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AIEEE – 2007
Max. Marks :360 No. of Questions : 120
SECTION I – PHYSICS
1. A circular disc of radius R is removed from a
bigger circular disc of radius 2R such that the
circumferences of the discs coincide. The centre
of mass of the new disc is a / R form the centre
of the bigger disc. The value of a is
(a) 1/4 (b) 1/3 (c) 1/2 (d) 1/6
2. A round uniform body of radius R, mass M and
moment of inertia I rolls down (without slipping)
an inclined plane making an angle q with the
horizontal. Then its acceleration is
(a)
2
gsin
1 MR / I
q
–
(b)
2
gsin
1 I /MR
q
+
(c) 2
gsin
1 MR / I
q
+
(d)
2
gsin
1 I /MR
q
–
3. Angular momentum of the particle rotating with
a central force is constant due to
(a) constant torque
(b) constant force
(c) constant linear momentum
(d) zero torque
4. A 2 kg block slides on a horizontal floor with a
speed of 4m/s. It strikes a uncompressed spring,
and compresses it till the block is motionless.
The kinetic friction force is 15N and spring
constant is 10,000 N/m. The spring compresses
by
(a) 8.5 cm (b) 5.5 cm
(c) 2.5 cm (d) 11.0 cm
5. A particle is projected at 60o to the horizontal
with a kinetic energy K. The kinetic energy at
the highest point is
(a) K/2 (b) K (c) Zero (d) K/4
6. In a Young’s double slit experiment the intensity
at a point where the path difference is
6
l (l being
the wavelength of light used) is I. If I0 denotes
the maximum intensity,
0
I
I
is equal to
(a) 3
4
(b)
1
2
(c) 3
2
(d) 1
2
7. Two springs, of force constants k1 and k2 are
connected to a mass m as shown. The frequency
of oscillation of the mass is f. If both k1 and k2
are made four times their original values, the
frequency of oscillation becomes
k1 k2
m
(a) 2f (b) f/2 (c) f/4 (d) 4f
8. When a system is taken from state i to state f
along the path iaf, it is found that Q =50 cal and
W = 20 cal. Along the path ibf Q = 36 cal. W
along the path ibf is
f
b
a
i
(a) 14 cal (b) 6 cal
(c) 16 cal (d) 66 cal
9. A particle of mass m executes simple harmonic
motion with amplitude a and frequency n. The
average kinetic energy during its motion from
the position of equilibrium to the end is
(a) 2p2ma2n2 (b) p2ma2n2
(c) 2 2 1
ma
4
n (d) 4p2ma2n2
10. The displacement of an object attached to a
spring and executing simple harmonic motion is
given by x = 2 × 10–2 cos pt metre.The time at
which the maximum speed first occurs is
(a) 0.25 s (b) 0.5 s
(c) 0.75 s (d) 0.125 s
11. In an a.c. circuit the voltage applied is
E = E0 sin wt. The resulting current in the circuit
is I I0 sin t
2
p
w= æç – ÷÷ö ççè ÷ø . The power consumption
in the circuit is given by
(a) P = 2E0I0 (b) E0I0
P
2 =
(c) P = zero (d) 0 0 E I
P
2 =
2007-2 AIEEE-2007 SOLVED PAPER
12. An electric charge 10–3 m C is placed at the origin
(0, 0) of X – Y co-ordinate system. Two points
A and B are situated at ( 2, 2) and (2, 0)
respectively. The potential difference between
the points A and B will be
(a) 4.5 volts (b) 9 volts
(c) Zero (d) 2 volt
13. A battery is used to charge a parallel plate
capacitor till the potential difference between the
plates becomes equal to the electromotive force
of the battery. The ratio of the energy stored in
the capacitor and the work done by the battery
will be
(a) 1/2 (b) 1 (c) 2 (d) 1/4
14. An ideal coil of 10H is connected in series with
a resistance of 5W and a battery of 5V. 2second
after the connection is made, the current flowing
in ampere in the circuit is
(a) (1 – e–1) (b) (1 – e)
(c) e (d) e–1
15. A long straight wire of radius a carries a steady
current i. The current is uniformly distributed
across its cross section. The ratio of the magnetic
field at a/2 and 2a is
(a) 1/2 (b) 1/4 (c) 4 (d) 1
16. A current I flows along the length of an infinitely
long, straight, thin walled pipe. Then
(a) the magnetic field at all points inside the
pipe is the same, but not zero
(b) the magnetic field is zero only on the axis
of the pipe
(c) the magnetic field is different at different
points inside the pipe
(d) the magnetic field at any point inside the
pipe is zero
17. If MO is the mass of an oxygen isotope 17
😯 ,MP
and MN are the masses of a proton and a neutron
respectively, the nuclear binding energy of the
isotope is
(a) (MO –17MN)c2
(b) (MO – 8MP)c2
(c) (MO– 8MP –9MN)c2
(d) MOc2
18. In gamma ray emission from a nucleus
(a) only the proton number changes
(b) both the neutron number and the proton
number change
(c) there is no change in the proton number and
the neutron number
(d) only the neutron number changes
19. If in a p-n junction diode, a square input signal
of 10 V is applied as shown
RL
5V
-5V
Then the output signal across RL will be
(a)
+5V
(b)
10 V
(c)
-10 V
(d)
-5V
20. Photon of frequency n has a momentum
associated with it. If c is the velocity of light,
the momentum is
(a) hn / c (b) n /c
(c) h n c (d) hn / c2
21. The velocity of a particle is v = v0 + gt + ft2. If
its position is x = 0 at t = 0, then its displacement
after unit time (t = 1) is
(a) v0 + g/2 + f (b) v0 + 2g + 3f
(c) v0 + g/2 + f/3 (d) v0 + g + f
22. For the given uniform square lamina ABCD,
whose centre is O,
O
A B
D C
E
F
(a) IAC = 2 IEF (b) 2IAC = IEF
(c) IAD = 3IEF (d) IAC = IEF
23. A point mass oscillates along the x-axis
according to the law x = x0 cos(wt-p/ 4) . If
the acceleration of the particle is written as
a = Acos(wt+d) ,then
(a) 2
A = x0w , d = 3p / 4
(b) A = x0, d=-p/ 4
(c) 2
A = x0w , d = p / 4
(d) 2
A = x0w , d=-p/ 4
AIEEE-2007 SOLVED PAPER 2007-3
24. Charges are placed on the vertices of a square
as shown. Let Eur be the electric field and V the
potential at the centre. If the charges on A and B
are interchanged with those on D and C
respectively, then
A B
D C
q
-q
q
-q
(a) Eur changes, V remains unchanged
(b) Eur remains unchanged, V changes
(c) both Eur and V change
(d) Eur and V remain unchanged
25. The half-life period of a radio-active element X
is same as the mean life time of another radioactive
element Y. Initially they have the same
number of atoms. Then
(a) X and Y decay at same rate always
(b) X will decay faster than Y
(c) Y will decay faster than X
(d) X and Y have same decay rate initially
26. A Carnot engine, having an efficiency of h = 1/
10 as heat engine, is used as a refrigerator. If the
work done on the system is 10 J, the amount of
energy absorbed from the reservoir at lower
temperature is
(a) 100 J (b) 99 J
(c) 90 J (d) 1 J
27. Carbon, silicon and germanium have four
valence electrons each. At room temperature
which one of the following statements is most
appropriate ?
(a) The number of free electrons for
conduction is significant only in Si and Ge
but small in C.
(b) The number of free conduction electrons
is significant in C but small in Si and Ge.
(c) The number of free conduction electrons
is negligibly small in all the three.
(d) The number of free electrons for
conduction is significant in all the three.
28. A charged particle with charge q enters a region
of constant, uniform and mutually orthogonal
fields Eur and Bur with a velocity v r perpendicular
to both Eur and Bur , and comes out without any
change in magnitude or direction of v r . Then
(a) v = B´ E / E2 r ur ur (b) v = E´B/B2 r ur ur
(c) v = B´ E / B2 r ur ur (d) v = E´B / E2 r ur ur
29. The potential at a point x (measured in m m) due
to some charges situated on the x-axis is given
by V(x) = 20/(x2 – 4) volt
The electric field E at x = 4 m m is given by
(a) (10/9) volt/ m m and in the +ve x direction
(b) (5/3) volt/ m m and in the –ve x direction
(c) (5/3) volt/ m m and in the +ve x direction
(d) (10/9) volt/ m m and in the –ve x direction
30. Which of the following transitions in hydrogen
atoms emit photons of highest frequency?
(a) n = 1 to n = 2 (b) n = 2 to n = 6
(c) n = 6 to n = 2 (d) n = 2 to n = 1
31. A block of mass m is connected to another block
of mass M by a spring (massless) of spring
constant k. The block are kept on a smooth
horizontal plane. Initially the blocks are at rest
and the spring is unstretched. Then a constant
force F starts acting on the block of mass M to
pull it. Find the force of the block of mass m.
(a) MF
(m+M)
(b)
mF
M
(c) (M m)F
m
+ (d) mF
(m+M)
32. Two lenses of power –15 D and +5 D are in
contact with each other. The focal length of the
combination is
(a) + 10 cm (b) – 20 cm
(c) – 10 cm (d) + 20 cm
33. One end of a thermally insulated rod is kept at a
temperatureT1 and the other at l2. The rod is
composed of two sections of length l1 and l2 and
thermal conductivities K1 and K2 respectively.
The temperature at the interface of the two
section is
T1 l1 l2 T2
K1 K2
(a) 111 2 2 2
11 2 2
(K T K T )
(K K )
+
+
l l
l l
(b) 2 21 11 2
11 2 2
(K T K T )
(K K )
+
+
l l
l l
(c) 2 11 12 2
21 1 2
(K T K T )
(K K )
+
+
l l
l l
(d) 1 21 2 1 2
12 2 1
(K T K T )
(K K )
+
+
l l
l l
2007-4 AIEEE-2007 SOLVED PAPER
34. A sound absorber attenuates the sound level by
20 dB. The intensity decreases by a factor of
(a) 100 (b) 1000
(c) 10000 (d) 10
35. If CP and CV denote the specific heats of nitrogen
per unit mass at constant pressure and constant
volume respectively, then
(a) CP – CV = 28R (b) CP – CV = R/28
(c) CP – CV = R/14 (d) CP – CV = R
36. A charged particle moves through a magnetic
field perpendicular to its direction. Then
(a) kinetic energy changes but the momentum
is constant
(b) the momentum changes but the kinetic
energy is constant
(c) both momentum and kinetic energy of the
particle are not constant
(d) both momentum and kinetic energy of the
particle are constant
37. Two identical conducting wires AOB and COD
are placed at right angles to each other. The wire
AOB carries an electric current I1 and COD
carries a current I2. The magnetic field on a point
lying at a distance d from O, in a direction
perpendicular to the plane of the wires AOB and
COD, will be given by
(a) 0 2 2
(I1 I2 )
2 d
m
+
p
(b)
1
0 I1 I2 2
2 d
m æ + ö
p ç ÷ è ø
(c) ( )1
0 2 2 2
I1 I2
2 d
m
+
p
(d) 0 ( )
I1 I2
2 d
m
+
p
38. The resistance of a wire is 5 ohm at 50°C and 6
ohm at 100°C. The resistance of the wire at 0°C
will be
(a) 3 ohm (b) 2 ohm
(c) 1 ohm (d) 4 ohm
39. A parallel plate condenser with a dielectric of
dielectric constant K between the plates has a
capacity C and is charged to a potential V volt.
The dielectric slab is slowly removed from
between the plates and then reinserted. The net
work done by the system in this process is
(a) zero (b) 1 2
(K 1) CV
2
–
(c)
CV2 (K 1)
K
– (d) (K -1) CV2
40. If gE and gM are the accelerations due to gravity
on the surfaces of the earth and the moon
respectively and if Millikan’s oil drop
experiment could be performed on the two
surfaces, one will find the ratio
electronic charge on the moon
to be
electronic charge on the earth
(a) gM / gE (b) 1
(c) 0 (d) gE / gM
SECTION II – CHEMISTRY
41. The equivalent conductances of two strong
electrolytes at infinite dilution in H2O (where
ions move freely through a solution) at 25°C are
given below :
3
2
LoCH COONa = 91.0 S cm / equiv.
2
LoHCl = 426.2 S cm / equiv.
What additional information/ quantity one needs
to calculate A° of an aqueous solution of acetic
acid?
(a) Lo of chloroacetic acid (ClCH2COOH)
(b) Lo of NaCl
(c) Lo of CH3COOK
(d) the limiting equivalent coductance of
H
H ( + )
+ l° .
42. Which one of the following is the strongest base
in aqueous solution ?
(a) Methylamine (b) Trimethylamine
(c) Aniline (d) Dimethylamine.
43. The compound formed as a result of oxidation
of ethyl benzene by KMnO4 is
(a) benzyl alcohol (b) benzophenone
(c) acetophenone (d) benzoic acid.
44. TheIUPAC nameof is
(a) 3-ethyl-4-4-dimethylheptane
(b) 1, 1-diethyl-2,2-dimethylpentane
(c) 4, 4-dimethyl-5,5-diethylpentane
(d) 5, 5-diethyl-4,4-dimethylpentane.
AIEEE-2007 SOLVED PAPER 2007-5
45. Which of the following species exhibits the
diamagnetic behaviour ?
(a) NO (b) O2
2– (c) O2
+ (d) O2.
46. The stability of dihalides of Si, Ge, Sn and Pb
increases steadily in the sequence
(a) PbX2 << SnX2 << GeX2 << SiX2
(b) GeX2 << SiX2 << SnX2 << PbX2
(c) SiX2 << GeX2 << PbX2 << SnX2
(d) SiX2 << GeX2 << SnX2 << PbX2.
47. Identify the incorrect statement among the
following.
(a) Br2 reacts with hot and strong NaOH
solution to give NaBr and H2O.
(b) Ozone reacts with SO2 to give SO3.
(c) Silicon reacts with NaOH(aq) in the
presence of air to give Na2SiO3 and H2O.
(d) Cl2 reacts with excess of NH3 to give N2
and HCl.
48. The charge/size ratio of a cation determines its
polarizing power. Which one of the following
sequences represents the increasing order of the
polarizing power of the cationic species, K+,
Ca2+, Mg2+, Be2+?
(a) Ca2+ < Mg2+ < Be+ < K+
(b) Mg2+ < Be2+ < K+ < Ca2+
(c) Be2+ < K+ < Ca2+ < Mg2+
(d) K+ < Ca2+ < Mg2+ < Be2+.
49. The density (in g mL–1) of a 3.60 M sulphuric
acid solution that is 29% H2SO4 (molar mass
= 98 g mol–1) by mass will be
(a) 1.45 (b) 1.64 (c) 1.88 (d) 1.22
50. The first and second dissociation constants of
an acid H2A are 1.0 × 10–5 and 5.0 × 10–10
respectively. The overall dissociation constant
of the acid will be
(a) 0.2 × 105 (b) 5.0 × 10–5
(c) 5.0 × 1015 (d) 5.0 × 10–15.
51. A mixtuve of ethyl alcohol and propyl alcohol
has a vapour pressure of 290 mm at 300 K. The
vapour pressure of propyl alcohol is 200 mm. If
the mole fraction of ethyl alcohol is
0.6, its vapour pressure (in mm) at the same
temperature will be
(a) 360 (b) 350 (c) 300 (d) 700
52. In conversion of lime-stone to lime,
CaCO3(s) ®CaO(s) +CO2(g)
the values of DH° and DS° are + 179.1 kJ mol-1
and 160.2 J/K respectively at 298 K and 1 bar.
Assuming that DH° and DS° do not change with
temperature, temperature above which
conversion of limestone to lime will be
spontaneous is
(a) 1118 K (b) 1008 K
(c) 1200 K (d) 845 K.
53. The energies of activation for forward and
reversereactionsforA2 + B2 2AB are 180
kJ mol–1 and 200 kJ mol–1 respectively. The
presence of a catalyst lowers the activation
energy of both (forward and reverse) reactions
by 100 kJ mol–1. The enthalpy change of the
reaction (A2 + B2® 2AB) in the presence of a
catalyst will be (in kJ mol–1)
(a) 20 (b) 300 (c) 120 (d) 280
54. The cell,
2 2
Zn | Zn (1 M) || Cu (1 M) | Cu (E cell 1.10 V) + + ° =
was allowed to be completely discharged at 298
K. The relative concentration of Zn2+ to Cu2+
2
2
[Zn ]
[Cu ]
+
+
æ ö
çç ÷÷
è ø
is
(a) 9.65 × 104 (b) antilog (24.08)
(c) 37.3 (d) 1037.3.
55. The pKa of a weak acid (HA) is 4.5. The pOH
of an aqueous buffer solution of HA in which
50% of the acid is ionized is
(a) 7.0 (b) 4.5 (c) 2.5 (d) 9.5
56. Consider the reaction, 2A + B ® products.
When concentration of B alone was doubled, the
half-life did not change. When the concentration
of A alone was doubled, the rate increased by
two times. The unit of rate constant for this
reaction is
(a) s–1 (b) L mol–1 s–1
(c) no unit (d) mol L–1 s–1.
57. Identify the incorrect statement among the
following:
(a) 4f and 5f orbitals are equally shielded.
(b) d-Block elements show irregular and erratic
chemical properties among themselves.
(c) La and Lu have partially filled d-orbitals
and no other partially filled orbitals.
(d) The chemistry of various lanthanoids is
very similar.
58. Which of the following has a square planar
geometry?
(a) [PtCl4]2– (b) [CoCl4]2–
(c) [FeCl4]2– (d) [NiCl4]2–
(At. nos.: Fe = 26, Co = 27, Ni = 28, Pt = 78)
2007-6 AIEEE-2007 SOLVED PAPER
59. Which of the following molecules is expected
to rotate the plane of plane-polarised light?
(a)
COOH
H2N H
H
(b)
CHO
HO
CH2OH
H
(c)
SH
(d)
NH2
Ph Ph
H N 2
H H
60. The secondary structure of a protein refers to
(a) fixed configuration of the polypeptide
backbone
(b) a - helical backbone
(c) hydrophobic interactions
(d) sequence of a - amino acids.
61. Which of the following reactions will yield
2, 2-dibromopropane?
(a) CH3 – CH = CH2 + HBr ®
(b) CH3 – C º CH + 2HBr ®
(c) CH3CH = CHBr + HBr ®
(d) CH º CH + 2HBr ®
62. In the chemical reaction,
CH3CH2NH2 + CHCl3 + 3KOH ® (A) + (B)
+ 3H2O, the compounds (A) and (B) are
respectively
(a) C2H5NC and 3KCl
(b) C2H5CN and 3KCl
(c) CH3CH2CONH2 and 3KCl
(d) C2H5NC and K2CO3.
63. The reaction of toluene with Cl2 in presence of
FeCl3 gives predominantly
(a) m-chlorobenzene
(b) benzoyl chloride
(c) benzyl chloride
(d) o- and p-chlorotoluene.
64. Presence of a nitro group in a benzene ring
(a) deactivates the ring towards electrophilic
substitution
(b) activates the ring towards electrophilic
substitution
(c) renders the ring basic
(d) deactivates the ring towards nucleophilic
substitution.
65. In which of the following ionization processes,
the bond order has increased and the magnetic
behaviour has changed?
(a) N2 ®N2+ (b) C2 ®C2+
(c) NO ® NO+ (d) O2 ®O2+ .
66. The actinoids exhibit more number of oxidation
states in general than the lanthanoids. This is
because
(a) the 5f orbitals extend further from the
nucleus than the 4f orbitals
(b) the 5f orbitals are more buried than the 4f
orbitals
(c) there is a similarity between 4f and 5f
orbitals in their angular part of the wave
function
(d) the actinoids are more reactive than the
lanthanoids.
67. Equal masses of methane and oxygen are mixed
in an empty container at 25°C. The fraction of
the total pressure exerted by oxygen is
(a) 1/2 (b) 2/3
(c) 1 273
3 298
´ (d) 1/3.
68. A 5.25% solution of a substance is isotonic with a
1.5% solution of urea (molar mass = 60 g mol–1)
in the same solvent. If the densities of both the
solutions are assumed to be equal to 1.0 g cm–3,
molar mass of the substance will be
(a) 210.0 g mol–1 (b) 90.0 g mol–1
(c) 115.0 g mol–1 (d) 105.0 g mol–1.
69. Assuming that water vapour is an ideal gas, the
internal energy change (DU) when 1 mol of
water is vapourised at 1 bar pressure and 100°C,
(given : molar enthalpy of vapourisation of water
at 1 bar and 373 K = 41 kJ mol–1 and R = 8.3 J
mol–1 K–1) will be
(a) 41.00 kJ mol–1 (b) 4.100 kJ mol–1
(c) 3.7904 kJ mol–1 (d) 37.904 kJ mol–1
AIEEE-2007 SOLVED PAPER 2007-7
70. In a saturated solution of the sparingly soluble
strong electrolyte AgIO3 (molecular mass = 283)
the equilibrium which sets in is AgIO3 (s)
Ag (aq) IO3(aq) + + - . If the solubility product
constant Ksp of AgIO3 at a given temperature is
1.0 × 10–8, what is the mass of AgIO3 contained
in 100 ml of its saturated saolution?
(a) 1.0 × 10– 4 g (b) 28.3 × 10–2 g
(c) 2.83 × 10–3 g (d) 1.0 × 10–7 g.
71. A radioactive element gets spilled over the floor
of a room. Its half-life period is 30 days. If the
initial velocity is ten times the permissible value,
after how many days will it be safe to enter the
room?
(a) 100 days (b) 1000 days
(c) 300 days (d) 10 days.
72. Which one of the following conformations of
cyclohexane is chiral?
(a) Boat (b) Twist boat
(c) Rigid (d) Chair.
73. Which of the following is the correct order of
decreasing SN2 reactivity?
(a) R2CH X > R3C X > RCH2 X
(b) RCH X > R3C X > R2CH X
(c) RCH2 X > R2CH X > R3C X
(d) R3C X > R2CH X > RCH2 X.
(X is a halogen)
74. In the following sequence of reactions,
P I2 Mg HCHO
3 2 ether
CH CH OH¾¾+¾®A ¾¾¾®B¾¾¾¾®
C¾H¾2O¾®D
the compound D is
(a) propanal (b) butanal
(c) n-butyl alcohol (d) n-propyl alcohol.
75. Which of the following sets of quantum numbers
represents the highest energy of an atom?
(a) n = 3, l = 0, m = 0, s = +1/2
(b) n = 3, l = 1, m = 1, s = +1/2
(c) n = 3, l = 2, m = 1, s = +1/2
(d) n = 4, l = 0, m = 0, s = +1/2.
76. Which of the following hydrogen bonds is the
strongest?
(a) O – H – – – F (b) O – H – – – H
(c) F – H – – – F (d) O – H – – – O.
77. In the reaction,
3
2A (s) 6HC (aq) 2A (aq) 6C (aq) 3H2(g) l + l ® l + + l- +
(a) 11.2 L H2(g) at STP is produced for every
mole HCl(aq) consumed
(b) 6 L HCl(aq) is consumed for every 3 L H2(g)
produced
(c) 33.6 L H2(g) is produced regardless of
temperature and pressure for every mole
Al that reacts
(d) 67.2 H2(g) at STP is produced for every
mole Al that reacts.
78. Regular use of the following fertilizers increases
the acidity of soil?
(a) Ammonium sulphate
(b) Potassium nitrate
(c) Urea
(d) Superphosphate of lime.
79. Identify the correct statement regarding a
spontaneous process:
(a) Lowering of energy in the process is the
only criterion for spontaneity.
(b) For a spontaneous process in an isolated
system, the change in entropy is positive.
(c) Endothermic processes are never
spontaneous.
(d) Exothermic processes are always
spontaneous.
80. Which of the following nuclear reactions will
generate an isotope?
(a) b – particle emission
(b) Neutron praticle emission
(c) Positron emission
(d) a – particle emission.
SECTION III – MATHEMATICS
81. The resultant of two forces Pn and 3n is a force
of 7n. If the direction of 3n force were reversed,
the resultant would be 19 n. The value of P is
(a) 3 n (b) 4 n
(c) 5 n (d) 6 n.
82. Two aeroplanes I and II bomb a target in
succession. The probabilities of I and II scoring
a hit correctly are 0.3 and 0.2, respectively. The
second plane will bomb only if the first misses
the target. The probability that the target is hit
by the second plane is
(a) 0.2 (b) 0.7
(c) 0.06 (d) 0.14.
2007-8 AIEEE-2007 SOLVED PAPER
83. If D =
1 1 1
1 1 x 1
1 1 1 y
+
+
for x ¹ 0, y ¹ 0 , then D
is
(a) divisible by x but not y
(b) divisible by y but not x
(c) divisible by neither x nor y
(d) divisible by both x and y
84. For the Hyperbola
2 2
2 2
x y
1
cos sin
– =
a a
, which of
the following remains constant when a varies =?
(a) abscissae of vertices
(b) abscissae of foci
(c) eccentricity
(d) directrix.
85. If a line makes an angle of p / 4 with the positive
directions of each of x- axis and y- axis, then the
angle that the line makes with the positive
direction of the z-axis is
(a)
4
p (b)
2
p (c)
6
p (d) 3
p
86. A value of c for which conclusion of Mean Value
Theorem holds for the function f (x) = loge x on
the interval [1, 3] is
(a) log3e (b) loge3
(c) 2 log3e (d)
1
2
log3e
87. The function f (x) = tan–1(sin x + cos x) is an
increasing function in
(a) 0,
2
æ pö
çè ÷ø
(b) ,
2 2
æ p pö ç- ÷ è ø
(c) ,
4 2
æ p pö
çè ÷ø
(d) ,
2 4
æ p pö ç- ÷ è ø
88. Let A =
5 5
0 5
0 0 5
a a
a a. If 2A25 = , then a
equals
(a) 1/5 (b) 5 (c) 52 (d) 1
89. The sum of series
1 1 1
2! 3! 4!
– + -……. upto
infinity is
(a) 1
e 2
– (b) 1
e 2
+ (c) e–2 (d) e–1
90. If ˆu and ˆv are unit vectors and q is the acute
angle between them, then 2 ˆu ×3 ˆv is a unit
vector for
(a) no value of q
(b) exactly one value of q
(c) exactly two values of q
(d) more than two values of q
91. A particle just clears a wall of height b at a
distance a and strikes the ground at a distance c
from the point of projection. The angle of
projection is
(a) 1 bc
tan
a(c a)
–
–
(b) 1 bc
tan
a
–
(c) 1 b
tan
ac
– (d) 45°.
92. The average marks of boys in class is 52 and
that of girls is 42. The average marks of boys
and girls combined is 50. The percentage of boys
in the class is
(a) 80 (b) 60
(c) 40 (d) 20.
93. The equation of a tangent to the parabola
y2 = 8x is y = x + 2. The point on this line from
which the other tangent to the parabola is
perpendicular to the given tangent is
(a) (2, 4) (b) (–2, 0)
(c) (–1, 1) (d) (0, 2)
94. If (2, 3, 5) is one end of a diameter of the sphere
x2 + y2 + z2 – 6x – 12y – 2z + 20 = 0, then the
cooordinates of the other end of the diameter
are
(a) (4, 3, 5) (b) (4, 3, – 3)
(c) (4, 9, – 3) (d) (4, –3, 3).
95. Let a = ˆi + ˆj+ kˆ , b = ˆi – ˆj+ 2kˆ r r and cr = xˆi + (x – 2)ˆj- kˆ .
If the vectors c r lies in the plane of ar and b r ,
then x equals
(a) – 4 (b) – 2
(c) 0 (d) 1.
96. Let A (h, k), B(1, 1) and C (2, 1) be the vertices
of a right angled triangle with AC as its
hypotenuse. If the area of the triangle is 1square
unit, then the set of values which ‘k’ can take is
given by
(a) {–1, 3} (b) {–3, –2}
(c) {1, 3} (d) {0, 2}
AIEEE-2007 SOLVED PAPER 2007-9
97. Let P = (–1, 0), Q = (0, 0) and R = (3, 3 3 ) be
three point. The equation of the bisector of the
angle PQR is
(a)
3
x y 0
2
+ = (b) x + 3y = 0
(c) 3x + y = 0 (d)
3xy 0
2
+ = .
98. If one of the lines of my2 + (1– m2) xy – mx2= 0
is a bisector of the angle between the lines xy =
0, then m is
(a) 1 (b) 2
(c) –1/2 (d) –2.
99. Let F(x) = f (x) + f 1
x
æ ö
çè ÷ø
,where
x
l
log t
f (x) dt,
1 t
=
+ ò Then F(e) equals
(a) 1 (b) 2
(c) 1/2 (d) 0,
100. Let f : R ® R be a function defined by
f (x) = min {x +1, x +1} ,Then which of the
following is true ?
(a) f (x) is differentiable everywhere
(b) f (x) is not differentiable at x = 0
(c) f (x) ³ 1 for all x ÎR
(d) f (x) is not differentiable at x = 1
101. The function f : R /{0}® R given by
2x
1 2
f (x)
x e 1
= –
–
can be made continuous at x = 0 by defining f
(0) as
(a) 0 (b) 1
(c) 2 (d) – 1
102. The solution for x of the equation
x
2
2
dt
t t 1 2
p
=
– ò is
(a) 3
2
(b) 2 2
(c) 2 (d) p .
103.
dx
cos x + 3 sin x ò equals
(a) log tan x
C
2 12
æ p ö ç + ÷ +
è ø
(b) log tan x
C
2 12
æ p ö ç – ÷ +
è ø
(c)
1
2
log tan x
C
2 12
æ p ö ç + ÷ +
è ø
(d)
1
2
log tan
x
C
2 12
æ p ö ç – ÷ +
è ø
104. The area enclosed between the curves y2 = x
and y = | x | is
(a) 1/6 (b) 1/3
(c) 2/3 (d) 1.
105. If the difference between the roots of the equation
x2 + ax + 1 = 0 is less than 5 , then the set of
possible values of a is
(a) (3,¥) (b) (-¥,-3)
(c) (– 3, 3) (d) (-3, ¥) .
106. In a geometric progression consisting of positive
terms, each term equals the sum of the next two
terms. Then the common ratio of its progression
is equals
(a) 5 (b) ( ) 1
5 1
2
–
(c) 1 ( )
1 5
2
– (d) 1
5
2
.
107. If 1 1 x 5
sin cosec
5 4 2
– æ ö + – æ ö = p ç ÷ ç ÷
è ø è ø
, then the values
of x is
(a) 4 (b) 5
(c) 1 (d) 3.
108. In the binomial expansion of (a – b)n, n ³ 5, the
sum of 5th and 6th terms is zero, then a/b equals
(a) n 5
6
– (b)
n 4
6
–
(c) 5
n – 4
(d)
6
n – 5
.
2007-10 AIEEE-2007 SOLVED PAPER
109. The set S : = {1, 2, 3, ……., 12} is to be partitioned
into three sets A, B, C of equal size. Thus A È
B È C = S, AÇB = BÇC = AÇC = f. The
number of ways to partition S is
(a)
3
12!
(4!)
(b)
4
12!
(4!)
(c) 3
12!
3!(4!)
(d) 4
12!
3!(4!)
110. The largest interval lying in ,
2 2
æ -p p ö
ç ÷
è ø
for which
the function,
x2 1 x
f (x) 4 cos 1 log(cos x)
2
= – + – æ – ö + ç ÷
è ø
, is
defined, is
(a) ,
4 2
é p p ö ê- ÷ ë ø
(b) 0,
2
é p ö
ê ÷ ë ø
(c) [0,p] (d) ,
2 2
æ p p ö ç – ÷
è ø
111. A body weighing 13 kg is suspended by two
strings 5m and 12m long, their other ends being
fastened to the extremities of a rod 13m long. If
the rod be so held that the body hangs
immediately below the middle point, then
tensions in the strings are
(a) 5 kg and 12 kg (b) 5 kg and 13 kg
(c) 12 kg and 13 kg (d) 5 kg and 5 kg
112. A pair of fair dice is thrown independently three
times. The probability of getting a score of
exactly 9 twice is
(a) 8/729 (b) 8/243
(c) 1/729 (d) 8/9.
113. Consider a family of circles which are passing
through the point (– 1, 1) and are tangent to xaxis.
If (h, k) are the coordinate of the centre of
the circles, then the set of values of k is given by
the interval
(a) 1 1
k
2 2
– £ £ (b) 1
k
2
£
(c) 1
0 k
2
£ £ (d)
1
k
2
³
114. Let L be the line of intersection of the planes
2x + 3y + z = 1 and x + 3y + 2z = 2. If L makes
an angle a with the positive x-axis, then cos a
equals
(a) 1 (b)
1
2
(c)
1
3
(d) 1
2
.
115. The differential equation of all circles passing
through the origin and having their centres on
the x-axis is
(a) 2 2 dy
y x 2xy
dx
= +
(b) 2 2 dy
y x 2xy
dx
= –
(c) 2 2 dy
x y xy
dx
= +
(d) 2 2 dy
x y 3xy
dx
= + .
116. If p and q are positive real numbers such that p2
+ q2 = 1, then the maximum value of (p + q) is
(a)
1
2
(b)
1
2
(c) 2 (d) 2.
117. A tower stands at the centre of a circular park. A
and B are two points on the boundary of the park
such that AB (= a) subtends an angle of 60° at
the foot of the tower, and the angle of elevation
of the top of the tower from A or B is 30°. The
height of the tower is
(a) a/ 3 (b) a 3
(c) 2a/ 3 (d) 2a 3.
118. The sum of the series
20 20 20 20
C0 – C1 + C2 – C3 + …..
20
-…..+ C10 is
(a) 0 (b) 20
C10
(c) 20
– C10 (d) 20
10
1
C
2
119. The normal to a curve at P(x, y) meets the xaxis
at G. If the distance of G from the origin is
twice the abscissa of P, then the curve is a
(a) circle (b) hyperbola
(c) ellipse (d) parabola.
120. If | z + 4 | £ 3, then the maximum value of
| z + 1 | is
(a) 6 (b) 0 (c) 4 (d) 10