CONCEPT RECAPITULATION TEST - I Paper 1

Question Paper 16 Pages

Joint Entrance Examination (Advanced)

Concept Recapitulation Test

SAS

Contributed by

Srinivasan Aayushman Sood

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
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CONCEPT RECAPITULATION TEST - I

Paper 1

Time Allotted: 3 Hours Maximum Marks: 180


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 is further divided into two sections: Section-A & Section-C
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 10) contains 10 multiple choice questions which have only one correct answer.
Each question carries +2 marks for correct answer. There is no negative marking.

Section-A (11 to 15) contains 5 multiple choice questions which have more than one correct

answer. Each question carries +4 marks for correct answer and – 1 mark for wrong answer.

(ii) Section-C (01 to 05) contains 5 Numerical based questions with answers as numerical value
and 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 (Advanced), 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 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D)
out of which ONLY ONE is correct.

1. Two balls are dropped from the same point after an interval of 1 second. Their separation 3
second after the release of the second ball. (g = 10 m/s
2
)
(A) 25 m (B) 30 m
(C) 35 m (D) 40 m

2. The upper half of an inclined plane of inclination  is perfectly smooth while the lower half is
rough. A block starting from rest at the top of the plane will come to rest at the bottom if the
coefficient of friction between the block and the lower half of the plane is
(A)  = 2 tan  (B)  = tan 
(C)
2
tan
 

(D)
1
tan
 


3. A spring is compressed between two blocks of masses m
1
and m
2
placed on a horizontal
frictionless surface. When the blocks are released. The blocks travel distance x
1
and x
2

respectively before coming to rest. The ratio x
1
/x
2
is
(A) m
1
/m
2
(B) m
2
/m
1

(C)
1
2
m
m
(D)
2
1
m
m

4. If A is the areal velocity of planet of mass M, its angular momentum is
(A) M (B) 2MA
(C) A
2
M (D) AM
2

5. A meteor of mass M breaks up into two parts. The mass of one part is m. For a given separation r
the mutual gravitational force between the two parts will be maximum if
(A) m = (M/2) (B) m = (M/3)
(C) m =
M
2
(D)
M
m
2 2

Space for Rough work

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6. A wire breaks when subjected to a stress S. If  is the density of the material of the wire and g,
the acceleration due to gravity, then the length of the wire so that it breaks by its own weight is
(A) gs (B) g/s
(C) gs/ (D) s/g

7. A cylinder has a radius r. To what height h should it be filled with water so that the thrust on its
walls is equal to that on its bottom
(A) h = 2r (B) h = r
(C) h = (r/2) (D) h = (r/4)
8 A swimmer can swim in still water with a speed of
5
m/s. While crossing a river his average
speed is 3 m/s. If he cross the river in the shortest possible time, what is the speed of flow of
water?
(A) 2 m/s (B) 4 m/s
(C) 6 m/s (D) 8 m/s

9 A car starting from rest is accelerated at constant rate until it attains a constant speed v. It is then
retarded at a constant rate until it comes to rest. Considering that the car moves with constant
speed for half of the time of total journey, the average speed of the car for the journey is
(A)
v
4
(B)
3v
4

(C)
3v
2
(D) Data insufficient

10. A smooth ring P of mass m can slide on a fixed horizontal rod. A string
tied to the ring passes over a fixed pulley and carries a block Q of mass
(m/2) as shown in the figure. At an instant, the string between the ring
and the pulley makes an angle 60 with the rod.
The initial acceleration of the ring is
(A)
2g
3
(B)
2g
6

(C)
2g
9
(D)
g
3

60

m

P

Q

m/2

Space for Rough work

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Multiple Correct Answer(s) Type

This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for
its answer, out of which ONE OR MORE is/are correct.

11. A particle having mass m and positive charge q whirls along vertical circle of radius R. At the
centre of circle, another positive charge 2q is fixed.
(A) The minimum velocity given at the lowest point to complete vertical circular motion is less
than
5gR
for motion in gravity.
(B) For any value of velocity given in horizontal direction at the lowest point in gravity free space it
will perform vertical circular motion.
(C) Tension in gravity free space cannot becomes zero at any point during motion.
(D) If the charge at the centre is removed and considering the motion in gravity tension will also
be function of charge on particle.

12. The potential energy of a particle of mass 0.1 kg, moving along the x-axis, is given by
U = 5x(x4)J, where x is in meters. It can be concluded that
(A) The particle is acted upon by a variable force.
(B) The minimum potential energy during motion is 20 J
(C) The speed of the particle is maximum at x = 2m.
(D) The period of oscillation of the particle is (/5) sec.
Space for Rough work

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13. A cubical block is floating in a liquid with one third of it’s volume immersed in the liquid. When the
whole system accelerates upwards with acceleration of g/2.
(A) The fraction of volume immersed in the liquid will change.
(B) The buoyancy force on the block will change.
(C) The buoyancy force will increase by 50 percent.
(D) The pressure in the liquid will increased.

14. Two concentric metallic shell’s of radius R and 2R, out of which the inner shell is having charge Q
and outer shell is uncharged. If they are connected with a conducting wire. Then,
(A) Q amount of charge will flow from inner to outer shell.
(B) Q/e number of electrons will flow from outer to inner shell, where e charge on electron.
(C)
2
KQ
4R
amount of heat is produced in the wire
(D)
2
KQ
2R
amount of heat is produced in the wire.

15. A sound wave of frequency n travels horizontally to the right. It is reflected from a large vertical
plane surface moving to the left with a speed v. The speed of sound in the medium is c. Then,
(A) The number of waves striking the surface pre second is
n(c v)
c

.
(B) The frequency of the reflected wave is
n(c v)
(c v)



(C) The wavelength of the reflected wave is
c(c v)
n(c v)



(D) The number of beats heard by a stationary listener to the left of the reflecting surface is
nv
c v


Space for Rough work

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SECTION –C
Integer Answer Type

This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0
to 9 (both inclusive).

1. A glass sphere having refractive index (3/2) is having a small
irregularity at its centre. It is placed in a liquid of refractive index
3
4
such that surface of liquid is r high above sphere where r is
radius of sphere. If irregularity is viewed from above normally, the
distance is 26/K cm from centre where eye will observe the
irregularity. Then find the value of K. (r = 20 cm)

r

=3/2
r

=4/3

2. Two block of masses m and M are connected by means of a metal wire passing over a
frictionless fixed pulley. The area of cross-section of the wire is 6.5  10

9
m
2
and its breaking
stress is 2  10
9
Nm

2
. If m = 1 kg, if the maximum value of M is K  1.86 kg for which the wire will
not break. Find the value of K. (g = 10 m/s
2
)

3. A small cubical block of mass 1 kg is placed inside a rough rectangular
groove
1
2
 
 
 
 
made in a circular table as shown in the figure. The table
starts rotating with angular acceleration 1 rad/sec
2
in a horizontal plane
about its axis. The time is
10 K
sec after which the blocks will start motion
with respect to table. Find the value of K. (Take g = 10 m/s
2
) Assume the
size of block slightly smaller then the width of groove.

4 cm

3 cm

4. Two particles of mass M = 3 kg each are kept on a horizontal circular platform on two mutually
perpendicular radii at equal distance R = 1 m from the centre of the table. The particles are
connected with a string, which is just taught when the platform is not rotating. Coefficient of
friction between the platform and block is  = 0.1. Then the maximum angular speed ( in
rad/sec) of platform about its centre so that the blocks remain stationary relative to platform. (take
g = 10 m/s
2
)

5. A uniform cylinder of radius R(= 3m) is spin about its axis at an angular
velocity 
0
(= 40

rad/sec) and placed between two perpendicular wall.
The coefficient of friction between the walls and cylinder is ( = 2). Then,
25 K turns will the cylinder make before it stops. Find the value of K.

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 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D)
out of which ONLY ONE is correct.

1. Which of the following reactions product is correct, correspondingly?
(A)
CH
3
H
Cl
Br
Alc. KOH

Cl
CH
3
major

(B)
CH N OAC


CN
OAC

(C)
OAC
OAC OAC


ACOH


(D)
CH CH
2 2
CH N



2.
O
2
NH OH
HCl
?


The major product of the following reaction is.....?
(A)
Cl

(B)
N
OH

(C)
N
O

(D)

N
OH

Space for Rough work

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3. What is the correct order of basic strength of the following amines?

NO
2
NO
2
Me
2
N
(I)
NH
2
(II)
N
N NH
H
H
(III) (IV)
N
CH
3

(A) (II) > (IV) > (III) > (I) (B) (IV) > (I) > (III) > (II)
(C) (IV) > (I) > (II) > (III) (D) (III) > (IV) > (II) > (I)

4. The complex [Fe(H
2
O)
5
(NO)]
2+
is formed in the ring test for nitrate when freshly prepared FeSO
4

solution is added to aqueous solution of
3
NO

followed by addition of conc. H
2
SO
4
. The complex
is formed by charge transfer, which of the following change occurs?
(A)
3 2
Fe Fe ; NO NO
  
  (B)
2 3
Fe Fe ; NO NO
  
 
(C)
2
Fe Fe ; NO NO
  
  (D)
2 3
Fe Fe ; NO NO
  
 

5.
CH
CH
3
O
CH
2
CH
3
CH
3
5
PCl
3
CH Cl A
  

(A) CH
3
Cl is formed by S
N
1 process.
(B) CH
3
Cl is formed by S
N
2 process
(C) A is
CH
3
CHCH
2
CH
3
Cl
,
which is formed by S
N
2 process
(D) A is
CH
3
CHCH
2
CH
3
Cl
, which is formed by S
N
1 process

6. For the following equilibria in a close container







5 3 2
PCl g PCl g Cl g




At a constant temperature, the volume of the container is halved suddenly. Which of the following
is correct for K
p
and ?
(A) Both K
p
and  changes (B) None of the K
p
and  change
(C) K
p
changes but  does not (D)  - changes but K
p
does not
Space for Rough work

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7. Aluminum chloride exists as a dimer
2 6
Al Cl
in solid state as well as in solution of non-polar
solvents such as C
6
H
6
. When dissolved in water, it gives
(A)
2 3
6
Al O HCl
 (B)
 
2
6
3
Al H O Cl


 

 

(C)
 
3
6
Al OH 6HCl

 

 

(D)
3
3
Al Cl
 


8. Resonance Energy of Toluene is 37.5 kcal/mol while that of Benzene is 36 kcal/mole then which
of the following explains this difference
(A) Zeeman effect (B) Electromeric effect
(C) Hyper-conjugation (D) – I effect

9. The ortho and para-hydrogens possess:
(A) Same physical properties but different chemical properties.
(B) Different physical properties but same chemical properties.
(C) Same chemical and physical properties.
(D) Different physical and chemical properties.

10. During extraction of Fe
(A) Carbon is ultimately converted to CO
2
in combustion zone in blast furnace.
(B) CO
2
is one of the by-products of reduction zone of blast furnace.
(C) Cast iron is obtained from blast furnace.
(D) Uppermost zone of blast furnace is slag formation zone.
Space for Rough work

Page 10

CONCEPT RECAPITULATION TEST - I Paper 1

CONCEPT RECAPITULATION TEST - I Paper 1

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