SJGHSHDJHF
VCPL – GMT – 12 – (Paper-I) – PCM – ADV. JEE - 2013
(SET -A)
PHYSICS
PART-I
SECTION – I
Single Correct Answer Type {Negative Marking(–1)}
This section contains 10 multiple choice questions numbered 01 to 10. Each question has 4 choices
(A), (B), (C) and (D), out of which ONLY ONE is correct.
(11 × 3 (–1) = 33)
01.
In Vernier calipers, m divisions of main scale coincide with (m + 1) divisions of vernier scale. If
each division of main scale is d units, the least count of the instrument is
(A)
d
m 1
(B)
d
m 1
(C)
d
m
(D)
md
m 1
02.
Consider two hollow glass spheres, one containing water and other containing mercury each
liquid fills about one tenth of the volume of sphere in zero gravity environment
(A) Water and Mercury floats freely inside sphere
(B) Water forms a layer on the Glass while Mercury floats
(C) Mercury forms a layer on the glass while water floats
(D) Water and Mercury both form a layer on glass
03.
Two Radioactive substances X and Y emit  and  particles respectively. Their disintegration
constants are in the ratio 2 : 3. To have equal rate of disintegration of getting emission of  and 
particles., the ratio of number of atoms of X to that of Y at any time instant is
(A) 2 : 3
(B) 3 : 2
(C) e : 1
(D) (e  1) : 1
04.
A concave lens is placed in the path of a uniform parallel beam of light falling on a screen as
shown, then
C
A
O
B
screen
D
(A) Intensity of light will be the same every where on the screen
(B) Intensity in region AB will be smaller than what it would be in the absence of the lens
(C) In the region AC and BD, the intensity will be smaller than what it would be in the absence
of the lens
(D) In the region AC and BO, the intensity will be greater than what it would be in the absence
of the lens
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SJGHSHDJHF
05.
VCPL – GMT – 12 – (Paper-I) – PCM – ADV. JEE - 2013
(SET -A)
A small body slides over the curved surface of a semicircular fixed cylinder of radius r, kept horizontally
on the ground as shown in the figure. At what height from the ground would the body lose contact with the
surface
body
06.
07.
(A)
2r
3
(B)
2r
5
(C)
r
2
(D)
3r
4
The third overtone of a closed pipe is observed to be in unision with the second overtone of an open pipe.
The ratio of the lengths of the pipes is
(A)
3/ 2
(B) 5 / 3
(C)
7/4
(D) 7/6.
A ray of light is incident normally on the diagonal face of a right–


3

is  sin 37º  
5

angled prism   
08.
5
 as shown. The net deviation suffered by the ray
3
(A) 127º
(B) 101º
(C) 90º
(D) 74º.
The time period of an orbiting satellite is (assuming spherical earth)
(A) Directly proportional to the density of earth
(B) Directly proportional to the square of density of earth
(C) Inversely proportional to the square root of density of earth
(D) Inversely proportional to the density of earth.
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09.
10.
VCPL – GMT – 12 – (Paper-I) – PCM – ADV. JEE - 2013
(SET -A)
Five persons A, B, C, D & E are pulling a cart of mass 100 kg on a smooth surface and cart is
moving with acceleration 3 m/s2 in east direction. When person ‘A’ stops pulling, it moves with
acceleration 1m/s2 in the west direction. When person ‘B’ stops pulling, it moves with
acceleration 24 m/s2 in the north direction. The magnitude of acceleration of the cart when only A
& B pull the cart keeping their directions same as the old directions, is (25/n) m/s2, value of n is
(A) 1
(B) 2
(C) 3
(D) 4
A wire of length L and of 3 identical cells of negligible internal resistance are connected in series.
Due to the current, temperature of wire rises T in time t. A number of N similar cells is now
connected in series with a wire of same material and crossection but length 2 L. The temperature
of wire is raised by same amount T in same time t. Find the value of N
(A) 2
(B) 4
(C) 6
(D) 8
SECTION - II
Linked Compherension Type {Negative Marking(–1)}
(3× 3 (–1) =9)
This section contain 1 paragraphs. Based upon paragraph, 3 multiple choice questions have to be
answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
Paragraph -1 for Question Nos.(11 to 13)
A beam of alpha particles is incident on a target of lead. A particular alpha particle comes in “head-on” to a
particular lead nucleus and stops 6.5 × 1014 m away from the centre of the nucleus. (This point is well outside the
nucleus ). Assume that the lead nucleus which has 82 protons, remains at rest. The mass of alpha particle is 6.6 ×
1027 kg.
11.
12.
13.
The electrostatic potential energy at the instant that the -particle stops is
(A) 3.63 MeV
(B) 40 MeV
(C) 45 MeV
(D) 36.3 MeV
The initial kinetic energy (in Joules) did the alpha particle have
(A) 3.82 × 1013 J
(B) 5.82 × 1013 J
(C) 1.32 × 1012 J
(D) 3.82 × 1012 J
What was the initial speed of alpha particle ?
(A) 1.32 × 107 m/s
(B) 13.2 × 102 m/s
(C) 0.13 × 107 m/s
(D) 132 × 102 m/s
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SJGHSHDJHF
VCPL – GMT – 12 – (Paper-I) – PCM – ADV. JEE - 2013
(SET -A)
SECTION - III
Multiple Correct Answer (S) Type (No Negative Marking)
This section contains 4 multiple choice questions numbered 14 to 17 Each question has 4 choices
(A), (B), (C) and (D) out of which ONE or MORE are correct.
(4× 4 (0) = 16)
14.
As a wave propagates
(A) the wave intensity remains constant for a plane wave
(B) the wave intensity decreases as the inverse of the distance from the source for a spherical wave
(C) the wave intensity decreases as the inverse square of the distance from the source for a
spherical
wave
(D) the wave intensity decreases as the inverse of the distance from the source for a cylindrical
wave
15.
A gas undergoes a process in which its pressure ‘P’ and volume ‘V’ are related as VPn  constant .
The bulk modulus of the gas in this process cannot be equal to
(A) nP
(B) P1/n
(C)
16.
P
n
(D) pn
Let the energy, magnitude of linear momentum and angular frequency of an electron in hydrogen
atom be E, P and  respectively. If n be the corresponding quantum number, then
E
varies as n

(C) P varies as n1/ 2
EP
is independent of n

(D) EP is independent of n
(A)
17.
(B)
Refer to the circuit diagram and corresponding graphs. The current rises when key K is pressed
with R  R1 and L  L1 . The rise of current is shown by curve (i) while curve (ii) shows the rise of
current when R = R2 and L = L2 then (in both the curves final steady current is i0)
i
R
L
l0
(1)
(2)
K
(A) R 1  R 2
(C) L1  L 2
V
O
(B) R 1  R 2
(D) L1  L 2
time
t
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SJGHSHDJHF
VCPL – GMT – 12 – (Paper-I) – PCM – ADV. JEE - 2013
(SET -A)
SECTION – IV
Matrix Match Type (No Negative)
(1 × 8 (0) = 8)
This section contains 1 questions. Each question contains statements given in two columns which
have to be matched. Statements (A, B, C, D) in Column I have to be matched with statement (p, q, r,
s) in Column II. The answers to these questions have to be appropriately bubbled as illustrated in
the following example.
If the correct matches are A–p, s, B–q, r, C–p, q and D–s, then the correctly bubbled 4 X 4
matrix should be as follows:
18.
(A)
A uniform rod of mass M and length L is hinged at one end in a
vertical plane. Rod is rotated with constant angular velocity 
such that it makes constant angle with vertical. In a rotating
frame associated with rod . Match the Column :
Column I
Toque of horizontal component of
hinge reaction about C.O.M.
q
Column II
(p)
MgL
9g2
1 2 4
2
4L 
3MgL
9g2
1 2 4
8
4L 
(B)
Torque of centrifugal force about
hinge
(q)
(C)
Torque of weight of rod about hinge
(r)
(D)
Torque of vertical component of
hinge reaction about C.O.M
(s)
(t)
MgL 1 
9g2
4L24
2MgL 1 
9g2
4L22
zero
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SJGHSHDJHF
VCPL – GMT – 12 – (Paper-I) – PCM – ADV. JEE - 2013
(SET -A)
ANSWNER –KEY
01.
(B)
Since m divisions of main scale is equivalent to (m + 1) divisions of vernier scale, one division of
vernier scale is equivalent to
m
divisions of main scale.
m 1
So, L.C. = 1 division of M.S.  1 division of V.S.

02.
03.
(B)
Cohesive force among Hg molecules is more than adhesive force between water and glass .
Molecules is greater than cohesive force among water molecules.
(B)
x 2
Since,

y 3
N x x  N y  y 
Nx 3

Ny 2
04.
(B)
Concave lens diverse the beam so more lights falls at AC and BD.
05.
(A)
Let normal reaction makes an angle q from vertical, then
mv 2
 mg cos q
r
2r
 height from ground h 
3
v2  2gr(1  cos q) and
06.
(D)
Frequency of the fundamental note in closed pipe is
v
 n1 . Only the odd harmonics,
4 1
3n1 (first overtone)
5n1 (second overtone)
7n1 (third overtone)
_______________________
are present
Frequency of the fundamental note in open pipe is
v
 n2 . All the harmonics
2 2
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SJGHSHDJHF
VCPL – GMT – 12 – (Paper-I) – PCM – ADV. JEE - 2013
(SET -A)
2n2 (second harmonic or first overtone)
3n2 (third harmonic or second overtone)
4n2 ( fourth harmonic or third overtone)
___________________________________
are present
Given that : 7n1  3n2
or
7

1
2
07.
v
v
3
4 1
2 2

7
6
(A)
1
C  sin 1    37º

i1 can be seen to be > 37º
 T.I.R. takes place.
i2 can be seen to be = 37º
 grazing emergence takes place.
 deviation = 127º.
90º
i1
37º
08.
(C)
T  2
09.
i2
r3
1
.

GM e

(1)
When all are pulling
Fnet  100  3iˆ
When ‘A’ stops
Fnet  FA  100 1(iˆ)
When ‘B’ stops
Fnet  FB  100  24 ˆj
…(1)
…(2)
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SJGHSHDJHF
VCPL – GMT – 12 – (Paper-I) – PCM – ADV. JEE - 2013
(SET -A)
From these three get
FA  FB and solve.
10.
(6)
2
V
V 2A
t  ms(T ) 
 dAL(T )
R
L
V 2 ds(T )
 2 
 constant
L
t
(3E )2 ( NE )2
 2 
 N 2  36  N  6
2
L
(2 L)
Passage
11.
(A)
U
1 q1q 2
,
40 r
U  9 10 .
9
q 1  2e, q 2  82.e
 2  82  1.6 1019 
14
2
 5.82 1013 J
6.5 10
 1eV 
U  5.82  1013 J
 3.63 MeV
19 
 1.6  10 
12.
(B)
Apply constant of energy K1 + U1 = K2 + U2
r1 =  and v1 = 0, alpha particle stops implies K2 = 0.
K1  U2  5.82  1013 J .
13.
(A)
1
2k
K  mv 2 so v 
 1.32  107 m/s .
2
m
More than
14.
(A,C,D)
15.
(ABD)
VPn  constant
 VPn  (V  V)(P  P)n
 V  P 
 VP 1 
1 

V 
P 

n
n
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SJGHSHDJHF
VCPL – GMT – 12 – (Paper-I) – PCM – ADV. JEE - 2013
(SET -A)
V
P
 n
V
P
or
Now Bulk modulus B  
16.
P
P

(V / V) n
(A, B)
E
1
n2
Angular momentum L  n
Radius r  n 2
Time period T  n3
Angular frequency  
Speed of electron v 
17.
1
n3
1
n
(A,C)
i  l0 1  e Rt / L  , time constant is
L
R
(1) is rising faster than (2)
L1 L2
V V

and l0 

 R1  R 2
R1 R 2
R1 R 2
 L1  L 2

Match type
18) A – q ; B - p ; C - p ; D - p
Torque due to pseudo force about hinge
RY
RX
q
x
dm( xsinq) 2
d 
M 2
 sin qx  xcos qdx
L
L

M 2
 sin q cos q  x 2dx
L
0
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SJGHSHDJHF

M 2
L3 ML2 
 sin q cos q  
 sin q cos q
L
3
3
VCPL – GMT – 12 – (Paper-I) – PCM – ADV. JEE - 2013
(SET -A)
Torque of Mg about hinge
L
  Mg  sin q
2
For equilibrium
MgL sin q M 2 L2
   sin q cos q
2
L
3
cos q 
g
2L2
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