1

Physics1. Consider the situation of figure. The work done

in taking a point charge from P to A is from P to B is and from P to C is .

AW ,

CWBW

A P

B

C q

(a) (b) W W A B CW W W< < A B CW> >A B CW W W= =(c) (d) none of these.

2. Figure shows a closed surface which intersects a

conducting sphere. If a positive charge is placed at the point P, the flux of the electric field through the closed surface

(a) will remain zero (b) will become positive (c) will become negative (d) will become undefined.

P

ClosedSurface

Conducting Sphere

1 2>

3. Figure shows two capacitors connected in series

and joined to a battery. The graph shows the variation in potential as one moves from left to right on the branch containing the capacitors.

(a) C C (b) 1 2C C=

C1 C2

V

x

(c) 1C C< 2 (d) The information is not sufficient to decide the relation between and . 1C 2C4. A capacitor of capacitance C is charged to a potential V. the flux of the electric field

through a closed surface enclosing the capacitor is

(a) 0

CV (b) 0

2CV

(c) 0

CV2 (d) zero.

5. A current passes through a resistor. Let and represent the average kinetic energy

of the conduction electrons and the metal ions respectively. 1K 2K

(a) (b) 1K K< 2 1 2K K= (c) (d) any of these three may occur. 1 2K K>

2

6. A uniform wire of resistance 50 is cut into 5 equal parts. These parts are now

connected in parallel. The equivalent resistance of the combination is (a) 2 (b) 10 (c) 250 (d) 6250 . 7. Two inductances L1 and L2 are placed far apart and in

parallel. Their combined inductance is

(a) 1 21 2

L LL L+ (b) 1 2( L L )+

(c) 11 22

L( L L )L

+

(d) 21 21

L( L L )L

+ .

L1

L2i2

E

i1

i

8. The current in an L R circuit builds up to 3 4 of its steady state value in 4 seconds. The time constant of this circuit is

th/

(a) 12sec

ln (b) 2

2sec

ln

(c) 32sec

ln (d) 4

2sec

ln.

9. Four particles, each having a charge q, are placed at

the four vertices of a regular pentagon. The electric field at the centre of the polygon is

(a) 204qa (b)

20

qa

(c) 20

2qa (d) 0

qa

.

C

0. Electric potential is given by : . Electric field at the origin

(b)

1 2 26 8 8 6 4V x xy y yz z= + is (a) 6 8 i j + 6 8 i j (c) i j zero. + (d)

3

11. Two identical capacitors have the same capacitance C. One of them is charged to potential and the other to . The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is

1V 2V

(a) 2 21 214C(V V ) (b) 2 21 214C(V V )+

(c) 21 214C(V V ) (d) 21 214C(V V )+ .

12. The electric field at the centre of an uniformly charged ring is zero. What is the electric field at the centre of a half ring if the charge on it be Q and its radius be R ?

(a) 20

14

QR (b) 20

14

QR

(c) 20

1 24

QR (d) 20

1 24

QR .

13. In the network shown in the figure, each resistance is equal to 2 the resistance between the points A and B is (a) 1 (b) 4 (c) 3 (d) 2 .

AB

14. Figure shows a network of 9 identical resistors. The

resistance of the whole circuit is 1.5 . The resistance R is :

(a) 1.1 (b) 3.3 (c) 1.4 (d) 1.8 .

A B

R RR

R

R

RRR

R

15. In the network shown in figure, the ring has zero

resistance. The equivalent resistance between the points A and B is :

(a) 2 R (b) 4 R (c) 7 R (d) 10 R.

ABR

3R3R

3R

16. A proton moving with a speed of 710 1ms enters the region of a uniform, perpendicular magnetic field of 0.4 T. The radius of the circular path described by proton is (mass of proton kg) 271 6 10. =

(a) 0.25 m (b) 0.25 mm (c) 4 mm (d) 4.25 mm.

4

17. Two capacitor C and 2C in parallel are charged with a battery of voltage V and then

isolated. Now a dielectric of relative permittivity k is filled in C

(a) the final p.d. across the combination is 3 1Vk +

(b) the final p.d. across the combination is 32

Vk +

(c) the final p.d. across the combination is 2Vk

(d) the final p.d. across the combination is 2 1Vk + .

18. A coil of inductance 8.4 mH and resistance 6 is connected to a 12 V battery. The

current in the coil is 1.0 A at approximately the time. (a) 500 s (b) 20 s (c) 35 s (d) 1 s. 19. The conductor AD moves to the right in a uniform

magnetic field directed into the paper. Mark the correct option.

(a) the free electrons in AD will move towards A (b) D will acquire a positive potential with respect to

A (c) If D and A are joined by a conductor externally, a

current will flow from A to D in AD (d) all the above.

A

D

B v

20. Lenzs law is consistent with law of conservation of (a) current (b) emf (c) energy (d) all of the above. 21. Two particles X and Y having equal charges, after being accelerated through the same

potential difference, enter a region of uniform magnetic field and describe circular paths of radii R1 and R2, respectively. The ratio of the mass of X to that of Y is

(a) 1

21 2( R / R ) (b) 2 1R / R

(c) (d) 21 2( R / R ) 1 2R / R . 22. A regular loop carrying a current i is situated near a

long straight wire such that the wire is parallel to one of the sides of the loop and is in the plane of the loop. If a steady current I established in the wire as shown in the figure, the loop will :

i

I

5

(a) rotate about an axis parallel to the wire (b) move away from the wire (c) move towards the wire (d) remain stationary.

23. Two equal point charges are fixed at x = - a and x = + a on the x-axis. Another point

charge Q is placed at the origin. The change in the electrical potential energy of Q, when it is displaced by a small distance x along the x-axis, is approximately proportional to :

(a) x (b) x2 (c) x3 (d) 1/x. 24. A certain charge Q is divided into two parts q and (Q-q). For the maximum coulomb

force between them, the ratio (q/Q) is : (a) 1/16 (b) 1/8 (c) 1/4 (d) 1/2. 25. A parallel plate capacitor of area A, plate separation d

and capacitance C is filled with three different dielectric materials having dielectric constants k1, k2 and k3 as shown. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by :

d

A/2A/2

k3

AA = area of plates

k1 k2 d/2

(a) 1 2

1 1 1 12k k k k

= + +3

(b) 1 2 3

1 1 12k k k k

= ++

(c) 1 2 31 2

2k kkk k

= ++ k 3 (d) 1 2 2k k k k= + +.

26. Find the charge flown through the switch when it is

closed (a) 20 C (b) 30

C (c) 42 C (d) 60

C.

10 F

5V

10V6F

2F

27. A solid conducting sphere of radius a having a charge

Q is surrounded by a concentric conducting spherical shell of inner radius 2a and outer radius 3a as shown in figure. Find the amount of heat produced when switch is closed.

(a) 2

2Kqa

(b) 2

3Kqa

3a 2a

sa

6

(c) 2

4Kqa

(d) 2

6Kqa

.

28. An uncharged sphere of metal placed inside a charged parallel plate capacitor. The lines

of force look like :

(a) (b)

-+--

++

-+ ---

+++

(c) (d) .

-+ ---

+++

-+ ---

+++

29. Consider two thin concentric shells of masses M and 2M and radii and ( < ). Magnitude of the gravitational force experienced by a particle of mass m placed at a

distance

1R 2R 1R 2R

1R R2+ 2 from the common centre will be

(A) 21 2

8GMm(R R )+ (B) 21 2

4GMm(R R )+

(C) 21 2

2GMm(R R )+ (D) 21 2

12GMm(R R )+

30. A uniform gravitational field ( ) E ai bj= +r N/kg exists in a region. Work done in displacing

a particle along a straight line represented by ax + by = c will be (a, b and c are constants)

(A) a 2 2x y+ (B) 2 2a b+ 2 2x y+ (C) ax+by (D) zero.

31. A pendulum oscillates with an angular amplitude 2

7

33. A power radiated by a black body is and the wavelength corresponding to the maximum energy is around

0P

0 . On changing the temperature of the black body, it was observed that the power radiated is increased to 0

256 P81

. The shift in the wavelength

corresponding to the maximum energy will be

(A) + 04

(B) 02+

(C) 04 (D) 0

2

34. A gas undergoes a process in which its pressure p and volume V are related as n mp Vstant, where m and n are dimensionless constants. The bulk modulus for the gas in

this process will be =con

(A) m pn

(B) n pm

(C) (m+n)p (D) (m n)p

35. The adiabatic exponent of a gas pv

CC

= and its molecular weight = M. The difference of its molar heat capacity and specific heat capacity (both at constant pressure) will be

(A) (R M 11

) (B) ( )M 1R

1 M

(C) RM1

(D) RM( 1)

36. Two organ pipes A and B have their lengths in the ratio n : m. Pipe A is open at both

ends while B is closed at one end only. The ratio of the frequencies of first overtones produced by each of them will be

(A) m2n

(B) 2mn

(C) 3n4m

(D) 4m3n

37. Match the following column (I) and (II).

(I) (II) (a) Conservative force field (i) Work done is stored. (b) Energy and frequency relationship (ii) Plancks law (c) sound waves (iii) decrease in temperature (d) Adiabatic expansion (iv) longitudinal wave motion.

(A) (a)-(i), (b)-(ii), (c)-(iii) and (d) - (iv) (B) (a)-(ii), (b)-(iii), (c)-(iv) and (d) - (i)

8

(C) (a)-(i), (b)-(ii), (c)-(iv) and (d) - (iii) (D) (a)-(iv), (b)-(iii), (c)-(ii) and (d) - (i)

38. Match the following column (I) and (II). (I) (II) (a) Periodic time of spring mass system (i) central forces (b) Escape velocity (ii) Doppler effect. (c) Conservation of angular momentum. (iii) independent of gravity. (d) Apparent change in pitch (iv) independent of mass of the object.

(A) (a)-(iii), (b)-(iv), (c)-(i) and (d) - (ii) (B) (a)-(iv), (b)-(iii), (c)-(ii) and (d) - (i) (C) (a)-(iv), (b)-(iii), (c)-(ii) and (d) - (i) (D) (a)-(i), (b)-(ii), (c)-(iii) and (d) - (iv) 39. From a solid sphere of radius R and mass

M a small sphere of radius R/4 is scooped out and placed on the surface of the original solid sphere on a diametrically opposite point as shown in the figure. The gravitational potential of the resulting system at a point P (as shown in the figure) is

R

O

R/4

R/4

P

d

R/4

(A) GMR

(B) +

22

GM

Rd4

(C) +2 2

4GM

16d R (D) zero.

40. Three particles are thrown at regular interval of 2 sec, with a speed of 60 m/s vertically

upward. The ratio of their speeds at the end of 7 sec is (A) 1 : 1 : 3 (B) 1 : 1 : 3 (C) 1 : 1 : 1 (D) 1 : 2 : 3 41. The velocity vector of a particle moving over a horizontal plane is given by v = 2t +

. The ratio of the magnitude of instantaneous acceleration of the particle at t = 2 sec to the magnitude of displacement of the particle during the interval of first 2 sec is

i23t i

(A) 3720

(B) 37 20

(C) 20 (D) cannot be determined 37

P 80t i 60tj= +

42. An external force is applied on a body of mass 10 kg placed over a rough horizontal surface having coefficient of friction 0.2. The momentum of the body is found to be r

. The applied force is (A) 80 i + 60 j (B) 74 + 48i j

9

(C) 16 i + 12 j (D) 96 + 72i j 43. A block of mass 2kg was moving along a straight line on a smooth surface with a speed

of 5 m/s. At t = 0, a force given by F = (3 + 2t)N directed in the direction of motion of the body starts acting on the block. The kinetic energy of the block after 2 sec is

(A) 20 J (B) 200 J (C) 100 J (D) none of these. 44. A wide vessel and a tube is connected as shown in the figure.

Water is filled inside vessel and tube. When tube is opened the water flows out as shown in the figure. The pressure at point P, at mid point of tube is (cross section of the tube is very-very small)

(A) P0 + 3gH (B) P0 + gH (C) P0 (D) P0 gH

H

2H P

F=kt

m

45. A block of mass m is placed on an inclined surface.

Coefficient of friction between plane and block is > tan. A force F = kt is applied on block at t = 0 then which of the following represents variation of magnitude of frictional force with time.

>tan

(A)

Time

fr (B)

Time

fr

(C)

(D)

Time

fr

Time

fr

46. A right circular cone of base radius R and height H is hanging horizontally via a string inside liquid of density . Tip of the cone is at a distance h below the free surface of liquid. The force due to liquid on the surface of cone is

(A) 2R gH 3

(B) ( )2 2R R H gH + 2R gH

(C) (D) zero

h

R H

10

47. Match the following column (I) and (II). (I) (II) (a) First law of thermodynamics (i) conservation of kinetic energy. (b) Elastic collision (ii) conservation of energy. (c) Absence of dissipative force (iii) conservation of volume. (d) equation of continuity (iv) conservation of mechanical energy.

(A) (a)-(iv), (b)-(i), (c)-(ii), (d)-(iii) (B) (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv) (C) (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii) (D) none of these 48. The time period of a simple pendulum is T for small oscillation. When the simple

pendulum is immersed in a fluid its time period is T, then the correct option is 0

0 0

0

ea

(A) T = T (B) T > T (C) T < T (D) none of these. 49. In the shown figure a cube of mass m is attached with a cylinder

of same mass and radius r through an ideal string-pulley system. The string is wound over the cylinder. If is the angular acceleration of the cylinder then the linear acceleration of

and the linear acceleration of cube A, are related as (A) = A (B) A = ea ea 2 (C) + r = A (D) = A + r ea ea

m

m

a

ae

50. A block of mass m, when placed on an incline plane fixed with an

elevator, which is moving with constant downward acceleration g/2, remain stationary. If the coefficient of friction between the plane and block is , the magnitude of force of friction acting on the block is

(A) mg cos (B) m g2

cos

g/2

m

(C) m g2

sin

Chemistry

(D) m g2

sin

51. The hydride ion H is stronger base than its hydroxide ion OH. Which of the following reaction will occur if NaOH is dissolved in water?

(a) H(aq) + H2O H2O (b) H(aq) + H2O(l) OH+H2 (c) H + H2O No reaction (d) None of these

11

52. The ionisation constant for CH3COOH is 1.75 105. What is the pH of a buffer solution

containing 0.1 mole of CH3COOH and 0.15 mole of CH3COONa? (a) 3 (b) 3.7 (c) 4.3 (d) 4.9 53. 2SO2 + O2 2SO3. Starting with 2 mol SO2 and 1 mol O2 in 1 L flask, mixture

required 0.4 mol MnO4 in acidic medium. Hence KC is (a) 2 (b) 0.4 (c) 1.6 (d) 2.6 54. For 3A + 2B 2C + D, initial mole of A is double of B. At equilibrium mol of A and

D are equal. Hence percentage dissociation of A is (a) 50% (b) 25% (c) 75% (d) none of these 55. Addition of solid potassium cyanide to water would cause (a) Increase in pH (b) Decrease in pH (c) No change in pH (d) no change in electrical conductivity 56. A certain buffer solution contains equal concentration of X and HX. The Kb for X is 10

10. The pH of the buffer is (a) 4 (b) 7 (c) 10 (d) 14 57. in increasing pKb values 3 2CH , N H ,O H,F

(a) (b) 3 2CH N H O H F

< < < 2 3F O H NH CH < <

CH2CH3

CH34. Hyperconjugation and Inductive

Codes a b c d (a) 2 3 4 1 (b) 3 1 4 2 (c) 4 3 1 2 (d) 3 4 2 1 67. Match list I with list II and select the correct answer using the codes given below: List I List II a. CH3COONa 1. Strong electrolyte with pH > 7 b. NH4Cl 2. Strong electrolyte with the pH < 7 c. Bi2S3 3. Weak electrolyte with Ksp = S2 d. CdS 4. Weak electrolyte with Ksp = 108S5 Codes a b c d (a) 2 3 1 4 (b) 1 2 4 3 (c) 1 3 2 4 (d) 1 3 4 2

15

68. Which one of the following has the lowest dipole moment?

(a) CH3

H H

CH3

(b) CH3 CH3

(c) CH3 CH (d) CH2 CH

69. 40% of a mixture of 0.2 mol of N2 and 0.6 mol of H2 react to give NH3 according to the

equation N2(g) + 3H2(g) 2NH3(g) at constant temperature and pressure. Then the ratio of the final volume to the initial volumes of gases is as

(a) 4:5 (b) 5:4 (c) 7:10 (d) 8:5 70. 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 71. The precipitate of CaF2(Ksp = 1.710-10) is obtained when equal volumes of the following

are mixed (a) 10-4 M Ca2+ + 10-4 MF- (b) 10-2 M Ca2+ + 10-3 MF- (c) 10-5 M Ca2+ + 10-3 MF- (d) 10-3 M Ca2+ + 10-5 MF- 72. The maximum number of isomers for an alkene with the molecular formula C4H8 is: (a) 2 (b) 3 (c) 4 (d) 5 73. In the following reaction 3 3BH CH COOH3 2CH CH CH A B = A and B are,

(a) BCH3

CH3

CH3CH3

,

3

(b) ,CH3 CH2 CH2 B CH3O C 3

O

H

3

(c) ,CH3 CH2 CH2 B CH3 CH33

16

(d) BCH3

CH3

CH3CH3

O

,

374. Which of the following is the diastereoisomer of the compound?

CH3

CH3

HO

H

H

I

(a)

CH3H O

H I

CH3

H

(b)

OH

CH3 H

H I

CH3

(c)

OH

CH3 H

I C 3H

H

(d)

OH

CH3 H

H C 3I

H

75. If the molecular weight of is M, then the equivalent weight of in acidic medium is:

4 2Ba(MnO ) 4 2Ba(MnO )

(A) M5

(B) M10

(C) M3

(D) M

76. 280 ml of reacts completely with 15.8g of in acidic medium, then the

volume strength of is: 2 2H O 4KMnO

2 2H O (A) 10 (B) 100 (C) 5 (D) 20 77. The velocity of electron in the second orbit of He+ will be (A) (B) 62.18 10 m/s 61.09 10 m/s (C) (D) None 64.36 10 m/s 78. If the 1.58g of in acidic medium completely reacts with ferrous oxalate

the what weight (in g) of ferrous oxalate is required? 4KMnO

2 4(FeC O ), (A) 2.73 (B) 4.73 (C) 11.19 (D) 8.5

17

79. Applying the principle of equipartition of energy, what will be total values of molecule, assuming 100% contribution of vibrational degree of freedom?

vC 2H

(A) 3.5R (B) 2.5R (C) 5R (D) 4.5R 80. The values of vander Waals constant `a for the gases and

are given 0.25, 3.5, 4.9 and 6.9 respectively. Which will have the highest ease of liquification?

2 2 2(atm L mol ) 2 2N , H 3NH

2SO

(A) (B) 2SO 3NH (C) (D) 2N 2H 81. The activation energy of the forward reaction and backward reaction decreases by 30

kcal then which of the following statement is correct? (A) will remain constant (B) H H will decrease (C) will increase (D) The reaction will be exothermic H

82. 30 ml of N5

is added in NaOH solution, then at the end point of the reaction, the equilibrium constant of the reaction at 25C (given that

3CH COOH

5a(CH COOH)3

K 10= ) will be

(A) (B) 910 910

(C) 91 105

(D) None 83. For the radioactive sequential chain reaction A B C for the steady state of B, assuming that the no. of atoms of A is half of the no. of atoms

of B then if the half life of B is 2 hours then the half of life of A (in hours) will be (A) 4 (B) 2 (C) 1 (D) 3 84. The compressibility factor for an ideal gas is: (A) 0 (B) 1 (C) 2 (D) 4 85. Two gram of hydrogen diffuse from a container in 10 minutes. How many grams of

oxygen would diffuse through the same container in the same time under similar conditions?

(A) 0.5 g (B) 4 g (C) 6 g (D) 8 g

18

86. for HCN is at 25C. For maintaining a constant pH = 9, the volume of 5 M KCN solution required to be added to 10 ml of 2 M HCN solution is

aK105 10

3COOH

3CH COONa a 3COOH

(A) 4 ml (B) 7.95 ml (C) 2 ml (D) 9.3 ml 87. A buffer solution is prepared by mixing 10 ml of 1.0 M CH and 120 ml of 0.5 M

and then diluted to 100 ml with distilled water. If pK of CH is 4.76, what is the pH of the buffer solution

(A) 5.53 (B) 4.76 (C) 4.34 (D) 5.8 88. The pH of solution formed by mixing 40 ml of 0.1 M HCl with 10 ml of 0.45 M of NaOH is (A) 10 (B) 12 (C) 8 (D) 6

89. Which of the following bromide will undergo faster dehydrobromination?

(A)

Br

(B)

Br

(C)

BrBr (D)

90. Which of the following carbocation is more stable?

(A) F CH2 (B) H2C

F

(C) CH3CH3

(D) CH3

OCH3

91. Which of the following keto compound will give the least stable enol?

(A) O

(B)

O

O

(C)

O

O

O

O

(D)

92. How many optically active fractions can be produced by monochlorination of the

compound

3

CH3

CH3 CH

19

(A) 1 (B) 3 (C) 4 (D) Zero 93. Which of the following is the least stable?

(A)

(B)

(C)

(D)

94. Which of the following is the most reactive towards electrophilic aromatic substitution?

(A)

O

(B)

OCH3

(C)

NH2 OH

(D)

95. Which of the following will show Friedal Crafts alkylation?

(A)

NH2

(B)

COO-

(C)

OHO NO2

(D)

96. Which of the following is most basic in protic polar solvent?

(A) NHCH3

CH3

(B) NCH3

CH3

CH3

(C) 3NHCH3 NH2 (D) 97. Which of the following is the correct order of reactivity towards nitration? (A) C H > (B) C D > 6 6 6 6 6 6C D C T> 6 6 6 6 6 6C H C T>

6 6 6 6 6 6 6T (C) (D) C C D C H6 6 6 6 6C T C D C H> > = =

N CH

O

98. Which of the following carbon has the most acidic hydrogen?

3345 2

20

(A) 5 (B) 4 (C) 3 (D) 1

99. Which of the following alkene has the lowest heat of hydrogenation?

(A)

H H

H H

(B)

H H

CH3

CH2

(C)

CH3 H H CH3

CH3 H CH3 H

(D)

100. Which of the following imene is least stable?

(A)

NH

NH

(B) NH

NH

(C)

NH NH

NHNH

(D)

Maths101. If ax2 y2 + 4x y = 0 represents a pair of lines, then a is equal to (a) 16 (b) 16 (c) 4 (d) 4 102. What is the equation of the locus of a point which moves such that 4 times its distance

from the x-axis is the square of its distance from the origin? (a) x2 + y2 4y = 0 (b) x2 + y2 4|y| = 0 (c) x2 + y2 4x = 0 (d) x2 + y2 4|x| = 0 103. Equation of the straight line making equal intercepts on the axes and passing through

the point (2, 4) is (a) 4x y 4 = 0 (b) 2x + y 8 = 0 (c) x + y 6 = 0 (d) x + 2y 10 = 0

21

104. If the area of the triangle with vertices (x, 0), (1, 1) and (0, 2) is 4 square units, then the value of x is

(a) 2 (b) 4 (c) 6 (d) 8

105. x

2

2limcot

(a) 0 (b) 1 (c) 1 (d) 106. The co-axial system of circles given by x2 + y2 + 2gx + c = 0 for c < 0 represetns (a) intersecting circles (b) non intersecting circles (c) touching circles (d) touching or non-intersecting circles 107. The radius of the circle passing through the point (6, 2) and two of whose diameters are

x + y = 6 and x + 2y = 4 is (a) 4 (b) 6 (c) 20 (d) 20 108. If (0, 6) and (0, 3) are respectively the vertex and focus of a parabola, then its equation

is (a) x2 + 12y = 72 (b) x2 12y = 72 (c) y2 12x = 72 (d) y2 + 12x = 72 109. For the ellipse 24x2 + 9y2 150x 90y + 225 = 0 the eccentricity e is equal to

(a) 25

(b) 35

(c) 45

(d) 15

110. If the foci of the ellipse 2 2

2x y 116 b

+ = and the hyperbola 2 2x y 1

144 81 25 = coincide, then the

value of b2 is (a) 1 (b) 7 (c) 5 (d) 9 111. The differential coefficient is f(sinx) with respect to x where f(x) = logx is (a) tan x (b) cot x (c) f(cos x) (d) 1/x

112. If 1 cos x , x 0

f(x) xk, x 0

= = is continuous at x = 0, then the value of k is

(a) 0 (b) (c) (d)

113. If 1 32

+ = i then is 2 4(3 3 )+ + (a) 16 (b) 16 (c) 16 (d) 162

22

114. If 1 dyy tan (sec x tanx), thendx

= is equal to (a) 2 (b) 2

(c) 12

(d) 12

115. If 1x 2cosx

+ = then n n1xx

+ is equal to (a) 2n cos (b) 2n cos n (c) 2isin n (d) 2cos n 116. is equal to 1

1|1 x |dx

(a) 2 (b) 0 (c) 2 (d) 4

117. 7dx

x(x 1)+ is equal to (a)

7

7xlog c

x 1

+ + (b)

7

71 xlog c7 x 1

+ +

(c) 7

7x 1log c

x

+ + (d)

7

71 x 1log c7 x

+ +

118. xxe dx is equal to (a) x x2 x e 4 xe c + (b) x(2x 4 x 4)e c + + (c) x(2x 4 x 4)e c+ + + (d) x(1 4 x )e c + 119. 2

dxx 2x 2+ + is equal to

(a) sin-1(x + 1) + c (b) sin h-1(x + 1) +c (c) tan h-1 (x + 1) +c (d) tan-1(x + 1) +c 120. If a tangent to the curve y = 6x x2 is parallel to the line 4x 2y 1 = 0, then the point

of tangency on the curve is (a) (2, 8) (b) (8, 2) (c) (6, 1) (d) (4, 2) 121. 0.5737373.... is equal to

(a) 284497

(b) 284495

(c) 568999

(d) 567990

23

122. The number of solutions for the equation x2 5|x| + 6 = 0 is (a) 4 (b) 3 (c) 2 (d) 1 123. How many numbers of 6 digits can be formed from the digits of the number 112233? (a) 30 (b) 60 (c) 90 (d) 120 124. The last digit in 7300 is (a) 7 (b) 9 (c) 1 (d) 3

125. If logx logy logza b b c c a

= = , then xyz is equal to (a) 0 (b) 1 (c) 1 (d) 2 126. The smallest positive integer n for which (1 + i)2n = (1 i)2n is (a) 1 (b) 2 (c) 3 (d) 4 127. If then p2 + q2 + r2 + 2pqr is equal to 1 1 1cos p cos q cos r + + = (a) 3 (b) 1 (c) 2 (d) 1

128. If 1 1x 5sin cosec5 4

+2

= , then x is equal to (a) 1 (b) 4 (c) 3 (d) 5 129. If , then x is equal to

2 2sin x cos x0 x and 81 81 30 + = (a)

6 (b)

2

(c) 4 (d) 3

4

130. The equation of the director circle of the hyperbola 2 2x y 1

16 4 = is given by

(a) x2 + y2 = 16 (b) x2 + y2 = 4 (c) x2 + y2 = 20 (d) x2 + y2 = 12 131. If Q1 is the set of all relations other than 1 with the binary operation * defined by a * b =

a + b ab for all a, b in Q1, then the identity in Q1 with respect to * is (a) 1 (b) 0 (c) 1 (d) 2 132. The circle x2 + y2 8x + 4y + 4 =0 touches (a) x-axis (b) y-axis (c) both axis (d) neither x-axis nor y-axis

24

133. Which of the following is true? (a) The set of all fourth roots of unity is a multiplicative group (b) The set of all cube roots of unity is an additive group (c) (ab)1 = a1b1 for all ab,b in any group G (d) If (ab)2 = a2b2 for all a, b in any group G, then the group G is non abelian 134. The set of all integral multiples of 5 is a subgroup of (a) The set of all reational numbers under multiplication (b) The set of all integers under multiplication (c) The set of all non zero rational numbers under multiplication (d) The set of all integers under addition 135. The value of k so that x2 + y2 + kx + 4y + 2 = 0 and 2(x2 + y2) 4x 3y + k = 0 cut

orthogonally is

(a) 103

(b) 83

(c) 103

(d) 83

136. 3x 1

x

4lim 1x 1

is equal to

(a) e12 (b) e12 (c) e4 (d) e3

137. If A + B + C = 180 then A Btan tan2 2

is equal to (a) 0 (b) 1 (c) 2 (d) 3 138. In a triangle ABC if b = 2, B = 30 then the area of the circumcircle of triangle ABC in

square units is (a) (b) 2 (c) 4 (d) 6 139. If sin x + sin2 x = 1, then cos12 x + 3cos10 x + 3cos8 x + cos6 x is equal to (a) 1 (b) 2 (c) 3 (d) 0 140. If R deontes the set of all real numbers, then the function f : R R defined f(x) = |x| is (a) one-one only (b) onto only (c) both one-one and onto (d) neither one-one nor onto 141. If 1, , 2 are cube roots of unity, then (1 + )3 (1 + 2)3 is (a) 0 (b) -1 (c) (d) 2 142. If z i

z i+ =1, then the locus of z is:

(a) x = 0 (b) y = 0 (c) x = 1 (d) y = 1

25

143. The condition that one root of the equation ax2 + bx + c = 0 may be square of the other, is: (a) a2c + ac2 + b3 3abc = 0 (b) a2c2 + ac2 + b2 3abc = 0 (c) ac2 + ac b3 3abc = 0 (d) a2c + ac2 b3 3abc = 0 144. If and are roots of the equation 4x2 + 2x 1 = 0, then the value of 2 + 2 is: (a) 2 (b) 3

4

(c) 3 (d) 14

145. If the root of the equation a b 1x a x b

+ = are equal in magnitude and opposite in sign, then: (a) a = b (b) a + b = 1 (c) a b = 1 (d) a + b = 0 146. The equation of smallest degree with real coefficients having 2 + 3i as one of the roots, is: (a) x2 + 4x + 13 = 0 (b) x2 + 4x 13 = 0 (c) x2 4x + 13 = 0 (d) x2 4x 13 = 0 147. If the expression a(b c) x2 + b(c a) xy + c (a b)y2 is a perfect square, then a, b, c are in: (a) AP (b) HP (c) GP (d) Both AP and GP

148. The value of n for which the expression n 1 n 1

n n

x yx y

+ +++ is arithmetic mean between x and y, is:

(A) 0 (b) 1 (c) -1 (d) 2 149. The angles A, B, C of a triangle ABC are in AP and side b and c are in the ratio 3 : 2 ,

then the angle A is: (a) 105 (b) 60 (c) 45 (d) 75 150. The sum of the series 1+ 2.2 + 3.22 + 4.23 + 5.24 + + 100.299 is (a) 99.2100 (b) 100.2100 (c) 99.2100 (d) 1000.2100 151. The sum to n terms of the series

1 3 7 15 ...2 4 8 16+ + + + is:

(a) 2n 1 (b) 1 2n (c) n + 2n 1 (d) n 1 + 2n 152. If A, G, H denotes respectively the AM, GM and HM between two unequal positive

numbers, then (a) A = G2H (b) G2 = AH (c) A2 = GH (d) A = GH 153. If nPr = 720 nCr, then r is equal to: (a) 6 (b) 5 (c) 4 (d) 7

26

154. Everybody is a room shakes hands with everybody else. The total number of handshakes is 66. The number of persons in the room is:

(a) 11 (b) 12 (c) 13 (d) 14 155. The number of four digit even numbers that can be formed using 0, 1, 2, 3, 4, 5, 6 without

repetition is: (a) 120 (b) 300 (c) 420 (d) 20 156. The number of circular permutations of n different objects is: (a) n! (b) n (c) (n 2)! (d) (n 1)!

157. The coefficient of x9 in the expansion of 92x 2

2 x

is:

(a) 512 (b) 512 (c) 521 (d) 251 158. If the coefficients of the rth term and the (r + 1)th term in the expansion of (1 + x)20 are in

the ratio 1 : 2, then r is equal to: (a) 6 (b) 7 (c) 8 (d) 9 159. The number of ways in which 21 objects can be grouped into three groups of 8, 7 and 6

objects, is:

(a) 20!8! 7! 6!+ + (b)

21!8!7!

(c) 21!8!7!6!

(d) 21!8! 7! 6!+ +

160. The value of

2 2 2

2 2 2

2 2 2

1 2 32 3 43 4 5

is:

(a) 8 (b) 8 (c) 400 (d) 1

161. If A = , then An is equal to: 1 20 1

(a) (b) 1 2n0 1

2 n0 1

(c) (d) 1 n0 1

1 n0 1

162. If A2 A + I = 0, then the inverse of A is: (a) A2 (b) A + I (c) I A (d) A I

27

163. If is a singular matrix, then x is: 2 x 3 4

1 1 2x 1 5

+

(a) 1325

(b) 2513

(c) 513

(d) 2513

164. If A and B are square matrices of order 3 such that |a| = 1, |B| = 3, then the determinant value of the matrix 3AB is equal to:

(a) -9 (b) -27 (c) -81 (d) 81

165. If value of is equal to: a a b a 2b

a 2b a a ba b a 2b a

+ + + + + +

(a) 9a2 (a + b) (b) 9b2 (a + b) (c) a2 (a + b) (d) b2 (a + b)

166. For the matrix A = which is correct? 1 1 01 2 12 1 0

(a) A3 + 3A2 I = 0 (b) A3 3A2 I =0 (c) A3 + 2A2 I = 0 (d) A3 A2 + I = 0 167. If are any three mutually perpendicular vectors of equal magnitude a, then | aa, b, c

rr rb c |+ +rr r :

(a) a (b) 2a (c) 3a (d) 2a 168. If are two unit vectors and the angle between them, then | xx and yr r y |r r is equal to: (a) 2sin

2 (b) 2cos 2

(c) sin2 (d) cos 2

169. If = (2, - 3, - 7), = (3, - 1, 2), car b

r r = (4, 5, -1), then the scalar triple product is equal to:

[a b c]rr r

(a) 180 (b) 184 (c) -184 (d) 84 170. The value of a . is equal to: {(b c) (a b c)} + +r rr r r rrr r (a) 0 (b) [a b c]

r (c) 2a (d) a r

171. If | a then | a| 6, | b | 8, | a b | 10,= = =r rr r b |+ rr is equal to: (a) 10 (b) 24 (c) 40 (d) 36

28

172. If | a and a b , then the angle between | 3, | b | 5, | c | 7= = =rr r c 0+ + =rr r ar and : br

(a) 15 (b) cos1 23

(c) 30 (d) 60 173. The area of a parallelogram with diagonals as a 3 i j 2k= + r and b i 3 j 4k= + r is: (a) 10 3 (b) 10

3

(c) 5 3 (d) 53

174. The position vectors of A, B and C are (1, 1, 1), (1, 5 1) and (2, 3, 5), then the greatest angle of the triangle is:

(a) 135 (b) 90

(c) cos1 23

(d) 1 5cos

7

175. If is a unit vector perpendicular to barr

and cr , then second unit vector perpendicular to br

and c is: r r (a) b (b) a b cr

r rrr r (c) c (d) a c r176. If , then is equal to: a.i a.( i j k) 1= + + =r r a

(a) (b) j i (c) (d) i j k +177. If is the angle between the planes 2x y + 2z = 3, 6x 2y + 3z = 5, then cos is equal to (a) 21

20 (b) 11

21

(c) 2021

(d) 1223

178. The direction cosines of the normal to the plane 6x 3y 2z = 1 are:

(a) 6 2, 3,7 7

(b) (6, -3, -2)

(c) 17

(6, -3, -2) (d) 17

(6, 3, 2)

179. If , , are the angles made by a straight line with the co-ordinate axes, then sin2 + sin2 + sin2 is equal to:

(a) 0 (b) 1

(c) 2 (d) 32

180. The equation of the plane through the intersection of the planes x + 2y + 3z 4 = 0 and 4x + 3y + 2z + 1 = 0 and passing through the origin, is:

(a) 17x + 14y + 11z = 0 (b) 7x + 14y + 11z = 0 (c) x + 14y + 11z = 0

29

(d) x + y + 11z =0 181. The number of real values of a satisfying the equation 01sin22 =+ xaa is (a) Zero (b) One (c) Two (d) Infinite 182. For positive integers 21 ,nn the value of the expression 2211 )1()1()1()1( 753 nnnn iiii +++++++

where 1=i is a real number if and only if (a) (b) 1121 += nn 21 = nn (c) 21 nn = (d) 0 ,0 21 >> nn183. If the angles of a quadrilateral are in A.P. whose common difference is , then the

angles of the quadrilateral are o10

(a) (b) (b) (d)

oooo 105,95,85,65oooo 115,105,95,65

oooo 105,95,85,75 oooo 95,85,75,65

184. If the sum of first n terms of an A.P. be equal to the sum of its first terms, m )( nm , then the sum of its first terms will be )n+(m

(a) 0 (b) n (c) m (d) nm + 185. If ,infinity to.......111 +++=x then x =

(a) 2

51 + (b) 2

51 (c) 2

51 (d) None of these

186. For the equation , the roots are 06|||| 2 =+ xx (a) One and only one real number (b) Real with sum

one (c) Real with sum zero (d) Real with product zero 187. The value of is )}12()32.....(5.3.1{2 nnn

(a) !

!)2(nn (b)

nn

2!)2( (c)

!)2(!nn (d) None of

these 188. A question paper is divided into two parts A and B and each part contains 5 questions. The

number of ways in which a candidate can answer 6 questions selecting at least two questions from each part is

(a) 80 (b) 100 (c) 200 (d) None of these

189. The value of 66 )12()12( ++ will be (a) 198 (b) 198 (c) 99 (d) 99 190. If then the value of a and n is ....,2481)1( 2 +++=+ xxax n (a) 2, 4 (b) 2, 3 (c) 3, 6 (d) 1, 2

191. If and , then

=abba

A

= 2A

(a) (b) (c) (d)

abba =+= ,2222,2 baab +==

abba 2,22 =+= 2222 , baba =+=

30

192. For non zero, if cba ,, 0111

111111

=+

++

=c

ba

, then the value of =++cba111

(a) abc (b) abc1 (c) )( cba ++ (d) None of

these

193. If ,24

tanlog

+= xu then is equal to uhcos (a) xsec (b) xcosec (c) xtan (d) xsin

194. If ,seccosh x= then =2

tan 2 x

(a) 2

cos 2 (b) 2

sin 2 (c) 2

cot 2 (d) 2

tanh 2 195. The number of integral values of m, for which the x-co-ordinate of the point of intersection

of the lines and 943 =+ yx 1+= mxy is also an integer is (a) 2 (b) 0 (c) 4 (d) 1 196. A ray of light coming from the point (1, 2) is reflected at a point A on the xaxis and then

passes through the point (5, 3). The coordinates of the point A are (a) ( (b) ( ) (c) ( 7, 0) (d) None of

these )0,5/13 0,13/5

197. The equation of the locus of foot of perpendiculars drawn from the origin to the line passing through a fixed point (a, b), is

(a) (b) (c) (d) None of these

022 =+ byaxyx 022 =+++ byaxyx 02222 =+ byaxyx

198. The orthocentre of the triangle formed by the lines 0=xy and 1=+ yx is (a) (b) (1/2, 1/2) (c) (1/3, 1/3) (d) (1/4, 1/4) )0,0(199. ABCD is a square, the length of whose side is a. Taking AB and AD as the coordinate

axes, the equation of the circle passing through the vertices of the square, is (a) (b) (c) (d)

022 =+++ ayaxyx

2222 =+ ayaxyx022 =+ ayaxyx 02222 =+++ ayaxyx

0

200. Locus of the point given by the equations 21

2tatx += , )11(1

)1(2

2+

= tttay is a

(a) Straight line (b) Circle (c) Ellipse (d) Hyperbola