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28th November 2014, 09:34 AM
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Join Date: Apr 2013
Re: AIIMS Exam Previous Year Question paper

AIIMS Exam Question paper has questions from following topics :

Physics
Chemistry
Biology (Botany and Zoology)
General Knowledge

Entrance Exam will consists of multiple choice & reason-assertion type question
Each correct answer will be awarded 1 mark
1/3(one-third) of negative marking will be given for each incorrect answer
More than one answer will be given negative marking

1. The radius of curvature of a spherical surface is measured using
A. a spherometer B. spectrometer C. screw gauge D. slide callipers
2. If the dimensions of length are expressed as Gx, Cy, h z, where G, C, h are universal
gravitational constant, speed of light and Plank's constant respectively, then
A. x = 1/2, y = 1/2 B. x = 1/2, z = 1/2 C. y = 1/2, z = 3/2 D. y = + 3/2, z = 1/2
3. The dimensional formula of electric field strength is:
A. MLT-2 I-1 B. MLT-3A-1 C. T-2A-1 D. MLTA-2
4. A man throws a ball in air in such a way that when the ball is in its maximum height he throws
another ball. If the balls are thrown after the time difference of 1 sec, then what wilt be the height
attained by them
A. 19.6 m B. 9.8 m C. 4.9 m D. 2.45 m
5. If the velocity time graph of a body is a straight line sloping downwards, the body has
A. acceleration B. declaration C. zero acceleration D. constant acceleration
6. Which one of the following equations represents the motion of body with finite constant
acceleration?
A. y = at B. y = at + bt2 C. y = at + bt 2 + ct3 D. y = at + bt
7. What is the magnitude of the velocity of the
body when it is projected horizontally from a
point above the ground after 0.2 seconds?
A. √2 ms-1 B. 2√2 ms-1 C. 3√2 ms-1 D. 4√2 ms-1
8. A string can withstand a tension of 25 N. What is the greatest speed at which a body of mass 1
kg can be whirled in a horizontal circle using 1 m length of the string?
A. 25 ms-1 B. 5 ms-1 C. 75 ms-1 D. 10 ms-1
9. An object tied to a piece of string is whirled in a vertical circle, at constant speed. The tention
in the string is maximum at
A. A B. B
C. C D. D
10. The maximum force of friction that comes into play is called
A. limiting friction B. kinetic friction C. static friction D. minimum friction
11. A body of mass 5 Kg is raised vertically to a
height of 10 m by a force of 170 N. The final
velocity of the body is
A. 15 ms-1 B. 17 ms-1 C. 20 ms-1 D. 22 ms-1
12. A cyclist moving at a speed of 17.64 km/h describes a circle of radius 9.8 m. If the cyclist is
held in balance, the co-efficient of friction between the tyre and the ground is
A. 0.25 B. 0.29 C. 0.36 D. 0.35
13. Two bodies with masses m1 and m2 have equal kinectic energies. If P1 and P2 are their
respective momenta, then P1 = P2 is
A. m1 : m2 B. m2 : m1 C. m1
2 : m2
2 D. √m1 : √m2
14. In elastic collision,
A. only energy is conserved B. only momentum is conserved
C. both energy and momentum is conserved D. none of these
15. The velocity of a particle whose kinetic
energy is equal to the rest energy is
A. (1/2) C B. C C. √3/3 D. √3 C
16. The propeller of a ship makes 350 rev. while its speed increases from 200 rpm to 500 rpm.
Then the time taken for this is
A. 1 min B. 1.2 minute C. 5.3 seconds D. 53 seconds
17. The K.E. needed to project a body from the earth's surface to infinity is
A. mgR B. 2 mgR C. 1/2 (mgR) D. 1/4 (mgR)
18. The distance of two planets from the sun are 1013 and 1012 meters respectively. The ratio of
time period of these two planets is
A. √10 B. 1/√10 C. 100 D. 10√10
19. Poisson ratio is the ratio of
A. the linear strain to the lateral strain B. the lateral strain to the linear strain
C. the linear stress to the lateral stress D. the lateral stress to the linear stress
20. Two wires L and M are of the same material
and of the same length, but the diameter of L is
twice that of M stretching force applied to L is
four times that of M. Then the ratio of the
elongation of L to that of M is
A. 1 : 4 B. 4 : 1 C. 1 : 1 D. 2 : 1
21. Which of the substance breaks just beyond the elastic limit?
A. Elastic B. Malleable C. Brittle D. Ductile
22. A stone of mass 16 kg is attached to a string 144-meter-long and is whirled in a horizontal
circle. The maximum tension the string can stand is 16 N. The maximum velocity of revolution
that can be given to the stone without breaking it will be
A. 12 ms-1 B. 14 ms-1

C. 16 ms-1 D. 20 ms-1
23. A vessel containing 0.1 m3 of air at 76 cm of Hg pressure is connected to an evacuated vessel
of capacity 0.09 m3. The resultant air pressure is
A. 20 cm of Hg B. 30 cm of Hg C. 40 cm of Hg D. 50 cm of Hg
24. Two gases A and B having the same temperature T, same pressure P and the same volume V
are mixed. If the mixture is at the same temperature T and occupies a volume V, the pressure of
the mixture is
A. P B. 2P C. P/2 D. 4P
25. A solid ball of metal has spherical cavity
inside it. If the ball is heated, the volume of the
cavity will
A. increase B. decrease C. remain
the same
D.
disappear
26. If the law of heat conduction is written in the form of Ohm's law, then the quantity similar to
electrical resistance is
A. A/dλ B. Ad/λ C. Aλ/d D. d/Aλ
27. The work done from 250 cals of heat is
A. 1045 ergs B. 1045 joules C. 1045 watt D. 1045 N
28. The time taken by a particle executing S.H.M of period T to move the mean position to half
the maximum displacement is
A. T/2 B. T/4 C. T/8 D. T/12
29. Let g be the acceleration due to gravity at
earth's surface and K be the rotational K.E. of
the earth. Suppose the earth's radius decreases
by 2%, then
A. g decreases by 2%
and K decreases by 4%
B. g decreases by 4%
and K increases by 2%
C. g increases by 4%
and K decreases by 4%
D. decreases by 4% and
K increases by 4%
30. A particle of mass m is hanging vertically by an ideal spring of force constant K. If the mass
is made to oscillate vertically, its total energy is
A. maximum at the extreme position B. maximum at the equilibrium
C. minimum at the equilibrium D. same at all position
31. Velocity of sound in CO2 is less than in hydrogen because
A. CO2 is heavier than hydrogen B. CO2 is a compound and hydrogen is an
element
C. CO2 is more soluble in water D. CO2 can be more easily liquefied
32. The velocity of sound in air at room temperature is 110 m/sec. The length of the wave
coming from a vibrating fork at frequency 275 is
A. 0.4 m B. 100 m C. 825 m D. 1375 m
33. The temperature at which velocity of sound in air is double its velocity at 0°C is
A. 435°C B. 694°C C. 781°C D. 819°C
34. Static electricity is produced by
A. induction B. friction
C. both induction and
friction
D. none of the above
35. Surface charge density on a pear shaped conductor is
A. maximum in the middle position B. maximum near the tapering end
C. maximum near the broad end D. equal throughout the surface
36. A given charge situated at a certain distance from an electric dipole in the end on position
experiences a force F. If the distance of the charge is doubled, the force acting on the charge will
be
A. 2F B. F/2 C. F/4 D. F/8
37. A piece of fuse wire melts when the current is 5 A. The energy produced then is 1 J/s. The
resistance of the fuse in ohm is
A. 0.04 B. 0.1 C. 0.5 D. 10
38. The gravitational force between two point masses m1 and m2 at separation r is given by
F = (m1m2)/r2 Then constant K
A. depends on systems of units only B. depends on medium between masses only
C. depends of both masses and units D. none of these
39. A piece of copper and another of germanium
are cooled from room temperature to 80 K. The
resistance of
A. each of them
increases
B. each of them
decreases
C. copper increases and
germanium decreases
D. germanium increases
and copper decreases
40. In a given thermocouple, the temperature of the cold junction is 20°C, while the neutral
temperature is 27°C. What will be the temperature of immersion ?
A. 420°C B. 425°C C. 520°C D. 525°C
41 When different parts of a metal are kept at different temperature and current is passed through
it, heat is either evolved or absorbed. The effect is called
A. Peltier effect B. Seebeck effect C. Thompson effect D. Joule effect
42. A storage battery is to be charged from a d.c. supply which terminal of the battery be
connected to the positive side of the line
A. positive B. negative

C. both positive and negative D. first negative and after the lapse of 5 minutes
positive
43. The force between two parallel wires carrying currents in the same direction is a
A. force of attraction B. force of repulsion
C. no resultant force between the wires D. resultant force acting perpendicular to the
flow of wires
44. The motion of an electric charge produces
A. only an electric field B. only a magnetic field
C. both magnetic and
electric field D. none of the above
45. An ammeter is connected in series with a 2V circuit containing a 2V battery when the switch
is closed, the ammeter shows high deflection and comes to zero. The circuit may contain a
A. resistance of 20Ω B. fuse C. diode D. triode
46. Ferromagnetic substances have
A. very high permeability and susceptibility B. low permeability but high susceptibility
C. high permeability and low susceptibility D. none of these
47. The permeability of the paramagnetic substance is
A. very large B. very small C. negative D. small but more than
1
48. When a material is subjected to a small field
H, the intensity of magnetisation is proportional
to
A. √H B. H C. H2 D. 1/√H
49. In a capacitance circuit the resistance is
A. ω C B. 1/ω C C. 1/√ω C D √ω x C
50. In electromagnetic induction, the induced e.m.f. is independent of
A. change of flux B. time
C. number of lines of force D. resistance of the cells
51. A coil of area A is kept perpendicular to a magnetic field B. If coil is rotated by 1800, then
change in the flux will be
A. BA B. zero C. 2BA D. 3BA
52. The displacement current flows in the dielectric of a capacitor when the P.D. across its plates
A. is increasing with time B. is not decreasing with time
C. has assured a constant value D. becomes zero
53. Electromagnetic waves
A. are longitudinal
waves
B. travel in free space at
the speed of light
C. are produced by D. travel with the same
charges moving with
uniform velocity
speed in all media
54. The frequency of visible light is of the order of
A. 108 Hz B. 1018 Hz C. 1015 Hz D. 1012 Hz
55. A concave mirror of focal length 15cm forms an image at a distance of 40 cm from it. The
distance of the object from the mirror is
A. 10 cm B. 20 cm C. 24 cm D. 30 cm
56. Binoculars are made conveniently short by making use of right angled isosceles prism of
glass. In a normal pair of binoculars, the number of prism is
A. 1 B. 2 C. 4 D. 5
57. A ray incident on a 60° prism of refractive
index √ 2 suffers minimum deviation. The angle
of incidence is
A. 0° B. 45° C. 60° D. 75°
58. Two electron beams having velocities in the ratio of 1 : 2 are subjected separately to identical
magnetic field. The ratio of deflection produced is
A. 4 : 1 B. 1 : 2 C. 1 : 4 D. 2 : 1
59. The ray used for determining the crystal structure of solid is
A. α -ray B. β -ray C. γ -ray D. X-ray
60. For the structural analysis of crystals X-ray are used because
A. X-rays have wavelength of the order of the inter-atomic spacing
B. X-rays are highly penetrating radiation
C. wavelength of X-rays is of order of nuclear size
D. X-rays are coherent radiation
61. The ratio of the molar amounts of H2S needed to precipitate the metal ions from 20 ml each
of 1 M Cd (NO3)2 and 0.5 M CuSO4 is
A. 2:1 B. 1:1 C. 1:2 D. indefinite
62. Among the following elements, which one has the highest value of first ionization potential?
A. Argon B. Barium C. Cesium D. Oxygen
63. Which of the following concepts best explains that o-nitrophenol is more volatile than pnitrophenol?
A. Resonance B. Conjugation C. Hydrogen binding D. Covalent bonding
64. Which of the following statements is false?
A. Ionic compounds generally have low m.p.and b.p.
B. Carbon tetrachloride is a non-polar molecule
C. Anhydrous AlCl3 is a covalent substance
D. A molecule represents a more stable state as compared to individual atoms
65. The chemical species having same number of electrons in the outermost and penultimate
shell is
A. Al3+ B. O2- C. Na+ D. Cl -
66. The solution was prepared by dissolving 0.0005 mol of Ba (OH)2 in 100 ml of the solution. If
the base is assume to ionize completely, the pOH of the solution will be
A. 10 B. 12 C. 2 D. unpredictable
67. In which of the following neutralization will
the enthalpy of neutralization be the smallest?
A. H3PO4
with NaOH
B. NaOH
and
CH3OOH
C. NaOH
with HCl
D. HCl
with
NH4OH
68. The pH of 10 -8 M NaOH will be
A. 6.96 B. 7.04 C. 12.0 D. 8
69. Gas deviates from ideal gas nature because molecules
A. attract each other B. contain covalent bond
C. show Brownian movement D. are colourless
70. Among the following reactions, the fastest one is
A. precipitation of silver chloride by mixing silver nitrate and sodium chloride solutions
B. burning of coal
C. rusting of iron in moist air
D. conversion of monoclinic sulphur to rhombic sulphur
71. When 5.0 g of BaCl2 is dissolved in water to have 106 g of solution. The concentration of
solution is
A. 5M B. 5gmL-1 C. 2.5 ppm D. 5 ppm
72. The unit of electrochemical equivalent is
A. coulomb/gram B. gm-ampere C. gm./coulomb D. gm-ampere-1
73. Adsorption increases when
A. temperature remains
constant
B. temperature
increases
C. temperature
decreases
D. none of the above
74. The number of hours required for a current of 3.0 A to decompose electrically 18 g of water
is
A. 12 hours B. 24 hours C. 6 hours D. 18 hours
75. The number of electrons per second, which pass through a cross section of a copper wire
carrying 10 -16 A, is
A. 16 x 10 -2 e/s B. 1.6 x 10 -3 C. 60 e/s D. 625 e/s
76. 20 ml of HCl having certain normality neutralizes exactly 1.0 g CaCO3. The normality of
acid is
A. 0.1 N B. 1.0 N C. 0.5 N D. 0.01 N
77. The alkali metal used in photoelectric cell is
A. Cs B. Fr C. K D. Rb
78. Calcium is extracted from
A. fused CaSO4 B. fused Ca3(PO4)3 C. fused CaCl2 D. aqueous CaCl2
solution
79. SbCl3 upon hydrolysis yields
A. Sb(OH)3 B. SbO+ C. Sb+3 D. None of the above
80. Which of the following trioxides can exist as
monomer molecule?
A. SO3 in
gaseous
state
B. TeO3 C. SeO3 in
all states
D. SO3 in
solid state
81. Pure chlorine is obtained
A. by heating PtCl4
B. by heating a mixture of NaCl and MnO2 with conc. H2SO4
C. by heating MnO2 with HCl
D. by treating bleaching powder with HCl
82. Which of the following gases is used in very low temperature thermometers?
A. N2 B. H2 C. Ne D. He
83. Number of nucleons in D2 molecule is
A. 4 B. 1 C. 2 D. 3
84. There is no s-s bond in
A. S2O7
2- B. S2O3
2- C. S2O4
2- D. S2O5
2-
85. The ratio of Cp/Cv for inert gas is
A. 1.66 B. 1.33 C. 1.99 D. 2.13
86. Electrolytic reduction method is used in the
extraction of
A. highly
electropositive elements B. transition metals
C. noble metals D. highly
electronegative
elements
87. The metal that is extracted from sea water is
A. Mg B. Au C. Ca D. Fe
88. The compound having blue colour is
A. HgSO4 B. PbSO4 C. CuSO4.5H2O D. CuSO4
89. Which of the following is known as ‘Wol-framite’?
A. Na2CO3 + K2CO3 B. FeWO4 C. SnO2 D. 98% pure Zinc
90. Within each transition series, the oxidation state
A. first decreases till the middle of period and then increases
B. decreases regularly in moving from left to right
C. first increases till the middle of period and then decreases
D. none of the trend is correct
91. Which of the following properties of graphite and diamond are identical?
A. Density B. Crystal structure C. Atomic weight D. Electrical
conductivity
92. Which of the following is an example of copolymer?
A. PAN B. PTFE C.
Polythene
D. Buna-S
93. The reagent which forms crystalline osazone derivative when reacted with glucose is
A. Hydroxylamine B. Benedict solution C. Fehling solution D. Phenylhydrazine
94. To which class of dyes does phenolphthalein belong?
A. Phthalein dyes B. Triphenyl methane
dyes C. Nitro dyes D. Azo dyes
95. Peroxo linkage is present in
A. H2S2O8 B. H2SO3 C. H2S2O7 D. H2SO4
96. Tautomerism is exhibited by
A. RCH2NO2 B. R3CNO2 C. (CH3)2NH D. (CH3)3CNO
97. Latest technique for purification, isolation and separation of organic substances is
A. chromatography B. sublimation C. crystallization D. distillation
98. Lactic acid looses optical activity when reduced with red P and HI because
A. racemic mixture is formed B. spatial arrangement is changed
C. symmetry of the molecule is destroyed D. chirality of the molecule is destroyed
99. In order to convert aniline into
chlorobenzene, the reagents needed are
A.
Cl2/AlCl3 B. Cl2/CCl4
C.
NaNO2/HCl
and CuCl
D. CuCl
100. Which of the following alcohol on dehydration with conc. H2SO4 will yield 2-butene?
A. 2-methyl-2-propanol B. 2-methyl-2-butanol C. 2-propanol D. Sec. Butyl alcohol
101. A compound A has a molecular formula C2Cl3OH. It reduces Fehling solution and an
oxidation gives a monocarboxylic acid B. It can be obtained by the action of chlorine on ethyl
alcohol. A is
A. Chloral B. Chloroform C. Methyl chloride D. Monochloroacetic
acid
102. Which of the following will yield Benzaldimine hydrochloride?
A. benzonitrile and SnCl2/HCl B. nitrobenzene and SnCl2/HCl
C. benzene and hydrazine D. hydrazine and HCl
103. Isopropyl alcohol is heated on a water bath with the suspension of bleaching powder. Which
of the following products will be formed?
A. Propene B. Ethanol C. Isopropyl chloride D. Trichloromethane
104. Which of the following compounds is least basic?
A. C6H5NH2 B. C2H5NH2 C. CH3NH2 D. NH3
105. Iodine dissolves in KI solution due to the
formation of
A. I+ B. I - C. I2
- D. I3
-
106. Hydrogen sulphide exhibits
A. acidic properties B. basic properties C. oxidising properties D. none of the above
107. White Phosphorus reacts with caustic soda. The products are pH3 and NaH2PO2. This
reaction is an example of
A. oxidation B. reduction C. oxidation and
reduction
D. neutralisation
108. Ammonia solution dissolves fairly in
A. Hg2Cl2 B. PbCl2 C. Cu(OH)2 D. AgI
109. Amongst the trihalides of nitrogen, which one is the least basic?
A. NF3 B. NCl3 C. NBr3 D. NI3
110. Among the various allotropes of carbon,
A. diamond is the
hardest
B. graphite is the
hardest
C. lamp black is the
hardest D. coke is the hardest
111. Bone charcoal is used for decolourising sugar because it
A. reduces colouring matter B. oxidises colouring matter
C. absorbs colouring matter D. none of the above
112. Tin (II) chloride is used as a
A. mordant
in dying B. catalyst
C.
oxidising
agent
D. none of
the above
113. Inert pair effect is most prominent in
A. aluminium B. boron C. gallium D. thallium
114. In the alumino thermite process, aluminium acts as
A. an oxidising agent B. a flux C. a reducing agent D. a solder
115. The correct structure of mercurous ion is
A. Hg+ B. Hg2+ C. Hg2
+ D. Hg2
2+
116. Which one of the following is purely ionic?
A. Sodium chloride B. Beryllium chloride C. Lithium chloride D. Carbon tetrachloride
117. A compound 'A' on heating gives a colourless gas. The residue is dissolved in water to
obtain B. Excess CO2 is passed through aqueous solution of B, when C is formed. C on gentle
heating gives back A. The compound A is
A. NaHCO3 B. Na2CO3 C. Ca(HCO3)2 D. CaCO3
118. A solution of sodium sulphate in water is
electrolysed using inert electrodes. The products
at the cathode and anode are respectively
A. H2, O2 B. O2, H2 C. O2, Na D. O2, SO2
119. The metals occurring in the form of their compound in the earth's crust are called
A. matters B. minerals C. alloys D. gangue
120. A commercial sample of hydrogen peroxide is labelled as 10 volume. Its percentage
strength is nearly
A. 1% B. 3% C. 10% D. 90%
121. If (1 + x)n = P0 + P1 + P2x + P2x2 + ...... + Pnxn, then the value of P0 - P2 + P4 - ....... is
A. 2n cosnπ/4 B. 2n/2 cosnπ/4 C. 2n/2 sinnπ/4 D. 2n sinnπ/4
122. If a, b, c and x are real numbers, then x2 + 2bx + c will be positive if
A. b2 > c B. b2 < c C. b2 > 4c D. b2 < 4c
123. The one of the values of (-i)1/3 is
A. (1/2)(√3 - i) B. (-1/2)(√3 + i) C. ± (1/2)(√3 + i) D. none of the above
124. Let A = R ≈ {m}and B = R ≈ {n}, where R is a set of real numbers. Let f(x) = (x - n)/(x - m),
then f is (where m, n are any integers)
A. one-one onto B. many one onto C. one-one into D. many one into
125. Cards are dealt one by one from a well shuffled pack until an ace appears. The probability
that exactly n cards are dealt with before the first ace appears is
A. [4(51 - n)(50 - n)(49 - n)]/(13.51.50.49) B. 4/(52 - n)
C. [48 - (n - 1)]/(52 - n) D. none of the above
126. A determinant is chosen at random from
the set all determinants of order 2 with element
0 and only. The probability that the value of
determinant chosen is positive, is
A. 11/18 B. 11/14 C. 13/16 D. 3/16
127. The value of the
integral | 1 - x | dx equals
A. 1 B. 2 C. 4 D. 0
128. The domain of the function f(x) =
sin -1
log2 (x2/2)
is
A. [-2, 2] ≈ {0} B. [-1, 1] ≈ {0} C. [-2, 2] D. [-1, 1]
129. Lt (1 - x) [(tanπx)/2] equals
x → 0
A. π/2 B. 2/π C. π - 2 D. π + 2
130. The function f(x) = | x |/x; x ≠ 0 and f(x) = 1; x = 0 is discontinuous
at
A. x = 0 B. x = 1 C. x = 2 D. x = -2
131. If x = a (t - sint), y = a (t - cost), then d2y/dx2 is equal to
A. (1/4a)(cosec2 t/2) B. (1/4a)(cosec3 t/2) C. - [(1/4a)(cosec2 t/3)] D. - [(1/4a)(cosec4 t/2)]
132. If x, y, and z are arithmetic, geometric, and harmonic means respectively of two distinct
position numbers, then
A. z < y < x B. x < y < z C. x < z < y D. x > z > y
133. All the solutions of the equation 16xy + x2 + y2 - 8x - 8y - 20 = 0 represents
A. a straight line B. pair of straight lines C. a circle D. a parabola
134. The solution set of an inequality 5 - 15y > 125, y ∈ R is
A. { y | y ∈ R } B. { y | y > 6 } C. { y | y < -8 } D. { y | y ∈ 8 & y ∈ 9 }
135. Unit vector in the xy-plane that makes an angle of 45o with the vector i + j and an angle of
60o with the vector 3i - 4j is
A. i B. 2i C. √2i D. none of the above
136. Given the line (x + 3)/2 = (y - 4)/3 = (z + 5)/2 and the plane 4x - 2y
- z = 1,then the line is
A. perpendicular to the
plane
B. inclined with 60o to
the plane
C. inclined with 45o to
the plane D. parallel to the plane
137. Lt [x sinx + log (1 - x)x]/x3
equals
x → 0
A. 1/2 B. - 1/2 C. 1/4 D. - 1/4
138. Four numbers are such that the first three are in A.P., while the last three are in G.P. The
first number is 6 and common ratio of G.P. is 1/2, then the numbers are
A. 2, 4, 6, 8 B. 6, 4, 2, 1 C. 6, 4, 3, 2 D. 6, 9, 3, 1
139. If the arithmetic and geometric mean of two distinct positive numbers are A and G
respectively, then their harmonic mean is
A. A/√G B. A/G2 C. G2/A D. √A/G
140. The area bounded by the straight lines y = 1, x + y = 2, and x - y = 2 is
A. 11 B. 11/2 C. 1/2 D. 2/11
141. The value of 52 log25 5 is
A. 4 B. 5 C. 6 D. 8
142. If the angle of intersection between the curves y = x2 and y2 = 4x, then the point of
intersection is
A. (0, 0) B. (0, 1) C. (1, 0) D. (1, 1)
143. The pair of points which lie on the same side of the straight line 3x - 8y = 7 is
A. (-4, -3), (1, 1) B. (0, 1), (3, 0) C. (-1, -1), (3, -7) D. (-1, -1), (3, 7)
144. The equation x2 - 8x + 16 = 0 has
A. coincident root B. imaginary root C. unequal root D. none of the above
145. If b = 3, c = 4 and B = π/4, then the number of triangles that can be formed is
A. 1 B. 2 C. 3 D. none of the above
146. Lim (tan mθ)/m equals
θ → 0
A. θ B. - θ C. θ2 D. 0
147. The range of the function f(x)[1 - x] - 1 = 0 is
A. a set of irrational
numbers
B. a set of rational
numbers
C. a set of real numbers D. none of the above
148. If a, b, c are in A.P., then
A. 1/(a - b) = 1/(b - c) B. (a - b)/(b - c) = 2 C. (a - c)/2 = b D. b + c = 2a
149. The sum of all numbers greater than 1000 formed by using the digits 1, 3, 5, 7, no digit
repeated in any number is
A. 106656 B. 101276 C. 82171 D. 81273
150. The vertices of a triangle are represented by the complex numbers 4 - 2i, -1 + 4i, and 6 + i,
then the complex number representing the centroid of a triangle is
A. 3 + i B. 3 - i C. 9 + i D. 9 - i
151. sin (π + θ) sin (π - θ) cosec2θ is equal to
A. sin θ B. cos θ C. 1 D. -1
152. In a triangle ABC, [(b2 - c2)/a]cos A + [(c2 - b2)/a]cos B + [(a2 - b2)/a]cos C is equal to
A. abc B. 1/abc C. a2b2c2 D. 0
153. If ex-radii r1, r2, r3 of a triangle ABC are in H.P., then the sides of
the triangle are in
A. A.P. B. G.P. C. H.P. D. none of
the above
154. The vertices of a triangle are A(6, 4), B(4, -3) and C(-2, 3), which one of the following is
true for triangle ABC?
A. an isosceles triangle B. an equilateral
triangle
C. a right angled
triangle D. none of the above
155. The length of tangent from (5, 1) to the circle x2 + y2 - 6x + 4y + 3 = 0 is
A. 7 B. 14 C. 28 D. 36
156. If a = i + 2j + k
and b = 4i + 3j - 2k, then the projection of b on a
is
A. 2/√29 B. 5/√29 C. 3/√29 D. 2
157. Which one is true?
A. P(A/B) = P(A) +
P(AB)
B. P(A/B) = P(A) -
P(B)
C. P(A/B) =
[P(AB)]/P(B)
D. P(A/B) = P(A) -
P(B/A)
158. If y = (1/2)[log (tanx)], then the value of dy/dx at x = π/4 is
A. 1 B. 0 C. -1 D. ∞
159. If y = (tanx + secx)x, then dy/dx is equal to
A. x secx B. y secx C. m secx D. mxy


160. The equation 2x2 + 3x + 1 = 0 has
A. rational root B. irrational root C. equal root D. none of the above
161. A bag contains 6 red, 5 green, and 7 white balls. The probability of choosing a red or a
white ball is
A. 1/3 B. 11/13 C. 13/18 D. 3/8
162. ∫ (x + 2)/(x + 4) dx is equal to
A. 1/2[tan -1(x - 2/x)] +
c B. tan -1x + c C. 1/2[tan -1(2/x)] + c D. none of the above
163. The length intercepted on the line 3x + 4y + 1 = 0 by the circle (x - 1)2 + (y - 4)2 = 25 is
A. 3 B. 4 C. 5 D. 6
164. The period of the function cos [(3/5)α] - sin [(2/7)α] is
A. 7π B. 10π C. 70π D. 3π
165. The minimum value of xx is attained when x is equal to
A. - e B. + e C. e2 D. 1/e
166. If a, b, c and u, v, w are complex numbers representing the vertices
of two triangles such that c = (1 - r)a + rb and w = (1 - r)u + rv, where r
is a complex number, then the two triangles are
A. similar B.
congruent
C. equal in
area
D. equal
bases
167. In a triangle ABC, if r and R are the in-radius and circum-radius respectively, then (a cos A
+ b cos B + c cos C)/(a + b + c) is
A. r/R B. R/r C. R2/r D. r2/R
168. ∫ [(x + sinx)/(1 + cosx)] dx is equal to
A. x tan(x/2) B. x tan(x/2) + c C. log (1 + cosx) + c D. x log (cos x) + c
169. The differential coefficient of f [log(x)] when f(x) log x is
A. x log x B. x/(log x) C. 1/(x log x) D. (log x)/x
170. If x = 9 sin 2θ (1 + cos 2θ) and y = b cos 2θ (1 - cos 2θ), then the value of dy/dx is
A. (b tan θ)/a B. a/(b tan θ) C. (a tan θ)/b D. ab tan θ
171. The number of solution of the equation (tan x + sec x = 2 cos x) lying in the interval (0, 2π)
is
A. 0 B. 1 C. 2 D. 3
172. If θ and φ are angles in the first quadrant such that tan θ = 1/7 and
sin φ = 1/√10, then
A. θ + 2φ =
90o
B. θ + 2φ =
60o
C. θ + 2φ =
30o
D. θ + 2φ =
45o
173. If a cos 2θ + b sin 2θ = c has a and b as its solution, then the value of tan α + tan β is
A. (c + a)/2b B. 2b/(c + a) C. (c - a)/2b D. b/(c + a)
174. The perimeter of a certain sector of a circle is equal to the length of the arc of a semi-circle
having the same radius, the angle of the sector is
A. 65o 24' B. 64o 24' C. 63o 24' D. 62o 24'
175. The value of tan -1x + cot -1x is
A. π/3 B. π/6 C. 2π/3 D. 2π
176. If a circle cuts a rectangular hyperbola xy = c2 in A, B, C, D and the parameters of these
four points be t1, t2, t3 and t4 respectively, then
A. t1 t2 = t3 t4 B. t1 t2 t3 t4 = 1 C. t1 = t2 D. t3 = t4
177. If the normal to y2 = 12x at (3, 6) meets the
parabola again in (27, -8) and the circle on the
normal chord as diameter is
A. x2 + y2 + 30x + 12y -
27 = 0
B. x2 + y2 + 30x + 12y
+ 27 = 0
C. x2 + y2 - 30x - 12y -
27 = 0
D. x2 + y2 - 30x + 12y -
27 = 0
178. If the normal any point P on the ellipse cuts the major and the minor axes in G and g
respectively and C be the centre of the ellipse, then
A. a2 (CG)2 + b2 (Cg)2 = (a2 - b2)2 B. a2 (CG)2 - b2 (Cg)2 = (a2 - b2)2
C. a2 (CG)2 - b2 (Cg)2 = (a2 + b2)2 D. none of the above
179. The point of intersection of the tangent at the end of the latus rectum of the parabola y2 = 4x
is
A. (-1, 1) B. (1, 1) C. (-1, 0) D. (0, 0)
180. If a, b, c are distinct positive numbers, then the expression (b + c - a)(c + a - b)(a + b - c) -
abc is
A. positive B. negative
C. both negative and positive D. none of the above


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