(Quiz) : AIEEE 2008 EXAMINATION PAPER Q&A Online Test

51. While measuring the speed of sound by performing a resonance column experiment, a student gets the
first resonance condition at a column length of 18 cm during winter. Repeating the same experiment
during summer, she measures the column length to be x cm for the second resonance. Then
(1) x > 54 (2) 54 > x > 36
(3) 36 > x > 18 (4) 18 > x
Ans. [1]

52. Shown in the figure below is a meter-bridge set up with null deflection in the galvanometer.
55Ω R
G
20 cm
The value of the unknown resistor R is
 (1) 220 Ω (2) 110 Ω
(3) 55 Ω (4) 13.75 Ω
Ans. [1]

53. A spherical solid ball of volume V is made of a material of density ρ1. It is falling through a liquid of
density ρ2 (ρ2 < ρ1). Assume that the liquid applies a viscous force on the ball that is proportional to the
square of its speed υ, i.e., Fviscous = – kυ2 (k > 0). The terminal speed of the ball is
(1)
k
Vgρ1
(2)
k
Vgρ1
(3)
k
Vg(ρ1 − ρ2 )
(4)
k
Vg(ρ1 − ρ2)
Ans. [4]

54. A thin rod of length 'L' is lying along the x-axis with its ends at x = 0 and x = L. Its linear density
(mass/length) varies with x as k
n
L
x 



 , where n can be zero or any positive number. If the position xCM of
the centre of mass of the rod is plotted against 'n', which of the following graphs best approximates the
dependence of xCM on n ?
(1)
xCM
O n
2
L (2)
xCM
O n
2
L
L
(3)
xCM
O n
2
L
L
(4)
xCM
O n
2
L
L
Ans. [4]

55. A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times
smaller. Given that the escape velocity from the earth is 11 km s–1, the escape velocity from the surface of
the planet would be
(1) 11 km s–1 (2) 110 km s–1
(3) 0.11 km s–1 (4) 1.1 km s–1
Ans. [2]

56. An insulated container of gas has two chambers separated by an insulating partition. One of the chambers
has volume V1 and contains ideal gas at pressure P1 and temperature T1. The other chamber has volume V2
and contains ideal gas at pressure P2 and temperature T2. If the partition is removed without doing any
work on the gas, the final equilibrium temperature of the gas in the container will be -
(1)
1 1 2 2
1 1 1 2 2 2
PV P V
P VT P V T
+
+
(2)
1 1 2 2
1 1 2 2 2 1
P V P V
P V T P V T
+
+
(3)
1 1 1 2 2 2
1 2 1 1 2 2
P V T P V T
T T (P V P V )
+
+
(4)
1 1 2 2 2 1
1 2 1 1 2 2
P V T P V T
T T (P V P V )
+
+
Ans.[4]

57. Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total
number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of
– 0.03 mm. While measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm
and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is -
(1) 3.73 mm (2) 3.67 mm
(3) 3.38 mm (4) 3.32 mm
Ans.[3]

58. A horizontal overhead powerline is at a height of 4 m from the ground and carries a current of 100 A from
east to west. The magnetic field directly below it on the ground is (μ0 = 4π × 10–7 T mA–1)
(1) 5 × 10–6 T northward (2) 5 × 10–6 T southward
(3) 2.5 × 10–7 T northward (4) 2.5 × 10–7 T southward
Ans.[2]

59. An experiment is performed to find the refractive index of glass using a travelling microscope. In this
experiment distances are measured by -
(1) a standard laboratory scale (2) a meter scale provided on the microscope
(3) a screw gauge provided on the microscope (4) a vernier scale provided on the microscope
Ans.[4]

60. A 5 V battery with internal resistance 2 Ω and a 2V battery with internal resistance 1Ω are connected to a
10Ω resistor as shown in the figure.
P2
P1
5V 10Ω
2Ω
2V
1Ω
The current in the 10 Ω resistor is -
(1) 0.03 A P1 to P2 (2) 0.03 A P2 to P1
(3) 0.27 A P1 to P2 (4) 0.27 A P2 to P1
Ans.[2]

61. A capillary tube (A) is dipped in water. Another identical tube (B) is dipped in a soap-water solution.
Which of the following shows the relative nature of the liquid columns in the two tubes ?
(1)
A B
(2)
A B
(3)
A B
(4)
A B
Ans.[2]

62. Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area
A = 10 cm2 and length = 20 cm. If one of the solenoids has 300 turns and the other 400 turns, their mutual
inductance is (μ0 = 4π × 10–7 T m A–1)
(1) 4.8 π × 10–4 H (2) 4.8 π × 10–5 H
(3) 2.4 π × 10–4 H (4) 2.4 π × 10–5 H
Ans.[3]

63. A student measures the focal length of a convex lens by putting an object pin at a distance 'u' from the lens
and measuring the distance 'v' of the image pin. The graph between 'u' and 'v' plotted by the student should
look like -
(1)
O u(cm)
v(cm)
(2)
O u(cm)
v(cm)
(3)
O u(cm)
v(cm)
(4)
O u(cm)
v(cm)
Ans.[2]

64. This question contains Statement-1 and Statement-2. Of the four choices given after the statements,
choose the one that best describes the two statements.
Statement-1 :
For a mass M kept at the centre of a cube of side 'a', the flux of gravitational field passing through its sides
is 4 πGM.
and
Statement-2 :
If the direction of a field due to a point source is radial and its dependence on the distance 'r' from the
source is given as r2
1 , its flux through a closed surface depends only on the strength of the source
enclosed by the surface and not on the size or shape of the surface.
(1) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
(2) Statement-1 is true. Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
(3) Statement-1 is true, Statement-2 is false.
(4) Statement-1 is false, Statement-2 is true.
Ans.[1]

65. This question contains Statement-1 and Statement-2. Of the four choices given after the statements,
choose the one that best describes the two statements.
Statement-1 :
Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion.
and
Statement-2 :
For heavy nuclei, binding energy per nucleon increases with increasing Z while for light nuclei it
decreases with increasing Z.
(1) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
(2) Statment-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
(3) Statement-1 is true, Statement-2 is false
(4) Statement-1 is false, Statement-2 is true
Ans.[3]

Directions : Questions No. 66 and 67 are based on the following paragraph.
Consider a block of conducting material of resistivity 'ρ' shown in the figure. Current 'I' enters at 'A' and
leaves from 'D'. We apply superposition principle to find voltage 'ΔV' developed between 'B' and 'C'. The
calculation is done in the following steps :
(i) Take current 'I' entering from 'A' and assume it to spread over a hemispherical surface in the block.
(ii) Calculate field E(r) at distance 'r' from A by using Ohm's law E = ρj, where j is the current per unit
area at 'r'.
(iii) From the 'r' dependence of E(r), obtain the potential V(r) at r.
(iv) Repeat (i), (ii) and (iii) for current 'I' leaving 'D' and superpose results for 'A' and 'D'.
a b a
I ΔV I
A B C D

66. For current entering at A, the electric field at a distance 'r' from A is -
(1) r2
ρI
(2) 2 r2
I
π
ρ
(3) 4 r2
I
π
ρ
(4) 8 r2
I
π
ρ
Ans.[2]

67. ΔV measured between B and C is -
(1)
a
ρI
–
(a b)
I
+
ρ
(2)
2 a
I
π
ρ
–
2 (a b)
I
π +
ρ
(3)
2 (a b)
I
π −
ρ
(4)
a
I
π
ρ
–
(a b)
I
π +
ρ
Ans.[2]
Directions : Questions No.68, 69 and 70 are based on the following paragraph.
Wave property of electrons implies that they will show diffraction effects. Davisson and Germer
demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal
is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere
constructively (see figure),
d
i
• • • • • • • •
• • • • • • • •
• • • • • • • •
Incoming
Electrons
Outgoing
Electrons
Crystal plane

68. If a strong diffraction peak is observed when electrons are incident at an angle 'i' from the normal to the
crystal planes with distance 'd' between them (see figure) de Broglie wavelength λdB of electrons can be
calculated by the relationship (n is an integer).
 (1) 2d cos i = n λdB (2) 2d sin i = n λdB
(3) d cos i = n λdB (4) d sin i = n λdB
Ans. [1]

69. Electrons accelerated by potential V are diffracted from a crystal. If d = 1Å and i = 30°, V should be about
(h = 6.6 × 10–34Js, me = 9.1 × 10–31 kg., e = 1.6 × 10–19 C)
(1) 50 V (2) 500 V
(3) 1000 V (4) 2000V
Ans. [1]

70. In an experiment, electrons are made to pass through a narrow slit of width 'd' comparable to their
de Broglie wavelength. They are detected on a screen at a distance 'D' from the slit (see figure).
d
D
y = 0
Which of the following graphs can be expected to represent the number of electrons 'N' detected as a
function of the detector position 'y' (y = 0 corresponds to the middle of the slit)?
(1) N
y
d (2) N
y
d
(3) N
y
d (4) N
y
d
Ans. [3]

71. Let f : N → Y be a function defined as f(x) = 4x + 3 where
Y = |y ∈ N : y = 4x + 3 for some x ∈ N|. Show that f is invertible and its inverse is
(1) g(y) = 4 +
4
y + 3
(2) g(y) =
4
y + 3
(3) g(y) =
4
y − 3
(4) g(y) =
3
3y + 4
Ans.[3]

72. Let R be the real line. Consider the following subsets of the plane R × R :
S = {(x, y): y = x + 1 and 0 < x < 2}
T = {(x, y) : x – y is an integer}.
Which one of the following is true ?
(1) Both S and T are equivalence relations on R
(2) S is an equivalence relation on R but T is not
(3) T is an equivalence relation on R but S is not
(4) Neither S nor T is an equivalence relation on R
Ans. [3]

73. The conjugate of a complex number is
i 1
1
−
. Then that complex number is
(1)
i 1
1
+
(2)
i 1
1
+
−
(3)
i 1
1
−
(4)
i 1
1
−
−
Ans. [2]

74. The quadratic equations
x2 – 6x + a = 0
and x2
– cx + 6 = 0
have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3.
Then the common root is
(1) 4 (2) 3
(3) 2 (4) 1
Ans. [3]

75. Let A be a square matrix all of whose entries are integers. Then which one of the following is true ?
(1) If det A ≠ ± 1 , then A–1 exists and all its entries are non-integers
(2) If det A = ± 1, then A–1 exists and all its entries are integers
(3) If det A = ± 1, then A–1 need not exist
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(4) If det A = ± 1, then A–1 exists but all its entries are not necessarily integers
Ans. [2]

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