The All India Institutes of Medical Sciences are a group of autonomous public medical colleges of higher education.
List of few questions are given below:
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
144.
k
a1
a2
a3
b1
b2
b3
c1
c2
c3
is
equal
to
A.
a1
a2
ka3
b1
kb2
b3
kc1
c2
c3
B.
ka1
ka2
ka3
kb1
kb2
kb3
kc1
kc2
kc3
C.
ka1
ka2
ka3
b1
b2
b3
c1
c2
c3
D.
ka1
a2
a3
b1
kb2
b3
c1
c2
kc3
145. One
root of the
equation
3x -
8
3
3
3
3x -
8
3
3
3
3x -
8
= 0 is which
of the
following?
A. 2/3 B. 8/3 C. 16/3 D. 1/3
146. If | A | =
a
x
p
b
y
q
c
z
r
and | B | =
q
-p
r
-b
a
-c
y
-x
z
, then
A. | A | = 2 | B | B. | A | = | B | C. | A | = - | B | D. none of the above
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