FIITJEE JEE (Advanced), 2015

FULL TEST – II
FIITJEE Students From All Programs have bagged 34 in Top 100, 66 in Top 200 and 174 in Top 500 All India Ranks. FIITJEE Performance in JEE (Advanced), 2014:
2521 FIITJEE Students from Classroom / Integrated School Programs & 3579 FIITJEE Students from All Programs have qualified in JEE (Advanced), 2014.

Paper 1

Time Allotted: 3 Hours Maximum Marks: 246

 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 l l 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 three sections: Section-A, Section-B & 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.

1. Section – A (01 – 07) contains 7 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 (08 – 11) contains 4 multiple choice questions which have one or more than one
correct answer. Each question carries +3 marks for correct answer. There is no negative
marking.
Section-A (12 – 16) contains 2 paragraphs. Based upon paragraph, 2 and 3 multiple choice
questions have to be answered. Each question has only one correct answer and carries
+3 marks for correct answer and – 1 mark for wrong answer.

2. Section – B (01 – 02) contains 2 Matrix Match Type questions containing statements given in 2
columns. Statements in the first column have to be matched with statements in the second
column. Each question carries +8 marks for all correct answer. For each correct row +2 marks
will be awarded. There may be one or more than one correct matching. No marks will be given for
any wrong matching in any question. There is no negative marking.
3. Section-C (01 – 06) contains 6 Numerical based questions with answers as numerical value from
0 to 9 and each question carries +3 marks for correct answer. There is no negative marking.

Name of the Candidate

Enrolment No.

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 2
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

Useful Data

PHYSICS
2
Acceleration due to gravity g = 10 m/s

Planck constant h = 6.6 1034 J-s

Charge of electron e = 1.6  1019 C

Mass of electron me = 9.1  1031 kg

2 2
Permittivity of free space 0 = 8.85  1012 C /N-m

Density of water water = 103 kg/m3

Atmospheric pressure Pa = 105 N/m2

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 Na = 6.023  1023
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.

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 3
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

Physics PART – I

SECTION – A
Straight Objective Type
This section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D)
out of which ONLY ONE option is correct.

 ( yiˆ  xj)
ˆ
1. Electric field at point P in a region whose coordinates are (x, y, z) is give by : E  E0
x2  y2
where E0 is constant. Which of the following can best represent the Electric field lines
corresponding to this field?
(A) y (B) y

O x
O x

(C) y (D) y

O x O x

Space for Rough work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 4
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

2. Net charge distributed on a ring shown in figure is zero. AA ' is axis of ring.
Then choose the correct statement
(A) Electrostatic field at all points an axis AA ' will be zero.
(B) Component of Electrostatic field along axis must be zero.
(C) Component of Electrostatic field perpendicular to the axis must be zero
(D) Electrostatic potential must be zero at all point inside ring in the plane of
ring

3. Figure shows a irregular shape conductor with

irregular cavity inside it. A charge Q is placed
inside cavity and a charge Q ' is placed outside
conductor. Let Q’ind be charge induced at outside
surface of conductor and Qind be the charge
induced at inside surface of cavity. A 'B ' is an
arbitrary line passing through charge Q and a, b, c
   
be the points on line as shown in figure. Let E, E', Eind and E'ind represent electric field at different
points due to charge Q, Q’ Qind, & Q’ind respectively. If Va,Vb and Vc represent potential at point a,
b, and c. Choose the incorrect statement

(A) Va  Vb  Vc

rb
     
(B) Vb 
 (E  E '  E ind  E 'ind ).dr , where rb = position vector of point b
–

rb
  
(C) Vb 
 (E '  E '

ind ).dr


(D) At point ‘b’, E'  0

Space for Rough work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 5
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

4. Two wires W 1 & W 2 carry current ‘2i’ and i respectively directed into the plane A

of paper as shown in figure. AA ' is line at some distance from wire. Let B be W1

  2i d
the net magnetic field due to wires. The magnitude of

 B .d will be equal to
W2
(A) 0i /2 (B) 0i /4 i
(C) 0i /8 (D) zero A

5. A conducting rod of square cross section is bent in a semi circular

shape of radius ‘r’ as shown in figure. Length of side of cross
section is equal to ‘a’. Resistivity of material is ‘’. The resistance
of rod across its end will be
 2
(A) (B)
aln 1 a / r  aln 1 a / r 
(r  a) 2  r
(C) 2
(D)
a a2

6. A charge ‘q’ is undergoing S.H.M. about

point ‘A’ along the line AB at distance ‘d’
from the center B of a conducting sphere of
radius R. Amplitude oscillation of charge is
‘a’ angular frequency is ‘’. The sphere is
grounded through conducting wire CC ' .
Choose the correct statement

 Ra 
(A) If a < < d then the maximum value of current in wire CC ' will be q  2 
d 
 qRa2 
(B) If a < < d then the maximum value of current in wire CC ' will be  3 
 d 
 2Ra 
(C) If a < < d then the maximum value of current in wire CC ' will be q  2 
 d 
 2qRa2 
(D) If a < < d then the maximum value of current in wire CC ' will be  3 
 d 

Space for Rough work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 6
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

7. A hollow cylindrical conductor (inner radius = a, outer radius = b) carries a current i uniformly
spread over its cross section. Which graph below correctly gives B as a function of the distance r
from the center of the cylinder?
(A) B (B) B

a r a r
b b
(C) B (D) B

a r a r
b b

(Multiple Correct Choice Type)

This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D)
out of which ONE or MORE THAN ONE are correct.

8. A rod is free to rotate in horizontal plane about one of its end hinged
at point ‘O’ as shown in figure. Point P & Q are fixed points located in
horizontal plane in such away that PO is perpendicular to rod & QO
is along length of rod. A bullet hits the rod perpendicularly at some
distance from point ‘O’ and gets imbedded into it. Then :
(A) Linear momentum of rod + bullet system will decrease after
collision.
(B) Linear momentum of rod + bullet system may increase
(C) Angular momentum of rod + bullet system about point ‘P’ will not
change before & after collision.
(D) Angular momentum of rod + bullet system about ‘Q’ may
increase after collision.

Space for Rough work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 7
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

9. Shape of string transmitting wave along x-

axis at some instant is shown
Velocity of point P is v = 4 cm/s and
  tan1(0.004)
(A) Amplitude of wave is 2 mm
(B) Velocity of wave is 10 m/s
(C) Max acceleration of particle is 80 2
cm/sec2
(D) Wave is traveling in –ve x-direction

10. A small ball of mass m is placed in a circular tube of mass M and radius R in v0
gravity free space. Friction is absent between tube and ball. Ball is given a
velocity v0 as shown. Then,
m
(A) Path of ball from centre of mass of system will be circular.
R
(B) Path of ball from centre of mass of system will be elliptical

MR
(C) Radius of curvature of ball at the time of projection of ball is
mM
2mV02
(D) Normal force between tube and ball if M = 2m, at the time of projection of ball is
3R

D
11. A system of rods is assembled such that each rod has a length 
2k k
and cross-sectional areas S. The mode of heat transfer is
A k C
conduction and the system is in steady state. The temperature of
Junction A is T and that of C is 2T. Now answer the following k 2k
question. B
(A) Temperature of junction B is 1.6 T.
(B) Temperature of junction D is 1.4 T.
1 kTS
(C) The rate of heat flow along BD is .
5 
21kTS
(D) The rate of heat flow along BD is .
5 

Space for Rough work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 8
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

Comprehension Type

This section contains 2 paragraphs. Based upon one of the paragraphs 2 multiple choice questions
and based on the other paragraph 3 multiple choice question have to be answered. Each of these
questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Paragraph for Questions 12 & 13

A square wire loop having side a, mass m and resistance R is moving y 

B
along positive x-axis with speed v 0 enters into uniform steady magnetic a

ˆ at t = 0 sec as shown in the figure.
field B  B0 (k)
a x
The magnitude of v0 is sufficient so that the loop comes out from region
of magnetic field with v1. Neglect any type of energy loss other than
3a
3B2 a3
heat loss in resistances of wires of square (given v0  )
mR
Read above passage carefully and answer the following questions.

12. The plot of speed of square versus position x will be represented by

(A) v (B) v

O a 2a 3a x O a 2a 3a x

(C) v (D) v

O a 2a 3a x O a 2a 3a x

13. The total amount of heat loss in the resistance will be

5 4
(A) mv 02 (B) mv 20
9 9
2 mv 20
(C) mv 02 (D)
9 9

Space for Rough work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 9
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

Paragraph for Questions 14 & 16

Figure shows intensity versus wavelength graph of X-rays coming from Coolidge-tube with molybdenum
as anticathode:

The two peaks shown in graph correspond to K & K X-rays

14. Wavelength of L X-rays from Coolidge tube will be (approximately)

(A) 5.60Å (B) 4.26 Å
(C) 0.33 Å (D) 1.34 Å

15. Voltage applied across Coolidge tube in (approximately)

(A) 20 kV (B) 16 kV
(C) 31 kV (D) 18 kV

16. In the potential difference across the Coolidge tube is increased such that the cut off wavelength
of x-ray becomes 0.2 Å. Find the value of    in this condition.
(A) 0.02 Å (B) 0.04 Å
(C) 0.06 Å (D) 0.08 Å

Space for Rough work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 10
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

SECTION - B
Matrix – Match Type
This section contains 2 questions. Each question contains statements given in p q r s t
two columns, which have to be matched. The statements in Column I are
p q r s t
labelled A, B, C and D, while the statements in Column II are labelled p, q, r, A
s and t. Any given statement in Column I can have correct matching with B p q r s t
ONE OR MORE statement(s) in Column II. The appropriate bubbles
corresponding to the answers to these questions have to be darkened as C p q r s t
illustrated in the following example:
D p q r s t
If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s
and t; then the correct darkening of bubbles will look like the following:

1. In the adjacent circuit shown, all ammeters 0.5 P 5V

+  0.5
A2
and batteries are ideal. Internal resistances 20 V 10 V
of all the batteries are negligible. Point R is 1
grounded. Then, match the following. 5V 20 V
Q +  + 

12.5  10 

A1
R

Column – I Column – II
(A)
Potential of point P (p) 6 SI unit
(B)
Potential of point Q (q) 25 SI unit
(C)
Reading of ammeter A1 (r) 18 SI unit
(D)
Reading of ammeter A2 (s) 47 SI unit

Space for Rough work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 11
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

2. A lens is made up of a material of refractive index  which is completely immersed in a medium of

refractive index 0. The power of lens is P. Match the properties in column I with the
corresponding type(s) of lens in column II
Column I Column II
(A) P  0 and  > 0 (p) Bi-convex
(B) P  0 and  < 0 (q) Bi-concave
(C) P  0 and  > 0 (r) Convexo concave
(D) P  0 and  < 0 (s) Concavo convex
(t) Plano convex

SECTION – C
(Integer Answer Type)

This section contains 6 questions. Each question, when worked out will result in one integer from 0 to 9
(both inclusive).

1. Conducting shell of radius R carrying charge Q, 3R

another charge Q is placed at 3R distance from
centre of shell. If the potential at point P due to R
11 KQ
charge on shell is , Then the value of n is O
3n R P Q
R/2

2. A liquid is kept in a cylindrical vessel. When the vessel is rotated about its axis, the liquid rises at
its sides. If the radius of the vessel is 0.05 m and the speed of rotation is 2 revolutions per
second, the difference in the heights (in cm) of the liquid at the centre and at the sides of the
vessel is (take g = 10 ms2 and 2 = 10)

Space for Rough work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 12
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

3. When a resistance R is connected in series with an element A, the electric current is found to be
lagging behind the voltage by V angle 30 When the same resistance is connected in series with
element B, current leads by 60. When R, A, B are connected in series, the current new leads
voltage by  . Which is equal to tan1(K/3), then the value of K is (assume same AC source is
used in all cases)

4. A ball of mass m = 2kg thrown from ground form point ‘O’ between
two walls, W1 & W2 at a distance 5 cm from ‘O’ an shown in figure.
Had the wall w2 not been there range of ball would have been 20 m.
Horizontal component of velocity of ball at the time of projection was
5 m/s. All collisions are elastic. Average force acting on one of the
walls (in newton) is

5. A small object at P oscillates infront of a concave mirror as R

shown in the figure perpendicular to principal axis according to
equation. P C
 
y = 4 sin  t   cm,
 3
3R/2
y is the displacement of particle perpendicular to principal axis.
The amplitude (in cm) of image is

6. A particle moves in a circle with a uniform speed, when it goes from a point A to a diametrically
 
opposite point B, the momentum of the particle changes by PA  PB  2kgm / s(ˆj) and the
 
ˆ where ˆi, ˆj are unit vectors. Then the
centripetal force acting on it changes by FA  FB  8N(i)
angular velocity (in rad/s) of the particle is

Space for Rough work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 13
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

Chemistry PART – II

SECTION – A
Straight Objective Type
This section contains 7 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for
its answer, out which ONLY ONE option is correct.
 Br  
1. At what does the following cell have its reaction at equilibrium?
CO32  
Ag(s) |Ag2CO3(s)| Na2CO3(aq)| |KBr(aq)| AgBr(s)| Ag(s)
–12 –13
Ksp = 8  10 for Ag2CO3 and Ksp = 4  10 for AgBr

(A) 1 107 (B) 2 107

7 7
(C) 3  10 (D) 4 10

2. A human body excretes [removes by waste discharges, sweating etc] certain material by a law
similar to radio activity. If technitium is injected in some form in the human body, the body
excrets half of the amount in 24 hours. A patient is given an injection confainingTc99. This
isotope is radioactive with a half life 6 hrs. The activity from the body just after the injection is 6
C. How many hours will elapse before the activity falls to 3 Ci?
(A) 24 hours (B) 6 hours
(C) 4.8 hours (D) 12 hours

3. Find the product of the following reaction

R R

CH2
R O
(A) R O (B) R
and H3C CH2 R
R R
O R
(C) R (D) R
and H2C CHO R CH2
R R
R
O

4. A big RED spherical balloon (radius = 6a) is filled up with gas. On this balloon six small GREEN
spherical balloons (radius = a) are stuck on the surface in a specific manner. As RED balloon is
slowly deflated, a point comes when all these six GREEN balloons touch and green balloons
arrange themselves in a 3-D closed packing arrangement. At that stage the radius of the RED
balloon would have reduced by approximately.
(A) 14.5 times (B) 1.414 times
(C) 6.0 times (D) 2.42 times
Rough Work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 14
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

5. Which of the following graphs represents the radial charge density for the electron of outer most
+2
sub shell of Cu ?

4r2 R2 4r2 R2

(A) (B)
r r

4r2 R2 4r2 R2

(C) (D)
r r

6. The order of reactivity towards Perkin reaction of the following aromatic aldehydes is
CHO CHO CHO CHO
CH3

N(CH3)2 NO2

(a) (b) (c) (d)

(A) (d) > (a) > (b) > (c) (B) (c) > (a) > (b) > (d)
(C) (b) > (c) > (a) > (d) (D) (d) > (a) > (c) > (b)

7. Which of the following represents the correct order for the wavelength of absorption in the visible
region for the following
[Ni(NO2 ) 6 ]4 [NiF6 ]4  [Ni(H 2O) 6 ]2  [Ni(NH 3 ) 6 ]2 
(I) (II) (III) (IV)
(A) I  IV  III  II (B) II  IV  III  I
(C) II  III  IV  I (D) I  III  II  IV
Rough Work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 15
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

Multiple Correct Choice Type

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

8. A + B   C + D is a stoichiometrically balanced reaction. The initial rate of the reaction is

doubled if the initial concentration of A is doubled, but is quadrupled if the initial concentration of
B is doubled.
Select the correct statement(s)
(A) The reaction is first order in B and second order in A
(B) The reaction is first order in A and second order in B
(C) The reaction can not be a single-step reaction
(D) The overall order of the reaction is 3

9. In which of the following cases will a violet colouration be observed

(A) An alkaline solution of sodium nitroprusside is treated with a solution of Na2S
(B) A solution of sodium cobaltinitrite is treated with KCl
(C) A solution of Mn(NO3)2 is treated with sodium bismuthate or red lead in the presence of
concentrated HNO3
(D) A solution of sodium nitroprusside in aqueous, NaOH is heated ith Na2SO3

?
10. CH 3  CH  NH   CH 3CH 2  NH 2 for this conversion suitable reagent
(A) Na  Hg H 2 O (B) H 2 Pd
(C) LiAlH 4 Et 2 O (D) NaBH 4 EtOH

11. X  H 2SO 4  Y (a colourless gas with pungent smell)

Y  K 2Cr2O 7  H 2SO 4  Green solution
(A) X is SO32– (B) X is CO3–2
(C) Y is H2S (D) Y is SO2

Rough Work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 16
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

Comprehension Type
This section contains 2 paragraphs. Based upon the first paragraph 2 multiple choice questions and
based upon the second paragraph 3 multiple choice questions have to be answered. Each of these
questions has four choices A), B), C) and D) out of WHICH ONLY ONE IS CORRECT.

Paragraph for Question Nos. 12 to 13

The process of eudiometry is used to calculate the volume of the various reacting gases present together
in a closed vessel, it is done by sparking the content and noting the volume change or pressure change
depending upon the conditions mentioned. Various reagents like alkaline pyrogallol, turpentine oil, caustic
potash, conc. H2SO4 are used to absorb the selective gases like O2, O3, CO2 and H2O (v) respectively.
A 2.0 mole mixture of H2(g), O2(g) and He(g) are placed together in a closed container at pressure equal
to 50 atm. An electric spark is passed and pressure is noted as 12.5 atm after cooling the content to
original temp. (room temp). Oxygen gas is introduced for pressure to change to 25 atm, keeping volume
and temp constant. Again electrical spark is passed and pressure drops to 10 atm under original temp.
conditions.

12. The moles of He(g) present in the mixture sample is

(A) 0.2 (B) 0.1
(C) 0.5 (D) 1.4

13. The mole fraction of H2(g) present in the initial mixture is:
(A) 0.05 (B) 0.7
(C) 0.5 (D) 1.25
Rough Work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 17
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

Paragraph for Question Nos. 14 to 16

An unknown organic compound (A) with the molecular formula C9H12O does not decolourize Br2 in CCl4,
reacts with sodium to give a colourless, odourless gas and can be oxidised by hot alkaline KMnO4 to give
benzoic acid. Then, following test were performed on the compound (A) is given sequence:
Test (a): The colour of the solution changes from orange to green when K2Cr2O7 is added to it.
Test (b): The compound can be resolved.
Test (c): No yellow precipitate of CHI3 is formed when reacted with I2 and OH–.
Test (d): Oxidation of the compound with CrO3 in pyridine gives another compound that gives
Tollen’s test.

14. Which of the following would be the structure of compound if test (a) is negative?
(A) PhCH(OH)CH2CH3 (B) PhC(OH)(CH3)2
(C) PhCH2CH(OH)CH3 (D) PhCH(CH3)CH2OH

15. Which of the following would not be the structure of compound (A) after test (b)?
(A) PhCH(OH)CH2CH3 (B) PhCH2CH(OH)CH3
(C) PhCH2CH2CH2OH (D) PhCH(CH3)CH2OH

16. The structure assigned to compound (A) after the test (d) would be
(A) PhCH(OH)CH2CH3 (B) PhCH2CH(OH)CH3
(C) PhCH(CH3)CH2OH (D) PhC(OH)(CH3)2
Rough Work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 18
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

SECTION-B
(Matrix-Match Type)
This section contains 2 questions. Each question contains statements given p q r s t
in two columns, which have to be matched. The statements in Column I are
A p q r s t
labelled A, B, C and D, while the statements in Column II are labelled p, q, r,
s and t. Any given statement in Column I can have correct matching with B p q r s t
ONE OR MORE statement(s) in Column II. The appropriate bubbles
corresponding to the answers to these questions have to be darkened as C p q r s t
illustrated in the following example:
D p q r s t
If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s
and t; then the correct darkening of bubbles will look like the following:

1. Match the following metals given in Column I with the appropriate metal extraction process(es)
listed below in Column II.
Column – I Column – II

(A) Silver (p) Fused salt electrolysis

(B) Lead (q) Cyanide process

(C) Iron (r) Carbon monoxide reduction

(D) Magnesium (s) Self reduction

(t) Frothflotation

Rough Work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 19
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

2. Column – I contain reaction and Column – II consist of reagent used in these reaction. Match the
following.
Column – I Column – II

(A) CHO CHO (p) X = Na/liq. NH3

 
X  
Y
Y = cold dil. KMnO4/OH
   

(B) OH CHO (q) X = Br2, CHCl3

Y = CH3ONa/CH3OH
  X  Y
   

OH

(C) (r) X = O3/H2O, Zn

Me Y = NaOH/

 
X  Y HC Me COCH3
   

CH(CH3)2

(D) O (s) X = HIO4

Y = NaOH/
H3 C C C CH 2 C CH3 X
  Y
  Racemic Mix.

(t) X= H2/Pd
Y=Zn-Hg/ conc. HCl

Rough Work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 20
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

SECTION –C
Integer Answer Type
This section contains 6 questions. Each question, when worked out will result in one integer from 0 to 9
(both inclusive).

1. How many of the following reactions are addition-elimination reactions of carbonyl compounds?
(I) Cyanohydrin formation
(II) Acetal formation
(III) Semicarbazone formation
(IV) Aldol formation
(V) Hemiacetal formation
(VI) Oximeformation
(VII) Ketal formation
(VIII) Imine formation
(IX) 2,4-DNPderivative formation

2. Total number of stereoisomers of the H

compound given below is x
C
C COCH3

And number of chiral carbons are there CH3CO

in the product ‘P’is y
H3C
 Br2 /CCl4
  ?  P

then the value of (x+y)/2 is?

3. A 50 ml 1.92% (W/V) solution of a metal ion Mn+ (atomic weight = 60) was treated with 5.332 g
hydrazinehydrate (90% pure) and mixture was saturated with CO2 gas when entire metal gets
precipitated as a complex [M(H2N – NHCOO)n]. The complex was filtered off and the filtrate was
M
titrated with KIO3 in the presence of conc. HCl according to the following equation:
10
N2H4  IO3  2H  2Cl   ICl  3H2O  N2 
M
The volume of KIO3 solution needed for the end point to arrive was 480 ml. Find the value of
10
n.
Rough Work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 21
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

4. How many statements are true in the given question of about?

(i) orthoboric acid It is a strong tribasic acid.
(ii) orthoboric acid does not act as a proton donor but behaves like a Lewis acid by accepting OH
ion.
(iii) orthoboric acid is prepared by the action of mineral acid on borax solution.
(iv) orthoboric acid has a layer structure in which hydrogen bonds unite B(OH)3 units.

(v) If the number of revolutions made by electron in1.0 s in H atom in its nth orbit is twice of the
number of revolution made by electron in 1.0 s in the 2nd orbit of Hatom, then n is 1.

(vi) Forms a colourless solution with coloured precipitate(r)CrCl3(s) + dil HNO3(aq)

(vii) Forms a coloured solution with no precipitate(s)K2CrO4(aq) + Ba(NO3)2(aq)

(viii) F > N > C > Si >Ca - metallic character

(ix) Saccharin (pKa = 2) is an artificial zero calorie sweetner added to toothpaste
O

C
+
N Na

S
O O
Sodium Saccharin Structure .Two flasks A&B both contain 18.3 gm of Saccharin dissolved in 100
ml solution. 2 grams of solid NaOH is added to A and 4 grams of solid NaOH is added to B. This
resulted in the formation of the above structure in both flasks. The difference in pH of the two
flasks after the experiment is: 6
(x) C > Si > P > N - electron affinity
(xi) O > N > F > C - second ionisation potential
(xii) I2 <F2  Br2  Cl2 Bond energy ORDER

(xiii) mixture of HCl and CH3COOH titrated against NaOH the correct graphical representation
is
Conductance

Vol. of titre

(xiv) The CORRECT ORDER OF basic character of the following alcohols is

CH2OH CH2OH CH2OH
CH 2OH
> > >

OCH3 Cl NO2

Rough Work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 22
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

5. In the given graph, the area of circle A

and B are 40 unit and 36 unit respectively,
total work done ‘X’ unit.
A B
P

V
When a system is taken from state A to B C B
along path ACB, as shown in the figure, 5
unit of heat flows into the system and the
system does 3 unit of work. If ‘y’unit heat
flows into the system along the path ADB,
and the work done by the system is 2 unit A D
?

Then the value of x + y is

6. Alkaline hydrolysis of chloral hydrate produces a compound (A) which is used as a solvent and
preservative for anatomical specimens and also has anesthetic properties. (A) is prone to aerial
oxidation in presence of sunlight to give a poisonous compound (B) which may be made non
poisonous by adding dilute solution of ethanol which converts it into a non poisonous compound
(C). How many moles of CH3MgBr will be added to (C) followed by acidic hydrolysis to give
alcohol?
Rough Work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 23
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

Mathematics PART – III

SECTION – A

Straight Objective Type

This section contains 7 multiple choice questions numbered 1 to 7. Each question has 4 choices (A), (B),
(C) and (D), out of which ONLY ONE is correct

1. The number of 6-digit numbers whose digits are selected from set {5, 6, 7, 8, 9} such that any
digit that appears in the number appears at least twice is
(A) 1100 (B) 1200
(C) 1400 (D) 1405

2. The equation of common tangent to the curve |z – 2i| = 2 and |z – 1 – 3i| + |z + 1 – 3i| = 2 2 is
(A) z  z  4 (B) z  z  8i
(C) z  z  8 (D) z  z  4i

n n
3. Let f  n    k Cr then total number of divisors of f(9) is equal to
r 0 k r
(A) 5 (B) 6
(C) 7 (D) 8

100 50
100   
4. 
Let 2 1  x 3    ai xi  cos  2  x  i    . If  a2i  2k
i0   i0
then the value of k is

(A) k = 100 (B) k = 200

(C) k = 310 (D) k = 410

5. Let M = {(x, y) : y  x2} and N = {(x, y) : x 2 + (y – a)2  1}. The necessary and sufficient condition
for M  N = N is
5 5
(A) a  (B) a 
4 4
(C) a  R+ (D) a  (0, 1)

Space for rough work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 24
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15


3
x loge  sin x  dx
0
6. The value of the ratio 
is
x
2
loge  
2 sin x dx
0

 2
(A) (B)
2 3
3 3
(C) (D)
4 2
2
7. A parabola y = ax + bx + c crosses the x-axis at (, 0) and (, 0) both to the right of the origin. A
circle also passes through these two points the length of tangent from the origin to the circle is
a c
(A) (B)
b a
2
b
(C) bc (D) 2
c

Multiple Correct Choice Type

This section contains 4 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

8. Positive integers are written on all the faces of a cube, one on each. At each corner (vertex) of
the cube, the product of the numbers on the faces that meet at the corner is written. The sum of
the numbers written at all the corner is 2004. If T denotes the sum of the number on all the faces,
the possible value of T are
(A) 174 (B) 175
(C) 339 (D) 505

9. If the equation x2 + (a – 2)x + 1 = 3|x| has exactly three distinct real solutions in x, the value of a
is/are
(A) 1 (B) 2
(C) 3 (D) 4

Space for rough work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 25
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

10. In an acute triangle ABC, O is circumcentre, H is orthocentre and G is the centroid. Let OD be
perpendicular to BC and HE be perpendicular to CA, with D on BC, E on CA. Let F be the mid-
point of AB. Suppose the area of triangle ODC, HEA and GFB are equal the possible value of
angle C is
 
(A) (B)
3 4
 
(C) (D)
6 2

11. A player throws an ordinary dice, whenever he throws 1, he gets an additional throw. Then
probability to get sum of score n is
1  64  1  1  65  1 
(A)  4  is n = 5 (B)  5  if n = 6
5 6  5 6 
1  65  1 
(C)   if n = 7 (D) 0 if n = 1
30  65 

Comprehension Type

This section contains 2 paragraphs. Based upon one of paragraphs 2 multiple choice questions and
based on the other paragraph 3 multiple choice questions have to be answered. Each of these questions
has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct

Paragraph for Question Nos. 12 to 13

Read the following write up carefully and answer the following questions:
A trapezium ABCD, in which AB is parallel to CD, is inscribed in a circle with centre O. Suppose the
diagonal AC and BD of trapezium intersect at M and OM = 2

12. If AMB = 60º then difference between length of parallel sides is

(A) 3 (B) 2
(C) 2 3 (D) 4

13. If AMD is 60º then difference between length of parallel sides is

(A) 2 (B) 3
(C) 2 3 (D) 4 3

Space for rough work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 26
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

Paragraph for Question Nos. 14 to 16

Read the following write up carefully and answer the following questions:
An ellipse whose major axis is parallel to x-axis such that segment of a focal chord are 1 and 2 units. The
x y 1
line    0 are the chords of the ellipse such that a, c, b are in H.P. and are bisected by the point
a b c
at which they are concurrent, the equation of auxiliary circle is 2x 2 + 2y2 + 4px + 4qy – 16p + 1= 0 then

14. The centre of ellipse is

(A) (1, –1) (B) (1, 1)
 1 1  1 1
(C)  ,  (D)   ,  
 2 2  2 2

15. Equation of director circle is

2 2 37 2 2 37
(A) x + y – x – y – 0 (B) x + y + x + y + 0
6 6
37 37
(C) x2 + y2 + x + y – 0 (D) x2 + b2 – x – y + 0
6 6

16. Eccentricity of ellipse is

1 1
(A) (B)
3 3
2 2
(C) (D)
3 3

Space for rough work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 27
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

SECTION-B
(Matrix-Match Type)
This section contains 2 questions. Each question contains statements given p q r s t
in two columns, which have to be matched. The statements in Column I are
A p q r s t
labelled A, B, C and D, while the statements in Column II are labelled p, q, r,
s and t. Any given statement in Column I can have correct matching with B p q r s t
ONE OR MORE statement(s) in Column II. The appropriate bubbles
corresponding to the answers to these questions have to be darkened as C p q r s t
illustrated in the following example:
D p q r s t
If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s
and t; then the correct darkening of bubbles will look like the following:

1. Match the following Column-I with Column-II

Column – I Column – II
(A) The number of all triples (a, b, c) such that all three term a,
b, c are in harmonic progression in which a = 20 and b
(p) 66
divides c (where a, b, c are strictly increasing positive
integers)
(B) The number of solutions of m + n + p = 10, (m, n, p are
(q) 20
non-negative integers)
(C) The number of ordered pair (a, b) satisfying the equation
(r) 4
ab + b – a + 1 = 0 are where a, b  I
(D) The number of ordered pairs (x, y) of real numbers such
(s) 5
that (x + iy)20 = x – iy is (where i = 1 )
(t) 22

2. Match the following Column-I with Column-II

Column – I Column – II
(A) Let f(x) = x 4 + ax3 + bx2 + cx + d (where a, b, c, d are real
coefficient) and f(x) = 0 has real roots, If |f(i)| = 1 and (p) 0
a = b = c = d = k then k can be (where i  1 )
x x2 x3 x4
(B) If x5 = 1 (x  1) then    equals (q) 1
1  x 2 1  x 4 1  x 1  x3
 1
(C) Let f  x   ln cos x   (where [.] denotes the greatest
 2
x2    f  x  n  

integer function), then  lim  2   dx is (r) 2
 n  x  tan2 x  
x1 
  
  
(where x1, x 2    ,  )
 6 6
(D) Let ABCD be a cyclic quadrilateral inscribed in a circle of
radius 2, such that BD = 2 3 , AB = 1. If BAD is acute (s) 3
and AD = a  b 5 , then the value of a + b is equal to
(t) 4

Space for rough work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
 28
AITS-FT-II-(Paper-1)-PCM-JEE(Advanced)/15

SECTION – C

(Integer Answer Type)

This section contains 6 questions. Each question, when worked out will result in one integer from 0 to 9
(both inclusive).

1. Let X be the set of all positive integers greater then or equal to 8 and let f : X  X be a function
such that f(x + y) = f(xy) for all x  4, y  4. If f(8) = 9 then f(9) is equal to _____

2. If f(x) and g(x) be two function such that f(x) = 2f(x) – 2f(x), g(x) = f(x) – f(x). Let F(x) be defined
as F(x) = [f2(x) + g2(x)][f 2(–x) + g2(–x)]. If F(0) = 1 then the value of F(1) is _____

5
3. Let f(x) = tan–1 (cot x – 2 cot 2x) and  f  r   a  b where a, b  N, then the value of b is _____
r 1

4. The least possible area of convex quadrilateral having two vertices on two branches of hyperbola
xy = 2 and other two vertices on the two branches of xy = –2 is _____

200 200
5. Consider two polynomial f(x) and g(x) given by f  x    r xr and g  x    r xr such that r = 1
r 0 r 0
200
 100  r  200 and f(x + 1) = g(x). Let A   r , then the remainder when A is divided by 15 is
r 100
equal to _____

6. Consider a square ABCD of diagonal length 2 3 . The square is folded along the diagonal AC so
that the plane of ABC is perpendicular to the plane of ADC. The shortest distance between AB
and CD is _____

Space for rough work

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com