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1. A particle of mass M and charge Q moving with velocity v
r describe a circular path of radius R when
subjected to a uniform transverse magnetic field of induction B. The work done by the field when the particle
completes one full circle is
(a) R2
R
Mv2
π
(b) Zero (c) BQ2 πR (d) BQ v2 πR
2. A particle of charge – 16×1018 coulomb moving with velocity 10ms1 along the xaxis enters a region where
a magnetic field of induction B is along the yaxis, and an electric field of magnitude 104
V/m is along the
negative zaxis. If the charged particle continues moving along the xaxis, the magnitude of B is
(a) 103
Wb/m2 (b) 105
Wb/m2 (c) 1016Wb/m2 (d) 103Wb/m2
3. A thin rectangular magnet suspended freely has a period of oscillation equal to T. Now it is broken into two
equal halves (each having half of the original length) and one piece is made to oscillate freely in the same
field. If its period of oscillation is T′ , the ratio T
T′
is
(a) 22
1
(b) 2
1
(c) 2 (d) 4
1
4. A magnetic needle lying parallel to a magnetic field requires W units of work to turn it through 600
. The
torque needed to maintain the needle in this position will be
(a) W3 (b) W (c) W
2
3 (d) 2W
5. The magnetic lines of force inside a bar magnet
(a) are from northpole to southpole of the magnet
(b) do not exist
(c) depend upon the area of crosssection of the bar magnet
(d) are from southpole to northpole of the magnet
6. Curie temperature is the temperature above which
(a) a ferromagnetic material becomes paramagnetic (b) a paramagnetic material becomes diamagnetic
(c) a ferromagnetic material becomes diamagnetic (d) a paramagnetic material becomes ferromagnetic
7. A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49
N, when the lift is stationary. If the lift moves downward with an acceleration of 5m/s2
, the reading of the
spring balance will be
(a) 24 N (b) 74 N (c) 15 N (d) 49 N
8. The length of a wire of a potentiometer is 100 cm, and the e.m.f. of its standard cell is E volt. It is employed
to measure the e.m.f of a battery whose internal resistance is 0.5 Ω . If the balance point is obtained at l = 30
cm from the positive end, the e.m.f. of the battery is
(a) 100 5.
E30
(b) 100( )5.0
E30
− (c) 100
− )i5.0E(30
, where i is the current in the potentiometer wire (d) 100
E30
9. A strip of copper and another of germanium are cooled from room temperature to 80 K. The resistance of
(a) each of these decreases (b) copper strip increases and that of germanium decreases
(c) copper strip decreases and that of germanium increases (d) each of these increases
AIEEE 2003
PHYSICS & CHEMISTRY
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10. Consider telecommunication through optical fibres. Which of the following statements is not true?
(a) Optical fibres can be of graded refractive index
(b) Optical fibres are subjective to electromagnetic interference from outside
(c) Optical fibres have extremely low transmission loss
(d) Optical fibres may have homogeneous core with a suitable cladding.
11. The thermo e.m.f. of a thermocouple is 25µV/ 0C at room temperature. A galvanometer of 40 ohm resistance,
capable of detecting current as low as 105 A, is connected with the thermo couple. The smallest
temperature difference that can be detected by this sytem is
(a) 160
C (b) 120
C (c) 80
C (d) 200
C
12. The negative Zn pole of a Daniell cell, sending a constant current through a circuit, decreases in mass by
0.13 g in 30 minutes. If the electrochemical equivalent of Zn and Cu are 32.5 and 31.5 respectively, the
increase in the mass of the positive Cu pole in this time is
(a) 0.180 g (b) 0.141 g (c) 0.126 g (d) 0.242 g
13. Dimension of
00
1
εµ , where symbols have their usual meaning, are
(a) [L1 T] (b) [L2 T2
] (c) [L2
T2] (d) [LT1]
14. A circular disc X of radius R is made from an iron plate of thickness t, and another disc Y of radius 4R is
made from an iron plate of thickness 4
t
. Then the relation between the moment of inertia IX and IY is
(a) IY = 32 IX (b) IY = 16 IX (c) IY = IX (d) IY = 64 IX
15. The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite is
increased to 4 times the previous value, the new time period will become
(a) 10 hours (b) 80 hours (c) 40 hours (d) 20 hours
16. A particle performing uniform circular motion has angular frequency is doubled & its kinetic energy halved,
then the new angular momentum is
(a) 4
L
(b) 2L (c) 4 L (d) 2
L
17. Which of the following radiations has the least wavelength?
(a) γ rays (b) β rays (c) αrays (d) Xrays
18. When a U238 nucleus originally at rest, decays by emitting an alpha particle having a speed ‘u’, the recoil
speed of the residual nucleus is
(a) 238
u4
(b) 234
u4 − (c) 234
u4
(d) 238
u4 −
19. Two spherical bodies of mass M and 5M & radii R & 2R respectively are released in free space with initial
separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then
the distance covered by the smaller body just before collision is
(a) 2.5 R (b) 4.5 R (c) 7.5 R (d) 1.5 R
20. The difference in the variation of resistance with temperature in a metal and a semiconductor arises essentially
due to the difference in the
(a) crystal structure (b) variation of the number of charge carriers with temperature
(c) type of bonding (d) variation of scattering mechanism with temperature
21. A car, moving with a speed of 50 km/hr, can be stopped by brakes after at least 6 m. If the same car is moving
at a speed of 100 km/hr, the minimum stopping distance is
(a) 12 m (b) 18 m (c) 24 m (D) 6 m
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22. A boy playing on the roof of a 10 m high building throws a ball with a speed of 10m/s at an angle of 300
with
the horizontal. How far from the throwing point will the ball be at the height of 10 m from the ground?
[g = 10m/s2
, sin300
= 2
1
, cos300
=
2
3
]
(a) 5.20m (b) 4.33m (c) 2.60m (d) 8.66m
23. An ammeter reads up to 1 ampere. Its internal resistance is 0.81 ohm. To increase the range to 10 A the value
of the required shunt is
(a) 0.03 Ω (b) 0.3 Ω (c) 0.9 Ω (d) 0.09 Ω
24. The physical quantities not having same dimensions are
(a) torque and work (b) momentum and Planck’s constant
(c) stress and Young’s modulus (d) speed and ( ) 2/1
00
− εµ
25. Three forces start acting simultaneously on a particle moving with velocity, v
r . These forces are represented
in magnitude and direction by the three sides of a triangle ABC. The particle will now move with velocity
A B
C
(a) less than v
r (b) greater than v
r (c) v in the direction of the largest force BC (d) v
r , remaining unchanged
26. If the electric flux entering and leaving an enclosed surface respectively is φ1 and φ2 , the electric charge
inside the surface will be
(a) ( ) 012 εφ−φ (b) ( ) 021 / εφ+φ (c) ( ) 012 / εφ−φ (d) ( ) 021 εφ+φ
27. A horizontal force of 10 N is necessary to just hold a block stationary against a wall. The coefficient of
friction between the block and the wall is 0.2. The weight of the block is
10N
(a) 20 N (b) 50 N (c) 100 N (d) 2 N
28. A marble block of mass 2 kg lying on ice when given a velocity of 6 m/s is stopped by friction in 10 s. Then
the coefficient of friction is
(a) 0.02 (b) 0.03 (c) 0.04 (d) 0.01
29. Consider the following two statements:
(A) Linear momentum of a system of particles is zero
(B) Kinetic energy of a system of particles is zero
Then (a) A does not imply B and B does not imply A
(b) A implies B but B does not imply A
(c) A does not imply B but B implies A (d) A implies B and B implies A
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30. Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon
(a) the rates at which currents are changing in the two coils
(b) relative position and orientation of the two coils (c) the materials of the wires of the coils.
(d) the currents in the two coils
31. A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. If a force P is applied
at the free end of the rope, the force exerted by the rope on the block is
(a) mM
Pm
+ (b) mM
Pm
− (c) P (d) mM
PM
+
32. A light spring balance hangs from the hook of the other light spring balance and a block of mass M kg hangs
from the former one. Then the true statement about the scale reading is
(a) Both the scales read M kg each (b) The scale of the lower one reads M kg and of the upper one zero
(c) The reading of the two scales can be anything but the sum of the reading will be M kg
(d) Both the scales read M/2 kg each
33. A wire suspended vertically from one of its ends is stretched by attaching a weight of 200 N to the lower end.
The weight stretches the wire by 1 mm. Then the elastic energy stored in the wire is
(a) 0.2 J (b) 10 J (c) 20 J (d) 0.1 J
34. The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body
is projected at an angle of 450
with the vertical, the escape velocity will be
(a) 11 2 km/s (b) 22 km/s (c) 11 km/s (d) 2
11
km/s
35. A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that
the mass executes SHM of time period T. If the mass is increased by m, the time period becomes 3
T5
. Then
the ratio of M
m
is
(a) 5
3
(b) 9
25
(c) 9
16
(d) 3
5
36. “Heat cannot by itself flow from a body at lower temperature to a body at higher temperature” is a statement
or consequence of
(a) second law of thermodynamics (b) conservation of momentum
(c) conservation of momentum (d) first law of thermodynamics
37. Two particles A and B of equal masses are suspended from two massless springs of spring constant k1
and k2
,
respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of A and B is
(a)
2
1
k
k
(b)
1
2
k
k
(c)
1
2
k
k
(d)
2
1
k
k
38. The length of a simple pendulum executing simple harmonic motion is increased by 21%. The percentage
increase in the time period of the pendulum of increased length is
(a) 11% (b) 21% (c) 42% (d) 10%
39. The displacement y of a wave travelling in the xdirection is given by
π
+−= −
3 600sin10y x2t 4
metres
where x is expressed in metres and t in seconds. The speed of the wavemotion, in ms1, is
(a) 300 (b) 600 (c) 1200 (d) 200
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40. When the current changes from +2A to 2A in 0.05 second, an e.m.f. of 8V is induced in a coil. The
coefficient of selfinduction of the coil is
(a) 0.2 H (b) 0.4 H (c) 0.8 H (d) 0.1 H
41. In an oscillating LC circuit the maximum charge on the capacitor is Q. The charge on the capacitor when the
energy is stored equally between the electric and magnetic field is
(a) 2
Q (b) 3
Q
(c) 2
Q
(d) Q
42. The core of any transformer is laminated so as to
(a) reduce the energy loss due to eddy currents (b) make it light weight
(c) make it robust and strong (d) increase the secondary voltage
43. Let F
r
be the force acting on a particle having position vector andr T r r
be the torque of this force about the
origin. Then
(a) and0T.r ≠= 0T.F r rrr (b) and0T.r =≠ 0T.F r rrr
(c) and0T.r ≠≠ 0T.F r rrr (d) and0T.r == 0T.F r rrr
44. A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After 5 minutes,
the rate is 1250 disintegrations per minute. Then, the decay constant (per minute) is
(a) 0.4 ln 2 (b) 0.2 ln 2 (c) 0.1 ln 2 (d) 0.8 ln 2
45. A nucleus with Z = 92 emits the following in a sequence:
αββαββαααααββα ++−−−−
,,,,,,,,,,,, . Then Z of the resulting nucleus is
(a) 76 (b) 78 (c) 82 (d) 74
46. Two identical photocathodes receive light of frequencies f1
and f2
. If the velocities of the photo electrons (of
mass m) coming out are respectively v1
and v2
, then
(a) )ff(
m
h2
vv 21
2
2
2
1 −=− (b)
2/1
2121 )ff(
m
h2
vv
+=+
(c) )ff(
m
h2
vv 21
2
2
2
1 +=+ (d)
2/1
2121 )ff(
m
h2
vv
−=−
47. Which of the following cannot be emitted by radioactive substances during their decay?
(a) Protons (b) Neutrinoes (c) Helium nuclei (d) Electrons
48. A 3 volt battery with negligible internal resistance is connected in a circuit as shown in the figure. The
current I, in the circuit will be
3Ω 3Ω
3Ω
V3
(a) 1 A (b) 1.5 A (c) 2 A (d) 1/3 A
49. A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance
of the capacitor
(a) decreases (b) remains unchanged (c) becomes infinite (d) increases
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50. The displacement of a particle varies according to the relation x = 4(cosπt + sin πt). The amplitude of the
particle is
(a) 4 (b) 4 (c) 24 (d) 8
51. A thin spherical conducting shell of radius R has a charge q. Another charge Q is placed at the centre of the
shell. The electrostatic potential at a point P a distance 2
R
from the centre of the shell is
(a) R4
Q2
πε0
(b) R4
q2
R4
Q2
πε00
− πε (c) R4
q
R4
Q2
πε00
+
πε (d) ( )
R4
2Qq
πε0
+
52. The work done in placing a charge of 8×1018 coulomb on a condenser of capacity 100 microfarad is
(a) 16×1032 joule (b) 3.1×1026 joule (c) 4×1010 joule (d) 32 ×1032 joule
53. The coordinates of a moving particle at any time ‘t’ are given by x = αt
3
and y = β t
3
. The speed of the
particle at time ‘t’ is given by
(a) 22 t3 β+α (b) 222t3 β+α (c) 222t β+α (d) 22 β+α
54. During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute
temperature. The ratio CP
/CV for the gas is
(a) 3
4
(b) 2 (c) 3
5
(d) 2
3
55. Which of the following parameters does not characterize the thermodynamic state of matter?
(a) temperature (b) Pressure (c) Work (b) Volume
56. A Carnot engine takes 3×106
cal. of heat from a reservoir at 6270
C, and gives it to a sink at 270
C. The work
done by the engine is
(a) 4.2×106
J (b) 8.4×106
J (c) 16.8×106
J (d) Zero
57. A spring of spring constant 5×103
N/m is stretched initially by 5 cm from the unstretched position. Then the
work required to stretch it further by another 5 cm is
(a) 12.50 Nm (b) 18.75 Nm (c) 25.00 Nm (d) 6.25 Nm
58. A metal wire of linear mass density of 9.8 g/m is stretched with a tension of 10 kgwt between two rigid
supports 1 metre apart. The wire passes at its middle point between the poles of a permanent magnet, and it
vibrates in resonance when carrying an alternating current of frequency n. The frequency n of the alternating
source is
(a) 50 Hz (b) 100 Hz (c) 200 Hz (d) 25 Hz
59. A tuning fork of known frequency 256 Hz makes 5 beats per second with the vibrating string of a piano. The
beat frequency decreases to 2 beats per second when the tension in the piano string is slightly increased. The
frequency of the piano string before increasing the tension was
(a) 256 + 2 Hz (b) 256 – 2 Hz (c) 256 – 5 Hz (d) 256 + 5 Hz
60. A body executes simple harmonic motion. The potential energy (P.E), the kinetic energy (K.E) and total
energy (T.E) are measured as a function of displacement x. Which of the following statements is true?
(a) K.E. is maximum when x = 0 (b) T.E is zero when x = 0
(c) K.E is maximum when x is maximum (d) P.E. is maximum when x = 0
61. In the nuclear fusion reaction nHeHH 4
2
3
1
2
1 +→+ given that the repulsive potential energy between the two
nuclei is ~7.7×1014 J, the temperature at which the gases must be heated to initiate the reaction is nearly
[Boltzmann’s Constant k = 1.38×1023 J/K]
(a) 107
K (b) 105
K (c) 103
K (d) 109
K
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62. Which of the following atoms has the lowest ionization potential?
(a) N14
7 (b) Cs 133
55 (c) Ar 40
18 (d) O16
8
63. The wavelengths involved in the spectrum of deuterium ( D) 2
1 are slightly different from that of hydrogen
spectrum, because
(a) the size of the two nuclei are different (b) the nuclear forces are different in the two cases
(c) the masses of the two nuclei are different
(d) the attraction between the electron and the nucleus is different in the two cases
64. In the middle of the depletion layer of a reverse biased pn junction, the
(a) electric field is zero (b) potential is maximum
(c) electric field is maximum (d) potential is zero
65. If the binding energy of the electron in a hydrogen atom is 13.6eV, the energy required to remove the
electron from the first excited state of Li++ is
(a) 30.6eV (b) 13.6 eV (c) 3.4 eV (d) 122.4 eV
66. A body is moved along a straight line by a machine delivering a constant power. The distance moved by the
body in time ‘t’ is proportional to
(a) t3/4 (b) t3/2 (c) t1/4 (d) t1/2
67. A rocket with a liftoff mass 3.5×104
kg is blasted upwards with an initial acceleration of 10m/s2
. Then the
initial thrust of the blast is
(a) 3.5×105
N (b) 7.0×105
N (c) 14.0×105
N (d) 1.75×105
N
68. To demonstrate the phenomenon of interference, we require two sources which emit radiation
(a) of nearly the same frequency (b) of the same frequency
(c) of different wavelengths (d) of the same frequency and having a definite phase relationship
69. Three charges q1
, +q2
and q3
are placed as shown in the figure. The xcomponent of the force on q1
is
proportional to
b
a
θ
q 1 + q 2
X
Y
q 3
(a) cosθ−
a
q
b
q
2
3
2
2 (b) sinθ+
a
q
b
q
2
3
2
2 (c) cosθ+
a
q
b
q
2
3
2
2 (d) sinθ−
a
q
b
q
2
3
2
2
70. A 220 volt, 1000 watt bulb is connected across a 110 volt mains supply. The power consumed will be
(a) 750 watt (b) 500 watt (c) 250 watt (d) 1000 watt
71. The image formed by an objective of a compound microscope is
(a) virtual and diminished (b) real and diminished (c) real and enlarged (d) virtual and enlarged
72. The earth radiates in the infrared region of the spectrum. The spectrum is correctly given by
(a) Rayleigh Jeans law (b) Planck’s law of radiation
(c) Stefan’s law of radiation (d) Wien’s law
73. To get three images of a single object, one should have two plane mirrors at an angle of
(a) 600 (b) 900 (c) 1200 (d) 300
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74. According to Newton’s law of cooling, the rate of cooling of a body is proportional to n θ∆ )( , where θ∆ is
the difference of the temperature of the body and the surroundings, and n is equal to
(a) two (b) three (c) four (d) one
75. The length of a given cylindrical wire is increased by 100%. Due to the consequent decrease in diameter the
change in the resistance of the wire will be
(a) 200% (b) 100% (c) 50% (d) 300%
76. Which of the following could act as apropellant for rockets?
(a) Liquid oxygen + liquid argon (b) Liquid hydrogen + liquid oxygen
(c) Liquid nitrogen + liquid oxygen (d) Liquid hydrogen + liquid nitrogen
77. The reaction of chloroform with alcoholic KOH and ptoluidine forms
(a) H3C N2Cl (b) H3C NHCHCl2 (c) H3C NC (d) H3C CN
78. Nylon threads are made of
(a) polyester polymer (b) polyamide polymer (c) polyethylene polymer (d) polyvinyl polymer
79. The correct order of increasing basic nature for the bases NH3
, CH3
NH2
and (CH3
)
2
NH is
(a) (CH3
)2
NH < NH3
< CH3
NH2 (b) NH3
< CH3
NH2
< (CH3
)2
NH
(c) CH3
NH2
< (CH3
)2
NH < NH3 (d) CH3
NH2
< NH3
< (CH3
)2
NH
80. Bottles containing C6
H5
l and C6
H5
CH2
I lost their original labels. They were labelled A and B for testing A
and B were separately taken in test tubes and boiled with NaOH solution. The end solution in each tube was
made acidic with dilute HNO3
and then some AgNO3
solution was added. Substance B gave a yellow
precipitate. Which one of the following statements is true for this experiment?
(a) A and C6
H5
CH2
I (b) B and C6
H5
I
(c) Addition of HNO3
was unnecessary (d) A was C6
H5
I
81. The internal energy change when a system goes from state A to B is 40 kJ/mole. If the system goes from A
to B by a reversible path and returns to state A by an irreversible path what would be the net change in internal energy?
(a)> 40 kJ (b) < 40kJ (c) Zero (d) 40 kJ
82. If at 298 K the bond energies of CH, CC, C = C and HH bonds are respectively 414, 347, 615 and 435 kJ
mol1, the value of enthalpy change for the reaction H2
C = CH2
(g) + H2
(g) →H3
C  CH3
(g) at 298 K will be
(a) 250 kJ (b) + 125 kJ (c) 125 kJ (d) + 250 kJ
83. The radionucleide Th 234
90 undergoes two successive β decays followed by one αdecay. The atomic number
and the mass number respectively of the resulting radionucleide are
(a) 94 and 230 (b) 90 and 230 (c) 92 and 230 (d) 92 and 234
84. The halflife of a radioactive isotope is three hours. If the initial mass of the isotope were 256 g, the mass of
it remaining undecayed after 18 hours would be
(a) 8.0 g (b) 12.0 g (c) 16.0 g (d) 4.0 g
85. If liquids A and B form an ideal solution
(a) the entropy of mixing is zero (b) the free energy of mixing is zero
(c) the free energy as well as the entropy of mixing are each zero (d) the enthalpy of mixing is zero
86. The radius of La3+ (Atomic number of La = 57) is 1.06Å. Which one of the following given values will be
closest to the radius of Lu3+ (Atomic number of Lu = 71) ?
(a) 1.40Å (b) 1.06Å (c) 0.85Å (d) 1.60Å
87. Ammonia forms the complex ion [Cu(NH3
)
4
]2+ with copper ions in alkaline solutions but not in acidic solutions.
What is the reason for it?
(a) In acidic solutions protons coordinate with ammonia molecules forming NH+
4
ions and NH3
molecules
are not available
(b) In alkaline solutions insoluble Cu(OH)2
is precipitated which is soluble in excess of any alkali
(c) Copper hydroxide is an amphoteric substance
(d) In acidic solutions hydration protects copper ions.
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88. One mole of the complex compound Co(NH3
)5
Cl3
, gives 3 moles of ions on dissolution in water. One mole
of the same complex reacts with two moles of AgNO3
solution to yield two moles of AgCl (s). The structure
of the complex is
(a) [Co(NH3
)3
Cl3
]. 2NH3
(b) [Co(NH3
)4
Cl2
] Cl. NH3
(c) [Co(NH3
)4
Cl]Cl2
. NH3
(d) [Co(NH3
)5
Cl] Cl2
89 In the coordination compound, K4
[Ni(CN)4
], the oxidation state of nickel is
(a) 0 (b) +1 (c) +2 (d) 1
90. In curing cement plasters water is sprinkled from time to time. This helps in
(a) developing interlocking needlelike crystals of hydrated silicates
(b) hydrating sand and gravel mixed with cement
(c) converting sand into silicic acid (d) keeping it cool
91. Which one of the following statements is not true?
(a) pH + pOH = 14 for all aqueous solutions (b) The pH of 1×108 M HCI is 8
(c) 96,500 coulombs of electricity when passed through a CuSO4
solution deposits 1 gram equivalent of
copper at the cathode
(d) The conjugate base of H2
PO4

is HPO2
4
92. On mixing a certain alkane with chlorine and irradiating it with ultravioletlight, it forms only one
monochloroalkane. This alkane could be
(a) pentane (b) isopentane (c) neopentane (d) propane
93. Butene1 may be converted to butane by reaction with
(a) Sn  HCI (b) Zn  Hg (c) Pd/H2 (d) Zn  HCI
94. What may be expected to happen when phosphine gas is mixed with chlorine gas?
(a) PCI3
and HCI are formed and the mixture warms up
(b) PCI5
and HCI are formed and the mixture cools down
(c) PH3
.Cl2
is formed with warming up (d) The mixture only cools down
95. The number of delectrons retained in Fe2+ (At.no.of Fe = 26) ion is
(a) 4 (b) 5 (c) 6 (d) 3
96. Concentrated hydrochloric acid when kept in open air sometimes produces a cloud of white fumes. The
explanation for it is that
(a) oxygen in air reacts with the emitted HCI gas to form a cloud of chlorine gas
(b) strong affinity of HCI gas for miosture in air results in forming of droplets of liquid solution which appears
like a cloudy smoke.
(c) due to strong affinity for water, concentrated hydrochloric acid pulls moisture of air towards it self. This
moisture forms droplets of water and hence the cloud.
(d) concentrated hydrochloric acid emits strongly smelling HCI gas all the time.
97. An ether is more volatile than an alcohol having the same molecular formula. This is due to
(a) alcohols having resonance structures (b) intermolecular hydrogen bonding in ethers
(c) intermolecular hydrogen bonding in alcohols (d) dipolar character of ethers
98. Graphite is a soft solid lubricant extremely difficult to melt. The reason for this anomalous behaviour is that
graphite
(a) is an allotropic form of diamond (b) has molecules of variable molecular masses like polymers
(c) has carbon atoms arranged in large plates of rings of strongly bound carbon atoms with weak interplate bonds
(d) is a noncrystalline substance
99. According to the Periodic Law of elements, the variation in properties of elements is related to their
(a) nuclear masses (b) atomic numbers (c) nuclear neutronproton number ratios (d) atomic masses
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100. Which one of the following statements is correct?
(a) From a mixed precipitate of AgCl and AgI, ammonia solution dissolves only AgCl
(b) Ferric ions give a deep green precipitate on adding potassium ferrocyanide solution
(c) On boiling a solution having K+, Ca2+ and HCO
3
ions we get a precipitate of K2
Ca(CO3
)2
.
(d) Manganese salts give a violet borax bead test in the reducing flame
101. Glass is a
(a) supercooled liquid (b) gel (c) polymeric mixture (d) microcrystalline solid
102. The orbital angular momentum for an electron revolving in an orbit is given by π
+
2
h l(l ).1 . This momentum
for an selectron will be given by
(a) zero (b) 2π
h
(c) 2π
h .2 (d) π
+
2
h .
2
1
103. How many unit cells are present in a cubeshaped ideal crystal of NaCl of mass 1.00 g?
[Atomic masses: Na = 23, Cl = 35.5]
(a) 5.14×1021 unit cells (b) 1.28×1021 unit cells
(c) 1.71×1021 unit cells (d) 2.57×1021 unit cells
104. In the anion HCOO
the two carbonoxygen bonds are found to be of equal length. What is the reason for it?
(a) The C = O bond is weaker than the CO bond
(b) The anion HCOO
has two resonating structures
(c) The anion is obtained by removal of a proton from the acid molecule
(d) Electronic orbitals of carbon atom are hybridised
105. Which one of the following characteristics is not correct for physical adsorption?
(a) Adsorption increases with incresae in temperature
(b) Adsorption is spontaneous (c) Both enthalpy and entropy of adsorption are negative
(d) Adsorption on solids is reversible
106. For a cell reaction involving a twoelectron change, the standard e.m.f. of the cell is found to be 0.295 V at
250
C. The equilibrium constant of the reaction at 250
C will be
(a) 29.5×102 (b) 10 (c) 1×1010 (d) 1×1010
107. In an irreversible process taking place at constant T and P and in which only pressurevolume work is being
done, the change in Gibbs free energy (dG) and change in entropy (dS), satisfy the criteria
(a) (dS)V,E > 0, (dG)T,P < 0 (b) (dS)V,E = 0, (dG)T.P = 0 (c) (dS)V,E = 0, (dG)T,P > 0 (d) (dS)V,E < 0, (dG)T,P < 0
108. The solubility in water of a sparingly soluble salt AB2
is 1.0×105 mol L1. Its solubility product number will be
(a) 4×1010 (b) 1×1015 (c) 1×1010 (d) 4×1015
109. What volume of hydrogen gas, at 273 K and 1 atm, pressure will be consumed in obtaining 21.6 g of
elemental boron (atomic mass = 10.8) from the reducti on of boron trichloride by hydrogen?
(a) 67.2 L (b) 44.8 L (c) 22.4 L (d) 89.6 L
110. For the reaction equilibrium N2
O4
(g) 2 NO2
(g) the concentrations of N2
O4
and NO2
at equilibrium are
4.8×102 and 1.2×102 mol L1 respectively. The value of Kc
for the reaction is
(a) 3×101 mol L1 (b) 3×103 mol L1 (c) 3×103
mol L1 (d) 3.3×102
mol L1
111. Consider the reaction equilibrium 2SO2
(g) + O2
(g) 2SO3 (g); ∆ H0
= 198 kJ. On the basis of Le Chatelier’s
principle, the condition favourable for the forward reaction is
(a) increasing temperature as well as pressure (b) lowering the temperature and increasing the pressure
(c) any value of temperature and pressure (d) lowering of temperature as well as pressure
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112. Which one of the following is an amphoteric oxide?
(a) Na2
O (b) SO2 (c) B2
O3 (d) ZnO
113. A red solid is insoluble in water. However it becomes soluble if some KI is added to water. Heating the red
solid in a test tube results in liberation of some violet coloured fumes and droplets of a metal appear on the
cooler parts of the test tube. The red solid is
(a) HgI2 (b) HgO (c) Pb3
O4 (d) (NH4
)2
Cr2
O7
114. Standard reduction electrode potentials of three metals A,B&C are respectively +0.5 V, 3.0 V & 1.2 V. The
reducing, powers of these metals are
(a) A > B > C (c) C > B > A (c) A > C > B (d) B > C > A
115. Which one of the following substances has the highest proton affinity?
(a) H2
S (b) NH3 (c) PH3 (d) H2
O
116. In a 0.2 molal aqueous solution of a weak acid HX the degree of ionization is 0.3. Taking kf
for water as 1.85,
the freezing point of the solution will be nearest to
(a) 0.3600
C (b) 0.2600
C (c) +0.4800
C (d) 0.4800
C
117. When during electrolysis of a solution of AgNO3
9650 coulombs of charge pass through the electroplating
bath, the mass of silver deposited on the cathode will be
(a) 10.8 g (b) 21.6 g (c) 108 g (d) 1.08 g
118. For the redox reaction Zn(s) + Cu2+(0.1 M) →Zn2+(1M) + Cu(s) taking place in a cell, 0 Ecell is 1.10 volt. Ecell
for the cell will be
= 0591.0
F
RT 303.2
(a) 1.80 volt (b) 1.07 volt (c) 0.82 volt (d) 2.14 volt
119. In respect of the equation a RT/E Aek − = in chemical kinetics, which one of the following statements is correct?
(a) A is adsorption factor (b) Ea
is energy of activation
(c) R is Rydberg’s constant (d) k is equilibrium constant
120. A reduction in atomic size with increase in atomic number is a characteristic of element of
(A) dblock (b) fblock (c) radioactive series (d) high atomic masses
121. The IUPAC name of CH3
COCH(CH3
)
2
is
(a) 2methyl3butanone (b) 4methylisopropyl ketone (c) 3methyl2butanone (d) Isopropylmethyl ketone
122. When CH2
= CH – COOH is reduced with LiAlH4
, the compound obtained will be
(a) CH2
= CH – CH2
OH (b) CH3
– CH2
– CH2
OH
(c) CH3
– CH2
– CHO (d) CH3
– CH2
– COOH
123. According to the kinetic theory of gases, in an ideal gas, between two successive collisions a gas molecule
travels
(a) in a wavy path (b) in a straight line path (c) with an accelerated velocity (d) in a circular path
124. The general formula Cn
H2nO2
could be for open chain
(a) carboxylic acids (b) diols (c) dialdehydes (d) deketones
125. Among the following four structures I to IV.
C2H5CH – C3H7
CH3
CH3C – CHC2H5
O CH3
(i) (ii)
H – C

H
H
⊕
C2H5CHC2H5

CH3
(iii) (iv)
, . It is true that
(a) only I and II are chiral compounds (b) only III i a chiral compound
(c) only II and IV are chiral compounds (d) all four are chiral compounds
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126. What would happen when a solution of potassium chromate is treated with an excess of dilute nitric acid?
(a) Cr2
O2
7
and H2
O are formed (b) CrO2
4
is reduced to +3 state of Cr
(c) CrO2
4
is oxidized to +7 state of Cr (d) Cr3+ and Cr2
O2
7
are formed
127. For making good quality mirrors, plates of float glass are used. These are obtained by floating molten glass
over a liquid metal which does not solidify before glass. The metal used can be
(a) tin (b) sodium (c) magnesium (d) mercury
128. The substance not likely to contain CaCO3
is
(a) calcined gypsum (b) sea shells (c) dolomite (d) a marble statue
129. Complete hydrolysis of cellulose gives
(a) Dribose (b) Dglucose (c) Lglucose (d) Dfructose
130. Which one of the following nitrates will leave behind a metal on strong heating?
(a) Copper nitrate (b) Manganese nitrate (c) Silver nitrate (d) Ferric nitrate
131. During dehydration of alcohols to alkenes by heating with conc. H2
SO4
the initiation step is
(a) formation of carbocation (b) elimination of water
(c) formation of an ester (d) protonation of alcohol molecule
132. The solubilities of carbonates decrease down the magnesium group due to a decrease in
(a) hydration energies of cations (b) interionic attraction
(c) entropy of solution formation (d) lattice energies of solids
133. When rain is accompanied by a thunderstorm, the collected rain water will have a pH value
(a) slightly higher than that when the thunderstorm is not there
(b) uninfluenced by occurence of thunderstorm
(c) which depends on the amount of dust in air
(d) slightly lower than that of rain water without thunderstorm
134. The reason for double helical structure of DNA is operation of
(a) dipoledipole interaction (b) hydrogen bonding (c) electrostatic attractions (d) van der Waals’ forces
135. 25 ml of a solution of barrium hydroxide on titration with a 0.1 molar solution of hydrochloric acid gave a
litre value of 35 ml. The molarity of barium hydroxide solution was
(a) 0.14 (b) 0.28 (c) 0.35 (d) 0.07
136. The correct relationship between free energy change in a reaction and the corresponding equilibrium constant
Kc
is
(a) ∆ G = RT ln Kc
(b) ∆ G0
= RT ln Kc (c) ∆ G0
= RT In Kc
(d) ∆ G = RT ln Kc
137. The rate law for a reaction between the substances A and B is given by Rate = k[A]n
[B]m On doubling the
concentration of A and halving the concentration of B, the ratio of the new rate to the earlier rate of the
reaction will be as
(a) (m + n) (b) ( n – m) (c) 2(n – m) (d) )nm( 2
1
+
138. Ethyl isocyanide on hydrolysis in acidic medium generates
(a) propanoic acid and ammonium salt (b) ethanoic acid and ammonium salt
(c) methylamine salt and ethanoic acid (d) ethylamine salt and methanoic acid
139. The enthalpy change for a reaction does not depend upon
(a) use of different reactants for the same product (b) the nature of intermediate reaction steps
(c) the differences in initial or final temperatures of involved substances
(d) the physical states of reactants and products
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140. A pressure cooker reduces cooking time for food because
(a) boiling point of water involved in cooking is increased
(b) the higher pressure inside the cooker crushes the food material
(c) cooking involves chemical changes helped by a rise in temperature
(d) heat is more evenly distributed in the cooking space
141. For the reaction system: 2NO(g) + O2
(g) → 2NO2
(g) volume is suddenly reduce to half its value by increasing
the pressure on it. If the reaction is of first order with respect to O2
and second order with respect to NO,
the rate of reaction will
(a) diminish to oneeighth of its initial value
(b) increase to eight times of its initial value
(c) increase to four times of its initial value
(d) diminish to onefourth of its initial value
142. Several blocks of magnesium are fixed to the bottom of a ship to
(a) make the ship lighter
(b) prevent action of water and salt
(c) prevent puncturing by undersea rocks
(d) keep away the sharks
143. Which one of the following pairs of molecules will have permanent dipole moments for both members?
(a) NO2
and CO2 (b) NO2
and O3 (c) SiF4
and CO2 (d) SiF4
and NO2
144. Which one of the following groupings represents a collection of isoelectronic species? (At. nos,: 55, Br:35)
(a) N3, F
, Na+ (b) Be, Al3+, Cl (c) Ca2+, Cs+, Br (d) Na+, Ca2+, Mg2+
145. Which one of the following processes will produce hard water?
(a) Saturation of water with MgCO3
(b) Saturation of water with CaSO4
(c) Addition of Na2
SO4
to water
(d) Saturation of water with CaCO3
146. Which one of the following compounds has the smallest bond angle in its molecule?
(a) OH2 (b) SH2 (c) NH3 (d) SO2
147. The pair of species having identical shapes for molecules of both species is
(a) XeF2
, CO2 (b) BF3
, PCl3
(c) PF5
, IF5 (d) CF4
, SF4
148. The atomic numbers of vanadium (V), Chromium (Cr), manganese (Mn) and iron (Fe) are respectively 23,
24, 25 and 26. Which one of these may be expected to have the highest second ionization enthalpy?
(a) Cr (b) Mn (c) Fe (d) V
149. In Bohr series of lines of hydrogen spectrum, the third line from the red end corresponds to which one of the
following interorbit jumps of the electron for Bohr orbits in an atom of hydrogen
(a) 5→2 (b) 4→1 (c) 2→5 (d) 3→2
150. The de Broglie wavelength of a tennis ball of mass 60 g moving with a velocity of 10 metres per second is
approximately
(a) 1031 metres
(b) 1016 metres
(c) 1025 metres
(d) 1033 metres Planck’s constant, h = 6.63×1034 Js.
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14
AIEEE 2003
MATHEMATICS
1. Let 0x,
x
e )x(F dx
d sinx
>
= . If dxe )1(F)k(F
x
3 3 sinx
4
1
−= ∫ then one of the possible values of k, is
(a) 64 (b) 15 (c) 16 (d) 63
2. The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is
increased by 2, then median of the new set
(a) remains the same as that of the original set (b) is increased by 2
(c) is decreased by 2 (d) is two times the original median
3. 5
333
lim
n 5
444
lim
n n
…321 n
n
n…321 +++ − +++ ∞→∞→
(a) 5
1 (b) 30
1 (c) Zero (d) 4
1
4. The normal at the point (bt1
2
, 2bt1
) on a parabola meets the parabola again in the point (bt2
2
, 2bt2
), then
(a)
1
12 t
2
tt += (b)
1
12 t
2
tt −−= (c)
1
12 t
2
tt +−= (d)
1
12 t
2
tt −=
5. If the two circles (x1)2
+ (y3)2
= r2
and x2
+ y2
– 8x + 2y + 8 = 0 intersect in two distinct point, then
(a) r > 2 (b) 2 < r < 8 (c) r < 2 (d) r = 2.
6. The degree and order of the differential equation of the family of all parabolas whose axis is Xaxis, are
respectively.
(a) 2, 3 (b) 2, 1 (c) 1, 2 (d) 3, 2
7. The foci of the ellipse 1
b
y
16
x
2
22
=+ and the hyperbola 25
1
81
y
144
x 22
=− coincide. Then the value of b2
is
(a) 9 (b) 1 (c) 5 (d) 7
8. If f(y) = ey
, g(y) = y; y > 0 and ∫ −=
t
0
)y(g)yt(f)t(F , then
(a) F(t) = tet (b) F(t) = 1 – tet (1 + t) (c) F(t) = et
– (1 + t) (d) F(t) = tet
.
9. The function
log)x(f ++= 1xx 2 , is
(a) neither an even nor an odd function (b) an even function
(c) an odd function (d) a periodic function
10. If the sum of the roots of the quadratic equation ax2
+ bx + c = 0 is equal to the sum of the squares of their
reciprocals, then b
c and
a
b
,
c
a are in
(a) Arithmetic – Geometric Progression (b) Arithmetic Progression
(c) Geometric Progression (d) Harmonic Progression
11. If the system of linear equations
x + 2ay + az = 0 x + 3by + bz = 0 x + 4cy + cz = 0
has a nonzero solution, then a, b, c
(a) satisfy a + 2b + 3c = 0 (b) are in A.P. (c) are in G.P. (d) are in H.P.
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12. A square of side a lies above the xaxis and has one vertex at the origin. The side passing through the origin
makes an angle
π <α<α
4
0 with the positive direction of xaxis. The equation of its diagonal not passing
through the origin is
(a) y(cos α + sin α ) + x(cos α sin α ) = a (b) y(cos α  sin α )  x(sin α  cos α ) = a
(c) y(cos α + sin α ) + x(sin α  cos α ) = a (d) y(cos α + sin α ) + x(sin α + cos α ) = a.
13. If the pair of straight lines x2
 2pxy  y2
= 0 and x2
 2pxy  y2
= 0 be such that each pair bisects the angle
between the other pair, then
(a) pq = 1 (b) p = q (c) p = q (d) pq = 1
14. Locus of a centriod of the triangle whose vertices are (a cos t, a sin t), (b sin t, b cost) and (1, 0), where t is a
parameter, is
(a) (3x + 1)2
+ (3y)2
= a2
 b2 (b) (3x  1)2
+ (3y)2
= a2
 b2
(c) (3x  1)2
+ (3y)2
= a2
+ b2 (d) (3x + 1)2
+ (3y)2
= a2
+ b2
15. If k x
lim log()x3log( )x3
0x = −−+ → , the value of k is
(a) 3
2 − (b) 0 (c) 3
1 − (d) 3
2
16. A couple is of moment G
r
and the force forming the couple is P
r
. If P
r
is turned through a right angle the
moment of the couple thus formed is H
r . If instead, the force P
r are turned through an angle α , then the
moment of couple becomes
(a) cosGsinH α−α r r (b) cosHsinG α−α r r (c) cosGsinH α+α r r (d) cosHsinG α+α r r
17. The resultant of forces andP isQ .R r r r If Q
r is doubled then R
r
is doubled. If the direction of Q
r is reversed, then
R
r
is again doubled. Then P2
: Q2
: R2
is
(a) 2 : 3 : 1 (b) 3 : 1 : 1 (c) 2 : 3 : 2 (d) 1 : 2 : 3
18. The mean and variance of a random variable X having binomial distribution are 4 and 2 respectively, then P
(X = 1) is
(a) 4
1 (b) 32
1 (c) 16
1 (d) 8
1
19. If f(x) = xn
, then the value of !n
)1(f)1( ................. !3
)1(f
!2
)1(f
!1
)1(f )1(f
nn − + ′′′ − ′′ + ′ − is
(a) 1 (b) 2n (c) 2n
 1 (d) 0
20. Let k
ˆ 3jˆ 2i w ˆ andjˆ i
ˆ v,jˆ i
ˆ u ++=−=+= rrr . If nˆ is a unit vector such that .u ˆ = 0nr and .v ˆ = 0nr , then .w nˆ r is equal to
(a) 3 (b) 0 (c) 1 (d) 2
21. A particle acted on by constant forces k
ˆ j
ˆ i
ˆ andk 3 ˆ 3jˆ i
ˆ 4 −+−+ to the point k
ˆ j 5ˆ 4i ˆ −+ . The total work done by
the forces is
(a) 50 units (b) 20 units (c) 30 units (d) 40 units
22. The vectors k
ˆ 4jˆ 2iˆ AC&k 5 ˆ 4iˆ 3AB +−=+= are the sides of a triangle ABC. The length of the median through
A is
(a) 288 (b) 18 (c) 72 (d) 33
23. The area of the region bounded by the curves and1xy −=−= x3y is
(a) 6 sq. units (b) 2 sq. units (c) 3 sq. units (d) 4 sq. units
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16
24. The shortest distance from the plane 12x + 4y + 3z = 327 to the sphere x2
+ y2
+ z2
+ 4x  2y  6z = 155 is
(a) 39 (b) 26 (c) 13
4 11 (d) 13
25. The two lines x = ay + b, z = cy + d and x = a′ y + b′ z = c′ y + d′ will be perpendicular, if and only if
(a) aa′ + c c′ + 1 = 0 (b) aa′ + bb′ + c c′ + 1= 0
(c) aa′ + bb′ + c c′ = 0 (d) (a + a′) (b + b′ ) + (c + c′ ) = 0
26. The lines k
4z
1
3y
1
2x
−
− = − = − and 1
5z
1
4y
k
1x − = − = − are coplanar if
(a) k = 3 or 2 (b) k = 0 or 1 (c) k = 1 or 1 (d) k = 0 or 3
27. If f (a + b  x) = f(x) then ∫
b
a
xf dx)x( is equal to
(a) ∫ −+
+ b
a
dx)xba(f 2
ba
(b) ∫ − + b
a
dx)xb(f 2
ba
(c) ∫ + b
a
dx)x(f 2
ba
(d) ∫ − b
a
dx)x(f 2
ab
28. A body travels a distance s in t seconds. It starts from rest and ends at rest. In the first part of the journey, it
moves with constant acceleration f and in the second part with constant retardation r. The value of t is given by
(a)
+
r
1
f
1 s2 (b)
+
r
1
f
1 s2 (c)
r
1
f
1
s2
+
(d) + )rf(s2
29. Two stones are projected from the top of a cliff h metres high, with the same speed u, so as to hit the ground
at the same spot. If one of the stones is projected at an angle θ to the horizontal then the θ equals
(a) gh
2
u (b) gh
u2
(c) h
u g2 (d)
g
u h2
30. If 1, 2 , ωω are the cube roots of unity, then
nn2
n2n
n2n
1
1
1
ωω
ωω
ωω
=∆ is equal to
(a) 2 ω (b) 0 (c) 1 (d) ω
31. The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a, is
(a)
π
n2
cot
4
a
(b)
π
n
cota (c)
π
n2
cot
2
a
(d)
π
n2
cota
32. If x1
, x2
, x3
and y1
, y2
, y3
are both in G.P. with the same common ratio, then the points (x1
, y1
), (x2
, y2
) and (x3
,
y3
)
(a) are vertices of a triangle (b) lie on a straight line (c) lie on an ellipse (d) lie on a circle
33. If z and ω are two nonzero complex numbers such that =ω 1z and Arg(z)  Arg(ω) = ω
π then, z
2 is equal to
(a) i (b) 1 (c) 1 (d) i.
34. Let Z1
and Z2
be two roots of the equation x2
+ aZ + b = 0 being complex. Further, assume that the origin, Z1
and Z2
form an equilateral triangle. Then
(a) a2
= 4b (b) a2
= b (c) a2
= 2b (d) a2
= 3b
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17
35. The solution of the differential equation ( ) 0
dx
dy ex)y1( tan2 y1
=−++ −
, is
(a) xe ketanytan2 y11
+= −−
(b) tan2 y 1
ke)2x( −
=− (c) xe2 ke tan2ytan y11
+= −−
(d) xe tan ky tan 1y1
+= − −
36. Let f(x) be a function satisfying f′(x) = f(x) with f(0) = 1 and g(x) be a function that satisfies f(x) + g(x) = x2
.
Then the value of the integral ∫
1
0
dx)x(g)x(f , is
(a) 2
5
2
e
e
2
++ (b) 2
5
2
e
e
2
−− (c) 2
3
2
e
e
2
−+ (d) 2
3
2
e
e
2
−−
37. The lines 2x  3y = 5 and 3x  4y = 7 are diameters of a circle having area as 154 sq. units. Then the equation
of the circle is
(a) x2
+ y2
 2x + 2y = 62 (b) x2
+ y2
+ 2x  2y =62
(c) x2
+ y2
+ 2x  2y = 47 (d) x2
+ y2
 2x + 2y = 47
38. Events A, B, C are mutually exclusive events such that 4
x21 and )C(P 4
1x )B(P, 3
1x3 )A(P − = − = + = . The
set of possible values of x are in the interval.
(a) [0, 1] (b)
2
1
,
3
1
(c)
3
2
,
3
1
(d)
3
13
,
3
1
39. Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr.
A selected the winning horse is
(a) 5
2
(b) 5
4
(c) 5
3
(d) 5
1
40. The value of ‘a’ for which one root of the quadratic equation (a2
 5a + 3)x3
+ (3a  1)x + 2 = 0 is twice as large
as the other is
(a) 3
1 − (b) 3
2
(c) 3
2 − (d) 3
1
41. If x is positive, the first negative term in the expansion of (1 + x)27/5 is
(a) 6th term (b) 7th term (c) 5th term (d) 8th term
42. The number of integral terms in the expansion of ( )256
+ 583 is
(a) 35 (b) 32 (c) 33 (d) 34
43. If n
Cr
denotes the number of combination of n things taken r at a time, then the expression n
Cr+1 + n
Cr1 +2xn
Cr
equals
(a) n+1Cr+1 (b) n+2Cr (c) n+2Cr+1 (d) n+1Cr
44. Two particles start simultaneously from the same point and move along two straight lines, one with uniform
velocity u
r and the other from rest with uniform acceleration f
r . Let α be the angle between their directions
of motion. The relative velocity of the second particle w.r.t. the first is least after a time.
(a) f
cosu α (b) f
sinu α (c) u
cosf α (d) u sin α .
45. The upper 4
3 th portion of a vertical pole subtends an angle 5
3
tan−1 at a point in the horizontal plane through
its foot and at a distance 40 m from the foot.
(a) 80 m (b) 20 m (c) 40 m (d) 60 m
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46. In a triangle ABC, medians AD and BE are drawn. If AD = 4, 3
and ABE
6
DAB π =∠ π =∠ , then the area of
the ∆ABC is
(a) 3
64 (b) 3
8 (c) 3
16 (d) 3
32
47. If in a triangle ABC a 2
b3
2
A
cosc
2
C
cos 22 =
+
, then the sides a, b and c
(a) satisfy a+ b = c (b) are in A.P. (c) are in G.P. (d) are in H.P.
48. c,b,a
r r r are 3 vectors, such that =++ 0cba r r r , c,2b,1ar r r == then a.cc.bb.a
rrr rr r ++ is equal to
(a) 1 (b) 0 (c) 7 (d) 7
49. The value of the integral ∫ −=
1
0
n dx)x1(xI is
(a) 2n
1
1n
1
+
+
+ (b) 1n
1
+ (c) 2n
1
+ (d) 2n
1
1n
1
+ − +
50. The value of sinx x
sec dtt
2 x
0
2
lim
0x
∫ → is
(a) 0 (b) 3 (c) 2 (d) 1
51. The radius of the circle in which the sphere
x2
+ y2
+ z2
+ 2x  2y  4z  19 = 0 is cut by the plane x + 2y + 2z + 7 = 0 is
(a) 4 (b) 1 (c) 2 (d) 3
52. A tetrahedron has vertices at O(0, 0, 0), A(1, 2, 1) B(2, 1, 3) and C(1, 1, 2). Then the angle between the
faces OAB and ABC will be
(a) 900 (b)
−
35
19
cos 1 (c)
−
31
17
cos 1 (d) 300
53. Let f(a) = g(a) = k and their nth derivatives fn
(a), gn
(a) exist and are not equal for some n. Further if
4
)x(f)x(g
)a(f)x(f)a(g)a(f)x(g)a(f lim
ax = −
+−− → then the value of k is
(a) 0 (b) 4 (c) 2 (d) 1
54.
[ ]
[ ] 3
lim
2 x
x2
2
x tan1
sin1 x 2
x tan1
−π
+
−
−
π → is
(a) ∞ (b) 8
1 (c) 0 (d) 32
1
55. If the equation of the locus of a point equidistant from the point (a1
, b1
) and
(a2
, b2
) is (a1
 b2
)x + (a1
 b2
)y + c = 0, then the value of ‘c’ is
(a) 2
2
2
2
2
1
2
1 −−+ baba (b) 2
1
2
1
2
2
2
2 baba
2
1
−−+
(c) 2
2
2
1
2
2
2
1 −+− bbaa (d) ( ) 2
2
2
1
2
2
2
1 bbaa
2
1
+++
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56. If 0
c1cc
b1bb
a1aa
32
32
32
=
+
+
+
and vectors (1, a, a2
), (a, b, b2
) and (a, c, c2
) are noncoplanar, then the product abc equals
(a) 0 (b) 2 (c) 1 (d) 1
57. The number of real solutions of the equation x2
 3x + 2 = 0 is
(a) 3 (b) 2 (c) 4 (d) 1
58. If the function f(x) = 2x2
 9ax2
+ 12a2
x + 1, where a > 0, attains its maximum and minimum at p and q
respectively such that p2
= q, then a equals
(a) 2
1 (b) 3 (c) 1 (d) 2
59. If
=
= ≠
+−
0x,0
)x(f xe 0x, x
1
x
1
then f(x) is
(a) discontinuous every where (b) continuous as well as differentiable for all x
(c) continuous for all x but not differentiable at x = 0 (d) neither differentiable nor continuous at x = 0
60. Domain of definition of the function log )xx( x4
3 )x(f 3
2 10 −+ − = , is
(a) (1, 0) ∪ (1, 2) ∪ (2, ∞ ) (b) (0, 2) (c) (1, 0) ∪ (0, 2) (d) (1, 2)∪ (2, ∞ )
61. If f: R →R satisfies f(x + y) = f(x) + f(y), for all x, ∈Ry and f(1) = 7, then ∑=
n
1r
)r(f is
(a) 2
+ )1n(n7 (b) 2
n7
(c) 2
+ )1n(7 (d) 7n+(n+1)
62. The real number x when added to its inverse gives the minimum value of the sum at x equal to
(a) 2 (b) 2 (c) 1 (d) 1
63. Let R1
and R2
respectively be the maximum ranges up and down an inclined plane and R be the maximum
range on the horizontal plane. Then R1
, R, R2
are in
(a) H.P (b) A.G.P (c) A.P (d) G.P.
64. In an experiment with 15 observations on x, the following results were available: 2830x , 2 =Σ =Σ 170x
One observation that was 20 was found to be wrong and was replaced by the correct value 30. The corrected
variance is
(a) 8.33 (b) 78.00 (c) 188.66 (d) 177.33
65. A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the
first five questions. The number of choices available to him is
(a) 346 (b) 140 (c) 196 (d) 280
66. If
αβ
βα =
= A2 and
ab
ba
A , then
(a) 22 ab2 +=β=α ba, (b) ab,ba 22 =β+=α (c) ab2,ba 22 =β+=α (d) 2222 −=β+=α ba,ba
67. The number of ways in which 6 men and 5 women can dine at a found table if no two women are to sit
together is given by
(a) ×57 (b) ×56 (c) 30 (d) ×45
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68. Consider points A, B, C and D with position vectors k
ˆ 4jˆ 3iˆ ,kˆ 10jˆ 6iˆ ,kˆ 7jˆ 4iˆ 7 +−−+−+− and k
ˆ 5jˆ i
ˆ 5 +−
respectively. Then ABCD is a
(a) parallelogram but not a rhombus (b) square (c) rhombus (d) rectangle
69. If andv,u w
rrr are three noncoplanar vectors, then ( )( ) ( ) wvvu.wvu
rrrrrrr −×−−+ equals
(a) wv.u3
rrr × (b) 0 (c) wv.u
rrr × (d) vw.u
rrr ×
70. The trigonometric equation sin1 x = 2sin1 a has a solution for
(a) 2
1
a ≥ (b) 2
1
a
2
1 << (c) all real values of a (d) 2
1
a <
71. Two system of rectangular axes have the same origin. If a plane cuts them at distances a,b,c and c,b,a ′′′ from
the origin then
(a) 0
c
1
b
1
a
1
c
1
b
1
a
1
222222 = ′ − ′ − ′ −++ (b) 0
c
1
b
1
a
1
c
1
b
1
a
1
222222 = ′ + ′ + ′ +++
(c) 0
c
1
b
1
a
1
c
1
b
1
a
1
222222 = ′ − ′ + ′ +−+ (d) 0
c
1
b
1
a
1
c
1
b
1
a
1
222222 = ′ − ′ − ′ +−−
72. If 1
i1
i1 x
=
−
+ then
(a) x = 2n+1, where n is any positive integer (b) x = 4n, where n is any positive integer
(c) x = 2n, where n is any positive integer (d) x = 4n+1, where n is any positive integer
73. A function f from the set of natural numbers to integers defined by
−
=
when, isn even
2
n
when, isn odd
2
1n
)n(f is
(a) neither oneone nor onto (b) oneone but not onto
(c) onto but not oneone (d) oneone and onto both.
74. Let f(x) be a polynomial function of second degree. If f(1) = f(1) and a, b, c are in A.P, then f′(a), f′(c) are
in
(a) ArithmeticGeometric Progression (b) A.P. (c) G.P. (d) H.P.
75. The sum of the series .................... toup. ∞+−
4.3
1
3.2
1
2.1
1
is equal to
(a)
e
4 loge (b) 2 loge
2 (c) loge
21 (d) loge
2
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