Physics
1. International unit of temperature is
a) Degree Celsius
b) Degree Fahrenheit
c) Kelvin
d) Both (a) and (b)

2. Electromagnetic waves are
a) longitudinal waves
b) transverse waves
c) neither longitudinal nor transverse
d) stationary waves

3. The frequency of AC mains in India is
a) 110 C/S
b) 50 C/S
c) 60 C/S
d) 120 C/S

4. Ampere Hour is the unit of
a) quantity of charge
b) strength of current
c) power
d) energy

5. The frequency of an electron circulating at right angles to a uniform magnetic field does not depend upon
a) speed of the charge
b) mass of the charge
c) charge of the particle
d) magnetic field ‘B’

6. ‘n’ cells each of emf ‘E’ and internal resistance ‘r’ send the same current through an external resistance R whether the cells are connected in the series or in parallel. Then
a) R = nr
b) R = r
c) r = nR
d) R = rn

7. One electron volt of energy is
a) 1.6×10?13J
b) 1.6×10?19J
c) 4.8×10?12J
d) 9×109J

8. Ampere-hour is the unit of
a) Charge
b) strength of electric current
c) energy
d) work

9. The ratio of KE required to be given to the satellite to escape from earth to the kinetic energy required to be given to the satellite to revolve around the earth in an orbit just above the earth’s surface is
a) 1:1
b) 2:1
c) 2:1
d) 4:1

10. Two satellites are moving in orbits, R1>R2; then the velocities associated with them is
a) V1
b) V1>V2
c) V1=V2
d) V1=2V2

11. Which of the following is a scalar quantity?
a) Electric current
b) Electric field
c) Acceleration
d) Linear momentum

12. A metallic ball has spherical cavity at its centre. If the ball is heated, what happens to the cavity
a) Its volume decreases
b) Its volume remains constant
c) Its volume decreases, and increases
d) Its volume increases

13. A body of mass m1moving with a uniform velocity of 40m/s collides with another mass m2at rest and then the too together begin to move with a uniform velocity 30 m/s. The ratio of their masses (m1/m2) is
a) 3
b) 4
c) 2
d) 1

14. Which of the following will not have have the dimensions of potential energy?
a) Torque x angular displacement
b) Rotational inertia x (angularfrequency)2
c) Position Vector x momentum
d) Displacement x momentum

15. A tank is filled with water upto a height H. Water is allowed to come out of a hole P in one of the walls at a depth h, below the surface. The horizontal distance is maximum when
a) h =H
b) h=0
c) h = H2
d) h=H3

16. The period of Satellite in a circular orbit of radius R is T. What is the period of another satellite in circular orbit of radius 4R?
a) 4T
b) T8
c) T4
d) 8T

17. A boat crosses the river in shortest possible time. The speed of the boat in still water is 13 m/s. The average speed of the boat while crossing the river comes out to be 12 m/s. What is the velocity of the flow of river
a) 2 m/s
b) 5 m/s
c) 6 m/s
d) none of the above

18. AC measuring instrument measures
a) peak value
b) rms value
c) any value
d) average value

19. A lamp is connected in series with a capacitor and an ac source. What happens if the capacity of the capacitor is reduced ?
a) the lamp shines more brightly
b) the lamp shines less brightly
c) there is no change in the brightness of the lamp
d) brightness may increases or decreases depending on the frequency of ac

20. In a nuclear reaction C611?B511+?++X, X stands for
a) an electron
b) a proton
c) a neutron
d) a neutrino

22. Matter waves are
a) e. m waves
b) transverse waves
c) longitudinal waves
d) waves which exhibit diffraction

23. A steel spring has an unstretched length of 8 cm and when a weight is hung from it, its length becomes 14cm. The period of oscillation of the weight is
a) 0.263 s
b) 0.491 s
c) 0.592 s
d) 2s

24. The current obtained from a rectifier circuit is
a) varying direct current
b) constant direct current
c) half current
d) eddy current

25. Two sources are said to be coherent if
a) they produce waves of the same wavelength
b) they produce waves of the same amplitude
c) they produce waves of the same wave length having constant initial phase difference
d) they are of the same amplitude and same frequency

26. Choose the correct statement
a) Brewsters angle is independent of the wavelength
b) Brewsters angle is independent of the material of the reflecting surface
c) Brewsters angle depends on wave length but not on the nature of the reflecting surface
d) Brewsters angle is different for different wave length

27. A thin layer of water is pressed between two glass plates so that it spreads over an area A. If d is the distance between the plates and Sthe surface tension, the normal force required to separate the plates is
a) AS/d
b) 2SA/d
c) Ad/S
d) S/Ad

28. The pressure energy per unit volume of fluid is (P is the pressure and d is the density)
a) P/d
b) P
c) Pd
d) d/P

29. The unit of electric field is
a) volt× metre
b) volt / Joule
c) volt × Joule
d) volt / metre

30. Which of the following is not an electromagnetic waves?
a) x- ray
b) alpha ray
c) gamma ray
d) light waves

31. Choose the wave relevant for telecommunication
a) ultra violet
b) micro wave
c) infrared
d) x -ray

32. The TV transmission tower in Delhi has a height 240m. The distance up to which the broadcast can be received (taking the radius of the earth as 6.4×106m) is
a) 100 km
b) 50 km
c) 55 km
d) 500 km

33. A parallel place capacitor has a capacitance of 50?F in air and 110?F when immersed in oil. The dielectric constant K of oil is
a) 0.45
b) 0.55
c) 1.10
d) 2.20

34. The lines of magnetic induction around an infinite straight conductor carrying current are
a) parallel to the conductor
b) circular
c) parabolie
d) none of the above

35. AM is used for broadcasting because
a) it is more noise immune than other modulated systems
b) it requires less transmitting power
c) its use avoids receiver complexity
d) no other modulating system can provide the necessary bandwith for high fidelity

36. The escape velocity from the surface of the earth is
a) 8?GdR2
b) 83G?R2d
c) 43G?R2d
d) 4?RG

37. The unit of magnetic induction is
a) oersted
b) weber
c) tesla
d) maxwell

38. A mass M is moving with a constant velocity parallel to the X-axis. Its angular momentum with respect to the origin
a) is zero
b) remains constant
c) goes on increasing
d) goes on decreasing

39. A biconvex lens of focal length 20cm is cut into two plano-convex lenses. The focal length of each part is
a) 10 cm
b) 20 cm
c) 30 cm
d) 40 cm

40. Holes exists in
a) Semiconductors
b) Insulators
c) Conductors
d) None of these

41. At OK, intrinsic semiconductor behaves as
a) a semiconductor
b) a perfect insulator
c) a perfect conductor
d) a superconductor

42. Viscosity of gas is
a) About hundred times less than those of liquids
b) About twenty times less than those of liquids
c) About five hundred times less than those of liquids
d) About ten hundreds times less than those of liquids

43. In a motion with constant acceleration, the velocity is reduced to zero in 5 seconds and after covering a distance of 100 m. The distance covered by the particle in next 5 seconds will be
a) zero
b) 250 m
c) 100 m
d) 500 m

44. The focal length of a concave mirror island the distance from the object to the principal focus is p. Then the ratio of the size of the image to the size of the object is
a) f2p2
b) fp
c) fp
d) f+pp

45. When a sphere rolls without slipping, the ratio of its kinetic energy of translation of its original kinetic energy is
a) 1 : 7
b) 1 : 2
c) 1 : 1
d) 5 : 7

46. The phenomenon of superconductivity was first discovered by
a) Ohm
b) H. Kammerlling Onnes
c) Andre M. Ampere
d) Kirchoff

47. Electric charges (q, q, -2q) are placed at the centers of an equilateral triangle ABC of side l. The magnitude of the dipole moment of the system is
a) 4ql
b) 3ql
c) 2ql
d) ql

48. Which of the following pairs of space and time varying electric field E and magnetic field B would generate a plane electromagnetic wave propagating in the Z- direction?
a) EX,BZ
b) EX,BY
c) EX,BX
d) EZ,BX

49. At a place horizontal component of earth’s magnetic field is equal to the vertical component then the place is situated at
a) poles

b) equator
c) at latitude 450
d) none of these

50. With a bar magnet P in the vibration magnetometer has time period 2 seconds. When an identical bar Q of the same mass and size is placed on the top of P then time period is unchanged. Which of the following statement is true?
a) Q is a bar magnet identical to P and similar poles of P and Q are placed together
b) Q is not a bar magnet
c) Q is a diamagnetic bar of the same dipole moment
d) Q is a bar magnet placed with opposite poles of P and Q together

51. A satellite can be in a geostationary orbit around a planet at a distance r from the centre of the planet. If the angular velocity of the planet about its axis double, a satellite can now be in a geostationary orbit around the planet if its distance from the centre of the planet is
a) r / 2
b) r / 21/3
c) r / (4)1/3
d) r / (8)1/3

52. If the pressure amplitude in a sound wave is tripled, then the intensity of sound is increased by a factor
a) 3
b) 6
c) 9
d) 3

53. V0 and VE represent the velocities, ?0 and ?E the refractive indices of ordinary and extraordinary rays for a doubly refracting crystal. Then
a) V0?VE, ?0??E, if the crystal is calcite
b) V0?VE, ?0??E, if the crystal is quartz
c) V0?VE, ?0??E, if the crystal is calcite
d) V0?VE, ?0??E, if the crystal is quartz

54. Path difference between two interfering waves at a point on the screen is ?/8. The ratio of intensity at this point and that at the central fringe will be
a) 0.853
b) 8.53
c) 85.3
d) 853

55. For what value of a, A?=2i^+aj^+k^ will be perpendicular to B?=4i^?2j^+k^ ?
a) 4
b) 0
c) 3
d) 1

56. If the magnitude of charge of proton and electron in a hydrogen atom were doubled, the energy emitted in the transition from n = 2 to n = 1 would change by a factor of
a) 8
b) 4
c) 1/4
d) 16

57. A capacitor of 2 ?F draws a current of 4 mA when connected across an a.c. of 300 Hz. The voltage drop across capacitor is
a) 1.06 V
b) 1.5 V
c) 2.1 V
d) 6.6 V

58. Photoelectrons are emitted from a metal surface only when
a) metal is initially charges
b) wavelength of incident light is less than some maximum limit
c) frequency of incident light is less than some minimum value
d) incident angle should be greater than the critical angle

59. X-ray tubes operates at 10KV. The ratio of x-ray wavelength to that of de-broglie wavelength is
a) 4.7
b) 6.87
c) 10.062
d) 8.34

60. M be the mass of a body at the surface of earth. What is the weight of the object at the centre of the earth?
a) 0
b) 3.9N
c) 5N
d) 4.9N

Chemistry

61. The reaction between alcohol and carboxylic acids is called
a) Esterification
b) Hydrolysis
c) Saponification
d) Hydrogenation

62. The reaction (CH3)3CBr?H2O(CH3)3C?OH is
a) elimination reaction
b) substitution reaction
c) free radical reaction
d) displacement reaction

63. Which of the following is extracted by the electrometallurgical method?
a) Cu
b) Fe
c) Na
d) Ag

64. Transition metals
a) exhibit diamagnetism
b) undergo inert pair effect
c) do not form alloys
d) show variable oxidation states

65. Enzymes are
a) micro-organism
b) proteins
c) inorganic compounds
d) moulds

66. Which of the following is not a colligative property?
a) ?Tf
b) ?
c) ?Tb
d) Kb

67. The conjugate base of HPO42? is
a) PO43?
b) H2PO4?
c) H3PO4
d) H3PO3

68. All the naturally occuring processes proceed spontaneously in a direction which leads to
a) Decrease of entropy
b) Increase of Enthalpy
c) Increase of free energy
d) Decrease of free energy

69. A F.C.C crystel contains how many atoms in each unit cell
a) 4
b) 6
c) 3
d) 8

70. Among the 2nd group elements, the metal forming predominently covalent compund is
a) Be
b) Mg
c) Sr
d) Ca

71. The quantum number for the outer electron of an atom is are given by n=2, l=0, m=0, s =+12
a) Lithium
b) Helium
c) Hydrogen
d) Boron

72. Which of the following compound does not react with metallic sodium?
a) CH3CH(OH)CH3
b) CH3?O?CH3
c) CH3COOH
d) C2H5OH

73. The type of isomerism exhibited byC6H5C?C6H5N=?C is
a) position
b) functional
c) enantiomerism
d) functional as well as tautomerism

74. In Wurtz reaction the reagent used is
a) Na
b) Na/liq.NH3
c) Na/dry ether
d) Na/dry alcohol

75. Synthetic detergents belong to the class of
a) macromolecular colloids
b) multi molecular colloids
c) associated colloids
d) multi atomic colloids

76. Milk is an example for
a) emulsion
b) gel
c) sol
d) gerosol

77. Which substance chars when heated with conc. H2SO4?
a) carbohydrate
b) hydrocarbon
c) fat
d) protein

78. Amoxillin is semi-synthetic modification of
a) pencillin
b) streptomycin
c) tetracycline
d) chloramphenicol

79. Methane gas producing field is
a) wheat field
b) paddy field
c) cotton field
d) groundnut field

80. Sea divers go deep in the sea water with a mixture of which of the following gases?
a) O2 and He
b) O2 and Ar
c) O2 and CO2
d) CO2 and Ar

81. Gun metal is an alloy of
a) Mg, Sn, Zn
b) Cu, Ni, Zn
c) cu, Sn, Zn, Pb
d) Cu, Sb, Zn, Pb

82. Water gas is produced by
a) passing steam through a red hot coke bed
b) saturating hydrogen with moisture
c) mixing oxygen and hydrogen in the ration of 1 : 2
d) heating a mixture of CO2and CH4 in petroleum refineries

83. A f.c.c. crystal contains how many atoms in each unit cell?
a) 4
b) 6
c) 3
d) 8

84. The equivalent weight of an acid is equal to
a) molecular weight ×acidity
b) molecular weight ×basicity
c) molecular weight /basicity
d) molecular weight /acidity

85. Washing soda has formula
a) Na2Co3.7H2O
b) Na2Co3.10H2O
c) Na2Co3.3H2O
d) Na2Co3

86. The first electron affinity of halogens vary in the order a) F>Cl>Br>I
b) Cl>Br>F>I
c) I>Br>Cl>F
d) Cl>F>Br>I

87. Which of the following metal is obtained by leaching its ore with dilute cyanide solution
a) silver
b) titanium
c) vanadium
d) zinc

88. The number of spherical nodes in 3p orbitals are
a) one
b) three
c) none
d) two

89. The equipment used to carry out nuclear reaction in a controlled manner is called
a) Breedor reactor
b) Nuclear reactor
c) Thermonuclear fission
d) Cyclotron

90. In an experiment set up for the measurement of e.m.f. of a half- cell using a reference electrode and a salt bridge, when the salt bridge is removed the voltage
a) does not change
b) increases to maximum
c) decreases to half the volume
d) drops to zero

91. “One gram molecule of a gas at N.T.P. occupies 22.4 litres.” This fact was derived from
a) Dalton’s theory
b) Avogadro’s hypothesis
c) Berzelius hypothesis
d) Law of gaseous volume

92. For most of the chemical reactions the rate of reaction
a) increases as the reaction proceeds
b) decreases as the reaction proceeds
c) may increase or decrease during the reaction
d) remians constant as the reaction proceeds

93. Which of the following is a colligative property
a) melting point
b) osmotic pressure
c) freezing point
d) sublimation temperature

94. A thermally isolated gaseous system can exchange energy with the surroundings. The mode of transference of energy can be
a) heat
b) work
c) heat and radiation
d) only radiation

95. Which thermodynamic property provides a measure of randomness in the system ?
a) enthalpy
b) PV- work
c) free energy
d) entropy

96. Antibonding MO is formed by
a) Addition of atomic orbitals
b) substraction of atomic orbitals
c) multiplication of atomic orbitals
d) none of these

97. The reaction 2H2O2+O2 is r =k[H2O2]
a) Zero order reaction
b) First order reaction
c) Second order reaction
d) Third order reaction

98. Natural rubber is which type of polymer
a) Condensation
b) addition
c) coordination
d) none of these

99. The ratio of the energy of a photon of 2000 A wavelength radiation to that of 4000 Aradiation is
a) 14
b) 4
c) 12
d) 2

100. Ozone is not
a) An allotrope
b) A powerful oxidising agent
c) Paramagnetic
d) A bent molecule

101. Which is not basic flux?
a) CaCO3
b) lime
c) SiO2
d) CaO

102. The process of converting hydrated alumina into anhydrous alumina is called
a) Roasting
b) Smelting
c) Dressing
d) Calcination

103. Pheromones are chemicals
a) Formed by fermentation process of fungi
b) Secreted by endocrine glands of man
c) Secreted outside the body of insects
d) Plant growth hormones

104. The kinetic theory of gases predicts that total kinetic energy of a gaseous assembly depends on
a) Pressure of the gas
b) Temperature of the gas
c) Volume of the gas
d) Pressure , temperature and volume of the gas

105. C-12 and C-14 isotopes are found as 98% and 2% respectively in any sample. Then, the number C-14 atoms in 12 g of the sample will be
a) 1.5 moles atoms
b) 1.032 x 1022 atoms
c) 2.06 x 1021 atoms
d) 2g atom

106. When enthalpy and entropy change for a chemical reaction are – 2.5 ×103 cals and 7.4 cals deg -1 respectively. Predict that reaction at 298 K is
a) Spontaneous
b) reversible
c) irreversible
d) non – spontaneous

107. Ametal which does not liberate H2(g) from acids is
a) Cu
b) Fe
c) Mn
d) Zn

108. Formaldehyde when treated with KOH (causic potash) gives methanol and potassium formate, the reaction is known as
a) Perkin’s reaction
b) Claisen’s reaction
c) Cannizzaro’s reaction
d) Knoevenagel’s reaction

109. [Co(NH3)4Cl2]No2 and [Co(NH3)4ClNo2]Cl exhibit which type of isomerism
a) Geometrical
b) Optical
c) Linkage
d) Ionisation

110. The enzyme which can catalyse the conversion of glucose to ethanol is
a) Zymase
b) Invertase
c) Maltase
d) Diastase

111. The volume of 0.1MH2SO4 required to neutralise completely 40 mL of 0.2 MNaOH solution is
a) 10 mL
b) 40 mL
c) 20 mL
d) 80 mL

112. The ionization energy and election affinity of an element are 13 eV and 3.8 eV respectively. Its electronegativity on the pauling scale is
a) 4
b) 3.5
c) 3
d) 2.8

113. Which of the following alkaline earth metals is the strongest reducing agent?
a) Ca
b) Sr
c) Ba
d) Mg

114. Which of the following statements are true?
a) Soap solution contains ionic micelles as the colloidal particles
b) A water in oil emulsion easily spreads over surface of water
c) Chemisorption is non-specific
d) Chemisorption occurs in the form of multimolecular layers

115. Asolution was prepared by mixing 50ml of 0.2 M HCl and 50 ml of 0.10 M NaOH. The Hp of the solution is
a) 7.0
b) 2.0
c) 3.0
d) 1.3

116. The function of AlCl3 in Friedal Craft’s reaction is
a) to absorb water
b) to absorb HCl
c) to produce electrophile
d) to produce nucleophile

117. A reducing agent is a substance which can
a) accept electrons
b) donate electrons
c) accept protons
d) donate protons

118. Tollen’s reagent is
a) Ammoniacal cuprous chloride
b) Ammoniacal Cuprous oxide
c) Ammoniacal Silver Bromide
d) Ammoniacal Silver Nitrate

119. In Wurtz reaction the reagent used is
a) Na
b) Na/Liquid NH3
c) Na/Dry ether
d) Na/Dry alcohol

120. Optically active isomers but not mirror images are called
a) Enantiomers
b) Mesomers
c) Tautomers
d) Diastereoisomers

MATHEMATICS

1. 9th term of the series 2 + 7 + 14 + 23 + 34 + —– is
a) 9998
b) 9999
c) 10000
d) none of these

2. f(x) = ?0x t smt dt , then f ‘ (x) =
a) x Cos x +sin x
b) x sin x
c) x Cos x
d) None of these

3. If f(x) is an even function, then f’(x) is
a) neither even nor odd
b) an odd function
c) 0
d) none of thes

4. Given positive integers r > 1, n > 2 and the coefficient of (3r)th and (r + 2)th terms in the expansion of (1+x)2nare equal, then
a) n = 2r
b) n = 3r
c) n = 2r + 1
d) none of these

5. How many different arrangements can be made out of the letters in the expansion A2B3C4, when written is full?
a) 9 !
b) 2 ! + 3 ! + 4 ! (2! 3! 4!)
c) 2 ! 3 ! – 4
d) 9 !________ 2 ! 3! 4 ! 2 ! + 3 ! + 4 !

6. The number of ways in which four men and four women can be seated at round table so that no two women may be together is
a) 576
b) 48
c) 16
d) 144

7. Sum of the focal distances of an ellipse x2a2 + y2b2 = 1 is equal to
a) 121
b) 23
c) 3
d) none of these

8. The slope of a chord of the parabola y2 = 4ax which is normal at one end and which subtends a right angle at the origin is
a) ± 12
b) ± 2
c) ± 2
d) none of these

9. Three normals are drawn to a parabola y2 = 4ax from a given point (x1, y1). The algebraic sum of the ordinates of their feet is
a) -a
b) a
c) 1
d) 0

10. The centres of a set of circles, each of radius 3, lie on the circle x2 + y2= 25 The locus of any point in the set is
a) 4? x2 + y2 ? 64
b) x2 + y2 ? 25
c) x2 + y2? 25
d) 3 ? x2 + y2 ? 9

11. If the distances from the origin of the centres of the three circles x2 + y2 – 2 ?i x = c2(i = 1, 2, 3) are in G.P., then the lengths of the tangents drawn to them from any point on the circle x2 + y2 = c2are in
a) A.P.
b) H.P
c) G.P.
d) none of these

12. The lines 3x – 4y + 4 + 0 and 6x – 8y – 7 = 0 are tangent to the same circle. The radius of this circle is
a) 45
b) 710
c) 34
d) 32

13. The equation of the chord of the circle x2 + y2 – 4x = 0 whose mid-point is (1, 0) is
a) y = 2
b) y = 1
c) x = 2
d) none of these

14. If the equation ax2 + by2+ 2hxy + 2gx + 2fy + c = 0 represents a circle, then the condition will be
a) a = b, c = 0
b) f = g and h = 0
c) a = b, h = 0
d) f = g and c = 0

15. A point equidistant from the lines 4x + 3y + 10 = 0, 5x – 2y + 26 = 0 and 7x + 24y – 50 = 0 is
a) (1, -1)
b) (1, 1)
c) (0, 0)
d) (0, 1)

16. The equations of the sides of a triangle are x = 0, y = m1 x + c1 and y = m2 x + c2. The area of the triangle is
a) C1?C2m1?m2
b) 12(c1?c2)2m1?m2
c) 12C1?C2(m1?m2)2
d) (c1?c2)2(m1?m2)2

17. The number of possible switching circuits with three switches is
a) 2
b) 3
c) 4
d) 5

18. If x,y are any two element of a Boolean algebra, then (x+y).(x+y’).(x’+y) is equal to
a) x+y
b) x.y
c) x’+y
d) x.y’

19. If a,b,c ?B then a+b+a’.b’ =
a) 0
b) 1
c) a’+b’
d) a+b

20. The statement with truth value T is,
a) A prime number greater than 100 is odd
b) The intersection of two nonempty sets is none mpty
c) Between two distinct natural numbers, there is a natural number.
d) 4 is aprime number

21. A statement among the following is,
a) Every rectangle is a parallelogram
b) Who is the father of geometry?
c) Is 1a a prime number?
d) Sit down.

22. The area of the curve ( x2/4) + (y2/9) = 1 in sq.units is
a) 6?
b) 4?
c) 3?
d) 7?

23. The function of f(x) = 2×3 – 3×2 – 12x + 4 has a
a) minima 1
b) maxima 1
c) maxima 11
d) minima 2

24. If y = log10x then dy/dx =
a) 1x
b) 0
c) log10x
d) 1xlog10

25. d/dx (sin?1 x + Cos?1 x) =
a) 1
b) ?/2
c) 0
d) 2

26. Ltx??>0X??>0 logCosxx2 equals
a) 0
b) 1
c) 2
d) 3

27. The value of ‘a’ for which the function f(x) = a sin x + (1/3) has an extremum ar x = ?/3 is
a) 1
b) -1
c) 2
d) 0

28. If x = a cos3? and y = a sin3? , then 1+ (dy/dx)2 =
a) tan2 ?
b) cot2?
c) sec2?
d) cosec2?

29. ?02 ddx [sin - 1[2x1+x2] ] dx ix equal to
a) 0
b) ?
c) ?/2
d) ?/4

30. The side of an equilateral triangle are increasing at the rate of 2 cms/sec. The rate at which the area increases, when the side is 10 cms is
a) 3 sq.units/sec
b) 10 sq.units/sec
c) 10 3sq units sec.
d) 103 sq.units.sec

31. Which of the following is not true ?
a) A polynomial function is always continuous
b) A continuous function is always differentiable
c) a differentiable function is always continuous
d) ex is continuous for all x

32. If the displacement s of a particle at time t is given by s2 = at2 + 2bt + c, then acceleration varies a
a) 1/s2
b) 1/s
c) 1/s3
d) s3

33. If a is such that ?0a x dx ? a + 4, then
a) 0 ? a ?4
b) -2 ? a ?0
c) a ? -2 or a ?4
d) -2 ? a ?4

34. Which of the following is equal to ?f02?(sinx)dx
a) 2?0? f (sinx)dx
b) ?f??(sinx)dx
c) 2?0? f (sinx)dx
d) None of the above

35. If n1, n2 are positive integers, then (1+i)n1 + (1+i3)n + (1+i5)n2 +(1+i7)n2 is a real number iff
a) n1 = n2 +1
b) n1 + 1 = n2
c) n1 = n2
d) n1, n2 are any two +ve integers

36. Let z1 and z2be two complex numbers such that z1 ? z2and ?z1???z2?. If z1has a positive real part and z2 has negative imaginary part, then z1 + z2 may be
a) zero or purely imaginary
b) real and positive
c) real and negative
d) none of these

37. The smallest positive integer which can be expressed as sum of two different cubes in two different ways is
a) 1000
b) 729
c) 1729
d) 1728

38. Irrational numbers are;
a) irrational decimals
b) non-terminating, recurring decimals
c) non-terminating, non recurring decimals
d) none of these

39. Which of the following is not a measure of dispersion?
a) variance
b) mean deviation
c) standard deviation
d) mode

40. The angle between the lines x = 1, y = 2 and y = -1 and z = 0 is
a) 90o
b) 30o
c) 60o
d) 0o

41. For every point (x, y, z) on xy-plane
a) x = 0
b) y = 0
c) z = 0
d) x = 0, z = 0

42. A tetrahedron of volume V = 5 has three of its vertices at the points. A (2, 1, -1), B (3, 0, 1) and C (2, -1, 1). The fourth vertex D lies on the y axis. Then D is the point
a) (0, 8, 0)
b) (0, -7, 0)
c) (0, 8, 0) or (0, -7, 0)
d) none of these

43. The numerical difference of the roots of x2 – 7x – 9 = 0 is
a) 5
b) 25
c) 97
d) 85

44. Both the roots of the equation ax2 + bx + c = 0, a ? 0, are zero if
a) b = 0, c = 0
b) b = 0, c ? 0
c) b ? 0, c = 0
d) b ? 0, c? 0

45. The angle of elevation of the top of a T.V. tower from three points A, B , C in a straight line through the foot of the tower are a, 2a, 3a respectively. If AB = a, the height of the tower is
a) a tan a
b) a sin a
c) a sin 2a
d) a sin 3a

46. The expression (a+b+c)(b+c?a)(c+a?b)(a+b?c)4b2c2 is equal to
a) cos 2 A
b) 1 – cos A
c) sin2 A
d) 1 + cos A

47. If sin A = sin B, cos A = cos B, then the value of A in terms of B is
a) n? + B
b) n? + (?1)n B
c) 2n?+ B
d) 2n? – B

48. The roots of the equation 4×2 – 25x + 1 = 0 are
a) sin 36o,sin 18o
b) sin 18o,cos 36o
c) sin 36o,cos18o
d) cos18o,cos 36o

49. If cos (a + b) = 0, then sin (a + 2b) is equal to
a) – sin a
b) cos a
c) sin b
d) cos b

50. If angle B of the triangle ABC is 45o, then (1 + cot A) (1 + cot C) is equal
a) -1
b) 0
c) 1
d) 2

51. The value of sin 2?8 + sin23?8+ sin25?8 + sin27?8 is
a) 1
b) 2
c) 118
d) 218

52. For m ? n, if tan m? = tan n?, then the different values of ? are in
a) no particular sequence
b) G.P.
c) H.P.
d) A.P.

53. The maximum value of 12sin? – 9sin2? is
a) 3
b) 4
c) 5
d) none of these

54. ?? and e are
a) natural numbers
b) integers
c) rational numbers
d) irrational numbers

55. Which of the following is the empty set?
a) { x : x is a real number x2 – 1 = 0}
b) { x : x is a real numberx2 + 1 = 0}
c) { x : x is a real number x2 – 9 = 0}
d) { x : x is a real number x2 = x + 2}

56. Sets of A and B have 3 and 6 elements respectively. What can be the minimum number of elements in A ? B?
a) 3
b) 6
c) 9
d) 18

57. If n ? 2, then the number of onto mappings or surjections that can be defined from { 1,2,3,…..,n} onto { 1, 2} is;
a) n2
b) 2n
c) n2 – 2
d) 2n2 – 2

58. Let ƒ: X ? Y be a given function, then f?1 exists (or ƒ is invertible) if;
a) ƒ is one-one
b) ƒ is onto
c) ƒ is one-one but not onto
d) ƒ is one-one and onto

59. Let S = { 0, 1, 5, 4, 7}. Then the total number of subsets of S is;
a) 64
b) 32
c) 40
d) 20

60. Two sets A, B are disjoint if:
a) A U B = ?
b) A ? B? ?
c) A ? B = ?
d) A – B = A

61. The number of log2 7 is
a) an integer
b) a rational number
c) an irrational number
d) a prime number

62. In the group (Z, *) of all integers, where a x b=a+b+1 for al a,b, ? Z, the inverse of -2 is
a) – 2
b) 0
c) – 4
d) 2

63. A plane which passes through the point (3, 2, 0) and the line
x ? 41 = y?75 = z ? 44 is
a) x – y + z=1
b) x + y +z=5
c) x+ 2y- z=1
d) 2x – y+z=5

64. The two lines x= ay + b, z= cy + d and x= a?y+b?, z=c?y+d? are perpendicular, if
a) aa?+cc?=?1
b) aa?+cc?=1
c) aa?+cc?=?1
d) aa?+cc?=1

65. The area of the triangle formed by the intersection of a line parallel to x-axis and passing through P(h, k) with the lines y = x and x+y =2 is 4h2. The locus of P is
a) 2x?y?1=0
b) 2x+y+1=0
c) 2x?y+1=0
d) 2x+y?3=0

66. The hyberbola x2a2?y2b2=1 has its conjugate axis 5 and passes through the point (2, -1). The length of a latus rectum is
a) 5429
b) 5829
c) 29
d) 294

67. If tangents are drawn to the ellipse x2+2y2=2then the locus of the midpoint of the intercept made by the tangents between the coordinate axes is
a) 12×2+14y2=1
b) 14×2+12y2=1
c) x22+y24=1
d) x24+y22=1

68. ?r=2431logrn=
a) logn43
b) log43n
c) log43!n
d) 1log43!n

69. If log0.3(x?1)
a) (1,2)
b) (2,?)
c) (?2,0)
d) none of these

70. The range of x2?2x+3×2?2x?8, x?R is
a) R
b) R?[?29,1]
c) R?(?29,1]
d) [?29,1]

71. If x2+px+q=0 and x2+p?x+q?=0 have one common root, then the common root is
a) q?q?p??p
b) q?q?p?p?
c) pq??p?qp?q?
d) pq??p?qq??q

72. If one root of the equation (a?b)x2+ax+1=0 isdouble the other and if a is real, then the greatest value of b is
a) 76
b) 87
c) 98
d) 109

73. If a
(x?a)(x?c)+2(x?b)(x?d)=0 has
a) imaginary roots
b) equal roots
c) distinct real roots
d) none of these

74. If a, b, c are the sides of a scalene triangle, then the expression (b+c?a) (c+a?b)(a+b?c)?abc is
a) non positive
b) non negative
c) positive
d) negative

75. In a triangle PQR,R=?2. If tanP2 and tanQ2 are the roots of the equation ax2+bx+c=0,then
a) a=b+c
b) b= c+ a
c) c= a+b
d) b=c

76. Let ?1, ?2 and ?1, ?2 be the roots of ax2+bx+c=0 and px2+qx+r=0 respectively. If the system of equations ?1y+?2z=0,?1y+?2z=0 has nontrivial solution, then
a) abc=pqr
b) ab2c=pq2r
c) acb=prq
d) acb2=prq2

77. If the difference between the roots of x2+ax+b=0 is same as that ofx2+bx+a=0,a?b, then
a) a +b+4=0
b) a+b-4=0
c) a- b- 4=0
d) a- b+4=0

78. If both the roots of the equation x2?2mx+m2?1=0 lie between ?2and4, then m?
a) (?1,3)
b) (1,4)
c) (?2,0)
d) (3,?)

79. The slopes of tangents to the circle (x?6)2+y2=2 which passes through the focus of the parabola y2=16x are
a) ±2
b) 12,?2
c) ?12,2
d) ±1

80. If two distinct chords of a parabola y2=4ax passing through the point (a, 2a) are bisected by the line x+y=1, then the length of the latus-rectum can be
a) 2
b) 7
c) 4
d) 5

81. The number of solution ofthe equation tanx+secx=2cosx in [0,2?] is
a) 0
b) 1
c) 2
d) 3

82. Which of the folowing data do not determine an acute angled triangle?
a) a, sin A, sin B
b) a, b, c
c) a, sin B, R
d) a, sin A, R

83. In ?ABC , if acos2C2+ccos2A2 = 3b2,then a, b, c
a) are in A.P
b) are in G.P
c) are in H.P
d) satisfy a + b = c

84. In a ?ABC , if r1=3s , then A=
a) ?3
b) ?2
c) 2?3
d) 3?4

85. The equation of the circle passing through (1,1) and the points of intersection of the circles x2+y2+13x?3y=0 and 2×2+2y2+4x?7y?25=0 is
a) 4×2+4y2?30x?10y?25=0
b) 4×2+4y2+30x?13y?25=0
c) 4×2+4y2?17x+10y+25=0
d) none

86. The centre of a circle passing through the points (0,0) and (1,0) and touching the circle x2+y2=9 is
a) (32,12)
b) (12,32)
c) (12,52)
d) (12,?2)

87. Let AB be a chord of the circle x2+y2=r2 subtending a right angle at the centre.Then the locus of the centroid of the triangle PAB as P moves on the circle is
a) parabola
b) circle
c) ellipse
d) pair of lines

88. If x>0,y>0,2x?5y=20,3x+my=m,thenm?
a) [0,30)
b) (?152,0)
c) (?152,30)
d) R?[?152,30]

89. If |(xr)(x+1r+1)(x+2r+2)(yr)(y+1r+1)(y+2r+2)(zr)(z+1r+1)(z+2r+2)|=|(xr)(xr+1)(xr+2)(yr)(yr+1)(yr+2)(zr)(zr+1)(zr