Concept Recap Test Mains 4

7/28/2019 Concept Recap Test Mains 4

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FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com

CONCEPT RECAPITULATION TEST(Set IV)

Time Allotted: 3 Hours Maximum Marks: 432

Please read the ins t ruct ions careful ly . You are al lot ted 5 minutesspec i f ical ly for th is purpose.

You are not al lowed to leave the Examinat ion Hal l before the end of the test .

INSTRUCTIONS

A. General Instructions

1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.

2. This question paper contains Three Parts.3. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics.

4. Each part has only one section: Section-A.

5. Rough spaces are provided for rough work inside the question paper. No additional sheets will beprovided for rough work.

6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronicdevices, in any form, are not allowed.

B. Filling of OMR Sheet

1. Ensure matching of OMR sheet with the Question paper before you start marking your answerson OMR sheet.

2. On the OMR sheet, darken the appropriate bubble with black pen for each character of yourEnrolment No. and write your Name, Test Centre and other details at the designated places.

3. OMR sheet contains alphabets, numerals & special characters for marking answers.

C. Marking Scheme For All Three Parts.

(i) Section-A (01 to 02 and 09 to 30) contains 24 multiple choice questions which have only onecorrect answer. Each question carries +4 marks for correct answer and 1 mark for wronganswer.

Section-A (03 to 08) contains 6 multiple choice questions which have only one correct answer.Each question carries +8 marks for correct answer and 2 mark for wrong answer.

Name of the Candidate

Enrolment No.

ALLINDIA

TESTSE

RIES

FIITJEE JEE (Main), 2013

FromLongTermC

lassroomProgramsandMedium/

ShortClassroomProgram4

inTop10,10inTop

20,43inTop100,

75in

Top200,159inTop500Ranks&3542

totalselec

tions

in

IIT-JEE

2012


2/24

AITS-CRT(Set-IV)-PCM-JEE(Main)/13


2

Useful Data

PHYSICS

Acceleration due to gravity g = 10 m/s2

Planck constant h = 6.6 1034 J-s

Charge of electron e = 1.6 1019 C

Mass of electron me = 9.1 1031 kg

Permittivity of free space 0 = 8.85 1012 C

2/N-m

2

Density of water water= 103

kg/m3

Atmospheric pressure Pa = 10

5

N/m

2

Gas constant R = 8.314 J K1

mol1

CHEMISTRY

Gas Constant R = 8.314 J K1

mol1

= 0.0821 Lit atm K1mol

1

= 1.987 2 Cal K1 mol1Avogadro's Number Na = 6.023 10

23

Plancks constant h = 6.625 1034 Js= 6.625 1027 ergs

1 Faraday = 96500 coulomb

1 calorie = 4.2 joule1 amu = 1.66 1027 kg1 eV = 1.6 1019 J

Atomic No: H=1, He = 2, Li=3, Be=4, B=5, C=6, N=7, O=8,N=9, Na=11, Mg=12, Si=14, Al=13, P=15, S=16,Cl=17, Ar=18, K =19, Ca=20, Cr=24, Mn=25,Fe=26, Co=27, Ni=28, Cu = 29, Zn=30, As=33,Br=35, Ag=47, Sn=50, I=53, Xe=54, Ba=56,Pb=82, U=92.

Atomic masses: H=1, He=4, Li=7, Be=9, B=11, C=12, N=14, O=16,F=19, Na=23, Mg=24, Al = 27, Si=28, P=31, S=32,Cl=35.5, K=39, Ca=40, Cr=52, Mn=55, Fe=56, Co=59,

Ni=58.7, Cu=63.5, Zn=65.4, As=75, Br=80, Ag=108,Sn=118.7, I=127, Xe=131, Ba=137, Pb=207, U=238.


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3

PPhhyyssiiccss PART I

SECTION ASingle Correct Choice Type

This section contains 30 multiple choice questions. Each question has four choices (A), (B), (C) and (D)out of which ONLY ONE is correct.

1. In the LCR circuit, the voltmeter and ammeter readings are(A) 200 volt, 20A (B) 200 volt, 50A(C) 1000 volt, 20A (D) 1000 volt, 20A

V

A

~

400V

1000V, 50 HzL50

400V

C

2. A collision occurs between two identical balls each of mass m , moving with velocities 1Gu and 2

Gu ,

colliding head-on. The coefficient of restitution is 0.5. The energy lost in the collision is

(A)2

1 2

1( )

4+

G Gm u u (B) 21 2

1( )

4

G Gm u u

(C)2

1 2

3( )

16

G Gm u u (D) 21 2

1( )

16

G Gm u u .

3. In the figure shown, the ammeter reads a current equal to

(A)V

R(B)

2V

R

(C)3

2

V

R(D)

2

V

R

V A

R R

R

RR

R R

Rough work


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4

4. From A conducting sphere of radius R a cavity of radius R/2 is

cut out as shown in the figure. At the centre of cavity a pointcharge q is placed then the field and potential at point P asshown in the figure is

R

Oq

R/2P d

(A)2

0 0

,2 2

q qV E

d d= =

(B)

2

0 0

,4 2

q qV E

d d= =

(C)2

0 0

,4 4

q qV E

d d= =

(D)

2

0 0

,2 4

q qV E

d d= =

5. The switch Sw of the circuit shown in the figure is closed at t = 0. i1 and i2 arethe electric current in the branch containing two ideal inductors L1 and L2respectively, at a certain instant. Choose the most appropriate statement.

(A) At t = 0,(just after the switch is closed) 1 2

1 2

di diand

dt L dt L

= =

(B) At t = 0, ,(just after the switch is closed) i1 = 0, i2 = 0

(C) After long time 2 11 2

1 2 1 2

L Li and i

(L L )r (L L )r

= =

+ +

L2

r Sw

L1

(D) All the above

6. A conical flask of mass 10 kg and base area as 10 cm isfloating in liquid of relative density 1.2, as shown in the figure.The force that liquid exerts on curved surface of conical flaskwill be(Given g = 10 m/s

2)

(A) 20 N downward direction

(B) 40 N in downward direction(C) can be determined only if is given(D) 20 N in upward direction

10cm

Rough work


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5

7. Potential difference across a resistance is measured as V = (20 .01) volts and current flowingthrough it is measured as i = (1 .01) A. Then the value of resistance measured by Ohms lawR = V/i is

(A) (20 1.2) (B) (20 0.8) (C) (20 1) (D) (20 0.6) .

8. A tunnel is made inside earth passing through center of earth. A particle isdropped from the surface of earth. Select the correct statement(A) Kinetic energy of particle is maximum at center and its potential

energy is zero at center(B) velocity of particle is proportional to x [where x is distance of particle

from center of earth(C) Kinetic energy of particle is maximum when it reaches on the other

side of tunnel.(D) kinetic energy of particle is maximum at center

m

9. The time period of a pendulum at temperature t1 C is T1 sec. Its time period at t2C is T2 sec. If

coefficient of linear expansion of material of pendulum is , then increase in time period is(A) (t2 t1) (B) (t2 t1)/3

(C) T1(t2 t1)/2 (D) none of these

10. A graph between the temperature read on the Celsius Scale and that on the Fahrenheit Scale,when plotted, gives the following:

(A)

C

F

(B)

C

F

(C)

C

F

(D)

C

F

Rough work


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6

11. A particle moving in the positive x-direction has initial velocity v0. The particle undergoesretardation kv

2, where v is its instantaneous velocity. The velocity of the particle as a function of

time is given by

(A) v = v0/(1 + kv0t) (B)kt1

v2v 0

+=

(C) kt

vv 0= (D) ( )tvk1

vv 2

0

20+=

12. A ray of light travelling along the positive zaxis is reflected twice :

(i) for the first time, by a mirror whose normal is along (i k)+

(ii) for the second time, by a mirror whose normal is along ( i j k)+ + ,

where the symbols have their usual meanings. The final ray is along

(A) j k+ (B) k i+

(C) 2 j 2k i+ (D) ( j k 2i)+ .

13. In the system shown, the acceleration of the

wedge of mass 5M is (there is no frictionanywhere)(A) zero(B) g/2(C) g/3(D) g/4

2M5M

M

60o

14. Two wires are placed at (2, 0, 0) and (-2, 0, 0) carrying equal currents along negativez-axis. Magnetic field at point (0, 2, 0) is along(A) positivex-axis (B) negative y-axis(C) positive y-axis (D) negative z-axis

Rough work


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7

15. In which of the following transitions will the wavelength be minimum ?(A) n = 5 to n = 4 (B) n = 4 to n = 3(C) n = 3 to n = 2 (D) n = 2 to n = 1

16. The angular momentum of electron in an orbit is quantized because it is(A) in accordance with particle nature of electron(B) in accordance with wave nature compatibility of electron(C) in accordance with Hunds rule(D) in accordance with Maxwells theory

17. A point object O is placed between two plane mirrors as shown infigure. If object is moved toward M1 with speed u then relative speedbetween first images of M1 and M2 is(A) Zero (B) u

(C)u

2(D) 2u

10mmM1 M2

O

18. A solid cylinder of mass m length land area of cross section A isplaced as shown in the figure. If Youngs modulus is Ythen strain

energy stored in the cylinder is

(A)

2 2

3

m g l

AY(B)

2 2

6

m g l

AY

(C)

2 2

2

m g l

AY(D)

2 2m g l

AY.

L

19. A rectangular block has a square base measuring a a, and its height is h. It moves on ahorizontal surface in a direction perpendicular to one of the edges of the base. The coefficient of

friction is . It will topple if (choose the most appropriate option)(A) a / 2 h > (B) 2 a /h > (C) a / h > (D) h / a >

Rough work


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8

20. A block of mass m is connected to two springs of spring constant 2k

and 3k respectively, such that the spring of spring constant 2k is

compressed by 3lwhen the block is in its mean position. If the block

is displaced slightly and allowed to oscillate, the frequency will be

smooth

2k 3k

fixed wall

m

fixed wall

(A) 1 k2 m

(B) 1 6k2 5m

(C)1 5k

2 6m(D) none of these

21. A wave1

y Asin 2x 4t3

= +

is superposed with a second waveform producing a standing

wave with a node at x = 0. In the equation of the waveform, x is in metre and t is in second. Theequation of the second waveform is

(A) ( )2y Asin 4t 2x / 3= (B) 2y Asin(2x 4t 5 / 3)= + +

(C) 2y Asin(2x 4t 5 / 3)= + (D) 2y Asin( 2x 4t / 3)= + .

22. A force2 2

yi xjF b N

x y

+=

+

G(b is a constant) acts on a particle as it undergoes counterclockwise

circular motion in a circle: x2

+ y2

= 16. The work done by the force when the particle undergoesone complete revolution is (x, y are in m)

(A) Zero (B) 2 bJ(C) 2 bJ (D) None of these.

23. The natural frequency of the circuit shown in the figure is (Assume thatequal currents i, i exist in the two branches, and the charges on thecapacitors are equal)

(A) 1 12 LC

(B) 1 12 3LC

(C)1 1

LC(D) none of the above

L

C

ii

LL

C

+ q

+

q

Rough work


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9

24. A block of mass m slides down an inclined wedge of same m shown in

the figure. Friction is absent everywhere. Magnitude of acceleration ofcenter of mass of the block and wedge is

(A) zero (B)2gsin

(1 sin )2

+

(C)2gcos

(1 sin )2

+ (D)

gsin

(1 cos )

+

m

m

25. In the figure shown, if Galvanometer shows no deflection then thevalue ofxis

(A) 4 (B) 3 (C) 2 (D) 8

G8

4 x

2 4

4

26. An arrangement of three metallic conductors is shown. What is the magnitude

of charge appearing on the left face of the conductor B?(A has a total charge Q1 and C has a total charge Q2)

(A) zero (B)1Q

(C)2

Q (D) 2 1Q Q

2

A B C

Q1 Q2

Rough work


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10

27. The potential difference (V) across the 2F capacitor increases

with time, and-11Vs=

dV

dtand

2-2

22Vs=

d V

dtat particular instant.

The p.d. across the 3H inductor is

(A) 6V (B) 12V (C) 6V (D) none of these.

2

1A i

2 F

3H

+

-

O

28. The rate of flow of glycerin of density through conical section of a pipe, if the area of cross-sectional of its ends are A1 and A2 and pressure drop across its length be P, is given by

(A)( )1 2 22

PA A

A21

(B)

( )1 2 222 P

A AA21

(C)

( )2

2

2 P

A

2

1

(D)

( )

1 2 2

2

2 PA A

A

2

1

3

29. Consider a particle of mass m0 enclosed by a closed imaginary surface S. Let E

be the

gravitational field intensity due to m0 at the surface element d S

directed as outward normal to it.

The surface integral of the gravitational field over S is

(A) m0G (B) 4m0G

(C)m G0

4

(D) None of these

30. For an adiabatic compression (for an ideal gas) the quantity PV(A) increases (B) decreases

(C) remains constant (D) depends on

Rough work


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11

CChheemmiissttrryy PART II

Straight Objective Type

This section contains 30 multiple choice questions numbered 1 to 30. Each question has 4 choices (A),

(B), (C) and (D), out of which ONLY ONE is correct.

1. In metal carbonyls the C O bond length(A) Decreases from double bond length to triple bond length(B) Increases from triple bond length to double bond length(C) Remain as triple bond length(D) Can not be predict

2. In the process of extraction of Al from bauxite coke powder is spreaded over the moltenelectrolyte to:(A) Prevent the loss of heat by radiation from the surface(B) Prevent the corrosion of graphite anode(C) Prevent oxidation of molten aluminium by air

(D) Both (A) and (C)

3. For the reaction:

( ) ( ) ( ) ( )2 2 2Hg Cl s H g 2Hg 2HCl aq. ;+ +A the correct representation of the cell and the

thermodynamic properties G and H at 298 K respectively are:(Given E298 = 0.2684 V and temperature coefficient = 3 10

-4V/K)

(A) Pt|H2 (g, 1 atm) | HCl(aq) | Hg2Cl2(g) | Hg(liq);1 1G 51.8 kJmol , H 69 kJ mol = =

(B) Pt|H2 (g, 1 atm) | HCl(aq) | Hg2Cl2(g) | Hg(liq);1 1G 25.9 kJmol , H 34.5 kJ mol = =

(C) Hg(liq)|Hg2Cl2(g) |HCl(aq) | H2(g, 1 atm)|Pt;1 1G 51.8 kJmol , H 69 kJ mol = =

(D) Hg(liq)|Hg2Cl2(g) |HCl(aq) | H2(g, 1 atm)|Pt;1 1G 51.8 kJmol , H 69 kJ mol = + =

Rough work


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12

4. The decomposition of O3 to O2 occurs by the following mechanism

(i) ( ) ( ) ( ) ( ) ( )11

K

3 2 aM g O g O g O g M g ; E+ + +

(ii) ( ) ( ) ( ) ( ) ( )22

K

2 3 aO g O g M g M g O g ; K+ + + +

(iii) ( ) ( ) ( )33

K

3 2 aO g O g 2O g ; E+

Where M is catalystIf K3[O3] >> K2[O2][M], then the activation energy of the overall reaction is:

(A) 1 2

2

a a

a

E E

E(B)

3 1 2a a aE E E+

(C)2a

E (D)1a

E

5. In the following reaction:

S

O

[ ]2Ac O/NaOAcheatMajor

X ; X is.....?

(A) (B)

S OAc

(C)

S COCH3

(D)

S

O

6. Which of the following statement is correct?

(A) Anti-conformer of BrCH2 CH2Br is more stable than its Gauche conformer

(B) N H

is less basic than N H

(C) Gauche conformer of butane dioic acid is more stable than its anti-conformer at high pH.(D) (A) and (B) are correct

Rough work


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13

7. The Major product formed in the reaction of 1,5-cyclooctadiene with 0.5 eq. of diborane is:(A) BH2

(B)

B

H

(C)

BH

(D) H2B

BH2

8. Buta-1,3-diene on heating with maleic and hydride would give

(A)

O

O

OH

H

(B)

O

O

OH

H

(C)

O

O

OH

H

(D)

O

O

OH

H

9. Which of the following is not the characteristic of interhalogen compounds?(A) They are more reactive than halogens(B) They are quite unstable but none of them is explosive(C) They are covalent in nature(D) They have low b.p. and high volatility

10. Which of the following has best leaving group ability?

(A) 3CH COO

(B) 3CH O

(C) HO (D) 2 3SO CF

11. Number of-bonds in cyclic trimer of solid SO3 is:(A) 4 (B) 3(C) 6 (D) 7

Rough work


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14

12. What is the probability density of the electron cloud at the nucleus of hydrogen. Given

0r/ a

1s3

0

1e

a

=

(A)3

0

1

a(B)

3

0

1

a

(C) 1 (D) 0

13. Which one is the most likely structure of CrCl3.6H2O, if1

3of total chlorine of the compound is

precipitated by adding AgNO3 of its aqueous solution?(A) CrCl3.6H2O (B) [Cr(H2O)3Cl3].3H2O(C) [CrCl2(H2O)4]Cl.2H2O (D) [CrCl(H2O)5]Cl2.H2O

14. In the equation:

[ ]2 2 24M 8CN 2H O O 4 M(CN) 4OH + + + +

Identify the metal M.(A) Cu (B) Fe

(C) Au (D) Zn

15. Which one has largest number of isomers?(A) [Co(en)2Cl2]

+(B) [Co(NH3)5Cl]

2+

(C) [Ir(PR3)2(H2O)]2+

: (R = alkyl) (D) [Ru(NH3)4Cl2]+

16. The compound (SiH3)3N is expected to be:(A) Pyramidal and more basic than (CH3)3N(B) Planar and less basic than (CH3)3N(C) Pyramidal and less basic than (CH3)3N(D) Planar and more basic than (CH3)3N

17. Which of the following combination of salt and solvent is correct, (such that salt is soluble in the

solvent):Salt Solvent(a) BeSO4 H2O(b) BaSO4 H2O(c) Be(OH)2 aq. NaOH(d) Ba(OH)2 aq. NaOH(A) a and b (B) b and c(C) a and c (D) b and d

Rough work


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15

18. van-der Waals constant b for Ar is 3.22 10-5

m3/mol. The molecular diameter of Ar is

(A) 0.1472 nm (B) 0.2944 nm(C) 0.2944 mm (D) 0.685 nm

19. Identify A, B and C from the following reactions:

( )2 2 2 2 3Na O CO Na CO A+ +

( ) ( )2 2 2 3Na O B Na CO A+ + ( ) ( )2 2 3KO B K CO A+ +

( )2 3 2Na O Cl carbon B NaCl+ + +

( )2 3CO NaCl C NaHCO white sublimative+ + +

( ) 2AgCl C H O soluble complex of Ag+ +

(A) A = CO; B = O2 ; C = PH3 (B) A = O2; B = CO; C = NH3(C) A = O2; B = CO2 ; C = NH3 (D) A = CO; B = CO2; C = NH3

20. The Bronsted acidity of boron hydrides follows the order:(A) B2H6 > B4H10 > B5H9 > B10H14 (B) B2H6 = B4H10 > B5H9 = B10H14(C) B10H14 > B5H9 > B4H10 > B2H6 (D) B5H9 > B4H10 > B2 H6 > B10H14

21. The change in entropy when two moles of Ar gas are heated at constant volume from 300 K to500 K is:(A) -12.74 J/K mol (B) - 6.37 J/K-mol(C) 6.37 J/K mol (D) 12.74 J/K mol

Rough work


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16

22. What is the product X of the following reaction?

Me

O

Me

[ ]H X+

(A)

Me

OH

Me

(B)

Me

Me

OH (C) Me

OH

Me

(D) Me Me

OH

23. The diene which undergo Diels-Alder reaction with maleic anhydride is:(A) (B)

(C) (D)

Rough work


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17

24.

o/ 490 C

(A) (B)

(C) (D)

25. The decreasing order of reactivity of the following compounds towards electrophiles is..

N

H

S N

(I) (II) (III)

(A) II > I > III (B) II > III > I(C) III > I > II (D) I > II > III

26. What are the correct stereochemical notations of the compound

OH

OH CH3

O (A) 2Z, 4R (B) 2Z, 4S(C) 2E, 4R (D) 2E, 4S

Rough work


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18

27. For the aldotetroes I, II and III, which of the given statements is true?CHO

CH2OH

OH

OH

(I)

CHO

CH2OH

OH

OH

(II)

CHO

CH2OH

OH

OH

(III) (A) I and II are diastereomers while II and III are enantiomers.(B) Only I is HIO4 cleavable(C) I and III are D-sugars(D) All above are true

28. Oxymercuration-Demercuration reaction of 1-methyl cyclohexene gives:(A) cis-2-methylcyclohexanol(B) trans-2-methylcyclohexanol(C) 1-methylcyclohexanol(D) mixture of cis and trans-2-methylcyclohexanol

29. Among the following the acid which undergoes fastest decarboxylation:

(A)

COOHPh

O

(B)Ph

O

COOH

(C) PhCOOH (D)

COOHPh

OH

30. Lithium dialkyl amide base on reaction with cyclohexanone, abstracts:

(A) axial H preferentially(B) equatorial H preferentially(C) any of the equatorial and axial H, non preferentially(D) neither axial nor equatorial H

Rough work


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19

MMaatthheemmaattiiccss PART IIISECTION A

Straight Objective Type

This section contains 30 multiple choice questions numbered 1 to 30. Each question has 4 choices (A),(B), (C) and (D), out of which ONLY ONE is correct.

1. Let R = {(x, y) : x, y R, x2 + y2 25}, 24

R' (x,y) : x,y R,y x9

=

, then

(A) Dom (R R) = {4, 4} (B) Range (R R) = [0, 4](C) Range (R R) = [0, 5] (D) R R does not define a function

2. If z1 and z2 are any two complex numbers, then which of the following is true?(A) |z1 + z2| = |z1| + |z2| (B) |z1 z2| = |z1| |z2|

(C) |z1 + z2| |z1| + |z2| (D) |z1 z2| |z1| |z2|

3. If minimum value of f(x) = (x2 + 2bx + 2c2) is greater than the maximum value of

g(x) = x2 2cx + b2, then (x R)

(A)| b |

| c |3

> (B)| c |

| b |2

>

(C) 1 c 2b < < (D) no real values of b and c exist

4. Let x be an irrational, then [ ]2m

m nlim lim cos(n! x)

equals

(A) 0 (B) 1(C) 1 (D) indeterminate

5. The angle of intersection of the normals at the point 5 3,2 2

of the curves x2 y2 = 8 and

9x2

+ 25y2

= 225 is

(A) 0 (B)4

(C)3

(D)

2

Rough work


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20

6.2

2 2

(x 1)dx

x (x x 1)(x x 1)

+ + + + is equal to

(A)2 2x x 1 x x 1

log cx

+ + + + + +

(B)2 2x x 1 x x 1

2log cx

+ + + + +

(C) 2 2log x x 1 x x 1 c + + + + + (D) none of these

7. Suppose values taken by a variable X are such that a xi b, where xi denotes the value of X inthe i

thcase for i = 1, 2, 3 . n, then

(A) a Var(X) b (B) a2 Var(X) b2

(C)2a

4 Var(X) (D) (b a)2 Var(X)

8. If sin1

x + sin1

y + sin1

z = , then x4 + y4 + z4 + 4x2y2z2 = k[x2y2 + y2z2 + z2x2], where k is equal to(A) 1 (B) 2(C) 4 (D) none of these

9. If |z| = Max. {|z 2|, |z + 2|}, then

(A) | z z | 1+ = (B) 2z z 2+ =

(C) | z z | 2+ = (D) none of these

10. The value of a for which the system of equationsa

3x + (a + 1)

3y + (a + 2)

3z = 0

ax + (a + 1)y + (a + 2)z = 0x + y + z = 0, has a non zero solution is(A) 1 (B) 0(C) 1 (D) none of these

11. If A, B and C are three square matrices of the same size such that B = CAC1

, then CA3C

1is

equal to(A) B (B) B

2

(C) B3

(D) B9

12. In a certain test, there are n questions. In this test, 2rstudents gave wrong answers to at least

(n r) questions, where r = 0, 1, 2, .. n. If the total number of wrong answer is 4095, then thevalue of n is(A) 11 (B) 12(C) 13 (D) 15

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21

13. If a, b, c are in A.P. p, q, r are in H.P. and ap, bq, cr are in G.P. thenp r

r p

+

is equal to

(A)a c

c a+ (B)

a c

c a

(C)b q

q b

+ (D)b a

q p

14. The function f(x) = p[x + 1] q[x 1], where [x] is the greatest integer function is continuous atx = 1, if(A) p q = 0 (B) p + q = 0(C) p = 0 (D) q = 0

15. If f(x) = g(x)(x a)2, where g(a) 0 and g(x) is continuous at x = a, then(A) f is increasing in the nbd of a if g(a) > 0 and f is decreasing in the nbd of a if g(a) < 0(B) f is increasing in the nbd of a if g(a) < 0(C) f is decreasing in the nbd of a if g(a) > 0(D) f is increasing in the nbd of a if g(a) < 0 and f is decreasing in the nbd of a if g(a) > 0

16. Rolles Theorem holds for the function f(x) = x3

+ bx2

+ cx, 1 x 2 at the point 4 ,3

the value of b

and c are

(A) b = 8, c = 5 (B) b = 5, c = 8(C) b = 5, c = 8 (D) b = 5, c = 8

17. If2

2 2 2 2 2 2

0

x dx

2(a b)(b c)(c a)(x a )(x b )(x c )

=+ + ++ + + then the value of 2 2

0

dx

(x 4)(x 9)

+ + is

(A)60

(B)

20

(C)40

(D)

80

18. The area of the region lying inside x2

+ (y 1)2

= 1 and outside c2x

2+ y

2= c

2, where c ( 2 1)=

is

(A)1

(4 2)4 2

+ (B)

1(4 2)

4 2

+

(C)1

(4 2)4 2

+ + (D) none of these

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22

19. If for the differential equationy x

y ' ,x y

= +

the general solution is

xy

log | cx |= , then

x

y

is

given by

(A)2

2

x

y (B)

2

2

y

x

(C)2

2

x

y(D)

2

2

y

x

20. If is the angle subtended by the circle S = x2 + y2 + 2gx + 2fy + c = 0 at a point (x1, y1) outsidethe circle and 2 21 1 1 1 1S x y 2gx 2fy c,= + + + + then cos = ?

(A)2 2

1

2 21

S c g f

S c g f

+

+ +(B)

2 21

2 21

S c g f

S c g f

+ +

+

(C)2 2

1

2 21

S c g f

S c g f

+ +

+ +(D)

2 21

2 21

S c g f

S c g f

+ +

+ +

21. The equation of the parabola whose focus is the point (0, 0) and the tangent at the vertex isx y + 1 = 0, is(A) x

2+ y

2 2xy 4x + 4y 4 = 0 (B) x

2+ y

2 2xy + 4x 4y 4 = 0

(C) x2

+ y2

+ 2xy 4x + 4y 4 = 0 (D) x2

+ y2

+ 2xy 4x 4y + 4 = 0

22. The locus of the middle points of the portion of the tangents of the ellipse2 2

2 2

x y1,

a b+ = included

between the axis is the curve

(A)2 2

2 2

x y4

a b+ = (B)

2 2

2 2

a b4

x y+ =

(C) a2x

2+ b

2y

2= 4 (D) b

2x

2+ a

2y

2= 4

23. If PQ is a double ordinate of the hyperbola2 2

2 2

x y1,

a b = such that OPQ is an equilateral triangle,

O being the centre of the hyperbola. Then the eccentricity e of the hyperbola satisfies

(A)2

1 e3

< < (B)2

e3

=

(C)3

e2

= (D)2

e3

>

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24. If the vector a and bGG

are perpendicular to each other, then a vector VG

in terms of a and b

satisfying the equations V.a 0,=G G

V.b 1=G G

and [V ab] 1,=G GG

is

(A)2 2

b (a b)

| b | | a b |

+

G GG

G GG (B) 2b (a b)

| b | | a b |

+

G GG

G GG

(C)

2

b / | b |(a b) / | a b |

G G

G GG G (D) none of these

25. A problem in mathematics is given to 3 students whose chances of solving individually are

1 1 1, and .

2 3 4The probability that the problem will be solved at least by one is

(A)1

4(B)

1

24

(C)23

34(D)

3

4

26. The mean and S.D. of a binomial variate X are 4 and 3 respectively. Then P(X 1) is equal to

(A)161

14

(B)163

14

(C)

162

13

(D)

161

13

27. If12

sin , 013 2

= <


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28. The general value of obtained from the equation cos 2 = sin, is ( )n ]

(A) 22

= (B) 2n

2

=

(C)nn ( 1)

2

+ = (D) n

4 2

=

29. If two towers of heights h1 and h2 subtend angles 60 and 30 respectively at the mid-point of theline joining their feet, then h1 : h2 is equal to(A) 1 : 2 (B) 1 : 3(C) 2 : 1 (D) 3 : 1

30. If a, b, c, d, e and f are G.P. then the value of

2 2

2 2

2 2

a d x

b e y

c f z

depends on

(A) x and y (B) x and z(C) y and z (D) independent of x, y and z

Rough work

Concept Recap Test Mains 4

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