As per your request here I am sharing the GUJCET Maths Previous year question papers:

1. The number of free electrons per 10 mm of an ordinary copper wire is 2 x 1021. The average

drift speed of the electrons is 0.25 mm/s. The current flowing is:

A. 0.8 A B. 8 A C. 80 A D. 5 A

2. Which of the following cells is more likely to be damaged due to short circuiting?

A. Daniel B. Dry C. Acid D. Fuel

3. A gas expands from 5 litre to 105 litre at a constant pressure 100N/m2. The work done is

A. 1 Joule B. 4 Joule C. 8 Joule D. 10 Joule

4. The Helium nuclei can be formed from

A. Hydrogen nuclei by process of chain reactionB. Hydrogen nuclei through nuclear fission

C. Hydrogen nuclei through nuclear fusion D. None of these

5. In the atom bomb dropped by Americans in 1945 on Nagasaki, Japan, the fissionable material

used was

A. Helium 4 B. Plutonium 239 C. Uranium 235 D. Uranium 233

6. The engine of a truck moving a straight road delivers constant power. The distance travelled

by the truck in time t is proportional to

A. t B. t 2 C. √t D. t 3/2

7. The velocity of electron in ground state of

hydrogen atom is

A. 2 x 105

m/s

B. 2 x 106

m/s

C. 2 x 107

m/s

D. 2 x 108

m/s

8. The radius of the first orbit of the electron in a hydrogen atom is 5.3 x 10-11 m; then the radius

of the second orbit must be

A. 15.9 x 10-11 m B. 10.6 x 10 m C. 21.2 x 10-11 m D. 42.4 x 10-11 m

9. A person pushes a rock of 1010Kg mass by applying a force of only 10N for just 4 seconds.

The work done is

A. 1000 Joule B. 0 J C. nearly zero D. positive

10. One can take pictures of objects which are completely invisible to the eye using camera films

which are sensitive to

A. ultra-violet rays B. sodium light C. visible light D. infra-red rays

11. Light from a 100 watt filament bulb is passed through an evacuated glass tube containing

sodium vapour at a high temperature. If the transmitted light is viewed through a spectrometer,

we will observe

A. D1 and D2 lines of sodium with good

intensity

B. dark lines where D1 and D2 lines should have

been observed

C. continuous radiation from the bulb only D. the entire emission spectrum of sodium

12. Under the action of a constant force, a

particle is experiencing a constant acceleration.

The power is

A. zero B. positive

C. negative D. increasing uniformly

with time

13. If in a plane convex lens the radius of curvature of the convex surface is 10 cm and the focal

length of the lens is 30 cm, the refractive index of the material of the lens will be

A. 1.5 B. 1.66 C. 1.33 D. 3

14. A plane convex lens has radius of curvature 30 cm. If the refractive index is 1.33, the focal

length of lens is

A. 10 cm B. 90 cm C. 30 cm D. 60 cm

15. A beam of light is converging towards a point I on a screen. A plane parallel plate of glass

(thickness in the direction of the beam = t, refractive index = µ ) is introduced in the path of the

beam. The convergence point is shifted by

A. t (µ - 1) away B. t (1 + 1/µ ) away C. t (1 - 1/µ ) nearer D. t (1 + 1/µ ) nearer

16 . In Young's double silt experiment the separation between the silts is halved and the distance

between the silts and screen is doubled. The fringe width will be

A. unchanged B. halved C. doubled D. quadrupled

17. Wavelength of red light is λ r, violet rays is λ v and X -ray is λ x then the order of

wavelengths is

A. λ x >λ v >λ r B. λ v >λ x >λ r C. λ r >λ x >λ v D. λ r >λ v >λ

18. The amount of work done by the labourer

who carries n bricks, each of mass m, to the roof

of a house whose height is h is

A. n mgh B. mgh/n C. zero D. ghn/m

19. In LCR circuit in the state of resonance, which of the following statements is correct ? (cos

φ)=

A. 0 B. 0.5 C. 1 D. None of these

20. In LCR circuit, phase difference between voltage and current cannot be

A. 80° B. 90° C. 145° D. 0°

21. If speed is plotted along x-axis and Kinetic energy against y-axis, then the graph obtained has

a shape similar to that of

A. circle B. ellipse C. hyperbola D. parabola

22. A magnetic needle lying parallel to a magnetic field requires w units of work to turn it

through 60°. The torque needed to maintain the needle in this position will be

A. (√ 3) w B. w

C. (√ 3w)/2 D. 2w

23. A vertical straight conductor carries a

current vertically upwards. A point p lies to the

east of it at a small distance and another point Q

lies to west of it at the same distance. The

magnetic field at p is

A. greater than at Q B. same as at Q

C. less than at Q

D. greater or less at Q

depending upon the

strength of the current

24. In a parallel arrangement if (R1 > R2), the power dissipated in resistance R1 will be

A. less than R2 B. same as R2 C. more than R2 D. none of these

25. For a fuse wire to be installed in the supply line in a house which one of the following is

immaterial ?

A. the specific resistance of the material of the

fuse wire B. the diameter of the fuse wire

C. the length of the fuse wire D. none of these

26. If V is voltage applied, Ea is emf drop across the armature, the armature current of a d.c.

motor Ia is given by

A. (V + Ea)/Ra B. Ea/Ra C. V- Ea/Ra D. V/Ra

27. The current of 2.0 amperes passes through a cell of e.m.f. 1.5 volts having internal resistance

of 0.15Ω . The potential difference measured in volts across both the terminals of the cell will be

A. 1.35 B. 1.50 C. 1.00 D. 1.20

28. In this circuit, current ratio i1/i2 depends upon

A. R1, R2

and R

B. R, R1,

R2 and E

C. R1 and

R2 D. E and R

29. A cell of emf E is connected across a resistance r. The potential difference between the

terminals of the cell is found to be V. The internal resistance of the cell must be

A. 2(E - V)V/r B. 2(E - V)r/E C. (E - V) r/V D. (E- V)/r

30. Copper and germanium are both cooled to 70 K from room temperature, then

A. resistance of copper increases while that of

germanium decreases

B. resistance of copper decreases while that of

germanium increases

C. resistance of both decreases D. resistance of both increases

31. The potential difference between the points A and B of the electrical circuit given is

A. 1.5 V B. 1.0 V

32. A moving coil galvanometer has a resistance

of 9.8Ω and gives a full scale deflection when a

current of 10 mA passes tbrough it. The value of

the shunt required to convert it into a mini

ammeter to measure current upto 500 mA is

A. 0.02Ω B. 0.2Ω C. 2Ω D. 0.4Ω

33. The total electrical resistance between the points A and B of the circuit shown in the figure is

A. 9.02 Ω A. 15 Ω

C. 30 Ω D. 100 Ω

34. If the plates of a charged parallel plate capacitor are pulled away from each other

A. capacitance

increases B. energy increases C. voltage increases D. voltage decreases

35. A parallel plate capacitor is charged by connecting its plates to the terminals of a battery. The

battery remains connected and a glass plate is interposed between the plates of the capacitor,

then

A. the charge on plates will be reduced

B. the charge on plates will increase

C. the potential difference between the plates of the capacitor will be reduced

D. the potential difference between the plates of the capacitor will increase

36. A person weighing 70Kg wt lifts a mass of 30 Kg to the roof of a building 10 m high. If he

takes 50 sec to do so,then the power spent is

A. 19.6 W B. 196 W C. 300 W D. 50 W

37. Work done in carrying a charge q from A to B along a semi-circle is

A. 2πrq B. 4πrq

C. πrq D. 0

38. A particle A has charge +q and particle B has charge +4q with each of them having the same

mass m. When allowed to fall from rest through same electrical potential difference, the ratio of

their speed VA :

VB will become

A. 2:1 B. 1:2 C. 1:4 D. 4:1

39. The electric field at a small distance R from an infinitely long plane sheet is directly

proportional to

A. R2/2 B. R/2 C. R-2 D. none of these

40. In the diagram, the electric field intensity will be zero at a distance

A. between -q and +2q charge B. towards +2q on the line drawn

C. away from the line towards

+2q D. away from the line towards -q

41. Wein's displacement law is given by

A. λ m =

constant

B. T/λ m =

constant

C. λ m T =

constant

D. T = λ m

= constant

42. If two electrons are forced to come closer to each to each other, then the potential energy

A. becomes zero B. increases C. decreases D. becomes infinite

43. The specific heat at constant pressure is greater than that of the same gas at constant volume

because

A. at constant volume work is done in expanding the gas

B. at constant pressure work is done in expanding the gas

C. the molecular attraction increases more at constant pressure

D. the molecular vibration increases more at constant pressure

44. The specific heats of CO2 at constant pressure and constant volume are 0.833 J/kg.K and

0.641 J/kg.K respectively. If molecular weight of CO2 is 44, what is the universal constant R?

A. 4.19 x 107 erg/cal B. 848.8 J/gm/K C. 8.448 J/mol/K D. 4.19 J/cal

45. The freezing point of the liquids decreases when pressure is increased, if the liquid

A. expands while freezing B. contracts while freezing

C. does not change in volume while freezing D. none

46. The equation of a transverse wave on a

stretched string is given by

y = 0.05 sin π (2t/0.002 -x/0.1 ) where x and y

are expressed in metres and t in sec.

The speed of the wave is

A.100

m/sec B. 50 m/s C. 200 m/s D. 400 m/s

47. The ratio of velocity of the body to the velocity of sound is called

A. Magic number B. Laplace number C. Natural number D. Mach number

48. Television signals on earth cannot be received at distances greater than 100 km from the

transmission station. The reason behind this is that

A. the receiver antenna is unable to detect the signal at a distance greater than 100 km

B. the TV programme consists of both audio and video signals

C. the TV signals are less powerful than radio signals

D. the surface of earth is curved like a sphere

49. A ball is thrown from a height of h m with an initial downward velocity v0. It hits the ground,

loses half of its Kinetic energy & bounces back to the same height. The value of v0 is

A. √2gh B. √gh C. √3gh D. √2.5gh

50. A thick rope of rubber of density 1.5 x 103

kg/m3 and Young's modulus 5 x 106 N/m2, 8m in

length, when hung from ceiling of a room, the

increase in length due to its own weight is

A. 9.6 x 10-

3m

B. 19.2 x

10-5m

C. 9.6cm D. 9.6mm

51. Water is falling on the blades of a turbine at a rate 6000Kg/min. The height of the fall

is100m. What is the power gained by the turbine?

A. 10KW B. 6KW C. 100KW D. 600KW

52. If momentum of alpha-particle, neutron, proton, and electron are the same, the minimum

K.E. is that of

A. alpha-particle B. neutron C. proton D. electron

53. An electric motor while lifting a given load produces a tension of 4500 N in the cable

attached to the load. If the motor winds the cable at the rate of 2m/s, then power must be

A. 9 kW B. 15 kW C. 225 kW D. 9000 H.P

54. If an electric iron electrons are accelerated through a potential difference of V volts. Taking

electronic charge and mass to be respectively e and m, the maximum velocity attained by the

electrons is

A. 2eV/√m B. √(2eV)/m C. 2m/eV D. v2/8em

55. A particle is moving on a circular track of radius 20 cm with a constant speed of 6 m/s. Its

acceleration is

A. 0 B. 180 m/s2 C. 1.2 m/s2 D. 36 m/s2

56. A satellite of the earth is revolving in a circular orbit

with a uniform speed v. If gravitational force suddenly

disappears, the satellite will:

A. continue to move with the speed v along the original orbit

B. move with the velocity v tangentially to the original orbit

C. fall downward with increasing velocity

D. ultimately come to rest somewhere on the original orbit

57. The kinetic energy K of a particle moving along a circle of radius R depends on the distance

covered s as K = as2. The force acting on the part1cle is

A. 2as2/R B. 2as(1 + s2/R)1/2 C. as(1 + s2/R2)1/2 D. None of these

58. Einstein was awarded Nobel Prize for his work in

A. Photoelectric effect B. Special theory of relativity

C. General theory of relativity D. None of these

59. One second is defined to be equal to

A. 1650763.73 periods of the Krypton clock B. 652189.63 periods of the Krypton clock

C. 1650763.73 periods of the Cesium clock D. 9192631770 periods of the Cesium clock

60. The dimensions of energy and torque respectively are

A. ML2T-2 and ML2T-2 B. MLT2 and ML2T-2 C. ML2T-2 and MLT-2 D. MLT-2 and MLT-2

61. When Benzene diazonium chloride reacts with hypophosphorous acid, it produces

A. benzene B. phenol C. phenylphosphite D. phenylphosphate

62. The reaction of aliphatic primary amine with nitrous acid in cold produces

A. nitrile B. alcohol C. diazonium salt D. secondary amine

63. Ethylamine can be prepared by the action of bromine and caustic potash on

A. acetamide B. propionamide C. formamide D. methyl cyanide

64. The aldol condensation of acetaldehyde results in the formation of

A. CH3COCHOHCH3 B. CH3CHOHCH2CHO C. CH3CH2CHOHCHO D. CH3CH2OH +

CH3COOH

65. Which compound reacts fastest with Lucas reagent at room temperature?

A. Butan-l-ol B. Butan-2-ol C. 2-Methyl propan-l-ol D. 2-Methyl propan-2-

ol

66. The reaction with D2O, (CH3)3CMgCl produces

A. (CH3)3CD B. (CH3)3CO C. (CD3)3CD D. (CD3)3COD

67. The reaction with alcoholic potash, l-chlorobutane gives

A. 1-Butene B. 1-Butanol C. 2-Butene D. 2-Butanol

68. The active nitrating agent during nitration of

benzene is

A. NO3

- B. HNO2

- C. NO2

- D. HNO3

69. The number of sigma and pi bonds in 1-buten-3-yne are

A. 5 sigma and 5 pi B. 7 sigma and 3 pi C. 8 sigma and 2 pi D. 6 sigma and 4 pi

70. The most stable carbonium ion among the cations is

A. sec-butyl B. ter-butyl C. n-butyl D. none of these

71. How many optically active stereo-isomers are possible for butane-2, 3-diol?

A. 1 B. 2 C. 3 D. 4

72. B.P. and M.P. of inert gases are

A. high B. low C. very high D. very low

73. [CO(NH3)5Br] SO4 and [CO(NH3)5 SO4] Br are examples of which type of isomerism ?

A. Linkage B. Geometrical C. Ionization D. Optical

74. The valency of Cr in the complex [Cr(H2O)4 Cl2] + is

A. 3 B. 1 C. 6 D. 5

75. In Nessler's reagent, the ion is

A. Hg+ B. Hg2+ C. HgI2

2 - D. HgI4

2 -

76. In solid CuSO4.5H2O, copper is co-ordinated to

A. five water molecules B. four water molecules C. one sulphate ion D. one water molecule

77. Which of the following is a weak acid?

A. HCl B. HBr C. HP D. HI

78. When SO2 is passed through acidified K2Cr2O7 solution,

A. the solution turns blue B. the solution is decolourised

C. SO2 is reduced D. green Cr2(SO4)3 is formed

79. Which of the following has lowest boiling point?

A. H2O B. H2S C. H2Se D. H2Te

80. Nitric oxide is prepared by the action of dil. HNO3 on

A. Fe B. Cu C. Zn D. Sn

81. The laughing gas is

A. nitrous

oxide

B. nitric

oxide

C. nitrogen

trioxide

D. nitrogen

pentaoxide

82. Ordinary glass is

A. sodium silicate B. calcium silicate

C. calcium and Sodium silicate D. copper silicate

83. The chemical name of phosgene is

A. Phosphene B. Carbonyl chloride C. Phosphorous

oxychloride

D. Phosphorous

trichloride

84. Which one of the following is strongest Lewis acid?

A. BF3 B. BCl3 C. BBr3 D. BI3

85. Three centred bond is present in

A. NH3 B. B2H6 C. BCl3 D. AlCl3

86. Plaster of Paris is

A. CaSO4.H2O B. CaSO4.2H2O C. CaSO4.1/2 H2O D. CaSO4.3/2 H2O

87. Rocky impurities present in a mineral are

called

A. flux B. gangue C. matte D. slag

88. Free hydrogen is found in

A. acids B. water C. marsh gas D. water gas

89. When zeolite, which is hydrated sodium aluminium silicate, is treated with hard water; the

sodium ions are exchanged with

A. H+ B. K+ C. SO4

2- D. Mg2+

90. On passing 0.3 faraday of electricity through aluminium chloride, the amount of aluminium

metal deposited on cathode is (Al = 27)

A. 0.27 g B. 0.3 g C. 2.7 g D. 0.9 g

91. The migration of colloidal particles under influence of an electric field is known as

A. Electro-osmosis B. Brownian movement C. Cataphoresis D. Dialysis

92. In a colloidal state, particle size ranges from

A. 1 to 10 Ao B. 20 to 50 Ao C. 10 to 1000 Ao D. 1 to 280 Ao

93. The half-life of a first order reaction is 69.35. The value of rate constant of the reaction is

A. 1.05-1 B. 0.15-1 C. 0.015-1 D. 0.0015-1

94. Heat of neutralisation of a strong acid and

strong base is always

A. 13.7

Kcal/mol

B. 9.6

Kcal/mol

C. 6

Kcal/mol

D. 11.4

Kcal/mol

95. In exothermic reactions,

A. HR =HP B. HR >HP C. HR < HP D. None of the above

96. Which is a buffer solution?

A. CH3COOH +

CH3COONa

B. CH3COOH +

CH3COONH4

C. CH3COOH + NH4Cl D. NaOH + NaCl

97. The pH of 0.01 M solution of HCl is

A. 1.0 B. 2.0 C. 10.0 D. 11.0

98. In which of the following case does the reaction go fastest to completion?

A. k = 102 B. k = 10 -2 C. k = 10 D. k = 1

99. What quantity of limestone (CaCO3) on heating will give 28 kg of CaO?

A. 1000 kg B. 56 kg C. 44 kg D. 50 kg

100. The percentage of oxygen in NaOH is

A. 40 B. 16 C. 18 D. 10

101. If we take 44 g of CO2 and 14 g of N2,

what will be the mole fraction of CO2 in the

mixture?

A. 1/5 B. 1/3 C. 1/2 D. 1/4

102. The molarity of a solution of Na2CO3 having 5.3 g/250 ml of solution is

A. 0.2 M B. 2 M C. 20 M D. 0.02 M

103. A gas is initially at 1 atm pressure. To compress it to 1/2th of its initial volume, pressure to

be applied is

A. 1 atm B. 4 atm C. 2 atm D. 1/4 atm

104. The value of R in calorie/degree/mole is

A. 0.0831 B. 8.31 C. 8.31 x 107 D. 1.987

105. Which of the following possesses zero resistance at 0 K?

A. Conductors B. Semi-conductors C. Super-conductors D. Insulators

106. CsCl has lattice of the type

A. ccp B. fcc C. bcc D. hcp

107. In the reaction between sodium and chlorine to form sodium chloride,

A. sodium atom is

reduced

B. sodium ion is

reduced

C. chlorine atom is

reduced

D. chloride ion is

reduced

108. Octahedral molecular shape exists in

______ hybridisation.

A. sp3d B. sp3d2 C. sp3d3 D. sp2d2

109. NH3 and BF3 form an adduct readily because they form

A. a co-ordinate bond B. a covalent bond C. an ionic bond D. a hydrogen bond

110. Diagonal relationship exists between

A. Li and Mg B. Na and Mg C. K and Mg D. Al and Mg

111. Which element has the highest electro-negativity?

A. F B. He C. Ne D. Na

112. Loss of a -particle is equivalent to

A. loss of two neutrons only B. loss of two protons only

C. loss of two neutrons and loss of two protons D. none of the above

113. Stable compounds in + 1 oxidation state are formed by

A. B B. Al C. Ga D. Th

114. Sodium hexametaphosphate is used as

A. a cleansing agent B. an insecticide C. a water softner D. an iron exchange

resin

115. The strongest acid is

A.

ClO3(OH)

B.

ClO2(OH)

C.

SO(OH)2

D.

SO2(OH)2

116. Which one among the following pairs of ions cannot be separated by H2S in dilute

hydrochloric acid?

A. Bi3+, Sn4+ B. Al3+, Hg2+ C. Zn2+, Cu2+ D. Ni2+, Cu2+

117. The alkane would have only the primary and tertiary carbon is

A. Pentane B. 2-methylbutane C. 2, 2-

dimethylpropane D. 2, 3-dimethylbutane

118. The product of reaction of alcoholic silver nitrite with ethy1 bromide is

A. ethane B. ethene C. nitroethane D. ethyl a1coho1

119. Formy1 chloride has not been so prepared. Which one of the following can function as

formyl chloride in formulation?

A. HCHO + HCl B. HCOOCH3 + HCl C. CO + HCl D. HCONH2 + HCl

120. Amongst the following, the most basic compound is

A. Benzylarnine B. Aniline C. Acetanilide D. p-Nitroaniline

121. If the roots of x2 - bx + c = 0 are

consecutive integers, then b2 - 4c is equal to

A. 4 B. 3 C. 2 D. 1

122. Condition that the two lines represented by the equation ax2 + 2hxy + by2 = 0 to the

perpendicular is

A. a = - b B. ab = 1 C. a = b D. ab = -1

123. If A ⊆ B, then A ∩ B is equal to

A. Bc B. Ac C. B D. A

124. In order that the function f(x) = (x + 1)cot x is continuous at x = 0, f(0) must be defined as

A. f(0) = 0 B. f(0) = e C. f(0) = 1/e D. none of the above

125. The eccentricity of the ellipse 16x2 + 7y2 = 112 is

A. 4/3 B. 7/16 C. 3/√7 D. 3/4

126. If z1, z2, z3 are three complex numbers in A.P., then they lie on

A. a circle B. an ellipse C. a straight line D. a parabola

127. If [(a2 + 1)2]/(2a - i) = x + iy, then x2 + y2 is

equal to

A. [(a2 +

1)4]/(4a2 +

1)

B. [(a +

1)2]/(4a2 +

1)

C. [(a2 -

1)2]/(4a2 -

1)2

D. none of

the above

128. The vertices of a triangle are (0, 0), (3, 0) and (0, 4). Its orthocentre is at

A. (3/2, 2) B. (0, 0) C. (1, 4/3) D. none of the above

129. The eccentricity of the conic 9x2 - 16y2 = 144 is

A. 5/4 B. 4/3 C. 4/5 D. √7

130. The vertices of a triangle are (0, 3), (-3, 0) and (3, 0). The co-ordinates of its orthocentre are

A. (0, 2) B. (0, -3) C. (0, 3) D. (0, -2)

131. If t is the parameter for one end of a focal chord of the parabola y2 = 4ax, then its length is

A. a [t - (1/t)] B. a [t + (1/t)] C. a [t - (1/t)]2 D. a [t + (1/t)]2

132. The value of cos2 θ + sec2 θ is always

A. equal to 1 B. less than 1

C. greater than or equal to 2 D. greater than 1, but less than 2

133. The number of points of intersection of 2y

= 1 and y = sin x, -2π ≤ x ≤ 2π is

A. 2 B. 3 C. 4 D. 1

134. If sin θ1 + sin θ2 + sin θ3 = 3, then cos θ1 + cos θ2 + cos θ3 =

A. 0 B. 1 C. 2 D. 3

135. The number of solutions in 0 ≤ x ≤ π/2 of the equation cos 3x tan 5x = sin 7x is

A. 5 B. 7 C. 6 D. none of the above

136. One end of a diameter of the circle x2 + y2 - 4x - 2y - 4 = 0 is (5, -6), the other end is

A. (4, -9) B. (-9, -4) C. (4, 9) D. (9, -4)

137. The set of values of m for which both the roots of the equation x2 - (m + 1)x + m + 4 = 0 are

real and negative consists of all m, such that

A. -3 ≥ m or m ≥ 5 B. -3 < m ≤ 5 C. - 4 < m ≤ -3 D. -3 < m ≤ -1

138. Let Pn(x) = 1 + 2x + 3x2 + ...... + (n + 1) xn be a polynomial such that n is even. Then the

number of real roots of P(x) = 0 is

A. 1 B. n C. 0 D. none of the above

139. The next term of the sequence 1, 3, 6, 10,

........ is

A. 16 B. 13 C. 15 D. 14

140. If H is the harmonic mean between P and Q, then H/P + H/Q is

A. (P + Q)/PQ B. PQ/(P + Q) C. 2 D. none of the above

141. A class is composed of two brothers and six other boys. In how many ways can all the boys

be seated at a round table so that the two brothers are not seated besides each other?

A. 4320 B. 3600 C. 720 D. 1440

142. The binomial coefficient of the 4th term in the expansion of (x - q)5 is

A. 15 B. 20 C. 10 D. 5

143. For x ≠ 0, the term independent of x in the expansion of (x - x -1) is equal to

A. 2nCn B. [(-1)n] [2nCn] C. [(-1)n] [2nCn + 1] D. 2nCn + 1

147. Equation of the sphere with centre (1, -1, 1) and radius equal to that of sphere 2x2 + 2y2 +

2z2 - 2x + 4y - 6z = 1 is

A. x2 + y2 + z2 - 2x + 2y - 2z + 1 = 0 B. x2 + y2 + z2 + 2x - 2y + 2z + 1 = 0

C. x2 + y2 + z2 - 2x + 2y - 2z - 1 = 0 D. none of the above

148. Equation of the line passing through the

point (1, 1, 1) and parallel to the plane 2x + 3y +

3z + 5 = 0 is

A. (x - 1)/1 = (y - 1)/2 =

(z - 1)/1

B. (x - 1)/-1 = (y - 1)/1

= (z - 1)/-1

C. (x - 1)/3 = (y - 1)/2 =

(z - 1)/1

D. (x - 1)/2 = (y - 1)/3 =

(z - 1)/1

149. If a, b, c are constants such that a and c are of opposite signs and r is the correlation

coefficient between x and y, then the correlation coefficient between ax + b and cy + d is

A. (a/c)r B. r C. - r D. (c/a)r

150. From a deck of 52 cards, the probability of drawing a court card is

A. 3/13 B. 1/4 C. 4/13 D. 1/13

151. A binomial probability distribution is symmetrical if p, the probability of success in a single

trial, is

A. > 1/2 B. < 1/2 C. < q, where q = 1 - p D. = 1/2

152. The binomial distribution whose mean is 10 and S.D. is 2√2 is

A. (4/5 + 1/5)50 B. (4/5 + 1/5)1/50 C. (4/5 + 5/1)50 D. none of the above

153. tan (cot -1x) is equal to

A. π/4 - x B. cot (tan -1x) C. tan x D. none of the above

154. If f(x) is an odd periodic function with

period 2, then f(4) equals

A. - 4 B. 4 C. 2 D. 0

155. The function f(x) = [(x3 + x2 - 16x + 20)]/(x - 2) is not defined for x = 2. In order to make

f(x) continuous at x = 2, f(2) should be defined as

A. 0 B. 1 C. 2 D. 3

156. Let f and g be differentiable functions satisfying g'(a) = 2, g(a) = b, and fog = 1 (identity

function). Then f'(b) is equal to

A. 0 B. 2/3 C. 1/2 D. none of the above

157. A cone of maximum volume is inscribed in a given sphere. Then the ratio of the height of

the cone to the diameter of the sphere is

A. 3/4 B. 1/3 C. 1/4 D. 2/3

158. The function is decreasing in the interval

A. - ∞ < x < -10/3 B. 0 < x < ∞ C. -3 < x < 3 D. -10/3 < x < 0

159. Suppose that f''(x) is

continuous for all x and

f(0) = f'(1). If

tf'(t) dt = 0,

then the value of f(1) is

A. 3 B. 2 C. 9/2 D. none of

the above

160. Integrating factor of differential equation cos x (dy/dx) + y sin x = 1 is

A. sin x B. sec x C. tan x D. cos x

161. If dx/(1 + 4x2) =

π/8, then the value of a is

A. π/2 B. 1/2 C. π/4 D. 1

162. The maximum value of (log x)/x is

A. 2/e B. 1/e C. 1 D. e

163. If one root of the equation x2 + px + 12 = 0

is 4, while the equation x2 + px + q = 0 has

equal roots, then the value of q is

A. 49/4 B. 4/49 C. 4 D. none of

the above

164. The sum of the series 1/2 + 1/3 + 1/6 + ....... to 9 terms is

A. -5/6 B. -1/2 C. 1 D. -3/2

165. The sum of all two digit numbers, which are odd is

A. 2475 B. 2530 C. 4905 D. 5049

166. How many ten digit numbers can be formed by using the digits 3 and 7 only?

A. 10C1 + 9C2 B. 210 C. 10C2 D. 10!

167. If x and y are real and different and u = x2 + 4y2 + 9z2 - 6xyz - 3zx - 2xy, then u is always

A. non-negative B. zero C. non-positive D. none of the above

168. If a be a non-zero vector, then which of the following is correct?

A. a . a = 0 B. a . a > 0 C. a . a ≥ 0 D. a . a ≤ 0

169. If two vectors a and b are parallel and have

equal magnitudes, then

A. they are equal B. they are not equal

C. they may or may not

be equal

D. they do not have the

same direction

170. In a triangle, the lengths of the two larger sides are 10 and 9 respectively. If the angles are

in A.P., then the length of the third side can be

A. 5 ± √6 B. 3√3 C. 5 D. none of the above

171. The three lines 3x + 4y + 6 = 0, √2x + √3y + 2√2 = 0, and 4x + 7y + 8 = 0 are

A. sides of a triangle B. concurrent C. parallel D. none of the above

172. The pole of the straight line 9x + y - 28 = 0 with respect to the circle 2x2 + 2y2 - 3x + 5y - 7

= 0 is

A. (3, 1) B. (1, 3) C. (3, -1) D. (-3, 1)

173. If the sets A and B are defined as A = { (x, y) : y = ex, x ∈ R }, B = { (x, y) : y = x, x ∈ R },

then

A. A ∪ B = A B. A ∩ B = φ C. A ⊆ B D. B ⊆ A

174. The

value of the

integral

{ f(x)/[f(x) + f(2a

- x)] }dx is equal

to

A. a B. 2a C. 3a D. none of

the above

175. The slope of the normal at the point (at2, 2at) of the parabola y2 = 4ax is

A. 1/t B. t C. - t D. -1/t

176. If z is any complex number such that | z + 4 | ≤ 3, then the greatest value of | z + 1 | is

A. 2 B. 6 C. 0 D. - 6

177. The equation cos x + sin x = 2 has

A. only one solution B. two solutions

C. no solution D. infinite number of solutions

178. The most general value of θ, which satisfies both the equations tan θ = -1 and cos θ = 1/√2

will be

A. nπ + (7π/4) B. nπ + (-1)n (7π/4) C. 2nπ + (7π/4) D. none of the above

179. A spherical ball of radius r placed on the

ground subtends an angle of 60o at a point A of

the ground. Then the distance of the point A

from the centre of the ball is

A. 3r B. 2r C. 4r D. none of

the above

180. In a triangle ABC, a2 cos 2B + b2 cos 2A + 2ab cos (A - B) is equal to

A. c B. c2 C. 2c D. none of the above

For complete question paper download the attachment given below: