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

CONCEPT RECAPITULATION TEST - II

/Integrated School Programs & 3723 Students from All Programs have been Awarded a Rank in JEE (Advanced), 2013

Paper 1

Time Allotted: 3 Hours Maximum Marks: 210

Pl ea s e r ea d t h e i n s t r u c t i o n s c a r ef u ll y . Yo u a r e a l l o t t ed 5 m i n u t es
s p ec i f i c a ll y f o r t h i s p u r p o s e.
ALL INDIA TEST SERIES

Yo u a r e n o t a ll o wed t o l ea v e t h e E xa m i n at i o n Ha l l b ef o r e t h e en d o f
t h e t es t .

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.

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2

Useful Data

PHYSICS
Acceleration due to gravity g = 10 m/s2

Planck constant h = 6.6 1034 J-s

Charge of electron e = 1.6 1019 C

Mass of electron me = 9.1 1031 kg

2 2
Permittivity of free space 0 = 8.85 1012 C /N-m

Density of water water = 103 kg/m3

Atmospheric pressure Pa = 105 N/m2

Gas constant R = 8.314 J K1 mol1

CHEMISTRY

Gas Constant R = 8.314 J K1 mol1

= 0.0821 Lit atm K1 mol1
= 1.987 2 Cal K1 mol1
Avogadro's Number Na = 6.023 1023
Plancks constant h = 6.625 1034 Js
= 6.625 1027 ergs
1 Faraday = 96500 coulomb
1 calorie = 4.2 joule
1 amu = 1.66 1027 kg
1 eV = 1.6 1019 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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 3 AITS-CRT-II(Paper-1)-PCM-JEE(Advanced)/14

Physics 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 yaxis 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
5
natural length of the spring is 0. If the block is slowly lifted up vertically to a height from its
12 0
initial position, which of the following is not correct:
5
(A) The work done by the gravity mg
12 0
k 2
(B) The work done by the spring force 0
288
5 k 2
(C) The work done by the lifting force mg 0 0
12 288
(D) The sum of works done by all the forces on the block is zero

3. A small hole of area 1 cm2 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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y
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 P(d, d)
(0, d)

and eye is placed at the level y = d.

(A) (d, d) (B) (d, +d ) (0, 0) x
(C) (2d, d) (D) (3d, 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 R
would be
(A) 0
1
(B) R cos 1/3
5
(C) R tan1 2
(D) 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) 105 poise (B) 102 poise
9
(C) 10 poise (D) 1015 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
2 4
(A) m (B) m
5 5
13 17
(C) m (D) m
5 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/sec2 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 XL = 2XC and phase difference between the
current and voltage is /4. If now capacitance is made 1/4th & the inductance and resistance are
doubled then which are not correct.
(A) voltage will lead current by a phase of tan1(1/2).
(B) voltage will lag behind current by a phase of tan1(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 P0. 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
X Y Z W

0 0 0 0

This section contains 5 questions. The answer to each of the questions is a single-digit 1 1 1 1
integer, ranging from 0 to 9. The appropriate bubbles below the respective question 2 2 2 2
numbers in the ORS have to be darkened. For example, if the correct answers to question 3 3 3 3
numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, then the correct darkening of
4 4 4 4
bubbles will look like the as shown.
5 5 5 5

6 6 6 6

7 7 7 7

8 8 8 8

9 9 9 9

m
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 R

disc through slack string as shown in the diagram. Find the 0

velocity of the block when string become taut.

2m
2. A block of mass 2 kg is tied to elastic thread of length 2 m and
O
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
4m
position is 2.5 K. Find the value of K.

m = 2kg

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
2 2
of the ring is parallel to the surface. A vertical magnetic field B = B0t where B0 = 4T/sec 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 101. Find the value of x.

4. In the circuit shown, the power factor of the circuit is 1, Box

power factor of box is 4/5, source voltage is 100V and

angular frequency = 100 rad/sec and current flowing in A
K 5 Amp 100 V, 100 rad/sec
circuit is 5 amp. Value of inductance of inductor is
20
henry then find value of K.

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 103 then find the value

of k. Breaking strength of dielectric is 5 108 V/m. (d is the distance
between plates of capacitor = 1 mm)

Space for rough work

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 9 AITS-CRT-II(Paper-1)-PCM-JEE(Advanced)/14

Chemistry 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) N OH (B) H3C CH3

HO OH

H3C CH3
O
(C) O (D) OH
H 5C 6 C 6H 5 HN C
NH2

H 5C 6 C 6 H5

2. Which of the following reactions represent developing in photography?

(A) AgNO3 + NaBr AgBr + NaNO3
(B) AgBr + 2Na2S2O3 Na3 Ag S2 O3 2 NaBa

(C) AgBr + h AgBr

(D) C6H4(OH)2 + 2AgBr C6H4O2 + 2HBr + 2Ag

3. In an adiabatic expansion of air (assume it a mixture of N2 and O2), 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 Mg2+, Al3+ and O2. 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)
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 20C. The slope of a plot of against C is found to be
3
4.65 10 . The molecular weight of the caffeine (g/mol) is:
(A) 3 105 (B) 9 105
5 6
(C) 4.5 10 (D) 5.16 10

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) PBr5 (B) N2O5
(C) PCl5 (D) Cl2O6

7. Arrange the following in increasing order of pko values:

Ha

Hc
Hd
Hb
(I) (II) (III) (IV)
(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 (PrNH2) till the pH
reaches 9.71. Calculate the ratio of [PrNH2]/[PrNH3]+ in this solution:

a 3
K Pr NH 1.96 10 11

(A) 0.01 (B) 0.002
(C) 0.1 (D) 103
Rough Work

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 11 AITS-CRT-II(Paper-1)-PCM-JEE(Advanced)/14

dil H acidic
9. Compound A
aq. NaOH
,
Na Cr O
Pr oduct C8H4 O3
2 2 7

The compound (A) is:

(A) Cl (B) Cl
CH3

COOH COOH
(C) (D) Cl
Cl
CH3
COOH

COOH

10. Me
C CH
H / Ni B P 2
H
2 2
B
C

Compound (C) is:

(A) Me (B) Me

Et
Et
(C) Me (D) Me

Me

Me

Rough Work

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AITS-CRT-II(Paper-1)-PCM-JEE(Advanced)/14
12

Multiple Correct Choice Type

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

11. Among the isomers of dimethylcyclohexane, the achiral ones are:

(A) 1, 2-trans and 1,3 cis (B) 1, 2-cis and 1. 3 trans
(C) 1, 3 trans and 1, 4 trans (D) 1, 2 and 1, 3 trans

12. Select the correct statement (s) about the compound NO[BF4]:
(A) Magnetic moment of the species is zero
(B) BF bond energy is lower in this compound than in BF3
(C) It has 5 and 2 bond
(D) Nitrogen oxygen bond order is same as in N2

13. The oxidation potential of hydrogen half-cell will be negative if:

+ +
(A) p(H2) = 1 atm and [H ] = 1 M (B) p(H2) = 1 atm and [H ] = 2 M
+
(C) p(H2) = 0.2 atm and [H ] = 1 M (D) p(H2) = 0.2 atm and [H+] = 0.2 M

14. O
O
H2 C CH2 H3C C H
Given: For ethylene oxide Hof and So are 51 kJ mol1 243 Jmol1K1 respectively and
acetaldehyde. Hof and So are 166 KJmol1 and 266 Jmol1K1 respectively, then select the
correct statements:
(A) Ho per the reation is 115 KJmol1
(B) So = 0.0236 KJmol1K1
(C) Reaction is thermodynamically favourable
(D) Low temperature can favour formation of more product.

15. Which of the following is/are correct about:

Tetramminedithiocyanato S cobalt (III) tris (oxalate) cobaltate (III)?
(A) Formula of the complex is [Co(SCN)2(NH3)4][Co(ox)3]
(B) It is a chelating complex and show linkage isomerism
(C) It shows optical isomerism
(D) It shows geometrical isomerism
Rough Work

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SECTION C

Integer Answer Type

X Y Z W

0 0 0 0

This section contains 5 questions. The answer to each of the questions is a single-digit 1 1 1 1
integer, ranging from 0 to 9. The appropriate bubbles below the respective question 2 2 2 2
numbers in the ORS have to be darkened. For example, if the correct answers to question 3 3 3 3
numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, then the correct darkening of
4 4 4 4
bubbles will look like the as shown.
5 5 5 5

6 6 6 6

7 7 7 7

8 8 8 8

9 9 9 9

1. AgNO3 gives white precipitate with hypo changing to black after some time, the oxidation number
of sulphur in the black precipitate is:

2. In the structure of (Sb2F11), the total number of hybrid orbitals present per Sb atom are

3. In the given reaction:

O
O
RCO H

3
Pr oduct X.

The number of sp2 carbon is X are expressed as a two-digit number AB, the sum of AB is:

4. The emf of the cell: M(s)|MnXn(0.01M)||MnXn (0.1M)/ Mcs) is found to be 0.0295V at 25C. If MnXn
is soluble salt. Find the value of n.

5. If the bond enthalpies of A2, AB and B2 are in the ratio. 1 : 1 : 0.5 and the enthalpy of formation of
AB from A2 and B2 is 100 KJmol1, the bond enthalpy of A2 is 504 kJ/mole. X will be y 102
kJ/mole, the value of y is:
Rough Work

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Mathematics PART III

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. Let u be a vector on rectangular coordinate system with sloping angle 60. Suppose that u i is

geometric mean of u and u 2i where i is the unit vector along xaxis then u has the value
3 3
equal to a b where a, b N, then the value of a b a b is
(A) 27 (B) 28
(C) 28 3 (D) 27 3

m n
2. One of the roots of equation 2000x 6 + 100x5 + 10x3 + x 2 = 0 is of the form , where m is
r
nonzero integer, and r and n are relatively prime natural number, then the value of (m + n + r) is
(A) 200 (B) 205
(C) 195 (D) 190

3. A perfectly rough plane is inclined at an angle to the horizontal. Then the least eccentricity of an
ellipse which can rest on the plane is
2sin
(A) 2 sin (B)
1 sin
2cos 2sin
(C) (D)
1 sin 1 cos

n 1 k k 1 k 1 k 2
1 120
4. If the value of limit lim
x
cos
k 2


k k 1
is equal to
k
then the value of k

is
(A) 360 (B) 700
(C) 720 (D) 240

Space for rough work

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5. In triangle ABC, |AB| = |AC| points D and E lie on ray BC such that A
|BD| = |DC| and |BE| > |CE|. Suppose that tan EAC, tan EAD
and tan EAB form a geometric progression, and that cot DAE,
cot CAE and cot DAB form an arithmetic progression. If |AE| =
10, then area of the triangle ABC is
50
(A) (B) 5 B D C E
3
10 25
(C) (D)
3 3

6. A circle C is tangent to the x and yaxis in first quadrant at the points P and Q respectively. BC
and AD are parallel tangents to the circle with slope 1. If the points A and B are on the yaxis
while C and D are on xaxis and area of figure ABCD is 900 2 sq. units. The radius of the circle
is
(A) 5 2 (B) 6 2
(C) 30 (D) 15

1 1 10 9 8 7 6 5 4 3 2
7. Let A be matrix then the matrix B = A A + 2A A + 4A 2A + 4A + A A + A +
1 1
I is
(A) A (B) A + I
(C) I (D) A I

8. Tangents are drawn to the incircle of ABC. Which are parallel to its sides, let p, q, r be the length
p q r
of the tangents opposite to a, b, c respectively, then the value of is
a b c
1 1
(A) (B)
4 2
(C) 1 (D) 2

9. A vector given by A = f(t) i + g(t) j + k moves such that it is always parallel to the vector

B f " t i f ' t j k then magnitude of A is
(A) constant (B) a quadratic function of time
(C) a linear function of time (D) a cubic function of time

a b c
10. Let A b c a such that |A| = 0. If a, b, c are distinct, then the sum of the coordinates of the
c a b
fixed point through which the line ax + by + c = 0 passes is
(A) 2 (B) 3
(C) 4 (D) 5

Space for rough work

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16

Multiple Correct Choice Type

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

x x
11. If a continuous function f(x) satisfies the relation t f x t dt t g t dt sin x cos x x 1 for

0 0
all x then which of the following does not hold good?
(A) f(0) = 1 (B) f(0) = 0
x

(C) f(0) = 2 (D) f x dx = e
0

12. From an urn containing x white and yx black balls, n balls have been lost, then probability of
drawing a white ball
x x
(A) before the loss is (B) after the loss is for n = 1
y y
x x
(C) after the loss is for n = 2 (D) after the loss is for n = 3
y y

v u z
13. Let u, v, w, z be complex number such that |u| < 1, |v| = 1 and w then
uz 1
(A) |w| 1 |z| 1 (B) |w| 1 |z| 1
(C) |w| 1 |z| 1 (D) |w| 1 |z| 1

cos2n x If x 0

14. The function defined as f(x) = lim n 1 x n 0 x 1 which of the following does not hold good
n
1 x 1
1 x n
(A) continuous at x = 0, but discontinuous at x = 1
(B) continuous at x = 1, but discontinuous at x = 0
(C) continuous at both x = 1 and x = 0
(D) discontinuous at both x = 1 and x = 0

15. Let 2sin x + 3 cos y = 3, and 3 sin y + 2 cos x = 4 then

(A) x y 4n 1 , n I
2

(B) x y 2n 1 , n I
2
(C) x and y can be two non right angle of a 345 triangle with x > y
(D) x and y can be two non right angles of a 345 triangle with y > x

Space for rough work

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website: www.fiitjee.com
 17 AITS-CRT-II(Paper-1)-PCM-JEE(Advanced)/14

SECTION C

Integer Answer Type

X Y Z W

0 0 0 0

This section contains 5 questions. The answer to each of the questions is a single-digit 1 1 1 1
integer, ranging from 0 to 9. The appropriate bubbles below the respective question 2 2 2 2
numbers in the ORS have to be darkened. For example, if the correct answers to question 3 3 3 3
numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, then the correct darkening of
4 4 4 4
bubbles will look like the as shown.
5 5 5 5

6 6 6 6

7 7 7 7

8 8 8 8

9 9 9 9

n 12
1
1. The value of lim
n
r
is _____
r n2

2. If r1, r2 and r3 are three values of r which satisfy the equation

/2 /2
4
sin x r cos x 3 dx 4r
x cos xdx 2 then the value of 7 r r22 r32 is equal to _____
2

0
2
0
1

3. Die A has four red faces and two white faces, die B has two red and four white faces. A fair coin
is tossed. If it shows head, then die A is rolled thrice, otherwise die B is rolled thrice. If the first
a
two throws of die shows red face, then the probability of getting red face in third throw is (in
b
lowest terms) then (a 1)b 3 is equal to _____

4. The set of all points where f(x) is increasing in (a, b) (c, ) then [a + b + c] is (where [.] denotes
x2
the greatest integer function). Given that f x 2f f 6 x 2 x R and f(x) > 0 x R
2
_____

5. A circle of radius R is tangent to the hypotenuse, the incircle and one leg of an isosceles right
a a
angle triangle with inradius r = 1 sin . If the value of Rr , where a is surd then (a +
8 b
b) is equal to _____

Space for rough work

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website: www.fiitjee.com