CONCEPT RECAPITULATION TEST - IV

Question Paper 23 Pages

Joint Entrance Examination (Main)

Concept Recapitulation Test

Contributed by

Baldev Mehan

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 - IV

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. The minimum and maximum magnitude which is possible by adding four forces of magnitudes
1N, 3N, 9N and 10N is
(A) 0 and 23 N (B) 1N and 23 N
(C) 2N and 23 N (D) 3N and 23 N

2. 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. Where
should a landing point be chosen on the other bank so that the
boat can cross in the minimum possible time?

0

37°

53°

B

A

(A) 1.2 km downstream from O (B) 2.4 km downstream from O
(C) 3.6 km downstream from O (D) 7.2 km downstream from O

3. A particle is moving in xy plane. At certain instant, the components of its velocity and
acceleration are as follows. V
x
= 3m/s, V
y
= 4m/s, a
x
= 2 m/s
2
and a
y
= 1 m/s
2
. The rate of change
of speed at this moment is
(A)
2
10m / s
(B)
2
4m / s

(C) 10 m/s
2
(D) 2 m/s
2

4. A body of mass ‘m’ is moving in a circle of radius with a constant speed ‘v’. Let work done by the
resultant force in moving the body over half circumference and full circumference is W and W’
then
(A)
2 2
mv mv
W ( r), W' (2 r)
r r
   
(B)
2
mv
W (2r), W ' zero
r
 
(C)
2
mv
W ( r), W' zero
r
   (D) W = 0, W’ = 0
Space for Rough work
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5. In the figure, one fourth part of uniform disc of radius ‘R’ is shown.
The distance of the centre of mass of this object from centre ‘O’ is
(A)
4R
3

(B)
2R
3


(C)
4R
2
3

(D)
2R
2
3


6. A force F is applied on the top of a cube as shown in the figure. The
coefficient of friction between the cube and ground is . If F is gradually
increased the cube will topple before sliding if
(A)  > 1 (B)
1
2
 

(C)
1
2
 
(D)  < 1

7. An observer starts moving with uniform acceleration ‘a’ towards a stationary sound source of
frequency 
o
. As the observer approaches the source, the apparent frequency ‘f’ heard by the
observer varies with time ‘t’ as
(A)

(B)

(C)

(D)

Space for Rough work


t


t


t


t
F
R

90
o

O
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8. A metallic cylinder of radius r and height h is totally
submerged in a liquid contained in a beaker as shown in the
figure. If force F is pulling the string at a constant velocity v,
the graph showing the variation of force F against
displacement of cylinder is best represented by

(A)

(B)

(C)

(D)

9. A particle starts moving with velocity
v i
 

(m/s), and acceleration
a i j
  
 
 
 
 
(m/s
2
). Find the
radius of curvature of the particle at t = 1sec.
(A) 5 m (B)
5 5
m
(C)
6 5
m (D) none

10. A block of mass m is lying at rest at point
P of a wedge having a smooth semi-
circular track of radius R. What should be
the minimum value of a
0
so that the mass
can just reach point Q.
(A)
g
2

(C) g
(D) not possible

Space for Rough work
m
Q
a
0

P
S

F

S

F

S

F

S

F

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11. 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 true weight of the person is
[Take g = 10 m/s
2
.]

Time in seconds

Velocity

(upward)

10

40

60

(A) 60 kg (B) 63 kg
(C) 61.5 kg (D) 65 kg

12. An x-ray tube is operating at 150 kV and 10 mA. If only 1% of the electric power supplied is
converted into X-ray, the rate at which heat is produced in the target is
(A) 3.55 cal/sec (B) 35.5 cal/sec
(C) 355 cal/sec (D) 3550 cal/sec

13. A parallel beam of light of monochromatic radiation of
cross-section area A (<b
2
), intensity I and frequency  is
incident on a solid, perfectly absorbing conducting
sphere of work function 
0
(h > 
0
) and radius b. The
inner sphere of radius a is grounded by a conducting
wire. Assume that for each incident photon one
photoelectron is ejected. Current through the conducting
wire just after the radiation is

a

b

I,
Insulated
stand

(A)
IAe b
h a

(B)
IAe
2h


(C)
2IAe
h

(D)
IAe a
h b


14. Two concentric rings of radius R = 8 cm and r = 2 cm
having charge Q = 8 C and q = 1 C are placed as
shown in diagram. Then electric field is zero at axis of
rings
(A) x =  43 cm
(B) x =  4 cm
(C) x =  2 cm
(D) x =  23 cm

R

x

P

q

Q

r

Space for Rough work
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15. A small sphere of mass m and radius r is placed inside a hollow cylinder of
radius R. Now cylinder rotating with some angular acceleration which slowly
increases from zero to certain value . There is no slipping between two
surfaces during motion.
(A) Maximum angle formed by line joining centre will be  =
1
2 R
sin
5g


 
 
 

R





(B) Angular velocity of sphere will be  =
r
R

where  is angular velocity of cylinder.
(C) sphere will keep rotating at lowest position.
(D) K.E. of sphere becomes constant when it reaches maximum height.

16. Suppose the potential energy between the electron and proton at a distance r is given by
2
3
Ke
3r
 .
Application of Bohr’s theory of hydrogen atom in this case shows that energy in the nth orbit is
proportional to
(A) n
6
(B) n

3

(C) n

2
(D) n

4

17. Block of mass m is placed on a wedge of mass M at height
H. All surfaces are smooth and system is released, then
which of the following is incorrect.
(A) Work done by normal reaction on the wedge is positive
and on block is negative.

M

m

H

(B) work done by normal reaction is zero for both the block and the wedge.
(C) change in gravitational potential energy is shared by the block and wedge in inverse ratio of
their masses.
(D) Centre of mass will not change position.

18. Following are some processes shown in V-T graph for ideal
gas. Which of following is incorrect.
(A) in process CD pressure continuously increases.
(B) in process EF pressure continuously decreases.
(C) Pressure remains constant in all process AB, CD, EF.
(D) Internal energy of gas increases in all three processes.

A

B

D

C

E

F

T

V

Space for Rough work
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19. A point positive charge q
0
is placed at a point C inside the cavity in
spherical conductor as shown in figure. Find the potential at P.
(A)
0
Kq
2a
(B)
0
Kq
a

(C)
0
2kq
a
(D)
0
3Kq
2a

0
1
here,k
4
 

 
 
 

20. In screw gauge; 5 complete rotations of circular scale give 1.5 mm reading on linear scale.
Circular scale has 50 divisions. Least count of the screw gauge is
(A) 0.006 mm (B) 0.003 mm
(C) 0.015 mm (D) 0.03 mm

21. A cubical block ‘A’ of mass m
1
and edge length ‘a’ lies on a smooth
horizontal floor. It has a groove with a flat base with an open end. On
the closed end of the groove there is a spring of natural leng
th ‘a’
attached to it. A small block ‘B’ of mass m
2
is pushed into the groove
compressing the spring by a/2. Coefficient of friction between B
and
groove is μ. System is now released from rest. Find speed of B as it
comes out of A. Assume that B is always sliding against the surface
of the groove. (m
1
= 3kg, m
2
= 1kg, a = 10 cm, k = 100N/m, μ = 0.13)

smooth
B
A
μ
Q
R
a
a/2

(A) 15 cm/s (B) 10 cm/s
(C) 5 cm/s (D) 20 cm/s

22. The end of capillary tube is immersed into a liquid. Liquid slowly rises in the tube up to a height.
The capillary-fluid system
(A) will absorb heat (B) will release heat
(C) will not be involved in any heat transfer (D) nothing can be said

23. The radius of a planet is n times the radius of earth, R. A satellite revolves around it in a circle of
radius 4nR with angular velocity . The acceleration due to gravity on planet’s surface is
(A) R
2
(B) 16 R
2

(C) 32 nR
2
(D) 64 nR
2
.

24. Some successive frequencies of an ideal organ pipe are measured as 150 Hz, 250 Hz, 350 Hz.
Velocity of sound is 340 m/s.
(A) it must be an open organ pipe of length 3.4 m
(B) it must be an open organ pipe of length 6.8 m
(C) it must be an closed organ pipe of length 1.7 m
(D) it must be an closed organ pipe of length 3.4 m.
Space for Rough work

2a

a
C
q
0

a/2

P
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25. Two identical blocks are kept on a frictionless horizontal table and connected by a spring of
stiffness ‘k’ and of original length
0

. A total charge Q is distributed on the blocks such that
maximum elongation of spring, at equilibrium, is equal to x. Value of Q is
(A)
0 0 0
2 4 k( x)
 
  (B)
0 0
2x 4 k( x)
 

(C)
0 0
2( x) 4 kx
  (D)
0 0
( x) 4 kx
  .

26. At t = 0, light of intensity 10
12
photons/s–m
2
of energy 6eV per photon start falling on a plate with
work function 2.5 eV. If area of the plate is 2 × 10
–4
m
2
and for every 10
5
photons one
photoelectron is emitted, charge on the plate at t = 25 s is
(A) 8 × 10
–15
C (B) 4 × 10
–15
C
(C) 12 × 10
–15
C (D) 16 × 10
–15
C.

27. Two resistances are measured in Ohm.
R
1
= 3  1%
R
2
= 6  2%
When they are connected in parallel, the percentage error in equivalent resistance is
(A)
14
%
3
(B)
1%

(C)
2%
(D)
4
%
3

28. If 
min
is minimum wavelength produced in X–ray tube and 
K
is the wavelength of K

line. As the
operating voltage is increased
(A) 
K
increases (B) 
K
decreases
(C) (
K
– 
min
) increases (D) (
K
– 
min
) decreases.

29. The filament current in the electron gun of a Coolidge tube is increased while the potential
difference used to accelerate the electron is decreased. As a result in the emitted radition.
(A) The intensity decreases while the minimum wavelength increases.
(B) The intensity increases while the minimum wavelength decreases.
(C) The intensity as well as the minimum wavelength increases.
(D) The intensity as well as the minimum wavelength decreases.

30. Monochromatic light of wavelength 900 nm is used in a young’s double slit experiment. One of
the slits is covered by a transparent sheet of thickness 1.8 x 10
-5
m made of material of refractive
index 1.6. How many fringes will shift due to introduction of the sheet.
(A) 18 (B) 12
(C) 10 (D) 6
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

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.

Compound
CH
3
HC
OEt
OEt
and
(p) (Acetal)
CH
3
CH
2
O CH
2
CH
3
(q)

can not be differentiated by
(A)
3
H O , Na

(B)
3
H O ,

Tollens test
(C)
3
H O ,

Fehling test (D) None of the above

2. If Ksp of AgX are in the order AgCl > AgBr > AgI, then what will be the order of

Ag/AgX/X
E

for
different half cells having different silver halides
(A) AgCl < AgBr < AgI (B) AgCl > AgBr > AgI
(C) AgCl = AgBr = AgI (D) E
0
is not related to Ksp

3. Which of the following compounds was unable to respond chromyl chloride Test?
(A) NaCl (B) SnCl
2

(C) SnCl
4
(D) AuCl

4. The activation energy for the decomposition of hydrogen iodide at 581 K is 209.5 cal. Then the
percentage of the molecules crossing over the barrier is:
Given that antilog (-1.07828) = 0.0835
(A) 83.5% (B) 8.35%
(C) 40% (D) 60%

5. A mixture of SO
3
, SO
2
and O
2
gases is maintained at equilibrium in 10 litre flask at a temperature
at which K
c
for the reaction






2 2 3
2SO g O g 2SO g



is 100. If number of moles of SO
2

and SO
3
are same at equilibrium, the number of moles of O
2
present is:
(A) 0.01 (B) 0.1
(C) 1 (D) 10
Space for Rough work

Page 10

CONCEPT RECAPITULATION TEST - IV

CONCEPT RECAPITULATION TEST - IV

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