Gillesania No Answers

8/16/2019 Gillesania No Answers

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MULTIPLE CHOICE

QUESTIONS in

ENGINEERING MATHEMATICS

By

Diego Inocencio T. Gillesania

Encoded y!

Sa"cia# Ma"c"is A.

Ma"asigan# $"ancis Ca"l B.Gan%&angco# C'a"les Lloyd G.


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Con(e"sion

P"ole) *

+'a% is %'e %e),e"a%&"e in deg"ee Celsi&s o- asol&%e e"o/

A. 012

B. 3

C. 241

D. 0241

P"ole) 2 5ME A,"il *6678

Ho9 )any deg"ees Celsi&s is *33 deg"ees $a'"en'ei%/

A. 14.: ;C

B. 2.774 ;C

C. *.11< ;C

D. *1.1< ;C

P"ole) 1 5ECE No(e)e" *6648

A co)-o"%ale "oo) %e),e"a%&"e is 42 ;$. +'a% is %'is %e),e"a%&"e# e=,"essed in deg"ees >el(in/

A. 271

B. 263

C. 26?

D. 24?

P"ole) <

2?? ;C is e@&i(alen% %o!A.


3/220

C. 11.11

D. *7.11

P"ole) 45EE Oc%oe" *6638

+'a% is %'e asol&%e %e),e"a%&"e o- %'e -"eeing ,oin% o- 9a%e" in deg"ee Ranine/

A. 012

B. 3

C.


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B. 243;

C. *:3;

D. 63;

P"ole) *1 5ECE No(e)e" *66?8

An ang&la" &ni% e@&i(alen% %o *


5/220

A.


6/220

T'e ,"e-i= nano is o,,osi%e %o!

A. )ega

B. %e"a

C. 'e=a

D. giga

P"ole) 2?5ME Oc%oe" *6678

*3 %o %'e *2%' ,o9e" is %'e (al&e o- %'e ,"e-i=!

A. gigaB. ,icoC. %e"aD. ,e%a

E=,onen%s and Radicals

P"ole) 27

Sol(e -o" =! = F 05*0248021

A. 6

B. *6

C. 06

D. 0*6

P"ole) 24

Sol(e -o" a in %'e e@&a%ion! a F 7


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C. √ 10=√ 5+√ 2

D. ??????????F?7

P"ole) 13

Sol(e -o" =! =F √ 18−√ 72+√ 50 .

A. 02 √ 2

B. 2 √ 2

C. <

D. < √ 3

P"ole) 1*

Sol(e -o" =!√

x−√

1− x=1−√

x .

A. 0*72? 3B. 2?*7 3C. 02?*7 3D. *72? 3

P"ole) 12

Si),li-y3√ 2 x4−

3√ 16 x4+2

3√ 54 x4 .

A. ?3√ x4

B. 23√ 5 x4

C. 53√ 2 x

4

D. 23√ x4

P"ole) 11

Sol(e -o" =! 1=?=* F 7=2

A. 2.*


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Si),li-y(a−2 b3)2

a2

b−1 .

A. a−2

b7

B. a−2

b5

C. a−6

b7

D. a−6

b5

P"ole) 1?

51=8= is e@&al %o!

A. 3 x

2

B. 1

=

=

=

C. 1==

D. 12=

P"ole) 17

Sol(e -o" =! 14=* F 7?7*.

A. *B. 2C. 1D. <

P"ole) 14

I- 1a F 4# %'en 1a242 F

A. *B. 14C. 41D.


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A. 06B. 7C. 6D. *7

P"ole)


10/220

P"ole)


11/220

C. x

3

y

D.1

x3 y

P"ole)


12/220

B. ?


13/220

B. 502=0y82

C. 502=y82

D. 52=0y82

P"ole) ?6

$ac%o" =


14/220

C. 5=0:85=28D. 5=:85=28

P"ole) 7?

$ac%o" %'e e=,"ession =70* as co),le%ely as ,ossile.

A. 5=*85=0*85=


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B. = F * y F 01C. = F 2 y F 2D. = F


16/220

B. 41*C. 21*D. :?*

P"ole) 47 5CE No(e)e" *6648

I- 1=1


17/220

C. 2a5a2 28D. 25a2 28

P"ole) :2

I- =0*= F *# -ind %'e (al&e o- =1 *=1.

A. *B. 2C. 1D. <

P"ole) :1

I- *= *y F 1 and 2= *y F *. T'en = is e@&al %o!

A. B. 21C.

D.


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T'e @&o%ien% o- 5=? 128 y 5=28 is!

A. =


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C. A F 1 B F 2D. A F 1 B F 2

P"ole) 6* 5ME Oc%oe" *6678

Resol(e

x+2

x2−7 x+12 in%o ,a"%ial -"ac%ion.

A.6

x−4−

2

x−3

B.6

x−4+

7

x−3

C.6

x−4−

5

x−3

D.6

x−4 + 5

x−3

P"ole) 62 5ECE A,"il *66:8

T'e a"i%')e%ic )ean o- :3 n&)e"s is ??. I- %9o n&)e"s na)ely 2?3 and :?3 a"e "e)o(ed 9'a%

is %'e a"i%')e%ic )ean o- %'e "e)aining n&)e"s/

A.


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P"ole) 6?

I- *a !* ! *c F 2 ! 1 !


21/220

P"ole) *3*

I-

log10 x

1−log10 2 F 2# 9'a% is %'e (al&e o- /

A. B. 2?C. <D. ?

P"ole) *32 5EE Oc%oe" *6628

Sol(e -o" =! log 7 = log < F log < log 512


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D. =y 0 *

P"ole) *34

log x

y

logy x is e@&al %o!

A. =yy=

B. y log = = log yC. 5y log =8 5= log y8D. *

P"ole) *3:

I- *3a= F P# 9'a% is %'e (al&e o- =/

A. 5*a85log P08B. 5*a8 log 5 P08

C. 5*a8 P*30

D. 5*a8 log P*3

P"ole) *36

$ind %'e (al&e o- log5aa8a.

A. 2a log aB. a2 log aC. a log a2

D. 5a log a8a

P"ole) **3Sol(e -o" =! = F log a

× logc d× logd c

A. log aB. loga cC. log cD. logd a

P"ole) ***

$ind %'e ,osi%i(e (al&e o- = i- log= 17 F 2.

A. 2

B. <C. 7D. :

P"ole) **2

$ind = i- log= 24 log= 1 F 2.

A. 6


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B. *2C. :D. 4

P"ole) **1

$ind a i- log2 5a28 log2 5a028 F ?A. 2B. <C. 7D. :

P"ole) **<

Sol(e -o" = i- log? = F 1.

A. **?B. *2?

C. *1?D. *


24/220

+'ic' o- %'e -ollo9ing is co""ec%/

A. 02 log 4 F *


25/220

P"ole) *2< 5CE No(e)e" *6648

Log7 :


26/220

B. "eal n&)e" C. i)agina"y n&)e" D. co),le= n&)e"

P"ole) *135ME A,"il *66:8

1:.? %o %'e = ,o9e" F 7.? %o %'e =02 ,o9e"# sol(e -o" = &sing loga"i%')s.A. 2.43B. 2.*3C. 02.*3D. 02.32

P"ole) *1* 5CE No(e)e" *6678

$ind %'e 7%' %e") o- %'e e=,ansion o- 5*2a 18*7.

A. 022113

256 a11

B. 066339

128a11

C. 022113

128a11

D. 066339

256 a11

P"ole) *12 5ECE A,"il *66:8In %'e e=,ansion o- 5=


27/220

C. 2?1


28/220

A. CAB. BAC. CAD. BA

P"ole) *


29/220

A. *2=2 4= * F 3B. *2=2 4= * F 3C. *2=2 4= * F 3D. *2=2 4= * F 3

P"ole) *


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B. *?

C. 23

D. *:

P"ole) *?2

Pe%e"Vs age *1 yea"s ago 9as *1 o- 'is age 4 yea"s 'ence. Ho9 old is Pe%e"/

A. *?

B. 2*

C. 21

D. 24

P"ole) *?1

A )an is


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D. 23

P"ole) *?4

T'e s&) o- %'e ,a"en%Vs ages is %9ice %'e s&) o- %'ei" c'ild"enVs ages. $i(e yea"s ago# %'e s&) o-

%'e ,a"en%Vs ages is -o&" %i)es %'e s&) o- %'ei" c'ild"enVs ages. In -i-%een yea"s %'e s&) o- %'e

,a"en%Vs ages 9ill e e@&al %o %'e s&) o- %'ei" c'ild"enVs ages. Ho9 )any c'ild"en 9e"e in %'e

-a)ily/

A. 2B. 1C. <D. ?

P"ole) *?:

T9o %'o&sand ilog"a) o- s%eel con%aining :W o- nicel is %o e )ade y )i=ing s%ell con%aining

*


32/220

B. *?

C. 23

D. 2?

P"ole) *72

A ,o&nd o- alloy o- lead and nicel 9eig'%s *


33/220

A. 2 'o&"s

B. 2.? 'o&"s

C. *.62 'o&"s

D. *.: 'o&"s

P"ole) *74

A s9i))ing ,ool is -illed %'"o&g' i%s inle% ,i,e and %'en e),%ied %'"o&g' i%s o&%le% ,i,e in a %o%al

o- : 'o&"s. I- 9a%e" en%e"s %'"o&g' i%s inle% and si)&l%aneo&sly allo9ed %o lea(e %'"o&g' i%s

o&%le%# %'e ,ool is -illed in 4 'o&"s. $ind 'o9 long 9ill i% %ae %o -ill %'e ,ool 9i%' %'e o&%le%

closed.

A. 7B. 2C. 1D. ?

P"ole) *7:

T'"ee ,e"sons can do a ,iece o- 9o" alone in 1 'o&"s# < 'o&"s and 7 'o&"s "es,ec%i(ely. +'a%

-"ac%ion o- %'e Yo can %'ey -inis' in one 'o&" 9o"ing %oge%'e"/

A. B.


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P"ole) *4* 5ECE No(e)e" *66?8

Ped"o can ,ain% a -ence ?3W -as%e" %'an X&an and 23W -as%e" %'an Pila" and %oge%'e" %'ey can

,ain% a gi(en -ence in < 'o&"s. Ho9 long 9ill i% %ae Pe%e" %o ,ain% %'e sa)e -ence i- 'e 'ad %o

9o" alone/

A. *3 '"s.

B. **'"s.C. *1'"s.D. *?'"s.

P"ole) *42

Nonoy can -inis' a ce"%ain Yo in *3 days i- I)elda 9ill 'el, -o" 7 days. T'e sa)e 9o" can e

done y I)elda in *2 days i- Nonoy 'el,s -o" 7 days. I- %'ey 9o" %oge%'e"# 'o9 long 9ill i% %ae

-o" %'e) %o do %'e Yo/

A. :.6B. :.<

C. 6.2D. :

P"ole) *41

A ,i,e can -ill &, a %an 9i%' %'e d"ain o,en in %'"ee 'o&"s. I- %'e ,i,e "&ns 9i%' %'e d"ain o,en

-o" one 'o&" and %'en %'e d"ain is closed i% 9ill %ae


35/220

B. 2*.


36/220

A. 2*B. 22C. 21D. 2<

P"ole) *:*Ho9 )any )in&%es a-%e" 1!33 9ill %'e )in&%e 'and o- %'e cloc o(e"%aes %'e 'o&" 'and/

A. *


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P"ole) *:7

I% is no9 e%9een 1 and < oVcloc and in %9en%y )in&%es %'e )in&%e 'and 9ill e as )&c' as %'e

'o&"0'and as i% is no9 e'ind i%. +'a% is %'e %i)e no9/

A. 1!37.37

B. 1!34.17C. 1!36.17D. 1!3:.17

P"ole) *:4 5EE Oc%oe" *6638

A )an le-% 'is 'o)e a% ,as% 1!33 oVcloc PM as indica%ed in 'is 9all cloc. Be%9een %9o %o %'"ee

'o&"s a-%e"# 'e "e%&"ned 'o)e and no%iced %'a% %'e 'ands o- %'e cloc in%e"c'anged. A% 9'a% %i)e

did 'e le-% 'is 'o)e/

A. 1!24.24B. 1!1*.


38/220

In a %9o0digi% n&)e"# %'e &ni%Vs digi% is 1 g"ea%e" %'an %'e %enVs digi%. $ind %'e n&)e" i- i% is <

%i)es as la"ge as %'e s&) o- i%s digi%s.

A.


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T'e s&) o- %'e digi%s o- %'e %'"ee0digi% n&)e" is *


40/220

Nonoy le-% Pii% %o d"i(e %o Da(ao a% 7!*? PM and a""i(ed a% **!


41/220

P"ole) 237

>i) and >en %"a(eled a% %'e sa)e %i)e a% %'e "a%e o-23))in#-"o) %'e sa)e ,oin%on a ci"c&la"

%"ac o- "adi&s 733 ). I- >i) 9als along a ci"c&)-e"ence and >i) %o9a"ds %'e cen%e"#-ind %'ei"

dis%ance a-%e" *3 )in&%es.

A.*61 )

B.232 )

C.2


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C. 13 )inD. 1? )in

P"ole) 2** 5CE May *6668

A% 2!33 ,)# an ai",lane %aes o-- a% 1

A. 7?7 )ilesB. 4:? )ilesC. ??4 )ilesD.


43/220

T'e elec%"ical "esis%ance o- a cale (a"ies di"ec%ly as i%s leng%' and in(e"sely as %'e s@&a"e o- i%s

dia)e%e". I- a cale 733 )e%e"s long and 2? )) in dia)e%e" 'as a "esis%ance o- 3.* o')# -ind %'e

leng%' o- %'e cale 4? )) in dia)e%e" 9i%' "esis%ance o- *7 o').

A. 7333 )B. 4333 )

C. :333 )D. 6333 )

P"ole) 2*7

T'e elec%"ical "esis%ance o--e"ed y an elec%"ic 9i"e (a"ies di"ec%ly as %'e leng%' and in(e"sely as

%'e s@&a"e o- %'e dia)e%e" o- %'e 9i"e. Co),a"e %'e elec%"ical "esis%ance o--e"ed y %9o ,ieces o-

9i"e o- %'e sa)e )a%e"ial# one eing *33 ) long and ? )) dia)e%e"# and %'e o%'e" is ?3 ) long

and 1 )) in dia)e%e".

A. R * F 3.?4 R 2B. R * F 3.42 R 2

C. R * F 3.:< R 2D. R * F 3.6? R 2

P"ole) 2*4

T'e %i)e "e@&i"ed -o" an ele(a%o" %o li-% a 9eig'% (a"ies di"ec%ly 9i%' %'e 9eig'% and %'e dis%ance

%'"o&g' 9'ic' i% is %o e li-%ed and in(e"sely as %'e ,o9e" o- %'e )o%o"s. I- i% %aes 23 seconds -o"

a ?0', )o%o" %o li-% ?3 ls. %'"o&g'


44/220

In a ce"%ain de,a"%)en% s%o"e# %'e sala"y o- saleslady is ,a"%ly cons%an% and (a"ies as %'e (al&e o-

'e" sales -o" %'e )on%'# 9'en %'e (al&e o- 'e" sales -o" %'e )on%' is P*3333.33# 'e" sala"y -o"

%'a% )on%' is P633.33. +'en 'e" sales goes &, %o P 2333.33 'e" )on%'ly sala"y goes &, %o

P*333.33. +'a% )&s% e %'e (al&e o- 'e" sales -o" %'e )on%' so %'a% 'e" sala"y -o" %'a% )on%'

9ill e P2333.33/

A. P2?333.33B. P2:333.33C. P12333.33D. P17333.33

P"ole) 223

A )an sold *33 eggs# eig'%y o- %'e) 9e"e sold a% gain o- 13W 9'ile %'e %9en%y eggs 9e"e sold

a% a loss o-


45/220

P"ole) 22<

>i) sold a 9a%c' -o" P1?33.33 a% a loss o- 13W on %'e cos% ,"ice. $ind %'e co""es,onding loss o"

gain i- 'e sold i% -o" P?3?3.33.

A. *W loss

B. *3W lossC. *W gainD. *3W gain

P"ole) 22?

By selling al&% a% P?.33 eac'# a (endo" gains 23W. T'e cos% ,"ice o- egg "ises y *2.?W. I- 'e

sells %'e al&% a% %'e sa)e ,"ice as e-o"e# -ind 'is ne9 gain in ,e"cen%.

A. 4.?WB. ?WC. :W

D. 7.2?W

P"ole) 227

T'e en"oll)en% a% college A and college B o%' g"e9 &, y :W -"o) *6:3 %o *6:?. I- %'e

en"oll)en% in college A g"e9 &, y :33 and %'e en"oll)en% in college B g"e9 &, y :


46/220

B. P*4.33C. P*?.33D. P22.?3

P"ole) 226

A ce"%ain ERO co,ie" ,"od&ces *1 co,ies e(e"y *3 seconds. I- %'e )ac'ine o,e"a%es 9i%'o&%in%e""&,%ion# 'o9 )any co,ies 9ill i% ,"od&ce in an 'o&"/

A. 4:3B.


47/220

A ce"%ain de,a"%)en% s%o"e 'as an in(en%o"y o- Q &ni%s o- a ce"%ain ,"od&c% a% %i)e %F3. T'e s%o"e

sells %'e ,"od&c% a% a s%eady "a%e o- QA &ni%s ,e" 9ee# and e='a&s%s %'e in(en%o"y in A 9ees.

T'e a)o&n% o- ,"od&c% in in(en%o"y a% any %i)e % is!

A. Q 5QA8 %B. Q 5QA8 %

C. Q% QAD. Q% 5QA8 %

P"ole) 21< 5ECE Ma"c' *6678

A )e"c'an% 'as %'"ee i%e)s on sale! na)ely# a "adio -o" P?3# a cloc -o" P13# and a -las'lig'% -o"

P*. A% %'e end o- %'e day# s'e 'as sold a %o%al o- *33 o- %'"ee i%e)s and 'as %aen e=ac%ly *333 on

%'e %o%al sales. Ho9 )any "adios did 'e sale/

A. :3B. <C. *7

D. 23

P"ole) 21?

T'e ,"ice o- : calc&la%o"s "anges -"o) P233 %o P*333.I- %'ei" a(e"age ,"ice is P6?3#9'a% is %'e

lo9es% ,ossile ,"ice o- any one o- %'e calc&la%o"s/

A. ?33

B. ??3

C. 733

D. 7?3

P"ole) 217

A dec o- ?2 ,laying ca"ds is c&% in%o %9o ,iles. T'e -i"s% ,ile con%ains 4 %i)es as )any lac

ca"ds as "ed ca"ds. T'e second ,ile con%ains %'e n&)e" o- "ed ca"ds %'a% is an e=ac% )&l%i,le as

%'e n&)e" o- lac ca"ds. Ho9 )any ca"ds a"e %'e"e in %'e -i"s% ,ile.

A. *<

B. *?

C. *7

D. *4

P"ole) 214 5ECE No(e)e" *6648

T'e ,o,&la%ion o- %'e P'ili,,ines do&led in %'e las% 13 yea"s -"o) *674 %o *664.Ass&)ing %'a%

%'e "a%e o- ,o,&la%ion "a%e inc"ease 9ill "e)ain %'e sa)e in 9'a% yea" 9ills %'e ,o,&la%ion %"i,le/

A. 2313

B. 2324

C. 232*


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D. 232?

P"ole) 21:

De%e")ine %'e &ni% digi% in %'e e=,ansion o- 1:??.

A. 1

B. 6

C. 4

D. *

P"ole) 216 5ECE A,"il *66:8

$ind %'e *6:4%' digi% in %'e deci)al e@&i(alen% o- *4:?6666 s%a"%ing -"o) %'e deci)al ,oin%.

A. *

B. 4

C. :

D. ?

P"ole) 2


49/220

A s'o"e sells *3 di--e"en% sies o- s'oes# eac' in o%' 'ig'0c&% and lo90c&% (a"ie%y# eac' ei%'e"

"&e" o" lea%'e"# and eac' 9i%' 9'i%e o" lac colo". Ho9 )any di--e"en% inds o- s'oes does 'e

sell/

A. 7<

B. :3

C. 42

D. 62

P"ole) 2


50/220


51/220

T'e s&) o- %'e ,"og"ession ?# :# **# *< J. is *32?. Ho9 )any %e")s a"e %'e"e/

A. 22B. 21C. 2<D. 2?

P"ole) 2?1 5CE May *66:8

T'e"e a"e se(en a"i%')e%ic )eans e%9een 1 and 1?. $ind %'e s&) o- all %e")s.

A. *76B. *4*C. *74D. *41

P"ole) 2?< 5CE May *6668

T'e"e a"e line 568 a"i%')e%ic )eans e%9een ** and ?*. T'e s&) o- %'e ,"og"ession is!

A. 246B. 1


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P"ole) 2?:

T'e s&) o- -i(e a"i%')e%ic )eans e%9een 1< and


53/220

C. 5=82=D. 2=5=8

P"ole) 27< 5ECE No(e)e" *6648

$ind %'e 13%' %e") o- %'e A.P.


54/220

C. ***D. 3.366

P"ole) 243

T'e *3%' %e") o- %'e ,"og"ession 7


55/220

C. 42D. **2

P"ole) 247 5ECE A,"il *66:8

$ind %'e s&) o- %'e -i"s% *3 %e")s o- %'e Geo)e%"ic P"og"ession 2#


56/220

T'e geo)e%"ic )ean and %'e 'a")onic )ean o- %9o n&)e"s a"e *2 and 17? "es,ec%i(ely. +'a%

a"e %'e n&)e"s/

A. 17 <B. 42 :C. 17 :

D. 42 <

P"ole) 2:2

I- =#


57/220


58/220

P"ole) 26* 5CE No(e)e" *6648

E(al&a%e %'e -ollo9ing de%e")inan%!

|1 5 −22 1 −33 −2 1 |

A. 02<B. 2<C. 0


59/220

B. |1 01 3|

C. |−1 30 1|

D. |−1 −10 3 |

P"ole) 26? 5CE May *6678

Ele)en%s o- )a%"i= B F |1 20 −5| Ele)en%s o- )a%"i= C F |3 64 1|$ind %'e ele)en%s o- %'e ,"od&c% o- %'e %9o )a%"ices# )a%"i= BC.

A.

| 11 8−20 −5|

B. | 15 9−22 4|

C. |12 1020 −4|

D. | 15 15−17 −6|

P"ole) 267 5CE Boa"d8

Sol(e -o" = and y -"o) %'e gi(en "ela%ions'i,!

|1 13 2|| x y|=|20|A. = F 02 y F 7B. = F 2 y F 7C. = F 02 y F 07D. = F2 y F 07

P"ole) 264 5EE Oc%oe" *6618

In a class o-


60/220

B. *<C. **D. *2

P"ole) 26:

A class o-


61/220

C. *23D. 2<

P"ole) 132 5CE No(e)e" *6678

Ho9 )any < digi% n&)e" can e -o")ed 9i%'o&% "e,ea%ing any digi%# -"o) %'e -ollo9ing digi%

*#2#1#< and 7.

A. *?3B. *23C. *


62/220

Ho9 )any 9ays can 4 ,eo,le e sea%ed a% a "o&nd %ale/

A. ?3


63/220

C. *2?


64/220

A. *B. 3C. *eD. 3.


65/220

P"ole) 12<

Ricy and Geo"ge eac' %'"o9 dice. I- Ricy ge%s a s&) o- -o&" 9'a% is %'e ,"oaili%y %'a%

Geo"ge 9ill ge% less %'an o- -o&"/

A. B. ?7

C. 6**D. **2

P"ole) 12?

T9o -ai" dice a"e %'"o9n. +'a% is %'e ,"oaili%y %'a% %'e s&) o- %'e dice is di(isile y ?/

A. 417B. *6C. **2D.

P"ole) 127 5ME A,"il *6678An &) con%ains < lac alls and 7 9'i%e alls. +'a% is %'e ,"oaili%y o- ge%%ing one lac all

and 9'i%e all in %9o consec&%i(e d"a9s -"o) %'e &"n/

A. 3.2<B. 3.24C. 3.?1D. 3.3<

P"ole) 124

I- %'"ee alls in d"a9n in s&ccession -"o) ? 9'i%e and a second ag# -ind %'e ,"oaili%y %'a% all

a"e o- one colo"# i- %'e -i"s% all is "e,laced i))edia%ely 9'ile %'e second is no% "e,laced e-o"e%'e %'i"d d"a9.

A. *3*2*B. *:*2*C. 2:*2*D. *:3*


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A. ?7B. *7C. 21D. *1

P"ole) 113I- se(en coins a"e %ossed si)&l%aneo&sly# -ind %'e ,"oaili%y %'a% 9ill Y&s% 'a(e %'"ee 'eads.

A. 11*2:B. 1?*2:C. 13*26D. 14*26

P"ole) 11*

I- se(en coins a"e %ossed si)&l%aneo&sly# -ind %'e ,"oaili%y %'a% %'e"e 9ill e a% leas% si= %ails.

A. 2*2:

B. 1*2:C. **7D. 2*7

P"ole) 112 5CE No(e)e" *66:8

A -ace o- a coin is ei%'e" 'ead o" %ail. I- %'"ee coins a"e %ossed# 9'a% is a"e %'e ,"oaili%y o-

ge%%ing %'"ee %ails/

A. *:B.

C. D. *7

P"ole) 111

T'e -ace o- a coin is ei%'e" 'ead o" %ail. I- %'"ee coins a"e %ossed# 9'a% is %'e ,"oaili%y o- ge%%ing

%'"ee %ails o" %'"ee 'eads/

A. *:B. C. D. *7

P"ole) 11<

$i(e -ai" coins 9e"e %ossed si)&l%aneo&sly. +'a% is %'e ,"oaili%y o- ge%%ing %'"ee 'eads and %9o

%ails/

A. *12B. **7C. *:D.


67/220

P"ole) 11?

T'"o9 a -ai" coin -i(e %i)es. +'a% is %'e ,"oaili%y o- ge%%ing %'"ee 'eads and %9o %ails/

A. ?12B. ?*7C. *12

D. 4*7

P"ole) 117 5ECE Ma"c' *6678

T'e ,"oaili%y o- ge%%ing c"edi% in an e=a)ina%ion is *1. I- %'"ee s%&den%s a"e selec%ed a%

"ando)# 9'a% is %'e ,"oaili%y %'a% a% leas% one o- %'e) go% a c"edi%/

A. *624B. :24C. 21D. *1

P"ole) 114T'e"e a"e %'"ee s'o"% @&es%ions in )a%'e)a%ics %es%. $o" eac' @&es%ion# one 5*8 )a" 9ill e

a9a"ded -o" a co""ec% ans9e" and no )a" -o" a 9"ong ans9e". I- %'e ,"oaili%y %'a% Ma"y

co""ec%ly ans9e"s a @&es%ion in a %es% is 21# de%e")ine %'e ,"oaili%y %'a% Ma"y ge%s %9o )a"s.

A.


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A. ?*2B. 14C. 4*2D. ?4

P"ole) 1


69/220


70/220

Co),le= N&)e"s# Ele)en%s

P"ole) 1?* 5CE May *66


71/220

A. ?B. *C. 2D. 1

P"ole) 1?7M&l%i,ly 5102i85


72/220

C. 0


73/220

P"ole)177

+'a% is %'e e=,onen%ial -o") o- %'e co),le= n&)e"


74/220

A. √ 17

B. √ 21

C. √ 20

D. √ 19

P"ole) 142 5ECE No(e)e" *6648

$ind %'e leng%' o- %'e (ec%o" 52#


75/220


76/220

D. E&le"Vs n&)e"

P"ole) 1:1 5ECE No(e)e" *66?8

T'e g"a,'ical "e,"esen%a%ion o- %'e co))&la%i(e -"e@&ency dis%"i&%ion in a se% o- s%a%is%ical da%a

is called!

A. Ogi(eB. His%og"a)C. $"e@&ency ,oly'ed"onD. Mass diag"a)

P"ole) 1:< 5ECE Ma"c' *6678

A se@&ence o- n&)e"s 9'e"e %'e s&cceeding %e") is g"ea%e" %'an %'e ,"eceding %e") is called!

A. Dissonan% se"iesB. Con(e"gen% se"iesC. Iso)e%"ic se"ies

D. Di(e"gen% se"ies

P"ole) 1:? 5ECE Ma"c' *6678

T'e n&)e" 3.*21*21*21J. is

A. I""a%ionalB. S&"dC. Ra%ionalD. T"anscenden%al

P"ole) 1:7 5ECE No(e)e" *6678

An a""ay o- ) × n @&an%i%ies 9'ic' "e,"esen% a single n&)e" sys%e) co),osed o- ele)en%s

in "o9s and col&)ns is no9 as!

A. T"ans,ose o- a )a%"i=B. De%e")inan%C. Co0-ac%o" o- a )a%"i=D. Ma%"i=

P"ole) 1:4

I- e@&als a"e added %o e@&als# %'e s&) is e@&al.

A. %'eo"e)B. ,os%&la%eC. a=io)D. co"olla"y

P"ole) 1:: 5ECE No(e)e" *6678

Te")s %'a% di--e" only in n&)e"ic coe--icien%s a"e no9n as!

A. &ne@&al %e")s


77/220

B. &nlie %e")sC. lie %e")sD. e@&al %e")s

P"ole) 1:6 5ECE No(e)e" *6678

ZZZZZZ is a se@&ence o- %e")s 9'ose "eci,"ocals a"e in a"i%')e%ic ,"og"ession.A. Geo)e%"ic ,"og"essionB. Ha")onic ,"og"essionC. Alge"aic P"og"essionD. Ra%io and ,"o,o"%ion

P"ole) 163 5ECE No(e)e" *6678

T'e loga"i%') o- a n&)e" %o %'e ase e 52.4*:2:*:2:J8 is called!

A. Na,e"ian loga"i%')B. C'a"ac%e"is%ic

C. Man%issaD. B"iggsian loga"i%')

P"ole) 16* 5ECE No(e)e" *6678

T'e "a%io o" ,"od&c% o- %9o e=,"essions in di"ec% o" in(e"se "ela%ion o- %'e o%'e" is called!

A. Ra%io and ,"o,o"%ionB. Cons%an% (a"ia%ionC. MeansD. E=%"e)es

P"ole) 162 5ECE No(e)e" *6678In any s@&a"e )a%"i=# 9'en %'e ele)en%s o- any %9o "o9s a"e %'e sa)e %'e de%e")inan% is!

A. [e"oB. Posi%i(e in%ege" C. Nega%i(e in%ege" D. Uni%y

P"ole) 161 5ECE No(e)e" *6678

T9o o" )o"e e@&a%ions a"e e@&al i- and only i- %'ey 'a(e %'e sa)e

A. Sol&%ion se%B. Deg"eeC. O"de" D. a"iale se%

P"ole) 16<

+'a% is %'e ,ossile o&%co)e o- an e=,e"i)en% called/

A. a sa),le s,aceB. a "ando) ,oin%


78/220

C. an e(en%D. a -ini%e se%

P"ole) 16?

I- %'e "oo%s o- an e@&a%ion a"e e"o# %'en %'ey a"e classi-ied as!

A. T"i(ial sol&%ionsB. E=%"aneo&s "oo%sC. Condi%ional sol&%ionsD. Hy,e"golic Sol&%ions

P"ole) 167

A co),le= n&)e" associa%ed 9i%' a ,'ase0s'i-%ed sine 9a(e in ,ola" -o") 9'ose )agni%&de is

in RMS and angle is e@&al %o %'e angle o- %'e ,'ase0s'i-%ed sine 9a(e is no9n as!

A. A"gandVs n&)e"B. I)agina"y n&)e"C. P'aso" D. Real n&)e"

P"ole) 164

In "a9 da%a# %'e %e")# 9'ic' occ&"s )os% -"e@&en%ly# is no9n as!

A. MeanB. MedianC. Mode

D. Q&a"%ile

P"ole) 16:

In-ini%y )in&s in-ini%y is!

A. In-ini%yB. [e"oC. Inde%e")ina%eD. None o- %'ese

P"ole) 166

Any n&)e" di(ided y in-ini%y is e@&al %o!A. IB. In-ini%yC. [e"oD. Inde%e")ina%e

P"ole)


79/220

A. A"i%')e%ic )eanB. MedianC. Middle %e")sD. Mean

P"ole)


80/220

T9o -ac%o"s a"e conside"ed essen%ially %'e sa)e i-!

A. One is )e"ely %'e nega%i(e o- %'e o%'e" B. One is e=ac%ly %'e sa)e o- %'e o%'e" C. Bo%' o- %'e) a"e nega%i(eD. Bo%' o- %'e) a"e ,osi%i(e

P"ole)


81/220


82/220

B. √ x

C. =2D. =

6. +'a% is %'e sine o- :23;/A. 3.6:<B. 03.:77C. 3.:77D. 03.?33

*3. csc 243; F /

A. −√ 3

B. −¿ *

C. √ 3

D. ***. I- co(e"sine is 3.*1


83/220


84/220

B. 3.2?3C. 3.*33D. 3.*?3

2


85/220


86/220

14. Sol(e -o" =! x=1−(sinѲ−cosѲ )2.

A. sin Ѳ cosѲ

B. 02 cos Ѳ

C. cos 2 Ѳ

D. sin 2 Ѳ

1:. Si),li-y cos4Ѳ – sin

4Ѳ .

A. 2B. *

C. 2 sin2Ѳ+1

D. 2 cos2Ѳ−1

16. Sol(e -o" =! x=1−tan2

a1+ tan2 a

A. cos aB. sin 2aC. cos 2aD. sin a


87/220

B. sin2Ѳ

C. sin2Ѳ sec

2Ѳ

D. cos2Ѳ


88/220


89/220

C.


90/220

D. 26< )e%e"s7


91/220


92/220

D. 77.6 )e%e"s47. A "ec%ang&la" ,iece o- land


93/220

B. *:.4


94/220

A. * ! <B. 1 ! *C. * ! <D. < ! *

::. T9o sides o- a %"iangle )eas&"e : c) and *2 c). -ind i%s a"ea i- i%s ,e"i)e%e" is 27 c).

A. 2*.11 s@. ).B. 12.?7 s@. c).C. 1.137 s@. in.D. 12.?7 s@. in.

:6. I- %'"ee sides o- a %"iangle o- an ac&%e %"iangle is 1 c)# < c)# and ^=] c)# 9'a% a"e %'e

,ossile (al&es o- =/A. * = ?B. 3 = ?C. 3 = 4D. * = 4

63. In %"iangle ABC# AB F :) and BC F 23). one ,ossile di)ension o- CA is!

A. *1B. 4C. 6D. **

6*. In a %"iangle BCD# BC F 2? ). and CD F *3 ). T'e ,e"i)e%e" o- %'e %"iangle )ay e.A. 42 ).B. 43 ).C. 76 ).D. 4* ).

62. T'e sides o- a %"iangle ABC a"e AB F 2? c)# BC F 16 c)# and AC F


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96/220

*31. A ,iece o- 9i"e o- leng%' ?2 c) is c&% in%o %9o ,a"%s. Eac' ,a"% is %'en en% %o -o") a

s@&a"e. I% is -o&nd %'a% %o%al a"ea o- %'e %9o s@&a"es is 64 s@. c). %'e di)ension o- %'e

igge" s@&a"e is!A. <B. 6

C. 1D. 7

*3


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***. T'e sides o- a @&ad"ila%e"al a"e *3)# :)# *7) and 23)# "es,ec%i(ely. T9o o,,osi%e

in%e"io" angles 'a(e a s&) o- 22?;. $ind %'e a"ea o- %'e @&ad"ila%e"al in s@. ).A. *


98/220

D. 2?23;**6. Eac' in%e"io" angle o- a "eg&la" ,olygon is *7?;. Ho9 )any sides/

A. 21B. 2<C. 2?

D. 27*23. T'e s&) o- %'e in%e"io" angles o- a ,olygon is ?


99/220

D. 1.?6: s@. &ni%s*2:. T'e co"ne"s o- a 20)e%e" s@&a"e a"e c&% o-- %o -o") a "eg&la" oc%agon. +'a% is %'e

leng%' o- %'e sides o- %'e "es&l%ing oc%agon/A. 3.?2?B. 3.727

C. 3.424D. 3.:2:

*26. I- a "eg&la" ,olygon 'as 24 diagonals# %'en i% is a!A. He=agonB. NonagonC. Pen%agonD. He,%agon

*13. One side o- a "eg&la" oc%agon is 2. $ind %'e a"ea o- %'e "egion inside %'e oc%agon.A. *6.1 s@. &ni%sB. *1.6 s@. &ni%sC. 2*.< s@. &ni%s

D. 1* s@. &ni%s*1*. A "eg&la" oc%agon is insc"ied in a ci"cle o- "adi&s *3. $ind %'e a"ea o- %'e oc%agon.A. 22:.2 s@. &ni%sB. 2::.2 s@. &ni%sC. 2:2.: s@. &ni%sD. 21:.2 s@. &ni%s

P"ole)s Ci"cles# Miscellaneo&s A,,lica%ions

Se% *1

*12. T'e a"ea o- a ci"cle is :6.< s@&a"e inc'es. +'a% is %'e ci"c&)-e"ence/A. 1?.11 inc'esB. 12.2? inc'esC. 11.?2 inc'esD. 1?.?? inc'es

*11. A ci"cle 9'ose a"ea is


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*1?. A @&ad"ila%e"al ABCD is insc"ied in a se)i0ci"cle 9i%' side AD coinciding 9i%' %'e

dia)e%e" o- %'e ci"cle. I- sides AB# BC# and CD a"e :c)# *3c)# and *2c) long#

"es,ec%i(ely# -ind %'e a"ea o- %'e ci"cle.A. 1*4 s@. c).B. 1?7 s@. c).

C.


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*


102/220


103/220

A. < π

B. ? π

C. 7 π

D. : π

*?


104/220

D. 7

Pa"% <

Solid Geo)e%"y

P"ole)s P"is)s# Py"a)ids# Cylinde"s# Cones

Se% *<

*73. I- %'e edge o- a c&e is do&led# 9'ic' o- %'e -ollo9ing is inco""ec%/A. T'e la%e"al a"ea 9ill e @&ad"&,ledB. T'e (ol&)e is inc"eased : %i)esC. T'e diagonal is do&ledD. T'e 9eig'% is do&led

*7*. T'e (ol&)e o- a c&e is "ed&ced y 'o9 )&c' i- all sides a"e 'al(ed/

A. *:B. ?:C. 7:D. 4:

*72. Eac' side o- a c&e is inc"eased y *W. By 9'a% ,e"cen% is %'e (ol&)e o- %'e c&e

inc"eased/A. 21.


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106/220


107/220

*:*. A cylind"ical gasoline %an# lying 'o"ion%ally# 3.63 ). in dia)e%e" and 1 ) long is

-illed %o a de,%' o- 3.73 ). Ho9 )any gallons o- gasoline does i% con%ain/ Hin%! One

c&ic )e%e" F 27? gallonsA. 2?3B. 173

C. 133D. 243

*:2. A closed cylind"ical %an is : -ee% long and 1 -ee% in dia)e%e". +'en lying in a

'o"ion%al ,osi%ion# %'e 9a%e" is 2 -ee% dee,. I- %'e %an is %'e (e"%ical ,osi%ion# %'e de,%'

o- 9a%e" in %'e %an is!A. ?.74 )B. ?.:2 )C. ?.:2 -%D. ?.74 -%

*:1. A ci"c&la" cylinde" is ci"c&)sc"ied ao&% a "ig'% ,"is) 'a(ing a s@&a"e ase one )e%e"

on an edge. T'e (ol&)e o- %'e cylinde" is 7.2:1 c&. ). -ind i%s al%i%&de in ). )e%e" on an

edge. T'e (ol&)e o- %'e cylinde" is 7.2:1 c&. ). $ind i%s al%i%&de in ).A. ?B.


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D. 1:?.2*::. A "ig'% ci"c&la" cone 9i%' an al%i%&de o- : c) is di(ided in%o %9o seg)en%s. One is a

s)alle" ci"c&la" cone 'a(ing %'e sa)e (e"%e= 9i%' %'e (ol&)e e@&al %o o- %'e o"iginal

cone. $ind %'e al%i%&de o- %'e s)alle" cone.A.


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B. 4422C. 44


110/220

B. 11WC.


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A. 72?1 cm3

B. 72? π /3 cm3

C. 72? π /2 cm3

D. 72? π cm3

236. A 9a%e" %an is in %'e -o") o- a s,'e"ical seg)en% 9'ose ase "adii a"e


112/220


113/220

C. 2.1D. 2.*

222. T'e (ol&)e o- %'e s,'e"e is 1 π cu.m . T'e s&"-ace a"ea o- %'is s,'e"e in s@. ). is!

A. 17 π

B. 2< π

C. *: π

D. *2 π

221. S,'e"ical alls *.? c) in dia)e%e" a"ea ,aced in a o= )eas&"ing 7 c) y 1 c) y 1

c). I- as )any alls as ,ossile a"e ,aced in %'e o=# 'o9 )&c' -"ee s,ace "e)ains in

%'e o=/A. 2:.


114/220

C. 1


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116/220


117/220

2


118/220

C.


119/220

27?. +'a% is %'e e@&a%ion o- %'e line %'a% ,asses %'"o&g' 5


120/220


121/220


122/220

D. 07

P"ole)s Pa"aola# Elli,se# Hy,e"ola# Pola"# S,ace

Se% *4

2:


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D. Do9n9a"d

26*. $ind %'e e@&a%ion o- %'e a=is o- sy))e%"y o- %'e -&nc%ion y F 2 x2−7 x+5.

A.


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2? x2+9 y2−300 x−144 y+1251=0

A. 1.<B. 1.2C. 1.7D. 1.3

26:. I- %'e leng%' o- %'e )aYo" and )ino" a=es o- an elli,se is *3 c) and : c)# "es,ec%i(ely#

9'a% is %'e eccen%"ici%y o- %'e elli,se/A. 3.?3B. 3.73C. 3.43D. 3.:3

266. T'e eccen%"ici%y o- %'e elli,se x2/4 y2 *7 F * is!

A. 3.42?B. 3.2?7C. 3.7:6D. 3.:77

133. An elli,se 'as %'e e@&a%ion *7 x2+9 y2 12= *2: F 3. I%s eccen%"ici%y is!

A. 3.?1*B. 3.77C. 3.:2<D. 3.61

13*. T'e cen%e" o- %'e elli,se < x2+ y2−16 x−6 y−43=0 is a%!

A. 52# 18B. 5


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126/220

1**. T'e c'o"ds o- %'e elli,se 7


127/220


128/220

D. " 2 ¿

8

cos2Ѳ+2

12:. %'e dis%ance e%9een ,oin%s 5?# 13;8 and 50:# 0?3;8 is!A. 6.:<

B. *3.*


129/220

P"ole)s Li)i%s# Di--e"en%ia%ion# Ra%e o- C'ange# Slo,e

Se% *:

11


130/220

D. 2

1


131/220

D.−4 x+ y x− y

1


132/220

D.2 e ln =

1?2. $ind %'e de"i(a%i(es 9i%' "es,ec% %o = o- %'e -&nc%ion √ 2−3 x2

A.02 x2

√ 2−3 x2

B. 01= √

2−3 x2

C. 02 x2

√ 2+3 x2

D. 01= √ 2+3 x2

1?1. Di--e"en%ia%e a=2 %o %'e ,o9e".A. 02a=B. 2a=C. 2a= D. a= 2

1?


133/220

D. 0< 5


134/220


135/220

D.3.4?147. $ind %'e ac&%e angle %'a% %'e c&"(e y F * 1=2 c&% %'e =0a=is.

A.44;B. 4?;C. 46;

D.*23;144. $ind %'e angle %'a% %'e line 2y 6= *: F 3 )aes 9i%' %'e =0a=is.A. 4


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1:


137/220


138/220


139/220

B.7 x

4

4 4 x

2

5 +C D. 7 x

4−4 x

2

2 +C

P"ole) 2 5CE May *6668

E(al&a%e! ∫ 4 (x3 x+2

A. 4 ln (3 x+2 )+C C.1

3 ln (3 x+2 )+C

B.4

3 ln (3 x+2 )+C

D. 2 ln (3 x+2 )+C

P"ole) 1 5CE May *66


140/220

In%eg"a%e

2

(¿ x2+7)(x . x cos¿

A. sin (2 x2

+7 )+C C. cos(2 x2

+7)+C

B. sin(2 x2+7)+C D. (sin−) ) ( x

2+7 )+C

P"ole) 4

E(al&a%e

x

ln ¿¿¿¿¿

tan ¿¿

∫¿

.

A.

x

ln ¿+C ¿¿

cos¿ln¿

C.

x

ln ¿+C ¿¿

tan2¿

B.

x

ln ¿+C ¿¿

sec¿ln¿

D.

x

ln ¿

¿¿2

¿¿

tan ¿

P"ole) :

E(al&a%e

x

xln sin ¿(x .

¿

cos¿¿¿∫ ¿


141/220

A.

x

1−lnsin¿+C ¿

x¿sin¿

C.

x−1ln sin ¿+C

¿ x¿

sin¿

B.

x1+ln sin ¿+C

¿ x ¿sin ¿

D. ln √ sin x+C

P"ole) 6

E(al&a%e ∫ tan ) ln sec)().

A. 2 ( ln sec) )

2

+C C. (ln

sec) )+C

B. (ln sec) )2+C D. (ln sec) )

2+C

P"ole) *3

E(al&a%e ∫ e

x(x

1+e2 x .

A. ln (1+e2 x )+C C. (1+e

2 x )2+C

B. ln (1+e2 x )+C D. arctan ( e

x)+C

P"ole) **

E(al&a%e∫ (x

ln x2√ (ln x )

2−1 .

A. arcsec ( ln x )+C C. ln √ (ln x )2−1+C

B. 5218 [ (ln x

)

2

−1

]

3 /2

+C

D.arctan ( ln x )+C

P"ole) *2

E(al&a%e ∫ x

3+1 x+2

(x .


142/220


143/220


144/220

P"ole) 22 5CE May *6678

$ind %'e in%eg"al o- 12sin5 x cos

5 x(x i- lo9e" li)i% F 3 and &,,e" li)i% F π /2 .

A. 3.2 C. 3.7B. 3.: D. 3.<

P"ole) 21 5CE No(e)e" *664# Si)ila" %o CE No(e)e" *66


145/220

P"ole) 26 5EE A,"il *6648

E(al&a%e %'e do&le in%eg"al o- r sin u(r (u # %'e li)i% o- " is -"o) 3 %o cos u and %'e li)i% o-

& is -"o) 3 %o ,i.A. 0*7 C. *1B. *7 D. *2

P"ole) 13

E(al&a%e ∫0

1

∫0

2

∫0

y

(x(y(z.

A. *1 C. *2B. *< D. *7


146/220

P"ole)s Plane A"eas# ol&)es# S&"-aces# Cen%"oid# E%c.

Se% 2*

P"ole) *

$ind %'e a"ea &nde" %'e c&"(e y ¿ x3+3 x2 and %'e =0a=is e%9een = F * and = F 1.

A. 2: s@. &ni%s C. 17 s@. &ni%sB.


147/220

B. a2

D. 2 a2

P"ole) 4 5CE No(e)e" *6648

+'a% is %'e a"ea 9i%'in %'e c&"(e r2=16cos ) !

A. 27 C. 13B. 2: D. 12

P"ole) : 5CE May *6668

$ind %'e a"ea enclosed y r2=2 a2 cos ) .

A. 2 a2

C. 4 a2

B. a2

D. 3 a2

P"ole) 6$ind %'e c&"(ed s&"-ace 5a"ea8 o- %'e solid gene"a%ed y "e(ol(ing %'e ,a"% o- %'e c&"(e y F =2

-"o) 53# 38 %o 5 √ 6 + 6¿ ao&% %'e y0a=is.

A. 62 π s@. &ni%s C. 62 π /5 s@. &ni%s

B. 62 π /3 s@. &ni%s D. 5/62 π s@. &ni%s

P"ole) *3$ind %'e (ol&)e gene"a%ed y "o%a%ing %'e "egion o&nded y y F =# = F *# and y2 F


148/220


149/220


150/220

P"ole)s Di--e"en%ial E@&a%ions A,,lica%ionSe% 22

P"ole) *O%ain %'e di--e"en%ial e@&a%ion o- %'e -a)ily o- s%"aig'% lines 9i%' slo,e and y0in%e"ce,% e@&al.

A y (y+ ( x+1 ) (x=0 C. y (x+ ( x+1 ) (y=0

B y (y−( x+1 ) (x=0 D. y (x−( x+1 )(y=0

P"ole) 2O%ain %'e di--e"en%ial e@&a%ion o- all s%"aig'% lines 9i%' alge"aic s&) o- %'e in%e"ce,%s -i=ed as.

A (1+ y,

)( x y,

− y )=#y C. (1− y,

) ( x y,

− y )=#y

B (1− y, ) ( x y , + y )=#y D. (1+ y

, ) ( x y , + y )=#y

P"ole) 1O%ain %'e di--e"en%ial e@&a%ion o- all s%"aig'% lines a% a -i=ed dis%ance , -"o) %'e o"igin.


151/220

A ( x y, − y )2= $[1+ ( y , )2] C. ( x y

, − y )2= $[1+ ( y , )2]

B ( x y, + y )2=[ 1+ ( y , )2 ] D. x y , − y ¿=[1+ y , ]

P"ole) < 5CE May *6648De%e")ine %'e di--e"en%ial e@&a%ion o- %'e -a)ily o- lines ,assing %'"o&g' %'e o"igin.

A x(y− y (x=0 C. x(y+ y (x=0

B x(x− y (y=0 D. x (x+ y (y=0

P"ole) ?O%ain %'e di--e"en%ial e@&a%ion o- all ci"cles 9i%' cen%e" on line y F 0= and ,assing %'"o&g' %'eo"igin.

A ( y2+2 xy− x2)(x−( y2−2 xy+ x2 )(y=0

B ( y2−2 xy− x2 ) (x−( y2−2 xy− x2 ) (y=0

C ( y2−2 xy− x2 ) (x−( y2−2 xy− x2 ) (y=0

D ( y2+2 xy− x2)(x+( y2−2 xy− x2 )(y=0

P"ole) 7O%ain %'e di--e"en%ial e@&a%ion o- a ,a"aola 9i%' a=is ,a"allel %o %'e =0a=is.

A 3 ( y,, )2− y , y , , , =0 C. 2 ( y

,, )2− y , y , , , =0

B 3 ( y,,

)2

+ y,

y, , ,

=0 D. 2 ( y, ,

)2

− y, ,

y, , ,

=0

P"ole) 4

O%ain %'e ,a"%ic&la" sol&%ion o-(r

(t =−4 rt

9'en t =0, r=r o.

A r=2 r o e−2t 2

C. r=r o e2t

2

B r=r o e−t 2

D. r=r o e−2t 2

P"ole) :

O%ain %'e gene"al sol&%ion o- %'e di--e"en%ial xy(x−( x+2 ) (y=0

A e x= y ( x+2 )2 C. e

x=cy ( x+2)


152/220

B e x=cy ( x+2 )2 D. e

x=2 cy ( x+2)

P"ole) 6

O%ain %'e gene"al sol&%ion o- y, = x y 2 .

A y ( x2+c )+2=0 C. ( x

2+c )+2=0

B y ( x2+c )−2=0 D. y ( x+c )−2=0

P"ole) *3

Sol(e %'e e@&a%ion xy(x−( x+2 y )2 (y=0 .

A e x / y=c y3 ( xy ) C. e

x / y=c y 3( x+ y )

B e x / y=c y3 ( x− y ) D. e

x / y=c y4 ( x−1 )

P"ole) **

O%ain %'e ,a"%ic&la" sol&%ion o- (3 x2−2 y2 ) y , =2 xy ; 9'en x=0, y=−1.

A x2=2 y2 ( y+1 ) C. x

2=2 y2( y−1)

B x2= y2 ( y+1 ) D. x

2= y2 ( y+1 )

P"ole) *2

Sol(e %'e e@&a%ion(2 xy+ y)(x+( x2− x )(y=0.

A y=cx ( x+1 )3+2 x C. y=3 x+cx ( x−1 )

3

B y=cx ( x+1 )−3−2 D. y=cx ( x−1 )

−3

P"ole) *1

Sol(e %'e e@&a%ion 5 6 x+ y2¿(x+ y (2 x−3 y ) (y=0.

A x y2+3 x2− y3=c C. x y

2+2 x2−3 y3=c

B 3 x y

2

−3 x2

− y3

=c D. x y2

+3 x2

− y2

=c

P"ole) *


153/220

Sol(e %'e e@&a%ion

)

)sin )+cos¿()=0.

r+sin )−¿cos¿(r+r ¿¿

A

)sin )+cos¿=c

r2+r ¿

C.

)sin )−cos¿=c

r−2r ¿

B

)

sin )−cos¿=cr

2+2r ¿D.

)

sin )+cos¿=cr

3+2r ¿

P"ole) *?

Sol(e ( x2+ y )(x+( y3+ x )(y=0.

A x

3

3 + x+

y4

4 =c C.

x3

3 + xy−

y4

4 =c

B x

3

3 + x+ y+

y4

4 =c D.

x3

3 − x y 2+

y4

4 =c

P"ole) *7

Sol(e %'e e@&a%ion x (y− y (x=2 x3

(x .

A y= x2+cx C. y= x

3+cx

B y= x3+c D. y= x

2+c x3

P"ole) *4

Sol(e %'e e@&a%ion x (y+ y (x=2 x2 y (x .

A ln| xy|= x3

+c C. ln| xy|= x2

+c

B ln| x+ y|= x2+c D. ln| x− y|=2 x

2+c

P"ole) *:

Sol(e %'e e@&a%ion(y

(x+

2

x y=6 x3.


154/220

A x2 y=6 x5+c C. x

2 y

2=6 x5+c

B x2=5 x6+c D. x

2 y= x6+c

P"ole) *6

Sol(e %'e e@&a%ion ( x5+3 y ) (x− x (y=0.

A 2 y= x5+c x3 C. 2 y= x

3+c x2

B y= x5+c x3 D. y

2=5 x4+c x3

P"ole) 23

T'e di--e"en%ial e@&a%ion(y

(x=

3 x2+ y2

2 xy can e )ade e=ac% y &sing %'e in%eg"a%ing -ac%o"!

A x2

C. y2

B 1/ x2

D. 1/ y2

P"ole) 2*

+'a% is no% %"&e -o" %'e di--e"en%ial e@&a%ion y, + y / x2=1 / x2!

A i% is linea" B i% is 'o)ogeneo&sC i% is se,a"ale

D i% can e sol(ed &sing %'e in%eg"a%ing -ac%o" e−1/ x

P"ole) 22A %an con%ains


155/220


156/220

D

t +(5/2) x−(3/2) y−(3 /2)# cos¿

(2/13 ) ¿

P"ole)s S%a%ics# T"ansla%ion# Ro%a%ionSe% 21

P"ole) *T'e 9eig'% o- a )ass o- *3 ilog"a)s a% a loca%ion 9'e"e g F 6.44 )s2 is!

A. 46.4 N C. 64.4 NB. 44.6 N D. 644 N

P"ole) 2 5ME A,"il *6648

+'a% is %'e "es&l%an% (eloci%y o- a ,oin% o- =0co),onen% - = ¿ t 3−1 # and y0co),onen%

- y ¿ t 2−t

a% %i)et =4 !

A. 71.*124 C. 7


157/220

A )an 9is'es %o c"oss d&e 9es% on a "i(e" 9'ic' is -lo9ing d&e no"%' a% %'e "a%e o- 1 ),'. I- 'ecan "o9 *2 ),' in s%ill 9a%e"# 9'a% di"ec%ion s'o&ld 'e %ae %o c"oss %'e "i(e"/

A. S *


158/220

A. 7 ) C. < )B. ? ) D. 1 )

P"ole) *1A loc o- 9ood is "es%ing on a le(el s&"-ace. I- %'e coe--icien% o- -"ic%ion e%9een %'e loc and

%'e s&"-ace is 3.13# 'o9 )&c' can %'e ,lane e inclined 9i%'o&% ca&sing %'e loc %o slide do9n/A. *7.4o C. 2*.2o

B. 13.2o D. 11.1o

P"ole) *<

A ?33 g loc is "es%ing on a 13o inclined ,lane 9i%' a =0.3 . $ind %'e "e@&i"ed -o"ce P

ac%ing 'o"ion%ally %'a% 9ill ,"e(en% %'e loc -"o) sliding.A. *323 N C.


159/220


160/220


161/220


162/220

P"ole)


163/220

A. *? C. 2?B. 23 D. *2

P"ole)


164/220


165/220

A ,ic0&, %"&c is %"a(eling -o"9a"d a% 2? )s. T'e %"&c ed is loaded 9i%' o=es# 9'ose

coe--icien% o- -"ic%ion 9i%' %'e ed is 3.


166/220

P"ole) 6 5ME A,"il *66:# CE No(e)e" *666 ^S%"&c%&"al]8

An ele(a%o" 9eig'ing 2#333 l a%%ains an &,9a"d (eloci%y o- *7 -,s in < sec 9i%' &ni-o")

accele"a%ion. +'a% is %'e %ension in %'e s&,,o"%ing cales/

A. *#6?3 l C. 2


167/220


168/220

B. 7.17 l D. 4.17 l

P"ole) 2*

An oYec% is ,laced 1 -ee% -"o) %'e cen%e" o- a 'o"ion%ally "o%a%ing ,la%-o"). T'e coe--icien% o-

-"ic%ion is 3.1. T'e oYec% 9ill egin %o slide o-- 9'en %'e ,la%-o") s,eed is nea"es% %o!

A. *4 ",) C. 22 ",)B. *2 ",) D. 24 ",)

P"ole) 22 5ME A,"il *66:8

A -o"ce o- 233 l- ac%s on a loc a% an angle o- 2:o 9i%' "es,ec% %o 'o"ion%al. T'e loc is

,&s'ed 2 -ee% 'o"ion%ally. +'a% is %'e 9o" done y %'is -o"ce/

A. 123 X C.


169/220


170/220


171/220

B. *:3 )s D. *.:3 )s

P"ole) 16

A 3.?30g all 9i%' a s,eed o- 23 )s s%"ies and s%ics %o a 430g loc "es%ing on a -"ic%ionless

s&"-ace. $ind %'e locVs (eloci%y.

A. *


172/220


173/220

S%eel a" 'a(ing a "ec%ang&la" c"oss0sec%ion *?)) × 23)) and *?3) long is s&s,ended

(e"%ically -"o) one end. T'e s%eel 'as a &ni% )ass o- 4:?3 g) 1 and a )od&l&s o- elas%ici%y E o-

233 GPa. I- a loa- o- 23 N is s&s,ended a% %'e o%'e" end o- %'e "od# de%e")ine %'e %o%al

elonga%ion o- %'e "od.

A.


174/220

T'e "o%a%ion o" %9is% in deg"ees o- a s'a-%# :33 )) long s&Yec%ed %o a %o"@&e o- :3 N0)# 23 ))

in dia)e%e" and s'ea" )od&l&s G o- :3#333 MPa is!

A. 1.31 C. 2.62B.


175/220

A *30)e%e" long si),ly s&,,o"%ed ea) ca""ies a &ni-o") load o- : N) -o" 7 )e%e"s -"o) %'e

le-% s&,,o"% and a concen%"a%ed load o- *? N 2 )e%e"s -"o) %'e "ig'% s&,,o"%. De%e")ine %'e

)a=i)&) s'ea" and )o)en%.

A. )a= F 11.2 N M)a= F :?.62 >N0) C. )a= F 17.7 N M)a= F :1.42 >N0)B. )a= F 1*.1 N M)a= F :*.4< >N0) D. )a= F N0)

P"ole) 2* 5ECE No(e)e" *6678

A si),le ea)# *3 ) long ca""ies a concen%"a%ed load o- ?33 N a% %'e )ids,an. +'a% is %'e

)a=i)&) )o)en% o- %'e ea)/

A. *2?3 N0) C. *?23 N0)B. *3?3 N0) D. *?*3 N0)

P"ole) 22 5CE May *6648

A s)all s@&a"e ?c) y ?c) is c&% o&% o- one co"ne" o- a "ec%ang&la" ca"doa"d 23c) 9ide y

13c) long. Ho9 -a"# in c) -"o) %'e &nc&% longe" side# is %'e cen%"oid o- %'e "e)aining a"ea/

A. 6.?7 C. 6.


176/220

P"ole)s P"ess&"e# B&oyancy# $l&id $lo9# Pi,esSe% 27

P"ole) *

T'e )ass o- ai" in a "oo) 9'ic' is 1) × ?) × 23) is no9n %o e 1?3 g. $ind i%s densi%y.

A. *.*74 g)1 C. *.7*4 g)1

B. *.*47 g)1 D. *.4*7 g)1

P"ole) 2 5ME Oc%oe" *6648

One '&nd"ed 5*338 g"a)s o- 9a%e" a"e )i=ed 9i%' *?3 g"a)s o- alco'ol 5 0=790 gc& )8.

+'a% is %'e s,eci-ic g"a(i%y o- %'e "es&l%ing )i=%&"es# ass&)ing %'a% %'e %9o -l&ids )i=

co),le%ely/

A. 3.67 C. 3.71B. 3.:2 D. 3.:7


177/220

P"ole) 1 5ME A,"il *66:8

One '&nd"ed g"a)s o- 9a%e" a"e )i=ed 9i%' *?3 g"a)s o- alco'ol 5 0=790 gc& )8. +'a% is

%'e s,eci-ic (ol&)e o- %'e "es&l%ing )i=%&"es# ass&)ing %'a% %'e -l&ids )i= co),le%ely/

A. 3.:: c& c)g C. 3.:2 c& c)g

B. *.23 c& c)g D. 3.71 c& c)g

P"ole) <

T'e ,"ess&"e 1< )e%e"s elo9 %'e ocean is nea"es% %o!

A. 23< Pa C. 1


178/220

B. 63 in1 D. 13.< in1

P"ole) *3

A %9o0)e%e" s@&a"e ,lane s&"-ace is i))e"sed (e"%ically elo9 %'e 9a%e" s&"-ace. T'e i))e"sion

is s&c' %'a% %'e %9o edges o- %'e s@&a"e a"e 'o"ion%al. I- %'e %o, o- %'e s@&a"e is * )e%e" elo9

%'e 9a%e" s&"-ace# 9'a% is %'e %o%al 9a%e" ,"ess&"e e=e"%ed on %'e ,lane s&"-ace/

A.


179/220


180/220

P"ole) 22

Ass&)e %'a% ?4 li%e"s ,e" second o- oil 5 0=860 g)18 is ,&),ed %'"o&g' a 133 ))

dia)e%e" ,i,eline o- cas% i"on. I- eac' ,&), ,"od&ces 7:? Pa# 'o9 -a" a,a"% can %'ey e ,laced/

5Ass&)e - F 3.31*8A. 21.4 ) C. *2.7 )B. 12.2 ) D. *6.: )

P"ole) 21

A 230)) dia)e%e" co))e"cial s%eel ,i,e# 13 ) long is &sed %o d"ain an oil %an. De%e")ine %'e

disc'a"ge 9'en %'e oil le(el in %'e %an is 1 ) ao(e %'e e=i% o- %'e ,i,e. Neglec% )ino" losses

and ass&)e - F 3.*2.

A. 3.3332?7 )1s C. 3.333**1 )1sB. 3.333*46 )1s D. 3.333:76 )1s

P"ole)s Si),le In%e"es%# Co),o&nd In%e"es%

Se% 24

P"ole) *

$ind %'e in%e"es% on P7:33.33 -o" 1 yea"s a% **W si),le in%e"es%.

A. P*#:4?.33 C. P2#*


181/220

A. P23#21


182/220

Acc&)&la%e P?#333.33 -o" *3 yea"s a% :W co),o&nded @&a"%e"ly.

A. P*2#


183/220


184/220

A. P*4:#1*1.76 C. P*43#*


185/220

A s%&den% 'as )oney gi(en y 'is g"and-a%'e" in %'e a)o&n% o- P23#333.33. Ho9 )&c' )oney in

%'e -o") o- in%e"es% 9ill 'e ge% i- %'e )oney is ,&% in a an %'a% o--e"s :W "a%e co),o&nded

ann&ally# a% %'e end o- 4 yea"s/

A. P1


186/220


187/220


188/220


189/220

B. P*2#1


190/220


191/220

A. P


192/220

A. 6.4?W C. 6.7:WB. 6.?3W D. 6.?4W

P"ole) *1 5ECE No(e)e" *6648

A )an 9is'es 'is son %o "ecei(e P?33#333.33 %en yea"s -"o) no9. +'a% a)o&n% s'o&ld 'e in(es%

no9 i- i% 9ill ea"n in%e"es% o- *2W co),o&nded ann&ally d&"ing %'e -i"s% ? yea"s and *?W

co),o&nded @&a"%e"ly d&"ing %'e ne=% ? yea"s/

A. P*1?#:7:.*6 C. P*21#


193/220

P"ole) *6

+'a% a)o&n% 9o&ld 'a(e %o e in(es%ed a% %'e end o- eac' yea" -o" %'e ne=% 6 yea"s a%


194/220

,ay)en%s o- P*2#?33.33 a% %'e end o- eac' )on%' -o" *: )on%'s 9'en in%e"es% is c'a"ged a% %'e

"a%e o- 7W co),o&nded )on%'ly/

A. P21#


195/220

+'a% is %'e ,"esen% 9o"%' o- a P*33 ann&i%y s%a"%ing a% %'e end o- %'e %'i"d yea" and con%in&ing %o

%'e end o- %'e -o&"%' yea"# i- %'e ann&al in%e"es% "a%e is :W/

A. *?1.


196/220


197/220


198/220

P"ole)


199/220

A ,iece o- )ac'ine"y can e o&g'% -o" P*3#333.33 cas'# o" -o" P2#333.33 do9n and ,ay)en%s

o- P4?3.33 ,e" yea" -o" *? yea"s. +'a% is %'e ann&al in%e"es% "a%e -o" %'e %i)e ,ay)en%s/

A.


200/220


201/220

An e@&i,)en% cos%ing P2?3#333 'as an es%i)a%ed li-e o- *? yea"s 9i%' a oo (al&e o- P13#333

a% %'e end o- %'e ,e"iod. Co),&%e %'e de,"ecia%ion c'a"ge and i%s oo (al&e a-%e" *3 yea"s &sing

declining alance )e%'od.

A. d F P6#


202/220

B. P


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P"ole) *4 5ME A,"il *66:8

An asse% is ,&"c'ased -o" P6#333.33. I%s es%i)a%ed li-e is *3 yea"s# a-%e" 9'ic' i% 9ill e sold -o"

P*#333.33. $ind %'e oo (al&e d&"ing %'e -i"s% yea" i- s&)0o-0%'e0yea"Vs digi% 5SO`D8

de,"ecia%ion is &sed.

A. P:#333.33 C. P7#?33.33

B. P4#?


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P"ole) 21 5CE May *6648

A co),any &ses a %y,e o- %"&c 9'ic' cos%s P2M# 9i%' li-e o- 1 yea"s and a -inal sal(age (al&e

o- P123#333. Ho9 )&c' co&ld %'e co),any a--o"d %o ,ay -o" ano%'e" %y,e o- %"&c -o" %'e sa)e

,&",ose# 9'ose li-e is < yea"s 9i%' a -inal sal(age (al&e o- P


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P"ole)s Recen% Boa"d E=a)s# Selec%ed P"ole)sSe% 12

P"ole) * 5CE No(e)e" 23338A line in a )a, 9as d"a9n a% a scale o- *!2?333. An e""o" o- 3.32 )) in %'e d"a9ing ise@&i(alen% %o 'o9 )any )e%e"s in ac%&al/

A. ? ) C. 3.3? )B. 3.? ) D. ?3 )

P"ole) 2 5ME Oc%oe" 23338

One day a Celsi&s %'e")o)e%e" and a $a'"en'ei% %'e")o)e%e" "egis%e"ed e=ac%ly %'e sa)en&)e"ical (al&e -o" %'e %e),e"a%&"e. +'a% 9as %'e %e),e"a%&"e %'a% day/A. 023 C.


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Sol(e -o" %'e gi(en e@&a%ion# 7.4 x 10−4=e−9.7 x .

A. 3.4


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T9el(e 9o"e"s co&ld do a Yo in 23 days. Si= 9o"e"s s%a"%ed %'e Yo. Ho9 )any 9o"e"s

s'o&ld e "ein-o"ced a% %'e eginning o- %'e 4%' day %o -inis' %'e Yo -o" a %o%al o- *: days -"o)

%'e s%a"%/

A. *3 C. 6B. *1 D. **

P"ole) *< 5ME Oc%oe" 23338

Bo= A 'as < 9'i%e alls# 1 alls# and 1 o"ange alls. Bo= B 'as 2 9'i%e alls# < l&e alls# and <

o"ange alls. I- one all is d"a9n -"o) eac' o=# 9'a% is %'e ,"oaili%y %'a% one o- %'e %9o alls

9ill e o"ange/

A. 27/50 C. 23/50

B. 27/50 D. 7/25

P"ole) *?

T9el(e oos consis%ing o- si= )a%'e)a%ics oos# 2 'yd"a&lics oos and -o&" s%"&c%&"al oos

a"e a""anged on a s'el- a% "ando). De%e")ine %'e ,"oaili%y %'a% oos o- %'e sa)e ind a"e all

%oge%'e".

A. *21*3 C. *1:*3B. *?723 D. **:73

P"ole) *7 5ME Oc%oe" *7 23338+'a% is %'e angle e%9een %9o (ec%o"s A and B/

A=4 i+12 4+6 #

B=24 i−8 4+6 #

A. *4?.


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Gi(en %'a% tanA=4 /5 # 9'a% is %'e (al&e o- 4 sinA−cosA3 cosA+sinA /

A. 3.?46 C. 3.7?<B. 3.4?2 D. 3.62?

P"ole) *6 5CE No(e)e" 23338A -lag,ole 1 ) 'ig' s%ands a% %'e %o, o- a ,edes%al 2 ) 'ig' loca%ed a% one side o- a ,a%'9ay. A%

%'e o,,osi%e side o- %'e ,a%'9ay di"ec%ly -acing %'e -lag,ole# %'e -lag,ole s&%ends %'e sa)e

angle as %'e ,edes%al. +'a% is %'e 9id%' o- %'e ,a%'9ay/

A.


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A. 7


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A. : c) C. 7 c)B. 6 c) D. *3 c)

P"ole) 12 5CE May 23338

T'e -"&s%&) o- a "eg&la" %"iang&la" ,y"a)id 'as e@&ila%e"al %"iangles -o" i%s ases and 'as an

al%i%&de o- : ). T'e lo9e" ase edge is 6 ). I- %'e (ol&)e is *1? c&. ).# 9'a% is %'e &,,e" ase

edge/

A. 2 ) C. < )B. ? ) D. 1 )

P"ole) 11 5CE May 23338

A cylinde" o- "adi&s 7 ) 'as i%s a=is along %'e =0a=is. A second cylinde" o- %'e sa)e "adi&s 'as

i%s a=is along %'e y0a=is. $ind %'e (ol&)e# in %'e -i"s% oc%an%# co))on %o %'e %9o cylinde"s.

A. 866m3

C. 144 m3

B. 1152m3

D. 288 m3

P"ole) 1< 5CE May 23338

$ind %'e (ol&)e o- a "ig'% ci"c&la" cylinde" 9'ose la%e"al a"ea is 2?.6*: m2

and ase a"ea o-

4.37: m2

.

A. *6.


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B. *


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B. y=8 D. y=4

P"ole)


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+'a% is %'e second de"i(a%i(e o- y=4 x2−2 x+1 a% x=2.

A. : C. *B. 3 D. No% de-ined

P"ole)


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+'e"e ' is %'e 'eig'% in -ee% and % is %'e %i)e in seconds. +'a% is %'e (eloci%y o- %'e ody 9'ent =2 seconds/

A. 2*.4 -,s C. 2


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A. 2.*


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P"ole) 7: 5ME Oc%oe" 23338A an o--e"s 3.?W e--ec%i(e )on%'ly in%e"es%. +'a% is %'e e--ec%i(e ann&al "a%e 9i%' )on%'lyco),o&nding/

A. 7.2W C. 4.2W

B. 7W D. 4W

P"ole) 76 5ME Oc%oe" 23338+'a% no)inal "a%e con(e"%ed @&a"%e"ly co&ld e &sed ins%ead o- *2W co),o&nded se)i0ann&ally/

A. *3.47W C. **.:2WB. **.


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