CONCEPT RECAPITULATION TEST - III

Question Paper 22 Pages

Joint Entrance Examination (Main)

Concept Recapitulation Test

BSP

Contributed by

Bishnu Singh Pau

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 - III

Time Allotted: 3 Hours Maximum Marks: 360


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 30) contains 30 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. An electron is released from rest at one point in a uniform electric field and travels a distance of
10 cm in 10
-7
seconds. Potential difference across the points is
(A) 11.375 volts (B) 10 volts
(C) 5 volts (D) 5.7 volts

2. A snapshot of a petrol engine is given in which piston is
moving downwards with velocity
40 3m / s.
Find the
angular velocity of the shaft.
(A) 400 rad/s
(B) 300 rad/s
(C) 200 rad/s
(D) 500 rad/s



40 3 m/s

30


120°

10 3 cm

3. A particle of mass m moves in the potential shown in the
figure. The particle has energy E. The period of the motion
the particle is
(A)
2
m 2E
2 2
k
mg
 
(B)
2
m 2E
2
k
mg
 
(C)
2
m 2E
2
k
mg
 
(D)
2
m 2E
k
mg
 

2
1
U kx
2


U = mgx

x > 0

x < 0

x
U

Space for Rough work

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4. A electron is projected normally from the surface of a sphere with
speed v
0
in a uniform magnetic field perpendicular to the plane of
the paper such that its strikes symmetrically opposite on the sphere
with respect to the x-axis. Radius of the sphere is ‘a’ and the
distance of its centre from the wall is ‘b’. What should be magnetic
field such that the charge particle just escapes the wall
(A)
0
2 2
2bmv
B
(b a )e



(B)
0
2 2
2bmv
B
(a b )e



wall

B

v
0
a

b
x

(C)
2 2
0
(a b )
B
2bmv


(D)
2 2
0
me(b a )
B
2bmv



5. A particle with positive charge Q and mass m enters a magnetic field of
magnitude B, existing only to the right of boundary YZ. The direction of
the motion of the particle is perpendicular to the direction of B. Let
m
T 2
QB
 
 
 
 
. The time spent by the particle in the field will be
(A) T
(B) 2T
(C)
2
T
2
  
 
 

 

(D)
2
T
2
  
 
 

 


×

B

m

Q

Y

Z

×

×

×

×

×

×

×

×

6. If net external torque, about a point, acting on the system is zero, then we can surely say
(A) Kinetic energy of the system remains constant
(B) Mechanical energy of the system remains constant
(C) Torque of Internal forces is zero
(D) Momentum of system will remain constant.
7. 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
Space for Rough work
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8. A metal block of mass m is placed on a smooth metallic plane in support with
string as shown in diagram. If, after long time due to corrosion, the contact
surface becomes rough with coefficient of friction

, then friction force acting
on the block will be
(A)
mgcos
 

(B)
mgsin


(C) mg
(D) None

m


9. A uniform rod of mass 2M and length 2L is bent at its mid point to form an L shape. Then,
moment of inertia of the system about an axis symmetrical to both straight parts of L shaped rod
is
(A)
2
7
ML
5
(B)
2
1
ML
3

(C)
2
7
ML
24
(D)
2
ML
2

10. Which of the following is correct about principle of conservation of momentum?
(A) Conservation of momentum can be applied only in absence of external forces
(B) Conservation of momentum can be applied only during collisions of bodies
(C) Conservation of momentum can be applied in a process even in the presence of external
forces
(D) Conservation of momentum is not applicable in rocket propulsion

11. A rod revolves with a constant angular velocity  about a vertical axis A.
The rod makes a fixed angle  with the horizontal. A body of mass m can
slide along the rod and it has tendency to slide down, the angle of friction
being . The value of  so that “m” remains at rest (relative to the rod) is
given by
(A)
2
L
tan( ) cos
g

    
(B)
2
L
tan( ) cos
g

    

(C) 
2
Lsin(+) = gcos (D) 
2
Lsin(  ) = g cos



A

m



L

12. Two long cylindrical coils with uniform winding of the same length and
nearly the same radius having inductances L
1
and L
2
. The coils are
coaxially inserted into each other and connected to a current source as
shown in the figure. The inductance L of the composite system is
(A) L
1
+ L
2

(B) L
1
L
2
(L
1
+L
2
)
(C) L
1
+ L
2
+
1 2
L L

(D) L
1
+ L
2
+ 2
1 2
L L

I

I

Space for Rough work
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13. A disturbance can be written as y(x, t) =
 
2
2
a
x b
2xt b t
e e e


 
 
. The disturbance is
(A) not a travelling wave
(B) a travelling wave with speed v = a
(C) a travelling wave with speed v = a/b
(D) a travelling wave with speed v = b

14. Which of the following is cause of dispersion of a white light by a prism
(A) waves of different frequencies lose energy at different rates.
(B) waves of different amplitudes lose energy at different rate.
(C) waves of different frequencies travel through the medium at different speeds
(D) waves of different amplitudes travels through the medium with different wavelengths.

15. A thick rope of length 2L and linear mass density 9 is joined at B
to a thin rope of length L and linear mass density 4. The system
is horizontally stretched by the two vertical wall A and C.
Assuming B to be a node, find the minimum number of loops in
the thick rope.
(A) 1 (B) 2
(C) 3 (D) 4

9


2
L

L

4


A

C

B

16. In an L-C-R series circuit, it is found that the power factor is maximum. Then the angular
frequency of the emf source must be equal to
(A)
1
LC
(B) zero
(C) a very large number (D) none of these

17. A car approaches an inclined wall (see in the figure) with speed v
0

an a horizontal road. When the horn of frequencies f
0
is sounded,
the beat frequencies heard by the person on the car is (v = speed
of sound)
(A)
0 0
0
v f
v v

(B)
0 0
0
2v f
2v v


(C)
 
0 0
0
v f
2 v v

(D)
0 0
0
2v f
v v


30


v
0
v
0

18. The speed of the colliding electron is increased in an X-ray tube, then
(A) the cutoff wavelength must increase
(B) the cutoff frequency must increase
(C) the intensity of the X-rays must increase.
(D) the types of characteristic X-rays must increase
Space for Rough work

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19. If white light is used in an YDSE setup, the nearest bright fringe from the central fringe will be
(A) white (B) violet
(C) red (D) yellow

20. A particle is placed in a cart. Initial location of the particle is taken as origin in ground frame. At
t = 0, the cart starts moving along x-axis with uniform velocity 2m/s and at the same instant the
particle starts moving with
ˆ
2xj
relative to cart where x is x-coordinate of the cart. Which of the
following is the radius of curvature of the trajectory of the particle in ground frame when it’s
tangential acceleration is equal to normal acceleration in magnitude?
(A)
1
m
2
(B)
2
2
m
(C)
3
2 2
m (D)
4
m
2

21. A boat crosses a 2.4km wide river to reach the a point A on the
opposite bank, located at 37° with the flow, in 500s. The same
boat takes the same time (500s) to reach another point B on the
opposite bank located at 53° with the flow. the speed of flow of
the river is
(A) 5 m/s
(B) 10 m/s
(C) 15 m/s
(D) none of these

0

37°

53°

B

A

22. A disc of mass M and radius R is wounded by massless inextensible thread.
One end of string is tied to ceiling and system is released. Then which of the
followings are/is false.
(A) Tension in the thread mg/3
(B) acceleration of disc 2g/3
(C) angular momentum of disc is conserved about point of contact on rim
with thread.
(D) angular momentum is conserved about any point on vertical line at

distance x = R/2 from centre toward left.

R/2

O

Space for Rough work

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23. A ball is thrown vertically upward at time t = 0. Viscous force of air resistance is not negligible and
the acceleration due to gravity is g. The ball reaches maximum height at t = T and then descends
attaining terminal speed. Which graph shows the best variation with time t of the acceleration a of
the ball.
(A)

a

t

(B)

a

t

(C)

a

t


g

T

(D)

a

t

t

g

24. An uncharged sphere of radius R is connected by zero
resistance wire to earth. A charged particle q
0
is moving towards
centre of sphere with constant velocity v
0
. Find current flowing in
wire. When charged particle is at distance x. q
0
= 10 C, R = 1 m,
v
0
= 10 m/s, x = 2 m.
(A) 25 A (B) 5A
(C) infinity (D) zero.

v
0
q
0
x

R

25. A rod and a block are of same mass. Initially rod is in
horizontal position. What will be acceleration of tip of the rod.
When system is released from this position
(A) zero (B)
3g
4

(C)
3g
8
(D)
3g
2

m

m

26. Two identical charges q are separated by distance 2d and
fixed at this position. Third charge q
0
is revolving in a circle
of radius x in plane perpendicular to line joining charges and
centre coincides with mid point of line joining charges. The
value of x for which speed of particle is maximum is [Consider
gravity free space.]
(A)
d
2
(B)
2
d
(C) d (D) 2d

x
2d
q

q

Space for Rough work
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27. A particle is thrown at an angle  with horizontal along the inclined
plane of inclination . Find the maximum height from the ground
reached by particle
(A)
2 2
u sin
2g

(B)
2 2
u sin sin
2g
 

(C)
2 2
u sin
2g sin


(D)
2 2 2
u sin sin
2g
 

u





28. A charged particle of charge q is revolving in a circle of radius R of time period T = 9 sec. A point
P at distance 2R from centre of circle in same plane record magnetic field. Find minimum time
interval between two successive times at which magnetic field is zero at that point
(A) 9 sec
(B) 4.5 sec
(C) 3 sec
(D) magnetic field at point P will always have non-zero value.

29. Two plates of capacitors are provided charges q
1
and q
2
and
connected with springs of constant k
1
and k
2
as shown in the
diagram. Find the ratio of elongation in two springs (x
1
/x
2
). (springs
are of dielectric material]
(A)
2
1
k
k
(B)
2
2
1
k
k
 
 
 

(C) 1 (D)
2
1
2
k
k
 
 
 

x
2
k
2
x
1
k
1
q
1
q
2

30. A body moves along a path PQR from P to R shown as a dashed line in
figure. When the particle is at Q, its speed is decreasing. The
acceleration of the particle at Q is best represented by the
(A) 1 (B) 2
(C) 3 (D) 4

P

R

Q

3

4

1

2

Space for Rough work

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C
C
h
h
e
e
m
m
i
i
s
s
t
t
r
r
y
y PART – II

SECTION – A

Straight Objective Type

This section contains 30 multiple choice questions numbered 1 to 30. Each question has 4 choices (A),
(B), (C) and (D), out of which ONLY ONE is correct.

1. The correct order of leaving group for aromatic nucleophilic substitution is:
(A)
2
F Cl I Br NO
    
    (B)
2
F NO Cl Br I
    
   

(C)
2
NO Cl Br I F
    
   
(D)
2
I Br Cl F NO
   
   

2.
O
O
 
3 4
H PO
P


(A)
O
O

(B)
O
OH

(C)
O
O

(D)
O
O

Rough Work

Page 10

CONCEPT RECAPITULATION TEST - III

CONCEPT RECAPITULATION TEST - III

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