CONCEPT RECAPITULATION TEST - II Paper 1

Question Paper 17 Pages

Joint Entrance Examination (Advanced)

Concept Recapitulation Test

Contributed by

Swati Kant

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CONCEPT RECAPITULATION TEST - II

Paper 1

Time Allotted: 3 Hours Maximum Marks: 210


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 +3 marks for correct answer and – 1 mark for wrong answer.

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. There is no negative marking.

(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. There is no negative marking.

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 mutually perpendicular infinitely long straight conductors carrying uniformly distributed
charges of 
1
and 
2
are at x = 0 along y–axis and at x = a parallel to z axis. Then:
(A) The force between them is infinite
(B) The force between them depends on ‘a’
(C) The force between them is independent of ‘a’
(D) The torque of force about x axis on any conductor is non zero

2. A block is attached to a horizontal spring of stiffness k. The other end of the spring is attached to
a fixed wall. The entire system lie on a horizontal surface and the spring is in natural state. The
natural length of the spring is 
0
. If the block is slowly lifted up vertically to a height

5
0
12
from its
initial position, which of the following is not correct:
(A) The work done by the gravity
mg

0
5
12

(B) The work done by the spring force –
2
0
k
288


(C) The work done by the lifting force
2
0
0
k
5
mg
12 288



(D) The sum of works done by all the forces on the block is zero

3. A small hole of area 1 cm
2
is punched on the
side of a cylindrical vessel containing water
upto a height H = 10 m as shown. The torque
of normal force about ‘Centre of the vessel O’
immediately after making the hole would be :
Assume that tank does not topple.
(A) 10 Nm
(B) 30 Nm
(C) 50 Nm
(D) Zero

Space for rough work

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4. Find the position coordinates of the image of the object P as seen
through the periscope. The mirrors are inclined at 45 with x-axis
and eye is placed at the level y = d.
(A) (d, d) (B) (d, +d )
(C) (2d, d) (D) (3d, d)

x
P(d, d)
y

(0, 0)
(0, d)
(0,

d)

5. The piston is massless and the spring is ideal and initially streched the
piston cylinder arrangement encloses an ideal gas. If the gas is heated
quasistatically the PV graph.

(A)

(B)

(C)

(D)

Space for rough work

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6. When an excited H atom goes to ground state it emits a photon.
Statement 1 : Mass has changed into energy.
Statement 2 : K.E. has increased.
(A) Both 1 and 2 are true (B) Both 1 and 2 are false
(C) Only 1 is true (D) Only 2 is true

7. The smooth circular pipe is kept fixed in a
horizontal plane. If mass m with change +q is
slightly displaced from the position shown,
then distance traveled by the ball when the
magnitude of normal becomes minimum
would be
(A) 0
(B) R cos
–1
1/3
(C) R tan
–1
5
2

(D) R

R

8. When a tangential force of 0.02 N is applied on a large wooden plate of area 10 m
2
floating on the
surface of river, plate moves with the speed 2 m/s on the river surface. The river is 1 m deep and
the water in contact with the bed is stationary. Assuming constant speed gradient, coefficient of
viscosity of water is
(A) 10
–5
poise (B) 10
–2
poise
(C) 10
–9
poise (D) 10
–15
poise

9. A car is moving towards an approaching bike. Bike is moving with velocity 30 m/s. Frequency of
horn sounded by car is 100 Hz while it is observed by bike rider as 120 Hz. The actual duration
of horn is 6 sec. The time the bike rider hears it, in seconds is (take velocity of sound in air as 330
m/s)
(A) 1 sec (B) 10 sec
(C) 5 sec (D) 12 sec

10. An empty plastic box of mass m is found to accelerate up at a rate of g/6 when placed deep
inside water. Then the mass of sand be filled in it so that it may accelerate down at a rate of g/6 is
(A)
2
m
5
(B)
4
m
5

(C)
13
m
5
(D)
17
m
5

Space for rough work

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Multiple Correct Answer(s) Type

This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D)
out of which ONE or MORE are correct.
11. A block of mass 2kg moves under the influence of external forces on a rough horizontal surface.
At some instant, it has a velocity of 1 m/sec. due south and acceleration of 1 m/sec
2
due east.
The force of friction acting on it is F.
(A) F acts due west
(B) F acts due north
(C) F acts in the south-west direction
(D) The magnitude of F can not be found from the given data.
12. In a certain series LCR A.C. circuit it is found that X
L
= 2X
C
and phase difference between the
current and voltage is /4. If now capacitance is made 1/4
th
& the inductance and resistance are
doubled then which are not correct.
(A) voltage will lead current by a phase of tan

1
(1/2).
(B) voltage will lag behind current by a phase of tan

1
(1/2).
(C) voltage will lag behind current by a phase of /4.
(D) voltage and current will be in same phase.

13. A vertical cylinder contains ideal gas with the help of two pistons whose
combined mass is M. Pistons are connected by an inextensible string. The
difference in the area of pistons is A. Atmospheric pressure is P
0
. Initially
the system is in equilibrium as shown in the figure. Now heat is supplied to
the system. Mark the correct statement(s).
(A) volume will increase
(B) Pressure will remain constant
(C) Temperature will increase
(D) Internal energy of gas will remain constant.

14. As shown in the fig. all surface are frictionless and block B is released
from top of the incline A then
(A) Linear momentum of (A + B) will remain constant in all direction.
(B) Linear momentum of (A + B) will remain constant in horizontal
direction.
(C) Linear momentum of A will remain constant in horizontal direction.
(D) Mechanical Energy of (A + B) system will remain constant

15. Choose the INCORRECT statement(s)
(A) The flux of electric field is equal to number of field lines crossing the surface
(B) The flux of electric field over a closed surface is always non-zero
(C) The flux of gravitational field over any closed surface can never be positive
(D) The flux is equal to
E.S
 


where
E

is electric field and
S

is area of surface.
Space for rough work

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SECTION –C

Integer Answer Type

This section contains 5 questions. The answer to each of the questions is a single-digit
integer, ranging from 0 to 9. The appropriate bubbles below the respective question
numbers in the ORS have to be darkened. For example, if the correct answers to question
numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, then the correct darkening of
bubbles will look like the as shown.

0

0

0

0

1

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

7

7

7

7

8

8

8

8

9

9

9

9

6

6

6

6

X

Y

Z

W

1. Disc of mass M = 10 kg and radius R = 50 cm is revolving about
fixed vertical axis on smooth horizontal surface with angular
velocity 
0
= 4 rad/sec. A block of mass m = 5kg is connected to
disc through slack string as shown in the diagram. Find the
velocity of the block when string become taut.

m


0
R

2. A block of mass 2 kg is tied to elastic thread of length 2 m and
suspended to point O. Initially block is horizontal level to this
point O. Now block is released and its speed is 5 m/s when
thread is vertical. If the acceleration of the block at the lowest
position is 2.5 K. Find the value of K.

2m
4m
m = 2kg

O

Space for rough work

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3. A non conducting ring of mass m = 1 kg and radius R = 10 cm has a charge Q = 2 C uniformly
distributed over its circumference. The ring is placed on rough horizontal surface such that plane
of the ring is parallel to the surface. A vertical magnetic field B = B
0
t
2
where B
0
= 4T/sec
2
is
switched on. After 5 sec, after switching on the magnetic field the ring is just about to rotate about
vertical axis through the centre. The coefficient of friction  between the ring and the surface is
found to be x  10

1
. Find the value of x.

4. In the circuit shown, the power factor of the circuit is 1,
power factor of box is 4/5, source voltage is 100V and
angular frequency  = 100 rad/sec and current flowing in
circuit is 5 amp. Value of inductance of inductor is
K
20

henry then find value of K.

5 Amp

Box

A

100 V, 100 rad/sec

5. A capacitor of capacitance 100 F is connected to smooth railing and
connector of mass 1 kg and length 1 m, whole system is in vertical plane
and a magnetic field of strength 100 T is applied perpendicular to plane of
circuit as shown. Connector is released under gravity. The time (in sec)
after which dielectric of capacitor will burn out is k  10
3
then find the value
of k. Breaking strength of dielectric is 5  10
8
V/m. (d is the distance
between plates of capacitor = 1 mm)

    

    

    

    

    

    

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 10 multiple choice questions numbered 1 to 10. Each question has 4 choices (A),
(B), (C) and (D), out of which ONLY ONE is correct.

1. Which of the following will not show tautomerism:
(A)
O
N OH

(B)
OH
CH
3
CH
3
CH
3
OH
CH
3

(C)
O
C
6
H
5
C
6
H
5
H
5
C
6
H
5
C
6

(D)

NH C
NH
2
OH

2. Which of the following reactions represent developing in photography?
(A) AgNO
3
+ NaBr

AgBr + NaNO
3

(B) AgBr + 2Na
2
S
2
O
3

 
3 2 3
2
Na Ag S O NaBa
 
 
 

(C) AgBr + h


AgBr


(D) C
6
H
4
(OH)
2
+
2AgBr



C
6
H
4
O
2
+ 2HBr + 2Ag

3. In an adiabatic expansion of air (assume it a mixture of N
2
and O
2
), the volume increases by 5%
the percentage change in pressure is:
(A) 3% (B) 4%
(C) 6% (D) 7%

4. In the normal spinel having one eighth of the tetrahedral holes, occupied by one type of metal ion
and one half of the octahedral holes occupied by another type of metal ion. Such a spinel is
formed by Mg
2+
, Al
3+
and O
2–
. If oxide ion is replaced by X
-8/3
, the number of anionic vacancies
per unit cell is;
(A) 1 (B) 2
(C) 3 (D) ¾
Rough Work

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5. Caffeine is dissolved in a suitable solvent and the osmotic pressure () of solutions of various
concentrations (g/cm
3
) C is measured at 20°C. The slope of a plot of  against C is found to be
4.65  10
–3
. The molecular weight of the caffeine (g/mol) is:
(A) 3  10
5
(B) 9  10
5

(C) 4.5  10
5
(D) 5.16  10
6

6. In which of the following molecule, the number of possible XAX angles is maximum in the
anionic part of their solid state? [A : central atom, X : surrounding atom]
(A) PBr
5
(B) N
2
O
5

(C) PCl
5
(D) Cl
2
O
6

7. Arrange the following in increasing order of pk
o
values:

(I)
(II)
(III)
(IV)
H
a
H
b
H
c
H
d

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

8. HCl gas is passed through an aqueous solution of 0.1 M 1 – aminopropane (PrNH
2
) till the pH
reaches 9.71. Calculate the ratio of [PrNH
2
]/[PrNH
3
]
+
in this solution:



11
a 3
K PrNH 1.96 10
 
 
 
 

(A) 0.01 (B) 0.002
(C) 0.1 (D) 10
–3

Rough Work

Page 10

CONCEPT RECAPITULATION TEST - II Paper 1

CONCEPT RECAPITULATION TEST - II Paper 1

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