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AIEEE–2011 (Set – Q)

IMPORTANT INSTRUCTIONS

1. Immediately fill in the particulars on this page of the Test Booklet with Blue/Black Ball Point Pen. Use of

Pencil is strictly prohibited.

2. The Answer Sheet is kept inside the Test Booklet. When you are directed to open the Test Booklet, take

out the Answer Sheet and fill in the particulars carefully.

3. The test is of 3 hours duration.

4. The Test Booklet consists of 90 questions. The maximum marks are 360.

5. There are three parts in the question paper A, B, C consisting of Physics, Mathematics, Chemistry having

30 questions in each part of equal weight age. Each question is allotted 4(four) marks for each correct

response.

6. Candidates will be awarded marks as stated above in instruction No. 5 for correct response of each

question 1⁄4 (one fourth) marks will be deducted for indicating incorrect response of each question. No

deduction from the total score will be made if no response is indicated for an item in the answer sheet.

7. There is only one correct response for each question. Filling up more than one response in each question

will be treated as wrong response and marks for wrong response will be deducted accordingly as per

instruction 6 above.

8. Use Blue/Black Ball Point Pen only for writing particulars/marking responses on Side-1 and Side-2 of the

Answer Sheet. Use of pencil is strictly prohibited.

9. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile

phone, any electronic device, etc., except the Admit Card inside the examination hall/room.

10. Rough work is to be done on the space provided for this purpose in the Test Booklet only. This space is

given at the bottom of each page and in 3 pages (Pages 21 – 23) at the end of the booklet.

11. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the

Room/Hall. However, the candidates are allowed to take away this Test Booklet with them.

12. The CODE for this Booklet is Q. Make sure that the CODE printed on Side-2 of the Answer Sheet is the

same as that on this booklet. In case of discrepancy, the candidate should immediately report the matter to

the Invigilator for replacement of both the Test Booklet and the Answer Sheet.

13. Do not fold or make any stray marks on the Answer Sheet.

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AIEEE−2011−2

PART A : PHYSICS

1. The transverse displacement y x,t ( ) of a wave on a string is given by ( ) ( ) 2 2 ax bt 2 ab xt y x,t e− ++

= .

This represents a

(1) wave moving in – x direction with speed b

a

(2) standing wave of frequency b

(3) standing wave of frequency 1

b (4) wave moving in + x direction with a

b

2. A screw gauge gives the following reading when used to measure the diameter of a wire.

Main scale reading : 0 mm

Circular scale reading : 52 divisions

Given that 1 mm on main scale corresponds to 100 divisions of the circular scale.

The diameter of wire from the above date is :

(1) 0.052 cm (2) 0.026 cm (3) 0.005 cm (4) 0.52 cm

3. A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley

has mass m and radius R. Assuming pulley to be a perfect uniform circular disc, the acceleration of the

mass m, if the string does not slip on the pulley, is

(1) g (2) 2

g

3 (3) g

3 (4) 3

g

2

4. Work done in increasing the size of a soap bubble from a radius of 3 cm to 5 cm is nearly (Surface

tension of soap solution = 0.03 Nm−1

):

(1) 0.2π mJ (2) 2π mJ (3) 0.4 π mJ (4) 4π mJ

5. A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at

rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its

other end. During the journey of the insect, the angular speed of the disc:

(1) continuously decreases (2) continuously increases

(3) first increases and then decreases (4) remains unchanged

6. Two particles are executing simple harmonic motion of the same amplitude A and frequency ω along the

x-axis. Their mean position is separated by distance XX A 0 0 ( > ) . If the maximum separation between

them is ( ) X A 0 + , the phase difference between their motion is :

(1) 3

π (2) 4

π (3) 6

π (4) 2

π

7. Two bodies of masses m and 4 m are placed at a distance r. The gravitational potential at a point on the

line joining them where the gravitational field is zero is:

(1) 4Gm

r − (2) 6Gm

r − (3) 9Gm

r − (4) zero

8. Two identical charged spheres suspended from a common point by two massless strings of length l are

initially a distance dd 1 ( ) << apart because of their mutual repulsion. The charge begins to leak from

both the spheres at a constant rate. As a result the charges approach each other with a velocity v. Then

as a function of distance x between them,

(1) 1 v x− ∝ (2) 1/ 2 v x ∝ (3) v x ∝ (4) 1/ 2 v x− ∝

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AIEEE−2011−3

9. A boat is moving due east in a region where the earth’s magnetic field is 5 11 5.0 10 NA m − −− × due north and

horizontal. The boat carries a vertical aerial 2m long. If the speed of the boat is 1.50 ms−1

, the

magnitude of the induced emf in the wire of aerial is :

(1) 0.75 mV (2) 0.50 mV (3) 0.15 mV (4) 1 mV

10. An object, moving with a speed of 6.25 m/s, is decelerated at a rate given by :

dv 2.5 v

dt = −

where v is the instantaneous speed. The time taken by the object, to come to rest, would be :

(1) 2 s (2) 4 s (3) 8 s (4) 1 s

11. A fully charged capacitor C with initial charge q0 is connected to a coil of self inductance L at t = 0. The

time at which the energy is stored equally between the electric and the magnetic field is :

(1) LC

4

π (2) 2 LC π (3) LC (4) π LC

12. Let the x – z plane be the boundary between two transparent media. Medium 1 in z ≥ 0 has a refractive

index of 2 and medium 2 with z < 0 has a refractive index of 3 . A ray of light in medium 1 given by

the vector A 6 3 i 8 3 j 10k → ∧ ∧∧

=+− is incident on the plane of separation. The angle of refraction in

medium 2 is

(1) 450

(2) 600

(3) 750

(4) 300

13. A current I flows in an infinitely long wire with cross section in the form of a semicircular ring of radius R.

The magnitude of the magnetic induction along its axis is

(1) 0

2

I

2 R

μ

π

(2) 0I

2 R

μ

π

(3) 0

2

I

4 R

μ

π

(4) 0

2

I

R

μ

π

14. A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats γ. It is

moving with speed υ and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its

temperature increases by :

(1) ( ) 2 1

M K

2 R

γ −

υ

γ

(2)

2 M K

2R

γ υ (3) ( ) 2 1

M K

2R

γ −

υ (4) ( )

( ) 2 1

M K

2 1R

γ −

υ

γ +

15. A mass M, attached to a horizontal spring, executes S.H.M. with amplitude A1. When the mass M passes

2

A

A

     

is :

(1) M m

M

+ (2)

1/ 2 M

M m

      +

(3)

1/ 2 M m

M

  +     (4) M

M m+

16. Water is flowing continuously from a tap having an internal diameter 3 8 10 m− × . The water velocity as it

leaves the tap is 0.4 ms−1

. The diameter of the water stream at a distance 1 2 10 m− × below the lap is

close to :

(1) 3 7.5 10 m− × (2) 3 9.6 10 m− × (3) 3 3.6 10 m− × (4) 3 5.0 10 m− ×

through its mean position then a smaller mass m is placed over it and both of them move together with

amplitude A2. The ratio of 1

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