CONCEPT RECAPITULATION TEST - I

Question Paper 22 Pages

Joint Entrance Examination (Main)

Concept Recapitulation Test

Contributed by

Anees Batta

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 - I

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 02 and 09 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.

Section-A (03 to 08) 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.

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

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. In a standard meter bridge experiment, to measure the specific resistance of a wire the following
data are found:-
Length (L)
(1 01)m
   measured by a meter scale
Radius of wire = 1mm .01mm. (measured by screw gauge).
Resistance of wire (R) = (5.01) 
The maximum possible error in the measurement of specific resistance is
(You may use the formula:-
2
r
R
L

  )
(A)
1 m
 
(B)
2 m
 

(C)
5024 m
 
(D)
6024 m
 

2. A physical quantity P is related to four measurable quantities as
3 2
3 4.
a b
P
c d
 . If the errors in
measurement of a, b, c, d are 0.1%, 0.2%, 0.3%, 0.1% respectively, what is the maximum
percentage error in measurement of P.
(A) 1% (B) 2%
(C) 3% (D) 4%

3. When
0
N
molecules of a radioactive nuclide are taken at t = 0, the activity reduces to ‘A’ in time
0
t
. When
o
3N
molecules of the same nuclide are taken, activity will become 3Ae in time t equal
to :-
(A)
0
t
(B)
0
1
t



(C)
0
1
t


(D) None of these
Where;  is decay constant of the Nuclide
Space for rough work
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4. A particle of mass m is projected from O with velocity

0 0
ˆ ˆ
v cos i v sin j
  
.
At the same instant, another particle of mass 2m is
projected from point P with
0
ˆ
v k.
The velocity of 2
nd

particle w.r.t first particle after time
0
v sin
t
g

 is

θ

(0,
0,
0)

y

X

Z

V
0
O

g

2 2 2
0 0
v sin2θ v sin θ
P , ,0
2g 2g
 
 
 

(A)
0 0
ˆ ˆ ˆ
v k gtj v cos i
  
(B)
0 0
ˆ ˆ ˆ
v k gtj v cos i
  

(C)
0 0
ˆ ˆ
v k v cos i
 
(D) None of the above

5. The plot of characteristics frequency ‘f’ in case of X – rays of K

wavelength, with the atomic
number ‘Z’ of an element may be best represented by :-
(A)

Z
→

f

(B)

Z


f


(C)

Z


f


(D)

Z


f


6. In the position shown, the spring is at its natural length. The block
of mass m is given a velocity
0
v
towards the vertical support at
t = 0. The coefficient of friction between the block and the surface
is given by:  = x, where  is a positive constant and x is the
position of the block from its starting position. The block comes to
rest for the first time at x =

F

μ

k

(A)
0
m
v
k mg
 
(B)
0
m
v
k

(C)
0
m
v
mg

(D) none of the above.
Space for rough work

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7. Two waves of Intensity
1
I
and
2
I
interfere. The maximum intensity produced to the minimum
intensity are in the ration
.

Then
1
I
/
2
I
is equal to
(A)
I
,
I
 
 
if I
1
> I
2
(B)
I
,
I
 
 
if I
1
> I
2

(C)
2
I
,
1
 
 
 
 
 
 
if I
1
< I
2
(D)
2
1
1
 
 
 
 
 
 
if I
1
> I
2

8. The current in the circuit at any time t is
(A) 20ampere.
(B) 20sin 50t
4

 

 
 

(C) 20sin 50t
4

 
 
 

(D)


20sin 50t

5


I

C = 0.004F

100 sin (50t) volts.
5

L = 0.1 H

9. All the surfaces & pulleys are frictionless in the shown
arrangement. Pulleys P and Q are massless. The force
applied by clamp on pulley P is
(A)
 
mg
ˆ ˆ
3i 3j
6
 
(B)
 
mg
ˆ ˆ
3i 3j
6

(C)
mg
2
6

(D) none of the above.

P

0
30


Y

m

2m

X

Q

10. The power factor, , for the above circuit and the peak
current, neglecting the mutual inductance of the coils,
is :-
(A)
,10 2
4

Ampere
(B)
,10 2
4

Ampere.
(C) 0, 20 Ampere
(D)
,10
4

Ampere

15


15


0.004F
0.05H
0.1H

0.1H

100 sin [50t]
15


Space for rough work
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11. A conducting square loop of length ‘L’ is placed in a
magnetic field of Induction
0
B

End ‘A’ and End ‘C’ are
moved away from each other. So that finally the square loop
becomes a straight line. The total charge flowing through
the loop, if its resistance is ‘R’ then :
(A)
2
0
B L
R

(B)
2
0
B L
R

(C)
2
0
B L
R
(D)
2
0
B L
R


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 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

D

A

B
C

L

B
0

12. A thin biconvex lens of focal length 30cm is Kept 90 cm away
from a plane mirror kept parallel to the plane of the lens. A point
object is placed on the optical axis of the lens 60cm away from
the lens as shown in the figure. Now, if the point object is slowly
moved towards the lens with a small velocity, the image of the
object in the mirror.

O

30cm
30
cm

90cm

X
Y
F

(A) Moves in the + ve x direction (B) Moves in – ve x direction
(C) Does not move (D) Data insufficient

13. ABCD is a square of side 4R and EFGH is a square loop of side 2R.
The loop carries a current I. The magnetic field at the centre O of the
loop
(A)
0
I
2 R



(B)
o
I
2 R




(C)
0
I
2 R



(D)
0
I
2 R




G

F

B

C

D

A

H

E

O

14. In the given circuit, if the voltmeter is ideal its reading is V
1

volts. If the voltmeter has a resistance of 100, the reading is
2
V .
Then
1 2
V V
 is equal to:-
(A) Zero (B) 0.3volts.
(C) 0.2volts (D) 0.1volts

V

10 volts

4


O

4


Space for rough work
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15. Two identical rods each of mass m and length

are placed on a
smooth horizontal surface. In case (1) a particle of mass m moving
with
0
V
strikes the rod perpendicularly at its centre. In case (ii), another
particle of mass m moving with V
0
strikes the rod perpendicularly
at
/ 4

from the centre. In both the cases, particles come to rest just
after collision. The ratio of velocity of center of mass of rod in case (i)
to that in case (ii) is
(A) 1:1 (B) 1:2
(C) 2:1 (D) 4:1

m


Cas
e
(i)

Case(ii)

/ 4


16. The charge on the capacitors A and B in steady state is :-
(A)
CE
,CE
2
(B)
CE CE
,
2 2

(C)
CE
CE,
2
(D)
CE,CE

R
R

R

R
R

E
L

S

P
C

B

C

A

17. In a region, uniform electric field exists as
ˆ ˆ
E 10i 10j N / C.
 
 
 

If the potential of origin is 0 volts,
the potential of point (10m, 10m, 10m) is
(A) 20 volts (B) – 200 volts
(C) 10 volts (D) – 10 volts

18. For
F
,
Mg
  the power applied by force F on the system as a function
of time t is
(A) Zero (B)
2
F
t
2M

(C)
2
F
t
M
(D) none of the above

F

μ o


M

M



Space for rough work
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19. There in a small source of heat radiations emitting energy at a
constant rate of P watts. At a distance r from the source a small thin
disc of mass ‘M’ surface area ‘A’ and specific heat capacity ‘c’ is
kept. The time required to raise the temperature of the disc by T
Kelvin is

O
r
A

P

(A)
mcT
P
(B)
2
4 r mcT
PA


(C)
2
r mcT
PA

(D) data insufficient.

20. There is a thin plate ABCD with an elliptical hole as shown in the
figure. The coefficient of linear expansion of the sheet is
.

When the
temperature of the plate is increased by T K, the area of the hole
increases by an amount :-
(A)b T (B) 2bT
(C) 3b T (D) Data insufficient.

2


2b

A
D

B

C

21. A rod of mass M and length

is falling vertically downwards. A
particle of m is projected with
0
V
at t = 0 at an angle

with
horizontal and it strikes the rod perpendicularly at


1
P att t
 and
comes to rest. The rod strikes the ground at
2
t t

. The angular
velocity of rod about its centre of mass (O)
(A) keeps on increasing from
1 2
t to t

V
0
B

O

A

O

P






/4



(B) keeps on decreasing for
1 2
t to t

(C) remains constant and is non – zero for t =
1 2
t to t

(D) remains constant and is zero for
1 2
t t to t


22. A spring block system (mass = m, spring constant k) is placed on a
smooth inclined plane
(
 
angle of inclination). The plane is
accelerated horizontally with a such that the block does not loose
contact with the plane. The time period of small oscillation of the
block is
(A)
m
2
k
 (B)
msin
2
k



m

θ

k
a

(C)
mg
2
ka
 (D) none of the above.
Space for rough work

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23. A spherical drop of radius r and density n is falling in air with terminal velocity. The density of air
is n
0
and its coefficient of viscosity . The power developed of by gravity is
(A)
 
5
2
0
r n
n n g



(B)
 
5
0
r
n n n
2




(C)
 
5 2
0
27
r n n n g
8


(D)
 
5
2
0
8 r
n n n g
27




24. A progressive mechanical longitudinal wave is represented by


y Asin t kx
    

For
1
k 100cm ,


phase difference between two particles at
1
x 2cm

and
2
x 4cm at t 0 is
 
(A) 1rad (B) 2rad
(C) 3rad (D) none of above.

25. In the given arrangement, two capillaries of glass having radii r and 2 r
are dipped in pure water of density , the surface tension of water is
(A)
2 hgr
 (B)
hgr

(C)
hgr
2

(D) None of these

h

2r


=density of water

r

26. A solid uniform sphere of mass M and radius R with centre C is
isolated in space. If in the sphere a cavity of radius
R
2
with centre C
1

is made, then the potential at a point P at a distance of 2R from
centre C is
(A)
2GM
5R
  (B)
2GM
5R
 
(C)
2GM
5R
  (D) None of these.

2R

R

P



R/2

C
1
C



Space for rough work

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27. Two concentric circles each of radius a (50m< a < 100m) lie in mutually perpendicular planes. A
source of sound moves with constant speed on one circle and an observer with same speed on
the other circle. If both cross each other simultaneously by at a point, then actual frequency


1
f
of sound and apparent frequency


2
f
received by observer are such that
(A)
1 2
f f

always (B)
1 2
f f

always
(C)
1 2
f f

always (D) none of above

28. A satellite of mass m is orbiting round the earth at a distance of 2R’ from the centre of the earth.
The amount of energy that must be given to the satellite in order to make its radius 6R must be :-
(A) less than
e
GM m
3R
(B) equal to
e
GM m
6R

(C) greater than
e
GM m
4R
(D) less than
e
GM m
4R

29. A person throws a ball (A) vertically upwards with 40 m/sec. After 4 sec, he throws another
identical ball (B) upwards with same speed. If the collision between balls is head-on perfectly
elastic, the speed of ball (A) just after collision is
(A) 0 (B) 10 m/sec
(C) 20 m/sec (D) 40 m/sec

30. Two blocks of mass m each are connected by a massless
string while block A is connected to point O by another
massless string. Both rotate with constant speed

on the
horizontal surface with O as centre. If
1
T
is the tension in
OA and
2
T
is tension in string AB, then the relation between
T
1
& T
2
is:-

m

r
1
m

A

B

r
2
O

(A)
1 2
T T

(B)
1 2
T T


(C)
1 2
T T

(D) data insufficient
Space for rough work

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CONCEPT RECAPITULATION TEST - I

CONCEPT RECAPITULATION TEST - I

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