1

PHYSICS

1. A force acts on a 30 gm particle in such a way that the position of the particle as a function of time is given by

2 3x 3t 4t t , where x is in metres and t is in seconds. The

work done during the first 4 seconds is (A) 5.28 J (B) 450 mJ (C) 490 mJ (D) 530 mJ

2. Two small drops of mercury, each of radius R, coalesce to

form a single large drop. The ratio of the total surface energies before and after the change is

(A) 1/31: 2 (B) 1/32 :1 (C) 2 : 1 (D) 1 : 2

3. The units of modulus of rigidity are

(A) N m (B) N/m

(C) 2N m (D) 2N/m

4. A river is flowing from west to east at a speed of 5 metre per

minute. A man on the south bank of the river, capable of swimming at 10 metre per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction

(A) due north (B) 30° east of north (B) 30° west of north (D) 60° east of north 5. A bird of mass 400 gm is flying horizontally at a certain height

with constant acceleration of 5 m/s2. The force exerted by surrounding air on the bird has magnitude (g = 10 m/s2)

(A) 4 N (B) 2 N

(C) 4 2N (D) 2 5N

6. In the figure shown initially spring is in unstretched state and blocks are at rest. Now 100 N force is applied on block A and B as shown in figure. After some time velocity of ‘A’ becomes 2 m/s & that of ‘B’ 4 m/s & block A displaced by amount 10 cm and spring is stretched by amount 30 cm. Then work done by spring force on A will be:

(A) 9/3 J (B) –6 J (C) 6 J (D) None of these

2

7. In the figure shown a lift goes downwards with a constant retardation. An observer in the lift observers a conical pendulum in the lift, revolving in a horizontal circle with time period 2 seconds. The distance between the centre of the circle and the point of suspension is 2.0 m. the retardation of the lift in m/s2 is:

Use 2 210 and g = 10 m/s

(A) 10 m/s2 (B) 20 m/s2

(C) 30 m/s2 (D) 40 m/s2

8. A body A of mass M while falling vertically downwards under

gravity breaks into two parts; a body B of mass 1

M3

and, a

body C of mass 2

M.3

The centre of mass of bodies B and C

taken together shifts compared to that of body A towards (A) depends on height of breaking

(B) does no shift (C) shift towards body C

(D) shift towards body B

9. The figure shows two parallel plane mirrors placed 10 cm apart. An object O is placed 7 cm from mirror M1. Then distance of final image formed from mirror M1 is

(A) 7 cm (B) 13 cm (C) 14 cm (D) 10. The angle of incidence at which reflected light is totally

polarized for reflection from air to glass (refractive index n), is (A) sin–1 (n) (B) sin–1 (1/n) (C) tan–1 (1/n) (D) tan–1 (n)

11. A plane mirror is moving with velocity ˆ ˆ ˆ4i 5j 8k. A point

object in front of the mirror moves with a velocity ˆ ˆ ˆ3i 4j 5k.

Here k̂ is along the normal to the plane mirror and facing towards the object. The velocity of the image is

(A) ˆ ˆ ˆ3i 4j 5k (B) ˆ ˆ ˆ3i 4j 11k

(C) ˆ ˆ ˆ3i 4j 11k (D) ˆ ˆ ˆ7i 9j 11k

3

12. A Galileo telescope has an objective focal length 100 cm and magnifying power 50. The distance between the two lenses in normal adjustment will be

(A) 150 cm (B) 100 cm (C) 98 cm (D) 200 cm

13. Light of wavelength 500nm is used to form interference

pattern in Young’s double slit experiment. A uniform glass

plate of refractive index 1.5 and thickness 0.1mm is

introduced in the path of one of the interfering beams. The number of fringes which will shift the cross wire due to this is

(A) 100 (B) 200 (C) 300 (D) 400

14. Two waves of equal amplitude and frequency interfere each

other. The ratio of intensity when the two waves arrive in

phase to that when they arrive 90 out of phase is

(A) 1 : 1 (B) 2 : 1

(C) 2 : 1 (D) 4 : 1

15. A racing car moving towards a cliff, sounds its horn. The driver observes that the sound reflected from the cliff has a pitch one octave higher than the actual sound of the horn. If v is the velocity of sound, then the velocity of the car is

(A) v / 2 (B) v / 2 (C) v / 3 (D) v / 4

16. Three waves of equal frequency having amplitudes 10 m, 4

m and 7 m arrive at a given point with successive phase

difference of

2. The amplitude of the resulting wave in m is

given by (A) 7 (B) 6 (C) 5 (D) 4

17. The two metallic plates of radius r are placed at a distance d

apart and its capacity is C . If a plate of radius r / 2 and

thickness d of dielectric constant 6 is placed between the

plates of the condenser, then its capacity will be

(A) 7C / 2 (B) 3C / 7 (C) 7C / 3 (D) 9C / 4

4

18. A charge q is fixed at each of the points

0 0 0x x ,x 3x ,x 5x ..... infinite, on the x axis and a

charge q is fixed at each of the points

0 0 0x 2x ,x 4x ,x 6x ,..... infinite. Here 0x is a positive

constant. Take the electric potential at a point due to a charge

Q at a distance r from it to be 0Q / (4 r) . Then, the

potential at the origin due to the above system of charges is

(A) 0 (B) 0 0

q

8 x ln2

(C) (D) 0 0

qln2

4 x

19. Charge q is uniformly distributed over a thin half ring of radius

R . The electric field at the centre of the ring is

(A) 2 2

0

q

2 R (B)

2 20

q

4 R

(C) 2

0

q

4 R (D)

20

q

2 R

20. There are three resistance coils of equal resistance. The maximum number of resistances you can obtain by connecting them in any manner you choose, using all at time is

(A) 3 (B) 4 (C) 6 (D) 5

21. In the circuit shown below E1 = 4.0 V, R1= 2 , E2 = 6.0 V, R2

= 4 and R3 = 2 . The current I1 is

(A) 1.6 A (B) 1.8 A (C) 1.25 A (D) 1.0 A

22. Three rods of the same dimension have thermal conductivities 3K, 2K and K. They are arranged as shown in fig. Given below, with their ends at 100oC, 50oC and 20oC. The temperature of their junction is

(A) 60C (B) 70 C

(C) 50° C (D) 35°C

5

23. A liquid of mass M and specific heat S is at a temperature 2t. If another liquid of thermal capacity 1.5 times, at a temperature

of t

3 is added to it, the resultant temperature will be

(A) 4

t3

(B) t

(C) t

2 (D)

2t

3

24. Two particles of mass m and 2m moving with velocity

ˆ ˆ ˆ ˆ2i 3j and 2i 3k collide at origin perfectly in-elastically. Find

the speed of the combined mass after impact (A) 2m/s (B) 3m/s (C) 4m/s (D) 5m/s 25. The P-V diagram of a system undergoing thermodynamic

transformation is shown in figure. The work done on the

system in going from A B C A is 50 J and 20 cal heat is given to the system. The change in internal energy between A and C is

(A) 34 J (B) 70 J (C) 84 J (D) 134 J

26. The mass m strikes the mass 2m and sticks to it after collision.

The minimum value of v0 so that combined mass may complete vertical circle about O is:

(A) 5gL (B) 2 5gL

(C) 3 5gL

(D)

15gL

2 27. A disc of mass 0.1Kg is kept floating horizontally in mid air by

firing bullets of mass 0.05 kg each vertically at it at the rate of 10 bullets per second. If the bullets rebound with the same speed what is the speed of the bullets with which they are fired? (g=9.8 m/s2)

(A) 0.5 m/s (B) 0.98 m/s (C) 2m/s (D) 2.3 m/s

6

28. A massless rope is wrapped around a ring (with a groove along its circumference) having a radius R and mass m. The ring is allowed to move downward. The linear acceleration of the ring is:

(A) 2g/3 (B) g/2

(C) g/3 (D) g 29. Three rings each of mass m kg and radius a are arranged as

shown in the figure. If moment of inertia of the arrangement about x x ' axis is n(ma2/2), the value of n is

(A) 3 (B) 5 (C) 7 (D) 9

30. A block A of mass m is placed over a plank B of mass 2m. Plank B is placed over a smooth horizontal surface. The

coefficient of friction between A and B is 1

2. Block A is given a

velocity v0 towards right. Acceleration of B relative to A is

(A) g

2 (B) zero

(C) 3g

4 (D)

g

4

B

v0A

7

3CH Ph

H

O 3CH

Ph

H

3CH

Ph

H

O 3CH

Ph

H

3CH

Ph

H O

3CH

Ph

H3CH

Ph

H O 3CH

Ph

H

CHEMISTRY

31. What is the mole ratio of benzene oB(P 150 torr) and toluene

oT(P 50 torr) in vapour phase, if the given solution has a

vapour pressure of 120 torr? (A) 7:1 (B) 7:3 (C) 8:1 (D) 7:8

32. The product in the given reaction is:

(A) (B) (C) (D)

33. What is leaving group ability order in the given compounds:

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

34. How many structural isomer is with formula 5 11C H Br yield

only a single alkene on dehydrohalogenation by alc.KOH. (A) 3 (B) 2 (C) 4 (D) 5

35. What is % s-character in hybridization of carbon when it exerts strongest –I effect? (A) 25% (B) 50% (C) 75% (D) 100%

36. Which of the following does not decolourise 2Br water?

(A) (B) (C) H C C H (D)

3CH

Ph

H ONa + 3CH

Ph

H

Br

?

O+

H

H

(I)

+

H

H(II)

S

(III)

OH

8

CH=C

3CH

3CH

3H C

O+

H

O + HH

O O O

O

37. LiAlH (excess)4

H O2

Product of the reaction is: (A) (B) (C) (D)

38. The antiaromatic compounds are:

(A) X, W (B) Y, Z (C) X, Z (D) Y,W

39. (1) O3

(2) Zn/H O2Y

Hydrocarbon (Y) in the above reaction can be: (A) (B) (C) (D) All of these

40. Using the standard electrode potential , find out the pair between which redox reaction is not feasible:

oE values : 3 2 22Fe /Fe 0.77; I /I 0.54; Cu /Cu

0.34; Ag /Ag 0.80V

(A) 3Fe and I (B) Ag and Cu

(C) 3Fe and Cu (D) 3Ag and Fe

(X)O

N

H

(Y)

(Z) (W)

9

H HO

3H CO 3CH

and OH

H 3OCH

3CH

3CHO

41. (I)

3 3 3CH O Na /CH OH H /CH OH(I) P, (I) Q

, Product P

and Q are respectively (A) &

(B) &

(C) & (D)

42. The magnitude of potential energy of electron in nth excited

state of He ion is 8

81 times the kinetic energy of electron in

the first excited state of 2Li ion. Hence the value of ‘n’ is: (A) 2 (B) 3 (C) 5 (D) 6

43. The correct order of bond angles is:

(A) 2 2 2NO NO NO

(B) 2 2 2NO NO NO

(B) 2 2 2NO NO NO

(D) 2 2 2NO NO NO

44. Select incorrect statement about complex

2 3 5 4[Cr(NO )(NH ) ][Zn(SCN) ] :

(A) It shows co-orindation isomerism (B) it shows optical activity (C) It shows linkage isomerism (D) IUPAC name of the compound is Pentaaminenitrito-N- chromium(III)tetrathiocyanato-S-zincate(II)

10

45. The correct sequence of the ionic radius of the following is:

(A) 2 2Br Cl S O F

(B) 2 2Br S Cl O F

(C) 2 2Br S Cl F O

(D) 2 2S Br Cl O F

46. O2

2 o400 C'A ' H O NaOH; 'A' B

H O22oat25 C

NaOH O

B is used for oxygenating in submarine. A and B are:

(A) 2 2 2Na O and Na O (B) 2 2 2Na O and Na O

(C) 2 2 2Na O and O (D) 2 2Na O and O

47. aK for HCN is 105 10 at o25 C. For maintaining a

constant pH of 9, the volume of 5M KCN solution required to be added to 10 mL of 2 M HCN solution is: (A) 4 mL (B) 7.95 mL (C) 2 mL (D) 9.3 mL

48. The accompanying figure depicts the change in concentration

of species A and B for the reaction A B , as a function

of time, the point of intersection of the two curves represent.

(A) 1/2t (B) 3/4t

(C) 2/3t (D) data insufficient

49. The correct graphical representation for ideal gas/ 2H gas at

o25 C is given by (Dotted line represents 2H (g) and solid line

represents ideal gas.) (A) (B) (C) (D)

time

Conc.

11

3N CH

50. Consider the following two cases:

Case I: 1V ml of NaCl solution (Having concentration

( 1 1 1M ,N and S ) is diluted by adding some amount of 2H O to

make a 2V ml NaCl solution (having concentration

2 2 2M ,N and S )

Case II: 3V ml of NaOH solution (having concentration

3 3 3M ,N and S ) is titrated with 4V ml of 2 4H SO solution

(having concentration 4 4 4M ,N and S ) for complete

neutralisation. (where M=molarity N=normality S=strength) Which of the following statements are correct.

(1) for Case I: 1 1 2 2M V M V , 1 1 2 2 1 1 2 2N V N V and S V S V

can be used can be used (2) for Case II: 3 3 4 4 3 3 4 4 3 3 4 4M V M V ,N V N V and S V S V

can be used

(3) for Case I: 1 1 2 2 1 1 2 2M V M V ,N V N V only can be used

and 1 1S V = 2 2S V is not valid

(4) for Case II: only 3 3 4 4N V N V can be used and other two

equations are not valid The correct choice is: (A) 1 & 2 (B) 3 & 4 (C) 1 & 4 (D) 2 & 3

51. Choose the incorrect statement:

(A) 6 6C H is more reactive than 6 6C D toward nitration

(B) 6 6C D is more reactive than 6 6C T towards sulphonation

(C) 6 6C H is more reactive than 6 6C D towards sulphonation

(D) 6 6C D and 6 6C H have equal reactivity towards nitration

52. Compound A 3 5(C H N) gives precipitate with Tollen’s reagent

and 2H gas is also evolved on addition of Na metal compound

A can be:

(A) 3 2CH CH C N

(B)

(C) 3 2CH CH N C

(D) 2 2H C C CH NH

12

53. Which of the following compounds contain at least one

secondary alcohol?

(A) I, II, IV, VI (B) I, III (C) I, II, III, V (D) I, III, V

54. CH SNaNBS 3(A) (B), Product (B) is:

(A) (B) (C) (D) None of these

55. In the given pair of reaction in which pair the second reaction

is more reactive than first towards 2NS reaction ?

(A) 3 2 3 2CH CH Cl CH CH O Et O Et

or

2 2 3 2CH CH Cl CH CH OH Et O Et

(B) 3 2CH CH Cl EtO Et O Et

or 3 2 3 2CH CH Cl EtS CH CH S Et

(C) 3 3(1m) (2m)

Et Cl CH O Et O CH or

3 3(2m) (1m)

Et Cl CH O Et O CH

(D) 3 3Et Br Ph P Et PPh

or 3 3Et Br Ph N E NPh

13

56. 40% (w /v) of NaCl solution (density = 1.12g/ml ) is equivalent

to:

(A) 53.57 10 ppm (B) 63.57 10 ppm

(C) 61 10 ppm (D) 54 10 ppm

57. The difference between the wave number of 1st line of Balmer series and last line of Paschen series for Li2+ ion is :

(A) R

36 (B)

5R

36

(C) 4R (D) R

4

58. Consider three one-litre flasks labeled A, B and C filled with

the gases NO, 2NO and 2N O, respectively, each at 1atm and

273K. In which flask do the molecules have the highest average kinetic energy (A) Flask C (B) All are the same (C) Flask A (D) None

59. The volume of a gas increases by a factor of 2 while the pressure decreases by a factor of 3. Given that the number of moles is unaffected, the factor by which the temperature changes is:

(A) 3

2 (B) 3 2

(C) 2

3 (D)

13

2

60. is a member of III group on losing forms a

new elements belonging to: (A) I group (B) II group (C) III group (D) IV group

90Th particle

14

MATHEMATICS

61. The minimum value of the expression 6 6sin x cos x3 3 is

(A) 1/82.3 (B) 7/82.3

(C) 1/83.2 (D) none of these

62. The value of

23 2

4 2 2r 1

r r 1

r r 1 r ris equal to

(A) 3

2 (B) 1

(C) 2 (D) infinite .

63. Period of 1

f x x x sin4 x cos4 x2

is (where {.}

denotes fractional part function) (A) (B) 1

(C) 1

2 (D) function is a periodic

64. If the solution set for f x 3 is 0, and the solution set

for f x 2 is ,5 , then the true solution set for

2f x f x 6 , is

(A) , (B) ,0

(C) 0,5 (D) ,0 5,

65. Domain of f x2

1/2 4 3log log log x 4 is ([.] denotes

the integer function)

(A) ,2 6, (B) ,2 6,8

(C) 2,6 (D) 2,6

66. The complete set of values of x for which

1 1tan x cot x2

is valid

(A) 3,3 (B) 1,1

(C) ,0 (D) 0,

67. If 1 1asin x bcos x c , then 1 1asin x bcos x is equal

to

(A) 0 (B) ab c b a

a b

(C) 2

(D) ab c a b

a b

15

68. The value of x 0

cos7x cos9xlim

cos x cos5x is equal to

(A) 1 (B) 2

(C) 4

3 (D)

1

4

69. Number of points of discontinuity of 3f x 2x 5 in 1,2 ,

is equal to: (where [x] denotes greatest integer less than or equal to x) (A) 14 (B) 13 (C) 10 (D) 8

70. If 2xf x log lnx , then f x at x e is

(A) 0 (B) 1

(C) 1

e (D)

1

2e

71. 2

xcos x lnx sinxdx

x lnx is equal to

(A) sinx

Clnx

(B) lnx sinx C

(C) lnx.sinx C (D) none of these

72. Primitive of 4

24

3x 1

x x 1

with respect to x is

(A) 4

xC

x x 1 (B)

4

xC

x x 1

(C) 4

x 1C

x x 1 (D)

4

x 1C

x x 1

73. The sum 10

k 1

k. k! equals:

(A) 10 ! (B) 11 !

(C) 10 ! 1 (D) 11 ! 1

74. Sum of series

10 1 10 21010 92 31

109 8 7

2. C .3 3. C .31. C... 10. C .3

2 2 2 is equal

to 8

k

2, then k is equal to

(A) 85 (B) 95

(C) 105 (D) 115

16

75. The system of equations: 22xcos ysin2 2sin 0 ,

2xsin2 2ysin 2cos , xsin ycos 0 , for all

values of , can

(A) have a unique non-trivial solution (B) not have a solution (C) have infinite solutions (D) have a trivial solution

76. If

2 0 0

A 2 2 0

2 2 2

, then adj. adj.A is equal to

(A)

1 0 0

8 1 1 0

1 1 1

(B)

1 0 0

64 1 1 0

1 1 1

(C)

1 0 0

16 1 1 0

1 1 1

(D) none of these

77. A circle passes through the point (–1, 1), (0, 6) and (5, 5). The

point(s) on this circle, the tangent(s) at which is parallel to the straight line joining the origin to its centre is (A) (1, –5) (B) (5, -1) (C) (–5, –1) (D) (–1, 5)

78. A six faced fair dice is thrown until 2 comes, then the

probability that 2 comes in even number of trials is (dice having six faces numbered, 1, 2, 3, 4, 5 and 6):

(A) 1

6 (B)

5

6

(C) 6

11 (D)

5

11

79. If R = {(6, 6), (9, 9), (6, 12), (12, 12), (12, 6)} is a relation on

set A = {3, 6, 9, 12} , then relation R is: (A) Only reflexive (B) Only symmetric (C) Symmetric and transitive but not reflexive (D) An equivalent relation

80. If a + 2b + 3c = 1 and a > 0, b > 0, c > 0 and the greatest value

of 3 2a b c is 1

k then (k – 5180) is

(A) 1 (B) 2 (C) 3 (D) 4

81. If the system of equations 2x + ay + 6z = 8, x + 2y + bz = 5 & x + y + 3z = 4 has unique solution, then:

(A) a 2 & b 3 (B) a 3 & b 2

(C) a 2 & b = 3 (D) a = 2 & b 3

17

82. Let is non-real root of the equation 10z 1 , then 23 53 40 is

(A) 1 (B) 2 (C) 3 (D) 4

83. The probabilities of Virat become man of the match in 1st, 2nd

and 3rd match of India in world cup 2015 are 3 2

,7 7

& 1

7

respectively. If Virat got a man of the match in exactly one match, then what is the probability that he got man of the match in 3rd match, is:

(A) 1

7 (B)

10

79

(C) 10

69 (D)

20

343

84. The probability of hitting a target by three marks men is 1 1

,2 3

and 1

4 respectively. If the probability that exactly two of them

will hit the target is and that at least two of them hit the target

is then + is equal to:

(A) 13

24 (B)

6

24

(C) 7

24 (D) None of these

85. tanx 2xe 2 xsec x dx is equal to

(A) tanx2e C (B) 2 tanxx e C

(C) tanxtanx xe C (D) 2 tanxx xe C

86. The number of ways in which we can choose 2 distinct

integers from 1 to 100 including 1 and 100 such that differences between them is at most 10 is:

(A) 100 90

2 2C C (B) 90 10

88 2C C

(C) 100 10

2 2C C (D)100

2C

87. The primitive of 3/2 1/2

1

x 4 3 x is (where ‘C’ is

integration constant):

(A) 1/2

3 xC

x 4 (B)

1/23 3 x

C4 x 4

(C) 1/2

x 4C

3 x (D)

3 x2 C

x 4

18

88. For any natural number 1

7m 2m m 6m m mm, x x x 2x 7x 14 dx (where

x 0 ), equals:

(A)

m 1

m7m 2m m7x 2x 14x

C14 m 1

(B)

m 1

m7m 2m m2x 14x 7x

C14 m 1

(C)

m 1

m7m 2m m2x 7x 14x

C14 m 1

(D)

m 1

m7m 2m m7x 2x x

C14 m 1

89. Value of integral

/2 7 5 3

2/2

2x 3x 4x x 1dx

sec x

(A) 2

(B) 2

(C) (D)

90. 18

12

xdx

30 x x is equal to

(A) 1 (B) 2

(C) 3 (D) 1

3