# (Paper) AIEEE 2008 EXAMINATION PAPER : Code-A6 (Paper -3)

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**AIEEE 2008 EXAMINATION
PAPER (Code-A6)**

**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]**

**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

(4) If det A = ± 1, then A–1 exists but all its entries are not necessarily
integers

**Ans. [2]**

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