119896119860 119905ℎ119890119899 119908119903119894119905119890 119905ℎ119890 119905ℎ119890 119907119886119897119906119890 119900119891 119896


2lt 119909 lt 120587 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119909 119891119900119903 119908ℎ119894119888ℎ 119905ℎ119890 119898119886119905119903119894119909 [

2 sin 119909 31 2 sin 119909

] is

singular matrix

12 If |119909 + 1 119909 minus 1119909 minus 3 119909 + 2

| = |4 minus11 3


13 If ∆= |5 3 82 0 11 5 minus7



119909 119909 minus 2] 119894119904 119886 119904119894119899119892119906119897119886119903 119898119886119905119903119894119909


|


|

17





19 If |119909 sin 120579 cos 120579




] [1199092

] = [56

]


119909 + 119910 + 119911119909 + 119911119910 + 119911

] = [957

]

22 If 2119883 + 3119884 = [2 34 0

] 119886119899119889 3119883 + 2119884 = [minus2 21 minus5

] find X and Y

23 If 119860 = [3 5] 119861 = [7 3] 119905ℎ119890119899 119891119894119899119889 119898119886119905119903119894119909 119862 119904119906119888ℎ 119905ℎ119886119905 119860119862 = 119861119862

24 If A=[0 05 0

] 119891119894119899119889 11986016

25 If A=[119888119900119904120572 119878119894119899120572

minus119904119894119899120572 119888119900119904120572] find 120572 119904119886119905119894119904119891119910119894119899119892 0 lt 120572 lt

120587

2 119908ℎ119890119899 119860 + 119860119879 = radic21198682 where 119860119879 is

transpose of A


skew-symmetric

27 if A=[1 24 2


28 If A=[120783 120782 120784120782 120784 120783120784 120782 120785

] find A(adj A)



] 119894119904 119894119899119907119890119903119904119890 119900119891 119905ℎ119890 119898119886119905119903119894119909 [minus7 minus9 10


]


30 If 119860 = [1 minus3 10 2 minus12 1 3

] 119861 = [minus1 0 15 4 62 1 1


] 119907119890119903119894119891119910 119905ℎ119886119905

(i) A(119861119862) = (119860119861)119862 (ii) (A+B)C=AC+BC

31 If A=[0 3

minus7 5] 119868 = [

1 00 1

] 119891119894119899119889 119896 119904119906119888ℎ 119905ℎ119886119905 1198961198602 = 5119860 minus 21119868


minus3 4] 119860 = [


]

33 Let A=[1 minus2 30 4 7

] 119886119899119889 119861 = [0 4 22 minus2 1





35 If A=[119886 1198870 1


119886minus1


18

36 If A=[352




38 If A=[1 2 22 1 22 2 1



(i)[1 23 7

](ii) [2 17 4

]



| = (119909 + 119910 + 119911)3


119909 119909 + 119910 119909 + 2119910119909 + 2119910 119909 119909 + 119910119909 + 119910 119909 + 2119910 119909

| = 91199102(119909 + 119910)

42 If 119891(119909) = |119886 minus1 0

119886119909 119886 minus11198861199092 119886119909 119886

| 119906119904119894119899119892 119901119903119900119901119890119903119905119894119890119904 119900119891 119889119890119905119890119903119898119894119899119886119899119905119904 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119891(2119909) minus

119891(119909)

43 Let f(t)=|119888119900119904119905 119905 1

2119904119894119899119905 119905 2119905119904119894119899119905 119905 119905

| 119905ℎ119890119899 119891119894119899119889 lim119905rarr0

119891(119905)

1199052


2 21198861199052) 119886119899119889 119862(11988611990532 21198861199053)



47 If 119860 = [2 31 4

] 119886119899119889119861 = [1 23 4

] 119907119890119903119894119891119910 119905ℎ119886119905 119886119889119895(119860119861) = (119886119889119895119861)(119886119889119895 119860)



] 119886119899119889 119907119890119903119894119891119910 119905ℎ119886119905 119860(119886119889119895119860) = (119886119889119895119860)119860 = |119860|1198683

49 Let 119860 = [3 72 5

] 119886119899119889119861 = [6 87 9





] 119904ℎ119900119908 119905ℎ119886119905 1198603 = 119860minus1



(i)A=[5 200 1

] (ii)A=[1 minus3 24 minus1 23 5 2

]


] 119883 [4 73 5

] = [1 00 1

]


19


| = 0


] and




2

57 If A=[1 0 20 2 12 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896





two types













-x+2y+5z=2 2x-3y+z=15 -x +y +z=-3


(i)[2 3 minus3


](ii) [2 0 minus15 1 00 1 3

]


(119887 + 119888)2 119887119886 119888119886

119886119887 (119888 + 119886)2 119888119887

119886119888 119887119888 (119886 + 119887)2

| =

2119886119887119888(119886 + 119887 + 119888)3

64 In a ∆119860119861119862 if |1 1 1

1 + 119904119894119899 119860 1 + 119904119894119899 119861 1 + 119904119894119899 119888119904119894119899 119860 + sin2 119860 119904119894119899 119861 + sin2 119861 119904119894119899 119861 + sin2 119861


isosceles triangle

65 If |119901 119887 119888119886 119902 119888119886 119887 119903

| = 0 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119901

119901minus119886+

119902

119902minus119887+

119903

119903minus119888 119901 ne 119886 119902 ne 119887 119903 ne 119888


119961minus

120783

119962+

120783

119963= 120787

120784

119961+

120785

119962minus

120786

119963= minus120789

120784

119961+

120783

119962minus

120784

119963= minus120785

20











| = 0









70 Prove that |






(119886 + 1)(119886 + 2) 119886 + 2 1

(119886 + 3)(119886 + 2) 119886 + 3 1

(119886 + 3)(119886 + 4) 119886 + 4 1| = minus2

If A=[1 0 2

0 2 1

2 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896

21

WORK SHEET I

CLASS XII

MATHEMATICS



1 MARK QUESTIONS






value of 24


2 MARK QUESTIONS







1 ) is two






22


13 If f(x) = 119909minus1



its inverse

( Ans 119891minus1(119909) = 5minus119909

7 )



4 MARK QUESTIONS


relation







120587













2]

23

WORKSHEET 12 IP

Q1 Table SchoolBus













order of rtno











24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




15


CLASS XII







119891(119909) = sin 119909+119909 cos 119909

119909



LONG ANSWER TYPE


1199092



(119909 minus 1)119909 119894119891 2 le 119909 lt 3 at x=2


119887 cos 119909+119886 sin 119909)minus

120587

2 lt 119909 lt

120587

2 and

119886



119889119909=

2119910

119909


119909)

119909

+ 119909(119909+1


11 Find 119889119910

119889119909 if y =

1199094radic119909+6

(3119909+5)2

12 If y= 31198902119909 + 21198903119909 prove that 1198892119910

1198891199092 - 5

119889119910

119889119909 +6y = 0



1198892119910

1198891199092 minus 3119909119889119910

119889119909minus 119910 = 0



16

WORK SHEET


CLASS-XII

VSA TYPE(1 marks)




for March


elements

3 If 119860 = [2 4 15 minus6 22 1 5



(i) aij=1

2(119894 minus 2119895)2 (ii) aij=

1

2|4119894 + 119895| (iii) aij=

119894 minus 119895 119894119891 119894 ge 119895119894 + 119895 119894119891 119894 lt 119895

(iv)119886119894119895 = 119894minus119895

119894+119895


7119860



) (10


8 If 2 [3 45 119909

] + [1 1199100 1

] = [7 0



minus2 0]=O


minus1 1] 119886119899119889 1198602 = 119896119860 119905ℎ119890119899 119908119903119894119905119890 119905ℎ119890 119905ℎ119890 119907119886119897119906119890 119900119891 119896


2lt 119909 lt 120587 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119909 119891119900119903 119908ℎ119894119888ℎ 119905ℎ119890 119898119886119905119903119894119909 [

2 sin 119909 31 2 sin 119909

] is

singular matrix

12 If |119909 + 1 119909 minus 1119909 minus 3 119909 + 2

| = |4 minus11 3


13 If ∆= |5 3 82 0 11 5 minus7



119909 119909 minus 2] 119894119904 119886 119904119894119899119892119906119897119886119903 119898119886119905119903119894119909


|


|

17





19 If |119909 sin 120579 cos 120579




] [1199092

] = [56

]


119909 + 119910 + 119911119909 + 119911119910 + 119911

] = [957

]

22 If 2119883 + 3119884 = [2 34 0

] 119886119899119889 3119883 + 2119884 = [minus2 21 minus5

] find X and Y

23 If 119860 = [3 5] 119861 = [7 3] 119905ℎ119890119899 119891119894119899119889 119898119886119905119903119894119909 119862 119904119906119888ℎ 119905ℎ119886119905 119860119862 = 119861119862

24 If A=[0 05 0

] 119891119894119899119889 11986016

25 If A=[119888119900119904120572 119878119894119899120572

minus119904119894119899120572 119888119900119904120572] find 120572 119904119886119905119894119904119891119910119894119899119892 0 lt 120572 lt

120587

2 119908ℎ119890119899 119860 + 119860119879 = radic21198682 where 119860119879 is

transpose of A


skew-symmetric

27 if A=[1 24 2


28 If A=[120783 120782 120784120782 120784 120783120784 120782 120785

] find A(adj A)



] 119894119904 119894119899119907119890119903119904119890 119900119891 119905ℎ119890 119898119886119905119903119894119909 [minus7 minus9 10


]


30 If 119860 = [1 minus3 10 2 minus12 1 3

] 119861 = [minus1 0 15 4 62 1 1


] 119907119890119903119894119891119910 119905ℎ119886119905

(i) A(119861119862) = (119860119861)119862 (ii) (A+B)C=AC+BC

31 If A=[0 3

minus7 5] 119868 = [

1 00 1

] 119891119894119899119889 119896 119904119906119888ℎ 119905ℎ119886119905 1198961198602 = 5119860 minus 21119868


minus3 4] 119860 = [


]

33 Let A=[1 minus2 30 4 7

] 119886119899119889 119861 = [0 4 22 minus2 1





35 If A=[119886 1198870 1


119886minus1


18

36 If A=[352




38 If A=[1 2 22 1 22 2 1



(i)[1 23 7

](ii) [2 17 4

]



| = (119909 + 119910 + 119911)3


119909 119909 + 119910 119909 + 2119910119909 + 2119910 119909 119909 + 119910119909 + 119910 119909 + 2119910 119909

| = 91199102(119909 + 119910)

42 If 119891(119909) = |119886 minus1 0

119886119909 119886 minus11198861199092 119886119909 119886

| 119906119904119894119899119892 119901119903119900119901119890119903119905119894119890119904 119900119891 119889119890119905119890119903119898119894119899119886119899119905119904 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119891(2119909) minus

119891(119909)

43 Let f(t)=|119888119900119904119905 119905 1

2119904119894119899119905 119905 2119905119904119894119899119905 119905 119905

| 119905ℎ119890119899 119891119894119899119889 lim119905rarr0

119891(119905)

1199052


2 21198861199052) 119886119899119889 119862(11988611990532 21198861199053)



47 If 119860 = [2 31 4

] 119886119899119889119861 = [1 23 4

] 119907119890119903119894119891119910 119905ℎ119886119905 119886119889119895(119860119861) = (119886119889119895119861)(119886119889119895 119860)



] 119886119899119889 119907119890119903119894119891119910 119905ℎ119886119905 119860(119886119889119895119860) = (119886119889119895119860)119860 = |119860|1198683

49 Let 119860 = [3 72 5

] 119886119899119889119861 = [6 87 9





] 119904ℎ119900119908 119905ℎ119886119905 1198603 = 119860minus1



(i)A=[5 200 1

] (ii)A=[1 minus3 24 minus1 23 5 2

]


] 119883 [4 73 5

] = [1 00 1

]


19


| = 0


] and




2

57 If A=[1 0 20 2 12 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896





two types













-x+2y+5z=2 2x-3y+z=15 -x +y +z=-3


(i)[2 3 minus3


](ii) [2 0 minus15 1 00 1 3

]


(119887 + 119888)2 119887119886 119888119886

119886119887 (119888 + 119886)2 119888119887

119886119888 119887119888 (119886 + 119887)2

| =

2119886119887119888(119886 + 119887 + 119888)3

64 In a ∆119860119861119862 if |1 1 1

1 + 119904119894119899 119860 1 + 119904119894119899 119861 1 + 119904119894119899 119888119904119894119899 119860 + sin2 119860 119904119894119899 119861 + sin2 119861 119904119894119899 119861 + sin2 119861


isosceles triangle

65 If |119901 119887 119888119886 119902 119888119886 119887 119903

| = 0 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119901

119901minus119886+

119902

119902minus119887+

119903

119903minus119888 119901 ne 119886 119902 ne 119887 119903 ne 119888


119961minus

120783

119962+

120783

119963= 120787

120784

119961+

120785

119962minus

120786

119963= minus120789

120784

119961+

120783

119962minus

120784

119963= minus120785

20











| = 0









70 Prove that |






(119886 + 1)(119886 + 2) 119886 + 2 1

(119886 + 3)(119886 + 2) 119886 + 3 1

(119886 + 3)(119886 + 4) 119886 + 4 1| = minus2

If A=[1 0 2

0 2 1

2 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896

21

WORK SHEET I

CLASS XII

MATHEMATICS



1 MARK QUESTIONS






value of 24


2 MARK QUESTIONS







1 ) is two






22


13 If f(x) = 119909minus1



its inverse

( Ans 119891minus1(119909) = 5minus119909

7 )



4 MARK QUESTIONS


relation







120587













2]

23

WORKSHEET 12 IP

Q1 Table SchoolBus













order of rtno











24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




16

WORK SHEET


CLASS-XII

VSA TYPE(1 marks)




for March


elements

3 If 119860 = [2 4 15 minus6 22 1 5



(i) aij=1

2(119894 minus 2119895)2 (ii) aij=

1

2|4119894 + 119895| (iii) aij=

119894 minus 119895 119894119891 119894 ge 119895119894 + 119895 119894119891 119894 lt 119895

(iv)119886119894119895 = 119894minus119895

119894+119895


7119860



) (10


8 If 2 [3 45 119909

] + [1 1199100 1

] = [7 0



minus2 0]=O


minus1 1] 119886119899119889 1198602 = 119896119860 119905ℎ119890119899 119908119903119894119905119890 119905ℎ119890 119905ℎ119890 119907119886119897119906119890 119900119891 119896


2lt 119909 lt 120587 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119909 119891119900119903 119908ℎ119894119888ℎ 119905ℎ119890 119898119886119905119903119894119909 [

2 sin 119909 31 2 sin 119909

] is

singular matrix

12 If |119909 + 1 119909 minus 1119909 minus 3 119909 + 2

| = |4 minus11 3


13 If ∆= |5 3 82 0 11 5 minus7



119909 119909 minus 2] 119894119904 119886 119904119894119899119892119906119897119886119903 119898119886119905119903119894119909


|


|

17





19 If |119909 sin 120579 cos 120579




] [1199092

] = [56

]


119909 + 119910 + 119911119909 + 119911119910 + 119911

] = [957

]

22 If 2119883 + 3119884 = [2 34 0

] 119886119899119889 3119883 + 2119884 = [minus2 21 minus5

] find X and Y

23 If 119860 = [3 5] 119861 = [7 3] 119905ℎ119890119899 119891119894119899119889 119898119886119905119903119894119909 119862 119904119906119888ℎ 119905ℎ119886119905 119860119862 = 119861119862

24 If A=[0 05 0

] 119891119894119899119889 11986016

25 If A=[119888119900119904120572 119878119894119899120572

minus119904119894119899120572 119888119900119904120572] find 120572 119904119886119905119894119904119891119910119894119899119892 0 lt 120572 lt

120587

2 119908ℎ119890119899 119860 + 119860119879 = radic21198682 where 119860119879 is

transpose of A


skew-symmetric

27 if A=[1 24 2


28 If A=[120783 120782 120784120782 120784 120783120784 120782 120785

] find A(adj A)



] 119894119904 119894119899119907119890119903119904119890 119900119891 119905ℎ119890 119898119886119905119903119894119909 [minus7 minus9 10


]


30 If 119860 = [1 minus3 10 2 minus12 1 3

] 119861 = [minus1 0 15 4 62 1 1


] 119907119890119903119894119891119910 119905ℎ119886119905

(i) A(119861119862) = (119860119861)119862 (ii) (A+B)C=AC+BC

31 If A=[0 3

minus7 5] 119868 = [

1 00 1

] 119891119894119899119889 119896 119904119906119888ℎ 119905ℎ119886119905 1198961198602 = 5119860 minus 21119868


minus3 4] 119860 = [


]

33 Let A=[1 minus2 30 4 7

] 119886119899119889 119861 = [0 4 22 minus2 1





35 If A=[119886 1198870 1


119886minus1


18

36 If A=[352




38 If A=[1 2 22 1 22 2 1



(i)[1 23 7

](ii) [2 17 4

]



| = (119909 + 119910 + 119911)3


119909 119909 + 119910 119909 + 2119910119909 + 2119910 119909 119909 + 119910119909 + 119910 119909 + 2119910 119909

| = 91199102(119909 + 119910)

42 If 119891(119909) = |119886 minus1 0

119886119909 119886 minus11198861199092 119886119909 119886

| 119906119904119894119899119892 119901119903119900119901119890119903119905119894119890119904 119900119891 119889119890119905119890119903119898119894119899119886119899119905119904 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119891(2119909) minus

119891(119909)

43 Let f(t)=|119888119900119904119905 119905 1

2119904119894119899119905 119905 2119905119904119894119899119905 119905 119905

| 119905ℎ119890119899 119891119894119899119889 lim119905rarr0

119891(119905)

1199052


2 21198861199052) 119886119899119889 119862(11988611990532 21198861199053)



47 If 119860 = [2 31 4

] 119886119899119889119861 = [1 23 4

] 119907119890119903119894119891119910 119905ℎ119886119905 119886119889119895(119860119861) = (119886119889119895119861)(119886119889119895 119860)



] 119886119899119889 119907119890119903119894119891119910 119905ℎ119886119905 119860(119886119889119895119860) = (119886119889119895119860)119860 = |119860|1198683

49 Let 119860 = [3 72 5

] 119886119899119889119861 = [6 87 9





] 119904ℎ119900119908 119905ℎ119886119905 1198603 = 119860minus1



(i)A=[5 200 1

] (ii)A=[1 minus3 24 minus1 23 5 2

]


] 119883 [4 73 5

] = [1 00 1

]


19


| = 0


] and




2

57 If A=[1 0 20 2 12 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896





two types













-x+2y+5z=2 2x-3y+z=15 -x +y +z=-3


(i)[2 3 minus3


](ii) [2 0 minus15 1 00 1 3

]


(119887 + 119888)2 119887119886 119888119886

119886119887 (119888 + 119886)2 119888119887

119886119888 119887119888 (119886 + 119887)2

| =

2119886119887119888(119886 + 119887 + 119888)3

64 In a ∆119860119861119862 if |1 1 1

1 + 119904119894119899 119860 1 + 119904119894119899 119861 1 + 119904119894119899 119888119904119894119899 119860 + sin2 119860 119904119894119899 119861 + sin2 119861 119904119894119899 119861 + sin2 119861


isosceles triangle

65 If |119901 119887 119888119886 119902 119888119886 119887 119903

| = 0 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119901

119901minus119886+

119902

119902minus119887+

119903

119903minus119888 119901 ne 119886 119902 ne 119887 119903 ne 119888


119961minus

120783

119962+

120783

119963= 120787

120784

119961+

120785

119962minus

120786

119963= minus120789

120784

119961+

120783

119962minus

120784

119963= minus120785

20











| = 0









70 Prove that |






(119886 + 1)(119886 + 2) 119886 + 2 1

(119886 + 3)(119886 + 2) 119886 + 3 1

(119886 + 3)(119886 + 4) 119886 + 4 1| = minus2

If A=[1 0 2

0 2 1

2 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896

21

WORK SHEET I

CLASS XII

MATHEMATICS



1 MARK QUESTIONS






value of 24


2 MARK QUESTIONS







1 ) is two






22


13 If f(x) = 119909minus1



its inverse

( Ans 119891minus1(119909) = 5minus119909

7 )



4 MARK QUESTIONS


relation







120587













2]

23

WORKSHEET 12 IP

Q1 Table SchoolBus













order of rtno











24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




17





19 If |119909 sin 120579 cos 120579




] [1199092

] = [56

]


119909 + 119910 + 119911119909 + 119911119910 + 119911

] = [957

]

22 If 2119883 + 3119884 = [2 34 0

] 119886119899119889 3119883 + 2119884 = [minus2 21 minus5

] find X and Y

23 If 119860 = [3 5] 119861 = [7 3] 119905ℎ119890119899 119891119894119899119889 119898119886119905119903119894119909 119862 119904119906119888ℎ 119905ℎ119886119905 119860119862 = 119861119862

24 If A=[0 05 0

] 119891119894119899119889 11986016

25 If A=[119888119900119904120572 119878119894119899120572

minus119904119894119899120572 119888119900119904120572] find 120572 119904119886119905119894119904119891119910119894119899119892 0 lt 120572 lt

120587

2 119908ℎ119890119899 119860 + 119860119879 = radic21198682 where 119860119879 is

transpose of A


skew-symmetric

27 if A=[1 24 2


28 If A=[120783 120782 120784120782 120784 120783120784 120782 120785

] find A(adj A)



] 119894119904 119894119899119907119890119903119904119890 119900119891 119905ℎ119890 119898119886119905119903119894119909 [minus7 minus9 10


]


30 If 119860 = [1 minus3 10 2 minus12 1 3

] 119861 = [minus1 0 15 4 62 1 1


] 119907119890119903119894119891119910 119905ℎ119886119905

(i) A(119861119862) = (119860119861)119862 (ii) (A+B)C=AC+BC

31 If A=[0 3

minus7 5] 119868 = [

1 00 1

] 119891119894119899119889 119896 119904119906119888ℎ 119905ℎ119886119905 1198961198602 = 5119860 minus 21119868


minus3 4] 119860 = [


]

33 Let A=[1 minus2 30 4 7

] 119886119899119889 119861 = [0 4 22 minus2 1





35 If A=[119886 1198870 1


119886minus1


18

36 If A=[352




38 If A=[1 2 22 1 22 2 1



(i)[1 23 7

](ii) [2 17 4

]



| = (119909 + 119910 + 119911)3


119909 119909 + 119910 119909 + 2119910119909 + 2119910 119909 119909 + 119910119909 + 119910 119909 + 2119910 119909

| = 91199102(119909 + 119910)

42 If 119891(119909) = |119886 minus1 0

119886119909 119886 minus11198861199092 119886119909 119886

| 119906119904119894119899119892 119901119903119900119901119890119903119905119894119890119904 119900119891 119889119890119905119890119903119898119894119899119886119899119905119904 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119891(2119909) minus

119891(119909)

43 Let f(t)=|119888119900119904119905 119905 1

2119904119894119899119905 119905 2119905119904119894119899119905 119905 119905

| 119905ℎ119890119899 119891119894119899119889 lim119905rarr0

119891(119905)

1199052


2 21198861199052) 119886119899119889 119862(11988611990532 21198861199053)



47 If 119860 = [2 31 4

] 119886119899119889119861 = [1 23 4

] 119907119890119903119894119891119910 119905ℎ119886119905 119886119889119895(119860119861) = (119886119889119895119861)(119886119889119895 119860)



] 119886119899119889 119907119890119903119894119891119910 119905ℎ119886119905 119860(119886119889119895119860) = (119886119889119895119860)119860 = |119860|1198683

49 Let 119860 = [3 72 5

] 119886119899119889119861 = [6 87 9





] 119904ℎ119900119908 119905ℎ119886119905 1198603 = 119860minus1



(i)A=[5 200 1

] (ii)A=[1 minus3 24 minus1 23 5 2

]


] 119883 [4 73 5

] = [1 00 1

]


19


| = 0


] and




2

57 If A=[1 0 20 2 12 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896





two types













-x+2y+5z=2 2x-3y+z=15 -x +y +z=-3


(i)[2 3 minus3


](ii) [2 0 minus15 1 00 1 3

]


(119887 + 119888)2 119887119886 119888119886

119886119887 (119888 + 119886)2 119888119887

119886119888 119887119888 (119886 + 119887)2

| =

2119886119887119888(119886 + 119887 + 119888)3

64 In a ∆119860119861119862 if |1 1 1

1 + 119904119894119899 119860 1 + 119904119894119899 119861 1 + 119904119894119899 119888119904119894119899 119860 + sin2 119860 119904119894119899 119861 + sin2 119861 119904119894119899 119861 + sin2 119861


isosceles triangle

65 If |119901 119887 119888119886 119902 119888119886 119887 119903

| = 0 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119901

119901minus119886+

119902

119902minus119887+

119903

119903minus119888 119901 ne 119886 119902 ne 119887 119903 ne 119888


119961minus

120783

119962+

120783

119963= 120787

120784

119961+

120785

119962minus

120786

119963= minus120789

120784

119961+

120783

119962minus

120784

119963= minus120785

20











| = 0









70 Prove that |






(119886 + 1)(119886 + 2) 119886 + 2 1

(119886 + 3)(119886 + 2) 119886 + 3 1

(119886 + 3)(119886 + 4) 119886 + 4 1| = minus2

If A=[1 0 2

0 2 1

2 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896

21

WORK SHEET I

CLASS XII

MATHEMATICS



1 MARK QUESTIONS






value of 24


2 MARK QUESTIONS







1 ) is two






22


13 If f(x) = 119909minus1



its inverse

( Ans 119891minus1(119909) = 5minus119909

7 )



4 MARK QUESTIONS


relation







120587













2]

23

WORKSHEET 12 IP

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order of rtno











24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




18

36 If A=[352




38 If A=[1 2 22 1 22 2 1



(i)[1 23 7

](ii) [2 17 4

]



| = (119909 + 119910 + 119911)3


119909 119909 + 119910 119909 + 2119910119909 + 2119910 119909 119909 + 119910119909 + 119910 119909 + 2119910 119909

| = 91199102(119909 + 119910)

42 If 119891(119909) = |119886 minus1 0

119886119909 119886 minus11198861199092 119886119909 119886

| 119906119904119894119899119892 119901119903119900119901119890119903119905119894119890119904 119900119891 119889119890119905119890119903119898119894119899119886119899119905119904 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119891(2119909) minus

119891(119909)

43 Let f(t)=|119888119900119904119905 119905 1

2119904119894119899119905 119905 2119905119904119894119899119905 119905 119905

| 119905ℎ119890119899 119891119894119899119889 lim119905rarr0

119891(119905)

1199052


2 21198861199052) 119886119899119889 119862(11988611990532 21198861199053)



47 If 119860 = [2 31 4

] 119886119899119889119861 = [1 23 4

] 119907119890119903119894119891119910 119905ℎ119886119905 119886119889119895(119860119861) = (119886119889119895119861)(119886119889119895 119860)



] 119886119899119889 119907119890119903119894119891119910 119905ℎ119886119905 119860(119886119889119895119860) = (119886119889119895119860)119860 = |119860|1198683

49 Let 119860 = [3 72 5

] 119886119899119889119861 = [6 87 9





] 119904ℎ119900119908 119905ℎ119886119905 1198603 = 119860minus1



(i)A=[5 200 1

] (ii)A=[1 minus3 24 minus1 23 5 2

]


] 119883 [4 73 5

] = [1 00 1

]


19


| = 0


] and




2

57 If A=[1 0 20 2 12 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896





two types













-x+2y+5z=2 2x-3y+z=15 -x +y +z=-3


(i)[2 3 minus3


](ii) [2 0 minus15 1 00 1 3

]


(119887 + 119888)2 119887119886 119888119886

119886119887 (119888 + 119886)2 119888119887

119886119888 119887119888 (119886 + 119887)2

| =

2119886119887119888(119886 + 119887 + 119888)3

64 In a ∆119860119861119862 if |1 1 1

1 + 119904119894119899 119860 1 + 119904119894119899 119861 1 + 119904119894119899 119888119904119894119899 119860 + sin2 119860 119904119894119899 119861 + sin2 119861 119904119894119899 119861 + sin2 119861


isosceles triangle

65 If |119901 119887 119888119886 119902 119888119886 119887 119903

| = 0 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119901

119901minus119886+

119902

119902minus119887+

119903

119903minus119888 119901 ne 119886 119902 ne 119887 119903 ne 119888


119961minus

120783

119962+

120783

119963= 120787

120784

119961+

120785

119962minus

120786

119963= minus120789

120784

119961+

120783

119962minus

120784

119963= minus120785

20











| = 0









70 Prove that |






(119886 + 1)(119886 + 2) 119886 + 2 1

(119886 + 3)(119886 + 2) 119886 + 3 1

(119886 + 3)(119886 + 4) 119886 + 4 1| = minus2

If A=[1 0 2

0 2 1

2 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896

21

WORK SHEET I

CLASS XII

MATHEMATICS



1 MARK QUESTIONS






value of 24


2 MARK QUESTIONS







1 ) is two






22


13 If f(x) = 119909minus1



its inverse

( Ans 119891minus1(119909) = 5minus119909

7 )



4 MARK QUESTIONS


relation







120587













2]

23

WORKSHEET 12 IP

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order of rtno











24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




19


| = 0


] and




2

57 If A=[1 0 20 2 12 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896





two types













-x+2y+5z=2 2x-3y+z=15 -x +y +z=-3


(i)[2 3 minus3


](ii) [2 0 minus15 1 00 1 3

]


(119887 + 119888)2 119887119886 119888119886

119886119887 (119888 + 119886)2 119888119887

119886119888 119887119888 (119886 + 119887)2

| =

2119886119887119888(119886 + 119887 + 119888)3

64 In a ∆119860119861119862 if |1 1 1

1 + 119904119894119899 119860 1 + 119904119894119899 119861 1 + 119904119894119899 119888119904119894119899 119860 + sin2 119860 119904119894119899 119861 + sin2 119861 119904119894119899 119861 + sin2 119861


isosceles triangle

65 If |119901 119887 119888119886 119902 119888119886 119887 119903

| = 0 119891119894119899119889 119905ℎ119890 119907119886119897119906119890 119900119891 119901

119901minus119886+

119902

119902minus119887+

119903

119903minus119888 119901 ne 119886 119902 ne 119887 119903 ne 119888


119961minus

120783

119962+

120783

119963= 120787

120784

119961+

120785

119962minus

120786

119963= minus120789

120784

119961+

120783

119962minus

120784

119963= minus120785

20











| = 0









70 Prove that |






(119886 + 1)(119886 + 2) 119886 + 2 1

(119886 + 3)(119886 + 2) 119886 + 3 1

(119886 + 3)(119886 + 4) 119886 + 4 1| = minus2

If A=[1 0 2

0 2 1

2 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896

21

WORK SHEET I

CLASS XII

MATHEMATICS



1 MARK QUESTIONS






value of 24


2 MARK QUESTIONS







1 ) is two






22


13 If f(x) = 119909minus1



its inverse

( Ans 119891minus1(119909) = 5minus119909

7 )



4 MARK QUESTIONS


relation







120587













2]

23

WORKSHEET 12 IP

Q1 Table SchoolBus













order of rtno











24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




20











| = 0









70 Prove that |






(119886 + 1)(119886 + 2) 119886 + 2 1

(119886 + 3)(119886 + 2) 119886 + 3 1

(119886 + 3)(119886 + 4) 119886 + 4 1| = minus2

If A=[1 0 2

0 2 1

2 0 3

] 119886119899119889 1198603 minus 61198602 + 7119860 + 1198701198683 = 119874 119891119894119899119889 119896

21

WORK SHEET I

CLASS XII

MATHEMATICS



1 MARK QUESTIONS






value of 24


2 MARK QUESTIONS







1 ) is two






22


13 If f(x) = 119909minus1



its inverse

( Ans 119891minus1(119909) = 5minus119909

7 )



4 MARK QUESTIONS


relation







120587













2]

23

WORKSHEET 12 IP

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order of rtno











24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




21

WORK SHEET I

CLASS XII

MATHEMATICS



1 MARK QUESTIONS






value of 24


2 MARK QUESTIONS







1 ) is two






22


13 If f(x) = 119909minus1



its inverse

( Ans 119891minus1(119909) = 5minus119909

7 )



4 MARK QUESTIONS


relation







120587













2]

23

WORKSHEET 12 IP

Q1 Table SchoolBus













order of rtno











24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




22


13 If f(x) = 119909minus1



its inverse

( Ans 119891minus1(119909) = 5minus119909

7 )



4 MARK QUESTIONS


relation







120587













2]

23

WORKSHEET 12 IP

Q1 Table SchoolBus













order of rtno











24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




23

WORKSHEET 12 IP

Q1 Table SchoolBus













order of rtno











24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




24












Table CLUB



27 1000 M

20

25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




25


20 1200 F

15


19 2000 M

2


01 1500 M

16


12 700 M

10


24 800 F

10


20 2200 F

5


22 1100 M

18


13 900 M

17


19 1700 M

17



















26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




26













Rno Fees

1 4000

2 4300

3 5000

4 Null





27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




27



Field







28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




28






29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




29




marks Grade

gt=90 A

lt90 and gt=80 B1

lt80 and gt=70 B2

lt70 and gt=50 C






30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




30










Class Char 15

Section Char 1

Fees Char 10


31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




31





Class Char 15

Section Char 1

Fees Char 15



32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




32





33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




33






1-15 Rs 50 Rs55

16-20 45 50

21-30 40 45

21-50 35 40

gt50 30 35




and Retailer



34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




34





HDFC 12

ICICI 15

CITY BANK 10

VISA 14

Master Card 18


35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




35





Medical gt=80 A

60-79 B

lt60 C

Non-Medical gt=75 A

lt75 and gt=50 B

lt50 C


the NCC cadets

36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




36

37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




37


38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




38


39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




39


FOR CLASS XII




lifestyle disease








40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




40

WORK SHEET

CLASS 12th BSt






ignored


















Name the process










of an organization

41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




41








down





country


lines
















above case


from the above case








42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




42

the employees





management





consequences














principle

43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




43

CLASS XII








PPCindicate











PPC







44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




44

CLASS XII






















(8-6)




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




45

CLASS XII










substitute




help of example





defend or refute






agree

46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




46




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




47

CLASS XII



2 DEFINE MPP






DIAGRAM


9 GIVE REASON

















48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




48




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




49

CLASS XII





4 DEFINE TCACMC





OUTPUT











PRODUCTION



LABOUR





50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




50




8

51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




51

CLASS XII




ORIGIN






__________________________________________

MR IS THE RATE OF ___________________________


______________________________________


________________________________________


_____________________________________________________





AR=0 WHEN TR IS MAX




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




52






53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




53

CLASS XII









CONDITION OF MR=MC



DIAGRAM







54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




54

CLASS XII






GOOD BY A FIRM









PRODUCT









LIFE



55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




55








56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




56

CLASS XII










8 WHAT IS CARTEL


ITWHY



MONOPOLY






MARKET COMPETITION


IT JUSTIFIED




INCREASE IN DEMAND

DECREASE IN DEMAND

INCREASE IN SUPPLY

57

DECREASE IN SUPPLY




57

DECREASE IN SUPPLY




CLASS XII SUBJECT- ENGLISH CORE WORK SHEET 1 ADVANCED...

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Transcript of CLASS XII SUBJECT- ENGLISH CORE WORK SHEET 1 ADVANCED...