SECTION I : PHYSICS waves having intensities in the ratio 25:4 produce interference. The ratio ... a single slit diffraction experiment with ... of the objective lens of a

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SECTION I : PHYSICS

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. An ideal gas is at absolute temperature T. Temperature coefficient of volume expansion for an

isobaric process is

(A) 2T

(B) 1T

(C) 2

1T

(D) None

2. The potential difference between points A and B is

(A) 0 V (B) 6 V (C) 3 V (D) 9 V 3. Two uniformly charged non-conducting hemispherical shells each having uniform charge density

and radius R form a complete sphere (not stuck together) and surround a concentric spherical conducting shell of radius R/2. If hemispherical parts are in equilibrium then minimum surface charge density of inner conducting shell is

(A) 2 (B) 2 (C) (D) / 2 4. An electromagnetic wave going through vacuum is described by 0 sin( )E E kx t ; 0 sin( )B B kx t , then

(A) 0 0E k B (B) 0 0E B k (C) 0 0E B k (D) None 5. A spring-block system undergoes simple harmonic motion on a

smooth horizontal surface. The block is now given some positive charge, and uniform horizontal electric field to the right is switched on. As a result,

(A) the time period of oscillation will increase (B) the time period of oscillation will decrease (C) the time period of oscillation will remain unaffected (D) the mean position of simple harmonic motion will shift to the left 6. A point source causes photoelectric effect from a small metal

plate. Which of the curves may represent the saturation photocurrent as a function of distance between the source and the metal?

(A) a (B) b (C) c (D) d


7. Two parallel long straight conductors lie on a smooth surface. Two other parallel conductors rest on them at right angles so as to form a square of side a initially. A uniform magnetic field B exists at right angles to the plane containing the conductors. Each wire starts moving with a constant velocity v perpendicular to its length increasing the size of the square uniformly. If r is the resistance per unit length of the wire, the current in the circuit will be

(A) 4Bvr

(B) 2Bvr

(C) Bv2r

(D) Bvr

8. Two stars of mass M and 5M, which are at a distance L apart rotate about their centre of mass due to

mutual gravitational attraction. The time of one rotation is

5MM

L

(A) 3

23

LGM

(B) 3

26

LGM

(C) 332 L

GM (D) None

9. In the P-V diagram shown in figure ABC is a semicircle. The work done by the gas in the process

ABC is

(A) Zero (B) ( )2

atm l (C) ( )

2atm l

(D) 4( )atm l

10. Two waves having intensities in the ratio 25:4 produce interference. The ratio of maximum to

minimum intensity is (A) 49 : 9 (B) 5 : 2 (C) 7 : 3 (D) 7 : 4 11. The energy radiated by a black body at 2300K is found to have the maximum at a wavelength 1260

nm, its emissive power being 8000 Wm-2. When the body is cooled to a temperature T K, the emissive power is found to decrease to 500 Wm-2. Find the temperature T

(A) 1200K (B) 1350K (C) 1050K (D) 1150K


12. A body A is thrown vertically upwards with such a velocity that it reaches a maximum height of h. Simultaneously another body B is dropped from height h. It strikes the ground and does not rebound. The velocity of A relative to B v/s time graph is best represented by: (upward direction is positive)

13. The current from the battery in circuit diagram shown is (A) 1 A (B) 2 A (C) 1.5 A (D) 3 A 14. Two resistances 1 3.0 0.1R and 2 6.0 0.2R are to be joined together.

(A) The maximum resistance obtainable is 9.0 0.2

(B) The maximum resistance obtainable is 9.0 0.1

(C) The minimum resistance obtainable is 2.0 0.3

(D) The minimum resistance obtainable is 2.0 0.07

15. Two particles are fired from the same point at same time, with speeds 100 m/sec and 100 m/sec, and

firing angles with horizontal = 60o and 120o respectively. The time after which their velocity vectors become perpendicular to each other, is [ g =10 m/s2]

(A) 5 sec (B) 5 3 1 sec (C) 5 3 sec (D) 5 3 / 2 sec

16. Yellow light is used in a single slit diffraction experiment with slit width of 0.6 mm. If yellow light is replaced by X-rays, then the observed pattern will reveal

(A) that the cental maximum is narrower (B) more number of fringes (C) less number of fringes (D) no diffraction pattern 17. A plastic circular disc of radius R is placed on a thin oil film, spread over a flat horizontal surface.

The torque required to spin the disc about its central vertical axis with a constant angular velocity is proportional to (A) R2 (B) R3 (C) R4 (D) R6

18. A metal ring of radius r = 0.5 m with its plane normal to a uniform magnetic field B of induction 0.2

Tesla carries a current I = 100 A. The tension in newtons developed in the ring is (A) 100 N (B) 50 N (C) 25 N (D) 10 N 19. In a transistor, (A) The emitter has the least concentration of impurity (B) The collector has the least concentration of impurity (C) The base has the least concentration of impurity (D) All the three regions have equal concentrations of impurity


20. Statement-1: If a convex lens is placed in liquid, it can behave as diverging lens. Statement-2: The focal length of a lens is independent of the refractive index of the material of the

lens. (A) Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1

(B) Statement1 is True, Statement2 is True; Statement2 is NOT a correct explanation for Statement 1 (C) Statement 1is True, Statement 2 is False, (D) Statement 1 is False, Statement -2 is True 21. Half-life of a radioactive substance A is two times the half-life of another radioactive substance B.

Initially the number of nuclei of A and B are NA and NB respectively. After three half lives of A number of nuclei of both are equal. Then the ratio NA/NB is:

(A) 1/4 (B) 1/8 (C) 1/3 (D) 1/6 22. A vessel containing a liquid is heated with its contents. The pressure at the bottom of vessel due to

the liquid (No evaporation and no spilling takes place) (A) increase (B) decrease (C) increase if vesselliq 3 (D)decrease if vesselliq 3

23. A particle of mass m moves along a circle of radius R with a normal acceleration varying with time

as an = kt4 where k is a constant. The average value of the power over the first t seconds after the beginning of the motion will be

(A) zero (B) mkRt2

(C) 3mkRt

2 (D) none

24. A cylinder is pure rolling up an incline plane. It stops momentarily and then rolls back. The force of

friction (A) on the cylinder is zero throughout the journey (B) is directed opposite to the velocity of the centre of mass throughout the journey (C) is directed up the plane throughout the journey (D) is directed down the plane throughout the journey 25. In an experiment of resonance tube to measure the velocity of sound, first resonance occurs at

l =10cm from the open end of the tube. End correction of the tube is 1.0cm and the frequency of tuning fork is 700Hz.

(I) Velocity of sound is 308m/s (II) Next resonance will occur at l = 32cm from the open end of the tube (III) Radius of resonance tube is 1.67cm The correct statement is/are (A) I, II (B) I, III (C) II, III (D) I. II. III 26. The focal length of the objective lens of a compound microscope (A) Equal to the focal length of its eye piece (B) Greater than the focal length of eye piece (C) Less than the focal length of eye piece (D) Any of the above three


27. A nucleus with mass number 220 initially at rest emits an α -particle. If the Q-value of the reaction is 5.5MeV, the kinetic energy of the α -particle is

(A) 4.4MeV (B) 5.4MeV (C) 5.6MeV (D) 6.5MeV 28. Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The

total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of − 0.03 mm while measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is

(A) 3.38 mm (B) 3.73 mm (C) 3.67 mm (D) 3.32 mm

29. The electric field intensity in a region is given by ˆ ˆ( )E yi xj

V/m where x, y are in metres. The shape of equipotential curves on X-Y plane is

(A) parallel lines making 45°with the positive X and Y axes. (B) concurrent lines passing through the origin. (C) concentric circles with origin as centre (D) rectangular hyperbola 30. Statement 1: A charged particle cannot be accelerated by magnetic field. Statement 2: Work done by magnetic field force on the moving charge particle is always zero. (A) Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1 (B) Statement 1 is True, Statement 2 isTrue; Statement 2 is NOT a correct explanation for Statement 1 (C) Statement 1is True, Statement 2 is False, (D) Statement 1 is False, Statement -2 is True


SECTION II : CHEMISTRY

This section contains 30 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out which ONLY ONE is correct.

31.

H (1)

S S

H (2)

O O

H

(3)

The correct order of acidity of the hydrogen’s represented above is

(A) (3) < (1) < (2) (B) (1) < (3) < (2) (C) (3) < (2) < (1) (D) (2) < (3) < (1) 32. How many stereoisomers can be formed by catalytic hydrogenation of both the double bonds in the

following compound?

H2 Ni

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

33.

N–NO2 Conc. H2SO4 ?

R

Product of this reaction is?

(A)

NH2

NO2 (B)

NHR

NO2 (C)

NHNO2

R (D) No reaction

34. A mixture of immiscible liquids (an organic liquid compound plus water) boils at 90ºC temperature.

The distillate contains 73% by weight of organic liquid. The molar mass of organic liquid (the vapor pressure of water at 90ºC is 526 mm and organic liquid is 732 mm) is :

(A) 34.9 g (B) 134 g (C) 114 g (D) 104 g 35. 25 mL of a solution of Na2CO3 having a specific gravity of 1.25 g mL–1 required 32.9 mL of a

solution of HCl containing 109.5 g of the acid per litre for complete neutralization. Find the volume of 0.84 N H2SO4 that will be completely neutralized by 125 g of Na2CO3 solution.

(A) 470 mL (B) 370 mL (C) 530 mL (D) 280 mL 36. Point out the false statement : (A) Brownian movement and Tyndall effect is shown by colloidal systems. (B) Gold number is a measure of the protective power of a lyophilic colloid. (C) The colloidal solution of liquid in liquid is called gel. (D) Hardy-Schulze rule is related with coagulation. 37. For the reactions, (i) kJx)g(HCl2)g(Cl)g(H 22 (ii) kJy)g(Cl)g(H)g(HCl2 22 which one of the following statements is correct ? (A) 0yx (B) 0yx (C) 0yx (D) None of these 38. Which of the following ions is responsible for the brown colour in the ring test for a nitrate? (A) [Fe(H2O)5NO]2+ (B) [Fe(CN)5NO]2– (C) [Fe(NO2)6]4– (D) [Fe(H2O)5NO2]+


39. When a nitrate is warmed with zinc powder and an NaOH solution, a gas is evolved. Which of the following reagents will be turned brown by the gas?

(A) Sodium nitroprusside (B) Sodium cobaltinitrite (C) Nessler’s reagent (D) Barium chloride 40. Pyridine is mixed with aqueous solution of NiSO4. NaNO2 solution is then added to mixture to get

dark blue precipitate ‘A’. Analysis show that A does not contain any 24SO ion but produce three

ions per molecule A is (A) 222 )NO()Py(Ni (B) 224 NO)Py(Ni (C) 4223 SONO)Py(Ni (D) 44 SO)Py(Ni 41. The following compounds have been arranged in order of their increasing thermal stabilities. Identify

the correct order : I. K2CO3 II. MgCO3 III. CaCO3 IV. BeCO3 (A) I < II < III < IV (B) IV < II < III < I (C) IV < II < I < III (D) II < IV < III < I 42. CH3CHO + NH2OH CH3CH = N – OH The above reaction occurs satisfactorily at

(A) pH = 1 (B) pH = 4.5 (C) pH = 12 (D)

any value of pH

43. The set with correct order of acidity is : (A) HClO < HClO2 < HClO3 < HClO4 (B) HClO4 < HClO3 < HClO2 < HClO

(C) HClO < HClO4 < HClO3 < HClO2 (D) HClO4 < HClO2 < HClO3 < HClO 44. Of the following species, one which is non-existent : (A) XeF6 (B) XeF5 (C) XeF4 (D) XeF2 45. Potassium hexachloroplatinate K2[PtCl6] adopts antifluorite crystal structure. Which of the following

ions adopts fcc arrangement? (A) Cl– ions (B) K+ ions (C) Pt4+ ions (D) [PtCl6]2– ions 46. When an ideal diatomic gas is heated at constant pressure the fraction of the heat energy supplied

which increases the internal energy of the gas is: (A) 2/5 (B) 3/5 (C) 3/7 (D) 5/7 47. Naturally occurring potassium consists of 0.01% K40, which has a half life of

1.28 109 yr. The activity of 1.0 g sample of KCl would be (A) 8 1017 yr1 (B) 4.37 108 yr1 (C) 5.42 1010 yr1 (D) 7.81 109 yr1

48. Two moles of an equimolar mixture of two alcohols, R1—OH and R2—OH are esterified with one

mole of acetic acid. If 80% of the acid is consumed and the quantities of ester formed under equilibrium are in the ratio of 3:2, the value of the equilibrium constant for the esterification of R1—OH with acetic acid is

(A) 3.3 (B) 3.7 (C) 3.5 (D) 3.9 49. Two systems PCl5(g) PCl3(g) + Cl2(g) and COCl2(g) CO(g) + Cl2(g) are

simultaneously in equilibrium in a vessel at constant volume. If some CO is introduced into the vessel, then at the new equilibrium the concentration of

(A) PCl5 is greater (B) PCl3 remains unchanged (C) PCl5 is less (D) Cl2 is greater


50. A real gas at a very high pressure occupies (A) more volume than that of an ideal gas under identical conditions. (B) less volume than that of an ideal gas under identical conditions. (C) same volume than that of an ideal gas under identical conditions. (D) can’t predict 51. A flask filled with CCl4 vapour was weighed at a temperature and pressure. The flask was then filled

with oxygen at the same temperature and pressure. The mass of CCl4 vapour would be about (A) the same as that of the oxygen (B) onefifth as heavy as oxygen (C) five times as heavy as oxygen (D) twice as heavy as oxygen 52. The frequency of certain line of the Lyman series of the atomic spectrum of hydrogen satisfies the

following conditions: (i) It is the sum of the frequencies of another Lyman line and a Balmer line. (ii) It is the sum of the frequencies of a certain line, a Balmer line and a Paschen line. (iii) It is the sum of the frequencies of a Lyman and a Paschen line but no Bracket line. To what transition does corresponds? (A) n2 = 3 to n1 = 1 (B) n2 = 3 to n1 = 2 (C) n2 = 2 to n1 = 1 (D) n2 = 4 to n1 = 1 53. A solution contains Na+, Sn2+,

3NO , Cl and 24SO ions, all at unit concentration, is electrolyzed

between a silver anode and a platinum cathode. Which of the following change does not occur when current is passed through the cell?

(A) Sn2+ will be oxidized to Sn4+ first, at the anode. (B) Sn2+ will be reduced to Sn first, at the cathode. (C) Cl will be oxidized to Cl2 first, at the anode. (D) Ag will be oxidized to Ag+ next, at the anode. 54. Consider the following sequence of reactions.

O

HOCH2 .CH2OH H+

COOCH3

A 1. LiAlH4, Et2O

2. H3O+ B

The products (A) and (B) are, respectively,

(A)

O

CH3OC

and

O O

OH

COOCH3

(B)

O O

COOCH3

and

CHO

O

(C)

O O

COOCH3

and

CH2OH

O

(D)

HO

COOCH3

and

CH2OH

OCH=CH2 OCH2CH2OH


55. In the reaction

BrCH2COOC2H5 H2O N

the main product obtained at the final stage is

(A)

CH2COOC2H5 N + Br– (B)

CH2COOC2H5 N +

Br–

(C)

CH2COOC2H5

O

(D)

CH2COOC2H5

HO

56. Ge (II) compounds are powerful reducing agents, whereas Pb(IV) compounds are strong oxidants. It

can be due to (A) lead is more electropositive than germanium. (B) the ionization potential of lead is less than that of germanium. (C) the ionic radii of Pb2+ and Pb4+ are larger than those of Ge2+ and Ge4+. (D) in lead the inert pair effect in more pronounced than in germanium. 57. Nitrogen (I) oxide is produced by (A) thermal decomposition of ammonium nitrate. (B) disproportionation of N2O4. (C) thermal decomposition of ammonium nitrite. (D) interaction of hydroxylamine and nitrous acid. 58. P4O10 has short and long PO bonds. The number of short P=O bonds present in P4O10 are (A) 1 (B) 2 (C) 3 (D) 4 59. In the nitrogen family, the HMH bond angle in the hybrides (MH3) gradually becomes closer to

90° on going from N to Sb. This shows that gradually (A) the basic strength of hydrides increases. (B) almost pure porbitals are used for MH bonding. (C) the bond energies of MH bond increases. (D) the bond pair of electrons become nearer to the central atom. 60. The conversion

O O

O

can be effected by using the reagent

(A) H2O2 (B) O3

(C) CO2H

Cl

(D)

CO3H

Cl


SECTION III : MATHEMATICS

This section contains 30 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out which ONLY ONE is correct.

61. A relation R on the set of complex numbers is defined by 1 21 2

1 2

z zz Rzz z

is real, then the relation R

“is real” is (A) equivalence (B) only reflexive (C) only transitive (D) none of these 62. If n U 60,n A 35,n B 24 and n A B ' 10 then n A B is

(A) 9 (B) 8 (C) 6 (D) none of these

63. The entire domain of the function 2f x 1 1 1 x is

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

64. If 1 13f x 5f 3, x 0 Rx x

, then f x

(A) 1 3 5x 616 x

(B) 1 3 5x 616 x

(C) 1 3 5x 616 x

(D) none of these

65. The inequality z 4 z 2 represents the region given by (z is a complex number)

(A) Re z 0 (B) Re z 0 (C) Re z 3 (D) none of these

66. The complex number z satisfying the equations z 4 z i z 5i 0 is

(A) 3 i (B) 2 3 2i (C) 2 3 2i (D) 0

67. The equation x x x125 45 2.27 has, x R (A) no solution (B) one solution (C) two solution (D) more than two solution

68. The roots of the equation 3x

x 2 x 12 .3 9 are given by

(A) 22log , 23

(B) 3, 3 (C) log 32,1log 2

(D) 21 log 3,2

69. If 1 2 1

A 1 1 22 1 1

, the det adj adjA is

(A) 414 (B) 314 (C) 214 (D) 114

70. If two events A and B are such that P A 0.3,P B 0.5 and P A B 0.3 , then P B A B is

equal to

(A) 58

(B) 78

(C) 38

(D) none of these


71. The value of in 0,2 such that the matrix

2sin 1 sin cos

sin 2cos 3 tancos tan 0

is skew-symmetric,

is (A) 2 (B) 3 (C) 4 (D) 6 72. 15 15 15 15

8 9 6 7C C C C (A) 2 (B) 3 (C) 4 (D) none of these 73. There are 10 lamps in a hall. Each one them can be switched on independently. The number of ways

in which the hall can be illuminated is (A) 210 (B) 18 (C) 102 (D) 1023 74. For natural number n nn,2 n 1 ! n , if

(A) n 2 (B) n 2 (C) n 2 (D) for no n

75. The greatest coefficient in the expansion of 2n1x

x

is

(A) 1.3.5... 2n 1n!

(B)

2n!n!

(C) 2nnC (D) None of these

76. The sum of positive terms of the series 4 110 9 9 ...7 7

is

(A) 3527

(B) 4377

(C) 8527

(D) none of these

77. For any odd integer n 1 , 3 n 13 3n n 1 ... 1 1

(A) 21 n 1 2n 12

(B) 21 n 1 2n 14

(C) 21 n 1 2n 12

(D) 21 n 1 2n 14

78. If 1f x1 x

, then the points of discontinuity of the function 3nf x in the domain of f(x),

where nf fof ... of (n times), are (A) x 2 (B) x 0 (C) x 1 (D) none of these

79. If 2y P x , a polynomial of degree n 3 , then 2

32

d d y2 ydx dx

(A) P x .P"' x (B) P x .P"' x (C) P x .P '' x (D) none of these

80. The tangent to the curve x y 4 is equally inclined to the axes at the point

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

81. If 02

then

(A) tantan

(B) tan

tan

(C) tan

tan

(D) None of these


82. 2

101

1 2

1 1cos ec x dxx x

(A) ¼ (B) 1 (C) 0 (D) 101/2

83. The value of the 2 2 2 2 2n 2

1 1 1 1lim ...n n 1 n 2 n n 1

is

(A) 4 (B)

3 (C)

2 (D) none of these

84. The degree of differential equation 2 3dy 1 dy 1 dyx 1

dx 2! dx 3! dx

….is

(A) three (B) one (C) not defined (D) none of these

85. If the points 3 2i i

ii i

a a 3P , ,i 1,2,3a 1 a 1

are collinear and 1 2a ,a and 3a are distinct real numbers, then

(A) 1 2 3 1 2 1a a a a a 3 a 0 (B) 1 2 3 1 2 1a a a a a 3 a 0

(C) 1 2 3 1 2 1a a a a a 3 a 0 (D) 1 2 3 1 2 1a a a a a 2 a 0

86. If 0 , the line 3 x y 2 0 passes through the fixed point

(A) 22,3

(B) 2 , 23

(C) 22,3

(D) none of these

87. If ii

1m , ,i 1,2,3,4m

are four con-cyclic points, then the value of 1 2 3 4m .m .m .m is

(A) 1 (B) – 1 (C) 0 (D) none of these 88. If the parabola 2x ay a 0 makes an intercept of length 40 on the line y 2x 1 , then a is

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

89. If bx 3ay 2ab touches the ellipse 2 2

2 2

x y 1a b

, then the eccentric angle of the point of contact is

(A) 6 (B)

4 (C)

3 (D) none of these

90. If

2 3

2 3

2 3

a a 1 ab b 1 b 0c c 1 c

and the vectors 2 2 2A 1,a,a , B 1,b,b ,C 1,c,c are non-coplanar then

the product abc (A) 1 (B) 1 (C) 0 (D) none of these

Documents

SECTION I : PHYSICS waves having intensities in the ratio 25:4 produce interference. The ratio ... a single slit diffraction experiment with ... of the objective lens of a