CONCEPT RECAPITULATION TEST - II

Question Paper 23 Pages

Joint Entrance Examination (Main)

Concept Recapitulation Test

ARK

Contributed by

Alex Ratan Khare

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com

CONCEPT RECAPITULATION TEST - II

Time Allotted: 3 Hours Maximum Marks: 432


Please read the instructions carefully. You are allotted 5 minutes
specifically for this purpose.
 You are not allowed to leave the Examination Hall before the end of
the test.

INSTRUCTIONS

A. General Instructions
1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.
2. This question paper contains Three Parts.
3. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics.
4. Each part has only one section: Section-A.
5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be
provided for rough work.
6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic
devices, in any form, are not allowed.

B. Filling of OMR Sheet
1. Ensure matching of OMR sheet with the Question paper before you start marking your answers
on OMR sheet.
2. On the OMR sheet, darken the appropriate bubble with black pen for each character of your
Enrolment No. and write your Name, Test Centre and other details at the designated places.
3. OMR sheet contains alphabets, numerals & special characters for marking answers.

C. Marking Scheme For All Three Parts.

(i) Section-A (01 to 03 and 10 to 12) contains 6 multiple choice questions which have only one
correct answer. Each question carries +8 marks for correct answer and – 2 mark for wrong
answer.

Section-A (04 to 09 and 13 to 30) contains 24 multiple choice questions which have only one
correct answer. Each question carries +4 marks for correct answer and – 1 mark for wrong
answer.

Name of the Candidate

Enrolment No.

ALL INDIA TEST SERIES

FIITJEE

JEE (Main), 2014

From Classroom/Integrated School Programs
7 in Top 20, 23 in Top 100, 54 in Top 300, 106 in Top 500 All India Ranks & 2314 Students
from Classroom
/Integrated School Programs & 3723 Students from All Programs have been Awarded a Rank in JEE (Advanced), 2013

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Useful Data

PHYSICS
Acceleration due to gravity g = 10 m/s
2

Planck constant h = 6.6 10

34
J-s
Charge of electron e = 1.6  10

19
C
Mass of electron m
e
= 9.1  10

31
kg
Permittivity of free space 
0
= 8.85  10

12
C
2
/N-m
2
Density of water 
water
= 10
3
kg/m
3

Atmospheric pressure P
a
= 10
5
N/m
2

Gas constant R = 8.314 J K

1
mol

1
CHEMISTRY

Gas Constant R = 8.314 J K

1
mol

1

= 0.0821 Lit atm K

1
mol

1

= 1.987  2 Cal K

1
mol

1

Avogadro's Number N
a
= 6.023  10
23

Planck’s constant h = 6.625  10

34
Js
= 6.625  10
–27
ergs
1 Faraday = 96500 coulomb
1 calorie = 4.2 joule
1 amu = 1.66  10
–27
kg
1 eV = 1.6  10
–19
J

Atomic No: H=1, He = 2, Li=3, Be=4, B=5, C=6, N=7, O=8,
N=9, Na=11, Mg=12, Si=14, Al=13, P=15, S=16,
Cl=17, Ar=18, K =19, Ca=20, Cr=24, Mn=25,
Fe=26, Co=27, Ni=28, Cu = 29, Zn=30, As=33,
Br=35, Ag=47, Sn=50, I=53, Xe=54, Ba=56,
Pb=82, U=92.
Atomic masses: H=1, He=4, Li=7, Be=9, B=11, C=12, N=14, O=16,
F=19, Na=23, Mg=24, Al = 27, Si=28, P=31, S=32,
Cl=35.5, K=39, Ca=40, Cr=52, Mn=55, Fe=56, Co=59,
Ni=58.7, Cu=63.5, Zn=65.4, As=75, Br=80, Ag=108,
Sn=118.7, I=127, Xe=131, Ba=137, Pb=207, U=238.

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P
P
h
h
y
y
s
s
i
i
c
c
s
s PART – I

SECTION – A
Single Correct Choice Type
This section contains 30 multiple choice questions. Each question has four choices (A), (B), (C) and (D)
out of which ONLY ONE is correct.

1. Two similar blocks A and B are riveted rigidly with a rigid rod
of length L such that block A can slide along an inclined
plane as shown in the figure. If masses of the both blocks
and the rod are each equal to m and kinetic friction between
A and inclined plane is 
k
= 0.25 then the magnitude of
acceleration of centre of mass of the block rod system is
(A) 6 m/s
2
(B) 4 m/s
2

(C) 5 m/s
2
(D) 2 m/s
2


k
= 0.25
 = sin

1
(3/5)
L

B

A

2. A wedge of mass M and dimensions as shown in the figure
is lying completely inside a region (I) of zero pressure. The
pressure inside region II is 1 Pa. The surfaces are smooth.
The wedge is imparted an initial velocity v
0
so that it just
travels a distance b inside region II before finally coming to
rest. The value of v
0
is

Region - II

Region
-
I


h

a

b

(A)
abh
M
(B)
3 abh
4 M

(C)
4 abh
3 M
(D)
4 abh
3 M

Space for Rough work
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3. A block A of mass m and a box B of same mass are
lying on a horizontal surface as shown in the above
figure. The coefficient of kinetic friction between the
block and horizontal surface is 
A
, while that
between the box and surface is 
B
. Given that 
B
>

A
. At t = 0, the position is as shown in the figure
and both are simultaneously given a velocity v
0
to
the right. The time after which block will collide with
the right end of the box is

B



L

A

(A)
 
 
B A
2 L
g

  

(B)
 
 
B A
2 L
g

  


(C)
 
 
B A
4 L
g

  

(D)
 
 
B A
4 L
g

  


4. It is observed that only 0.39% of the original radioactive sample remains undecayed after eight
hours. Hence choose the incorrect statement.
(A) The half life of that substance is 1 hr.
(B) The mean life of that substance is 1/ln 2 hr
(C) The decay constant of the substance is ln 2 hr

1
(D) The half life of the substance is 1/2 hr

5. The figure shows a hollow circular tube fixed to a frictionless
horizontal table. It is the top view of the arrangement. A ball
is shot into end A of the tube to leave the other end B at high
speed. The balls diameter is slightly less than the internal
diameter of the tube. Which of the paths below will the ball
follow on the table after it leaves the tube?

A

B

(A)

(B)

(C)

(D) None of these
Space for Rough work
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6. A mass m on the end of an ideal spring stretches the spring
to a length  when at rest. The mass is now set into motion
so that it executes up and down vibrations while swinging
back and forth as a simple pendulum. The mass moves in a
figure eight pattern in a vertical plane a shown in the figure.
The force constant of the spring assuming small oscillations
is

m

m



(A)
mg

(B)
2mg
k

(C)
4mg

(D)
mg
2


7. When an ultrasonic waves travels from air into water,
(A) waves bends towards the normal
(B) frequency of waves changes from air to water.
(C) speed of ultrasonic wave is greater in water than that in air.
(D) speed of ultrasonic wave is less in water than that in air.

8. A narrow tunnel is made through the earth of mass M and radius R from the centre to the surface.
The speed (in m/s) with which a particle should be projected from the centre of the earth through
the tunnel so that it escapes to the space is
(A)
2gR
(B)
gR

(C)
3gR
(D)
2 gR

9. A cubical block of volume v and density 3 is placed inside a
liquid of density  and attached to a spring of spring
constant k as shown in the figure. Assuming ideal spring and
pulley and spring is attached at A which is at R/2 from
centre. The compression in the spring at equilibrium is

A

C

k

(A)
4 vg
k

(B)
2 vg
k


(C)
3 vg
k

(D)
vg
k


Space for Rough work
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10. A conductor having uniform linear charge density

is placed in
circular form in 3 quadrants with different polarities as shown in
the figure. Let
0
E

be the electric field at O. Then the angle
made by
0
E

with the line along y-axis is
(A)
1
1
tan
2

 
 
 
(B)


1
tan 1


(C)
1
1
tan
3

 
 
 
(D) None

O
y

R

+
+
+
+
+

+

+
+
–
–
–
–

–
–
–
–
–

–
–

–
–
–
–
–
x

11. The pulley and the string are light and all the surfaces are frictionless.
The system is initially held at rest and The string is just taut. The 1kg
block on the plane is suddenly imparted a velocity of 5m/s to the left,
and the system is simultaneously released. Find the displacement of
the 1kg block (on the plane) after 3s. [Take g = 10 m/s
2
]

1 kg

1 kg

(A) 10 m (B) 20 m
(C) 30 m (D) 40 m

12. A light thread is wound on a disk of mass m and other end of
thread is connected to a block of mass m, which is placed on a
rough ground as shown in diagram. Find the minimum value
of coefficient of friction for which block remain at rest:
(A)
1
3
(B)
1
4

(C)
1
2
(D)
1
5

m

m
r

13. A milli ammeter of range 5 mA and resistance 0.5

is joined
in a circuit as shown. Find the value of current for which
meter gives full scale deflection when A & B are used as
Terminal:
(A) 50 mA (B) 5 mA
(C) 100 mA (D) 1 A

S

0.5
B

C

D

0.1
0.2 0.3
5 mA

Space for Rough work
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14. In the circuit shown, the batteries E
1
= E
2
= 1 V, E
3
= 2.5 V
and the resistances R
1
= 10

, R
2
= 20

. The potential
difference across the capacitor is
(A) 0.2 V (B) 0.4 V
(C) 0.5 V (D) 1.2 V

E
1

E
2

E
3

R
1

R
2

C

15. A horizontal spring mass system of mass M performs simple harmonic motion of amplitude a
0

and time period T
0
. When the mass M passes through mean position another stationary mass M
sticks to it and both move together. If a and T be new amplitude and time period. Then
(A)
0
a
a
2
 (B)
0
a a 2

(C)
0
T
T
2
 (D) None

16. System is shown in figure. Assume the cylinder
remains in contact with the two wedges. The velocity
of cylinder is

u m/s
2u m/s
30
o
30
o

(A)
u
19 4 3
2
 m/s (B)
13
v
2
m/s
(C)
3v
m/s (D)
7u
m/s

17. Consider the following statements for a particle moving in an elliptic orbit under the influence of a
central force:
(1) The radius vector covers equal area in equal time.
(2) The motion takes place in a plane.
(3) The angular momentum is constant of motion.
Which of options given above are correct?
(A) 1 & 2 only (B) 2 & 3 only
(C) 1 & 3 only (D) all
Space for Rough work
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18. A person is standing on a weighing
machine placed on the floor of an elevator.
The motion of the elevator is shown in the
adjacent diagram. The maximum and the
minimum weights recorded are 66 kg and
57 kg. The magnitude of the upward
accelerations is [Take g = 10 m/s
2
.]

Time in seconds

Velocity

(upward)

10

40

60

(A) 1 m/s
2
(B) 0.5 m/s
2

(C) 2 m/s
2
(D) 0.25 m/s
2

19. When a charge particle of charge 2

c and mass 1 gm is released at origin in gravity free space
having
0
ˆ
E E j


and
0
ˆ
B B j
 

(E
0
= 10
3
N/c and B0 = 5T). Then its speed
(A) depends only of X co-ordinate (B) depends only on Y co-ordinate
(C) depends only on z co-ordinate (D) depends only on X, Y, Z co-ordinate

20. A neutral metallic finite block is placed at large but finite distance from a large charged sheet in
the middle space in front of sheet. Then the block will be
(A) Attracted towards the sheet (B) Repelled away from the sheet
(C) Depend on nature of charge on the sheet (D) Zero force on the block

21. Two equal masses hang on either side of a pulley at the same
height from the ground. The mass on the right is given a
horizontal speed, after some time.
(A) The mass on the left will be nearer to ground.
(B) The mass on the right will be nearer to ground.
(C) Both the masses will be at equal distance from the ground.
(D) Nothing can be said regarding their positions.

u

Ground

22. O is the centre of mass of a body of mass M as shown in the figure.
A, B, C are three different point on the body. OB = 8 cm, OC = 10
cm, BC = 6 cm and OA = 10 cm. Which of the following can be
written by using parallel axis theorem? I
0
is the moment of inertia
about the axis passing through point O and perpendicular to plane of
object.
(A) I
B
= I
C
+ M(BC)
2
(B) I
C
= I
B
+ M(BC)
2

(C) I
A
= I
0
+ M(OB)
2
(D) None of these

O

B

C

A

Space for Rough work

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23. A solid sphere of radius R, and dielectric constant ‘k’ has spherical cavity of radius R/4. A point
charge q
1
is placed in the cavity. Another charge q
2
is placed outside the sphere at a distance of
r from q. Then Coulombic force of interaction between them is found to be ‘F
1
’. When the same
charges are separated by same distance in vacuum then the force of interaction between them is
found to be F
2
then
(A) F
1
= F
2
/k (B) F
2
= F
1
/k
(C) F
1
. F
2
=
1
k
(D) F
1
= F
2

24. The relation between R and r (internal resistance of the battery) for
which the power consumed in the external part of the circuit is
maximum.
(A) R = r (B)
r
R
2


(C) R = 2r (D) R = 1.5 r



R

R

R

R

R

R

4
R

r

25. An equilateral triangular loop having a resistance R and length of each side ‘’ is
placed in a magnetic field which is varying at
dB
dt
= 1 T/s. The induced current
in the loop will be

x x x x

x x x x x x
x x x x x x
x x x x x x
x x x x x x

x x x

(A)
3
4
2
R

(B)
4
3
2
R


(C)
3
4
2
R

(D)
4
3
2
R


26. The temperature of a mono-atomic gas in an uniform container of
length ‘L varies linearly from T
0
to T
L
as shown in the figure. If the
molecular weight of the gas is M
0
, then the time taken by a wave
pulse in travelling from end A to end B is

A B
T
L
T
0
L

(A)
L 0
2L 3M
5R
( T T )
(B)
L 0
0
3(T T )
5RM L


(C)
L 0
2L 3M
5R
( T T )
(D) L
0
L 0
M
2R(T T )


Space for Rough work
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27. 12 identical rods made of same material are arranged in the
form of a cube. The temperature of ‘P’ and ‘R’ are maintained
at 90
0
C and 30
0
C respectively. Then the temperature of
point ‘V’, when steady state is reached,
(A) 65C (B) 60C
(C) 20C (D) 50C

T

U

S

R

V

W

a

30
0
C
90
0
C
Q

P

28. A spring block system with mass of block m and spring constant K (all
the surfaces of block are perfectly reflecting and smooth) is placed on a
smooth horizontal plane as shown in the diagram. A light beam of
intensity I is switched on from rightwards. Find the amplitude of
oscillations of the block.
(A)
I
KC
(B)
2I
KC

(C)
4I
KC
(D) Zero

m

29. A rod of mass M and length L is placed on a smooth horizontal table and is hit by a ball moving
horizontally and perpendicular to length of rod and sticks to it. Then conservation of angular
momentum can be applied
(A) About any point on the rod (B) About a point at the centre of the rod
(C) About end point of the rod (D) None

30. Magnetic force on a spiral carrying current I
0
and placed in magnetic
field B
0
parallel to the plane of spiral as shown in diagram, will be
nearly (initial point, final point and centre lie on a line)
(A) Zero (B)


0 0 2 1
I B r r


(C)


0 0 2 1
I B r r

(D)
0 0 2
1
I B r
r

I
0

r
2

r
1

B
0

Space for Rough work

Page 10

CONCEPT RECAPITULATION TEST - II

CONCEPT RECAPITULATION TEST - II

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