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April 9th, 2015, 04:11 PM
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Re: Previous year question papers of B.Tech entrance exam of Guru Gobind Singh Indraprast

As you want I ma here providing you question papers of B.Tech entrance exam of Guru Gobind Singh Indraprastha University Common Entrance Test.

Sample paper :
B.Tech entrance exam Sample paper

1. If the ground state energy of H-atom is 13.6 eV, the energy required to ionize an H-atom from
second excited state is :
A. 1.51 eV B. 3.4 eV C. 13.6 eV D. 12.1 eV
2. The binding energy per nucleon is maximum in case of:
A. 2He4 B. 26Fe56 C. 56Ba14 D. 92U23
3. The energy of a photon of wavelength λ is :
A. hc λ B. hc/λ C. λ /hc D. hλ /c
4. Radio waves of constant amplitude can be generated with :
A. rectifier B. filter C. FET D. oscillator
5. Great bear is a
A. Star B. Galaxy C. Constellation D. Planet
6. Monoclinic crystal lattice has dimensions
A. α = β = γ B. α = β = 90°, γ ≠ 90°
C. α ≠ β ≠ γ D. None of these
7. Which of the following relations is correct ?
A. E2 = pc2 B. E2 = p2c C. E2 = p2c2 D. E2 = p2/c2
8. During nuclear disintegration, the following is true
A. mass in conserved B. energy is conserved
C. kinetic Energy is conserved D. momentum is conserved
9. The nucleus forces are
A. charge-dependent B. spin-dependent C. charge-symmetric D. long range
10. During radio-active decay, the negative charged particle is emitted because of
A. X-rays B. β emissions
C. Transmutation of neutron into proton D. None of these
11. Particle in β - decay is
A. Neutron B. Proton C. Electron D. Photon
12. Energy in stars is produced by
A. fusion B. fission C. radioactive decay D. artificial
transmutation
13. Atomic packing fraction in bcc lattice is
A. 1/√ π B. √ π C. π /√ 2 D. None of these
14. The count of α - particles decreases from 28,800 to 1,800 in 48 hours, the half-life of this
radioactive element will be
A. 4 hours B. 8 hours C. 12 hours D. 16 hours
15. Binding energy will be maximum in the case of
A. He3 B. He2 C. H2 D. He4
16. Binding energy per nucleon in heavy nuclei is of the order of
A. 8 MeV B. 8 eV C. 80 eV D. 80 MeV
17. Complete the series He6 ---> e + Li6 + ?
A. nutrino B. anti-nutrino C. proton D. neutron
18. Line spectrum can be obtained from
A. Sun B. Candle C. Mercury Vapour
Lamp D. Electric Bulb
19. What is radius of 1st Bohr's orbit in a Hydrogen atom ?
A. 0.53 x 10-10 cm B. 0.53 x 10-8 cm
C. 2.73 x 10-10 cm D. 2.73 x 10-12 cm
20. What is the energy of an electron of Hydrogen in its ground state ?
A. -13.6 eV B. 0 C. infinity D. 13.6 eV
21. What is the rest mass of a photon ?
A. 0 B. 13.6 eV C. 1 MeV D. 3.1 x 10-27 kg
22. Two lenses of powers 12D and - 2D are placed together, the combined focal length will be
A. 1 cm B. 10 cm C. 100 cm D. 1000 cm
23. The critical angle is maximum when light travels from
A. water to air B. glass to air C. glass to water D. air to water
24. A rider on a horse back falls forward when the horse suddenly stops. This is due to
A. inertia of horse B. inertia of rider
C. large weight of the horse D. losing of the balance
25. Fundamental particle in an electro-magnetic wave is
A. photon B. electron C. phonon D. proton
26. The wavelength is least in case of
A. γ -rays B. X-rays C. infrared D. ultraviolet
27. The speed of electro-magnetic radiation in vacuum is
A. µ0 ε0 B. √ (µ0 ε0) C. 1/µ0 ε0 D. 1/√ (µ0 ε0)
28. Power factor in LC oscillations is
A. 0 B. 1 C. 1/4 D. 1/√ 2
29. 220 V is changed to 2,200 V through a step-up transformer. Th current in primary is 5 A,
what is the current in the secondary ?
A. 5 A B. 50 A C. 0.5 A D. 500 A
30. When a bar is placed near a strong magnet, it is repelled, then the material of the bar is
A. Dimagnetic B. Ferromagnetic
C. Paramagnetic D. Anti-ferrimagnetic
31. Electron enters into a magnetic field at an angle of 60°, its path will be
A. straight line B. circle C. parabola D. helix
32. One electron is moving in electric and magnetic fields, it will gain energy from:
A. electric field B. magnetic field C. both of these D. none of these
33. Force acting on a conductor of length 5 m carrying current 8 amperes kept perpendicular to
the magnetic field of 1.5 tesla is
A. 10 N B. 100 N C. 15 N D. 50 N
34. If E = at - bt3 , the neutral temperature is
A. -2a/b B. -2b/a C. √ (a/3b) D. -b/2a
35. The charge carriers in an electrolyte are
A. negative ions B. positive ions C. both A and B D. none of these
36. When 4 equal resistors are connected in series with a battery and dissipate a power of 10 W,
what will be the power dissipated through any of them if it is individually connected across the
same battery?
A. 40 W B. 10/3 W C.90W D.10W
37. Cell of emf 1 volt is connected across a potentiometer, balancing length is 600 cm. What will
be the balancing length for 2.5 volts ?
A. 400 cm B. 600 cm C. 1500 cm D. 1200 cm
38. A Wire of resistance R is stretched to twice its original length, what is its new resistance ?
A. 4 R B. R/9 C. 3 R D. R/3
39. The charge carriers in super-conductors are
A. electrons B. protons
C. phonons D. photons
40. 8 drops of mercury are combined to form a bigger single drop. The capacitance of a single
big drop and of the single small drop will be in the ratio
A. 2 : 1 B. 1 : 8 C. 8 : 1 D. 1 : 2
41. A dipole is placed in a uniform electric field, its potential energy will be minimum when the
angle between its axis and field is
A. 0 B. π C. π /2 D. 2π
42. Charge of 2 c is placed at the centre of a cube of volume 8 cc, what is electric flux passing
through one face ?
A. 1/(3ε0) B. (1/2) ε0 C. 2/ε0 D. 3/ε0
43. 1 MeV is
A. 1.6 x 10-
19 J
B. 1.6 x 10-
13 J
C. 1.6 x 10-
16 J
D. 1.6 x 10-
9 J
44. Fundamental frequency of a sonometer wire is n, if the tension is made 3 times and length
and diameter are also increased 3 times, what is the new frequency ?
A. n/3√ 3 B. 3n C. √ 3 n D. 3√ 3 n
45. What is the number of beats heard by the driver of a taxi which is approaching a wall at a
speed 30 km/hr and emitting a sound of frequency 300 Hz ? Velocity of sound = 330 m/s.
A. 10 B. 15
C. 20 D. 25
46. A person is standing on a railway platform and a train is approaching, what is the maximum
wavelength of sound he can hear ? Given wavelength of whistle = 1 m; speed of sound in air =
330 m/s; speed of the train = 36 km/hr.
A. 1 m B. 32/33 m C. 33/32 m D. 12/13 m
47. Velocity of sound in open-ended tube is 330 m/s, the frequency of waves is 1.1 kHz and the
length of tube = 30 cm, which harmonic will it emit ?
A. 2nd B. 3rd C. 4th D. 5th
48. If both sprong constants K1 and K2 are
increased to 4K1 and K2 respectively, what will
be the new frequency, if f was the original
frequency?
A. f B. 2f
C. (1/2) f D. 4f
49. The radii of two drops are in the ratio 3 : 2, their terminal velocities are
A. 9 : 4 B. 2 : 3 C. 3 : 2 D. 2 : 9
50. When a body is raised to a height R (which is the radius of earth), the change in its P.E. will
be
A. mgR B. 2 mgR C. mgR/2 D. 4 mgR
51. If the length of a simple pendulum is tripled, what will be its new time period? (T = original
time period)
A. 0.7 T B. 1.7 T C. T/2 D. T
52. A pendulum of length 2m left at P. When it reaches Q, it looses 10% of its total energy due
to air resistance. The velocity at Q is
A. 6m/s B. 1m/s
C. 2m/s D. 8m/s
53. A lift is falling freely under gravity, what is
the time period of a pendulum attached to its
ceiling ?
A. zero B. infinity C. one
second
D. two
second
54. What is the ratio of the moment of inertia of two rings of radius r and nr respectively about
an axis perpendicular to their plane and passing through their centres?
A. 1 : n2 B. 1 : n C. 1 : 2n D. n2 : 1
55. Beta-particle is emitted from the nucleus of mass number A, with velocity V, what is the
recoil speed of the nucleus?
A. Me V/(A - Me) B. 4V/(A + 4) C. V D. V/(A - 4)
56. If an alpha particle collides head-on with the nucleus, what is the impact parameter ?
A. zero B. infinity C. 10-10m D. 1010m
57. If momentum decreases by 20%, kinetic energy will decrease
A. 40% B. 36% C. 18% D. 8%
58. If two balls are projected at angles 60° and 45° and the total heights reached are same, what
is the ratio of their initial velocities ?
A. √ 3 : √ 2 B. √ 2 : √ 3 C. 3 : 2 D. 2 : 3
59. Which one is a vector quantity ?
A. heat B. couple C. energy D. volume
60. Gravel is dropped on to a conveyor belt at a rate of 0.5Kg s-2. The extra force in Newton
required to keep the belt moving at 2 ms-2 is
A. 1 B. 2 C. 4 D. 5
61. An element with atomic number 20 is
A. an alkali
metal
B. an
alkaline
earth metal
C. a
halogen
D. a noble
gas
62. When supercooled water suddenly freezes, the free energy of the system
A. increases B. decreases C. remains same D. becomes zero
63. The density of neon is highest at
A. STP B. 0oC, 2 atm C. 273°C, 1 atm D. 273°C, 2 atm
64. Cadmium in a nuclear reactor acts as
A. nuclear fuel B. neutron absorber
C. a moderator D. neutron liberator to start the chain
65. The end product of 4π series
A. 82Pb203 B. 92Pb207 C. 82Pb208 D. 82Bi204
66. Haemoglobin is a co-ordination compound in which the central metal atom is
A. iron B. cobalt C. sodium D. manganese
67. The element californium belongs to the family of
A. actinide
series
B. alkaline
earth
family
C.
lanthanide
series
D. alkali
metal
family
68. The coloured discharge tube for advertisements contain
A. argon B. xenon C. helium D. neon
69. Which of the following is the strongest base?
A. PH3 B. AsH3 C. NH3 D. SbH3
70. Canizzaro reaction is not given by
A.
Triethylacetaldehyde B. Acetaldehyde C. Benzaldehyde D. Formaldehyde
71. Which of the following statements is not true for alcohols?
A. Lower alcohols have fiery pungent and strong smell
B. As molecular mass increases, boiling point also increases
C. Lower alcohols are water insoluble and their solubility increases with molecular weight
D. Lower alcohols are water insoluble and their solubility decreases with molecular weight
72. Formaldehyde when heated with CH3CH2CH2MgBr gives
A. Primary alcohol B. Secondary alcohol C. Tertiary alcohol D. Acetone
73. A compound of molecular formula C3H8O on oxidation gives a
compound of formula C3H6O2. The original compound is
A. Primary
alcohol
B.
Secondary
alcohol
C.
Aldehyde
D. Tertiary
alcohol
74. The increasing order of size of F-, Cl - , Br -, I - is
A. I - < Br - < Cl - < F - B. I - < Cl - < Br - < F - C. F - < Cl - < Br - < I - D. Br - < Cl - < F - < I -
75. Which of the following series contains only nucleophiles?
A. NH3, H2O, AlCl3 B. NH3, ROH, H2O C. H2O, H3O+, SO3 D. None of these
76. The formula of acetonitrite is
A. CH3COCH B. CH3CN C. CH3CH2CN D. CH3CONH2
77. The IUPAC name of CH3CONH2 is
A. Propionaldehyde B. Acetamide C. Ethanamide D. Ethylamine
78. The rate of reaction increases with temperature because
A. threshold energy increases B. kinetic energy of molecules increases
C. effective collision increases D. none of the above
79. If the graph of concentration of A versus
time for completion of reaction is a straight line,
then the order of the reaction is
A. zero B. second C. first D. third
80. The decomposition of hydrogen peroxide 2H2O2 → 2H2O + O2 is
A. zero order reaction B. first order reaction C. second order
reaction D. third order reaction
81. The half-life period of a first order process is 1.6 min -1. It will be 90% complete in
A. 0.8 min B. 3.2 min C. 5.3 min D. 1.6 min
82. Which of the following is an electrophile?
A. AlCl3 B. CN - C. NH3 D. CH3OH
83. Molarity of a solution is the number of
A. moles of solute per litre of solution
B. moles of solute per 100 gm of the solution
C. gram molecular weight of solute dissolved per litre of the solution
D. gram equivalents of solute dissolved per litre of solution
84. The hybridisation in PF3 is
A. sp3 B. sp2 C. dsp3 D. d2sp3
85. Which of the following is present in DNA?
A.
Deoxyribose B. Starch C.
Riboflavin
D. None of
these
86. Propyne when treated with H2SO4 in presence of HgSO4 gives
A. Acetone B. Propionaldehyde C. Acetaldehyde D. Propanoic acid
87. The general formula for alkyne is
A. CnH2n + 2 B. CnH2n C. CnH2n - 2 D. CnHn
88. Mesotartaric acid is optically inactive due to the presence of
A. molecular symmetry B. molecular asymmetry
C. external compensation D. two asymmetric carbon atoms
89. Which of the following electronic configuration in the outermost shell is characteristic of
alkali metals?
A. (n - 1) s2p6ns2s1 B. (n - l) s2p6d10ns1 C. (n - l) s2p6ns1 D. ns2p6d1
90. Lead chloride is soluble in
A. cold water B. hot water C. HCl D. acetic acid
91. When a copper wire is placed in a solution of silver nitrate, the
solution acquires blue colour. This is due to the formation of
A. a
soluble
complex of
copper with
AgNO3
B. Cu+ ions
C. Cu2+
ions
D. Cu2+ by
reduction
of Cu
92. The pyrites are heated with hydrochloric acid. The solution so obtained will give blood red
colour with
A. K4Fe(CN)6 B. KCN C. K3Fe(CN)6 D. KSNC
93 The ignition mixture in alumino thermite process contains a mixture of
A. magnesium powder and BaO2 B. magnesium powder, aluminium powder and
BaO2
C. magnesium and aluminium powders D. magnesium and aluminium oxides
94. One of the most important use of quick lime is
A. as a purgative B. drying gases and
alcohols C. in bleaching silk D. dyeing cotton
95. In preparing Cl2 from HCl, MnO2 acts as a/an
A. dehydrating agent B. reducing agent C. catalytic agent D. oxidising agent
96. Seaweed is an important source of
A. chlorine B. iodine C. fluorine D. bromine
97. Nitrates of all metals are
A. unstable B. stable C. coloured D. soluble
98. Ostwald’s method is used for manufacture of
A. HNO3 B. NO2 C. NO D. P2O5
99. Magnesium reacts with acids producing hydrogen and corresponding magnesium salts. In
such reactions, magnesium undergoes
A. oxidation B. reduction
C. neither oxidation nor reduction D. simple dissolution
100. An acidic buffer solution can be prepared by mixing solution of
A. ammonium chloride and HCl B. H2SO4 and Na2SO4
C. acetic acid and sulphuric acid D. ammonium acetate and acetic acid
101. Which of the following is not a Lewis acid?
A. BF3 B. AlCl3 C. SnCl4 D. CCl4
102. Equal weights of methane and oxygen are mixed in an empty container at 25°C. The
fraction of total pressure exerted by oxygen is
A. 1/2 B. 1/3 C. 2/3 D. 1/3 x (273/298)
103. HI was heated in a sealed tube at 440oC till the equilibrium was
reached. HI was found to be 22% decomposed. The equilibrium constant
for dissociation is
A. 0.282 B. 1.99 C. 0.0199 D. 0.0796
104. The molar heat of vaporisation ∆ Hvap for water is 2079 cal mol -1, therefore, molar heat of
condensation of water is
A. + 2079 cal mol -1 B. - 2079 cal mol -1
C. greater than 2079 cal mol -1 D. smaller than 2079 cal mol -1
105. Which of the following is an insulator?
A. Diamond B. Graphite C. Aluminium D. Silicon
106. The purest coal is
A. Anthracite B. Bituminous C. Peat D. Lignite
107. Among N 3-, O 2-, F -, and Na+, which one has largest size?
A. N 3- B. O 2- C. F - D. Na+
108. Ni, Pt, Pd belong to which group of the periodic table?
A. 12th B. 14th C. 8th D. 10th
109. A mixture of 200 ml of dry hydrogen and oxygen in equal
proportion at STP is exploded in an audiometer. What will be the nature
of components in the audiometer immediately after the explosion?
A. 50 ml of
steam only
B. 50 ml of
steam and
50 ml of
hydrogen
C. 50 ml of
steam and
50 ml of
oxygen
D. 100 ml
of steam
and 50 ml
of oxygen
110. If 9.8 gm of hexane bums completely in oxygen, how many moles of CO2 is produced?
A. 6 B. 0.6 C. 0.9 D. 1.2
111. Which one of the following nitrates does not give NO2 on heating?
A. NaNO3 B. Pb(NO3)2 C. AgNO3 D. Cu(NO3)2
112. Which has lowest 1st I.P.?
A. N B. Be C. B D. C
113. The oxidation states of phosphorus vary from
A. - 3 to + 5 B. - 1 to + 1 C. - 3 to + 3 D. - 5 to + 1
114. The molecular velocity of any gas is
A. proportional to the absolute temperature B. proportional to the square of the absolute
temperature
C. proportional to the square root of the
absolute temperature D. independent of the absolute temperature
115. Which of the following is an endothermic
reaction?
A. 2H2 +
O2 →
2H2O
B. N2O2 →
2NO
C. 2NaOH
+ H2SO4 →
Na2SO4
D. C2H5OH
+ 3O2 →
2CO2 +
+2H2O 3H2O
116. A solution of sodium sulphate in water is electrolysed between inert electrodes. The product
at the cathode and anode are respectively
A. H2, O2 B. O2, H2 C. H2, Na D. O2, SO2
117. Bauxite mineral containing iron as impurity is purified by
A. Baeyer’s process B. Electrolytic process C. Hoope's process D. Serpeck's process
118. Butter of tin is represented by
A. SnCl2.3H2O B. SnCl2.5H2O C. SnCl2.6H2O D. SnCl2.8H2O
119. Which group activates the benzene ring towards electrophilic substitution?
A. bezo group B. amino group C. acetyl group D. carbyl group
120. Phenol is less acidic than
A. ethanol B. propenol C. p-nitrophenol D. none of the above
121. The lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0
are tangents of the same circle. The radius of
this circle is
A. 1/2 B. 1/4 C. 3/4 D. 2
122. The three dice are thrown simultaneously, then the probability of getting a score of 7 is
A. 1/6 B. 5/216 C. 1/36 D. none of the above
123. Set A has 3 elements and set B has 4 elements. This number of injections (one to one
mapping) that can defined from A to B is
A. 24 B. 144 C. 12 D. none of the above
124. If θ is the angle between vectors a and b and | a x b | = | a.b |, then θ is equal to
A. 0o B. 180o C. 135o D. 45o
125. The number log20 3 lies in
A. (3/4, 4/5) B. (1/3, 1/2) C. (1/2, 3/4) D. (1/4, 1/3)
126. For x1, x2, y1, y2 ∈ R, if 0 < x1 < x2, y1 = y2 and z1 = x1 + i y1, z2 = x2 + i y2 and z3 = 1/2(z1 +
z2), then z1, z2, and z3 satisfy
A. | z1 | < | z3 | < | z2 | B. | z1 | > | z2 | > | z3 | C. | z1 | < | z2 | < | z3 | D. | z1 | = | z2 | = | z3 |
127. The complex number which satisfies the
equation z + √2 | z + 1 | + i = 0 is
A. 2 - i B. -2 - i C. 2 + i D. -2 + i
128. The equation of the line with slope -3/2 and which is concurrent with lines 4x + 3y - 7 = 0
and 8x + 5y - 1 = 0 is
A. 2y - 3x - 2= 0 B. 3x + 2y - 2 = 0 C. 3x + 2y - 63 = 0 D. none of the above
129. The parabola y2 = 4ax passes through the point (2, -6), then the length of its latus rectum is
A. 9 B. 16 C. 18 D. 6
130. The equation of the conic with focus at (1, -1) directrix along x - y + 1 = 0 and with
eccentricity √2 is
A. xy = 1 B. 2xy + 4x - 4y - 1 = 0 C. x2 - y2 D. 2xy - 4x + 4y + 1 =
0
131. If the radical axis of the circles x2 - y2 + 2gx + 2fy + c = 0 and 2x2 + 2y2 + 3x + 8y + 2c = 0
touches the circle x2 + y2 + 2x + 2y + 1 = 0, then
A. g = 3/4 or f = 2 B. g ≠ 3/4 and f = 2 C. g = 3/4 or f ≠ 2 D. none of the above
132. If tan θ + sec θ = √3, θ < π, then θ is equal to or least positive value of θ is
A. 5π/6 B. 2π/3 C. π/6 D. π/3
133. The roots of the equation 4x2 + 2√5x + 1 =
0 are
A. cos 18o,
cos 36o
B. sin 18o,
cos 18o
C. sin 18o,
cos 36o
D. sin 36o,
sin 18o
134. From the bottom of a pole of height h, the angle of elevation of the top of a tower is α. The
pole subtends an angle β at the top of a tower. The height of the tower is
A. [h sin α sin(α -
β)]/sin β
B. [h sin α cos(α +
β)]/cos β
C. [h sin α cos(α -
β)]/sin β
D. [h sin α sin(α +
β)]/cos β
135. If sin(π cos θ) = cos(π sin θ), then the value of cos(θ + π/4) is
A. 2/√2 B. 1/√2 C. -1/√2 D. 1/2/√2
136. If 4 ≤ x ≤ 9, then
A. (x - 4) (x - 9) ≤ 0 B. (x - 4) (x - 9) ≥ 0 C. (x - 4) (x - 9) < 0 D. (x - 4) (x - 9) > 0
137. The circle x2 + y2 + 4x - 7y + 12 = 0 cuts an intercept on y-axis equal to
A. 7 B. 4 C. 3 D. 1
138. If α and β are the roots of the equation x2 - p(x + 1) - q = 0, then the value of [(α2 + 2α +
1)/(α2 + 2αv + q)] + [(β2 + 2β + 1)/(β2 + 2β + q)] is
A. 1 B. 0 C. 3 D. 2
139. For x ∈ R, if mx2 - 9mx + 5m + 1 > 0, then
m lies in the interval
A. [-61/4,
0]
B. [4/61,
61/4] C. [0, 4/61] D. - [-4/61,
0]
140. If a, b, c are positive real numbers, then the number of real roots of the equation ax2 + b| x |
+ c = 0 is
A. 0 B. 2 C. 4 D. none of the above
141. If ax = by = cz and a, b, c are in G.P., then x, y, z are
A. G.P. B. A.P. C. H.P. D. none of the above
142. Let cos x = b. For what b do the roots of the equation form an A.P.?
A. √3/2 B. 1/2 C. -1 D. none of the above
143. Coefficient of x4 in the expansion of (1 - 3x - x2)/ex is
A. 5/24 B. 4/25 C. 24/25 D. 25/24
144. If C (10, 4) + C (10, 5) = C (11, r), then r equals
A. 6 B. 5 C. 4 D. 3
145. In a steamer, there are stalls for 12 animals
and there are cows, horses, and calves (not less
than 12 of each) ready to be shipped. The total
number of ways in which the shipload can be
made is
A. 12C3 B. 12P3 C. 312 D. 123
146. The coefficient of xn in the binomial expansion of (1 - x) -2 is
A. 2n/2! B. n + 1 C. n D. 2n
147. The largest coefficient in the expansion of (1 + x)24 is
A. 24C13 B. 24C11 C. 24C24 D. 24C12
148. The sum of first n terms of two A.P. are 3n + 8, 7n + 15, then the ratio of their 12th term is
A. 7/16 B. 8/15 C. 4/9 D. 3/7
149.
If A
=
12
21
, then Adj. A is
equal to
A.
-1
2
2
-1
B.
1
-2
-2
-1
C.
2
1
1
1
D.
1
-2
-2
1
150. If a, b, c are different, then the value of x
satisfying the determinant
0
x2 +
a
x4 +
b
x2 -
a
0
x - c
x3 -
b
x2 +
c
0
= 0 is
A. a B. c C. b D. 0
151. If the system of equations x = a(y + z), y = b(z + x), z = c(x + y) (a, b, c ≠ -1) has a non-zero
solution, then the value of [a/(1 + a)] + [b/(1 + b)] + [c/(1 + c)] is
A. -1 B. 0 C. 1 D. 2
152. Two lines with direction cosines < l1, m1, n1 > and < l2, m2, n2 > are at right angles if
A. l1 l2 + m1 m2 + n1 n2 = 1 B. l1 l2 + m1 m2 + n1 n2 = 0
C. l1/l2 = m1/m2 = n1/n2 D. l1 = l2, m1 = m2, n1 = n2
153. Given the line L : [(x - 1)/3] = [(y + 1)/2] =
[( z - 3)/-1] and the plane π : x - 2y = 0. Of the
following assertions, the only one that is always
true is
A. L is
perpendicular
to π
B. L lies in
π
C. L is
parallel to
π
D. none of
the above
154. Quartile deviation for a frequency distribution
A. Q = 1/4 (Q2 - Q1) B. Q = 1/3 (Q3 - Q1) C. Q = 1/2 (Q3 - Q1) D. Q = (Q3 - Q1)
155. For a symmetrical distribution, Q1 = 20 and Q3 = 40. The value of 50th percentile is
A. 20 B. 30 C. 40 D. none of the above
156. The area bounded by the curve y = x3, the x-axis and the ordinates x = -2 and x = 1 is
A. -9 B. -15/4 C. 15/4 D. 17/4
157. A random variable X has the following probability distribution:
X: 0 1 2 3 4 5 6 7 8
p(X =
x): a 3a 5a 7a 9a 11a 13a 15a 17a
then the value of a is
A. 7/81 B. 5/81 C. 2/81 D. 1/81
158. Dialing a telephone number, an old man
forgets the last two digits remembering only that
these are different, dialed at random. The
probability that the number dialed correctly is
A. 1/90 B. 1/100 C. 1/45 D. none of
the above
159. Three identical dice are rolled. The probability that the same number will appear on each of
them is
A. 1/18 B. 3/28 C. 1/36 D. 1/6
160. The value of n ∈ I for which the function f(x) = sin nx/[sin(x/n)] has 4π as its period is
A. 5 B. 4 C. 3 D. 2
161. Lt (log cosx)/x is equal to
x → 0
A. 0 B. 1 C. ∞ D. none of the above
162. Lt [ex - (1 + x)]/x2 is equal to
x → 0
A. 1/2 B. 1 C. 0 D. 1/4
163. For the curve x = t2 - 1, y = t2 - t, tangent is
parallel to x-axis where
A. t = 1/√3 B. -1/√3 C. t = 0 D. 1/2
164. The function f(x) = Kx3 - 9x2 + 9x + 3 is monotonically increasing in each interval, then
A. K > 3 B. K < 3 C. K ≤ 3 D. none of the above
165. The area of the region bounded by the curve y = x - x2 between x = 0 and x = 1 is
A. 5/6 B. 1/2 C. 1/3 D. 1/6
166. If f(x) dx = 1,
x f(x) dx = a, x2 f(x) dx = a2, then (a - x)2 f(x) dx equals
A. 4a2 B. 0 C. 2a2 D. none of the above
167. The area between the curve y = 1 - | x | and x-axis is
A. 1/3 B. 2 C. 1/2 D. 1
168. The equations ax + by + c = 0 and dx + ey + f = 0 represents the same straight line if and
only if
A. a/d = b/e B. c = f C. a/d = b/e = c/f D. a = d, b = e, c = f
169. If a + b + c = 0, | a | = 3, | b | = 5, | c | = 7,
then the angle between a and b is
A. π/6 B. 2π/3 C. 5π/3 D. π/3
170. The differential coefficient of log tan x is
A. 2 sec3 2x B. 2 cosec3 2x C. 2 sec x D. 2 cosec x
171. The differential coefficient of f(log x) where f(x) = log x is
A. x/(log x) B. (log x)/x C. (x log x)-1 D. none of the above
172. The number of solutions 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
173. In a triangle ABC, the angle B is greater than the angle A. If the values of the angles A and
B satisfy the equation 3 sin x- 4 sin3 x - k = 0, 0 < k < 1, then the value of C is
A. π/3 B. π/2 C. 2π/3 D. 5π/6
174. If one root of 5x2 + 13x + k = 0 is reciprocal of the other, then
A. k = 0 B. k = 5 C. k = 1/6 D. k = 6
175. The number of quadratic equations, which
are unchanged by squaring their roots is
A. 2 B. 4 C. 6 D. none of
the above
176. If x2 -3xy + λy2 + 3x - 5y + 2 = 0 represents a pair of straight lines, then the value of λ is
A. 1 B. 4 C. 3 D. 2
177. If each element of a determinant of third order with value A is multiplied by 3, then the
value of newly formed determinant is
A. 3A B. 9A C. 27A D. none of the above
178. If A, B, and C are non-empty set subsets of the sets, then (A - B) ∪ (B - A) equals
A. (A ∩ B) ∪ (A ∪ B) B. (A ∪ B) - (A ∩ B) C. A - (A ∩ B) D. (A ∪ B) - B
179. A and B are two independent events. The probability that both A and B occur is 1/6 and the
probability that neither of them occurs is 1/3. The probability of the occurence of the event A is
A. 2/3 B. 5/6 C. 1/2 D. none of the above
180. The number of divisors of 9600 including 1 and 9600 is
A. 60 B. 58 C. 48 D. 46


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