Physics PART – I

SECTION – A
(One or More than One Options Correct Type)
This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C)
and (D) out of which ONLY ONE is correct.

1. Find the angular frequency of oscillation of the show

system (the pulley is massless).
K K 2K
(A) (B)
M 3M
K 2K
(C) (D)
2M 3M

K M

2. An object is placed at a distance of 20 cm from an equi-concave lens of focal length 30

cm whose one side is silvered. If a virtual image is formed at 20/3 cm from the lens then
what is the radius of curvature of the curved surface?
(A) 30 cm (B) 40 cm
(C) 60 cm (D) 15 cm

3. Find the current i in the circuit.

E E R R R
(A) i  (B) i  i
2R R
E
E 2E
(C) i  (D) i 
4R R R R

R
E

Space for Rough work

 4
Review Test-11-(Paper-1)-PCM-JEE(Advanced)

4. Four particles each of mass ‘m’ are located at equal distance from each other. If the
separation between any two particles is a then their gravitational potential energy is:
4Gm2 Gm2
(A) (B)
a 8a
Gm2 6Gm2
(C) (D)
6a a

5. A parallel beam of light is incident on a perfectly absorbing small cube of side a. The
beam is directed along one of the body diagonals of the cube and has sufficiently large
aperture. What is the total radiation force experienced by the cube. I is the intensity of
radiation.
I I
(A) a2 (B) 3a2
c c
I I
(C) 3a2 (D) 2a2
c c

6. A cylinder is released from top of an inclined plane

which itself rests on a smooth horizontal surface. The m
initial velocity of the cylinder as well as the incline is
zero. (Assume no slipping in each case where the
incline is rough). M
(A) As the cylinder reaches the bottom most point, the
inclined plane will acquire a greater speed if it
were rough as compared to the case if it were 0
smooth.
(B) As cylinder reaches the bottom-most point of the inclined plane it will acquire a
greater speed if it were smooth as compared to the case when it were rough.
(C) The cylinder will have a lower kinetic energy i the case when the inclined plane is
rough as compared to the case when it is smooth.
(D) Inclined plane will have a higher kinetic energy in the case when it is rough as
compared to the case when it is smooth.

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
Review Test-11-(Paper-1)-PCM-JEE(Advanced)

Multi Correct Choice Type

This section contains 3 multiple choice questions. Each question has four choices (A), (B), (C)
and (D) out of which ONE or MORE THAN ONE are correct.

7. Four stationary observers have positions (a, 0), (0, a), (–a, 0) and (0, –a) respectively. A
moving source, moving along +x-axis is crossing origin at t = 0. Which of the followings
are correct at t = 0?
(A) Wavelength is same for all the observers.
(B) Speed of wave is same for all observers.
(C) Frequency is same for all observers.
(D) Frequency observed is more than emitted by source for three observers.

8. A parallel plate capacitor is dipped

in an insulated liquid, vertically so
that half of capacitor is in liquid. A A'
Plates of capacitor are joined to
an ideal battery of emf , A, B, A’,
B’ are four points on plate at B'
facing surface as shown. Which of
B
the following is/are correct?
(A) VA – VB’ = VA – VA’
(B) VB – VB’ = VB – VA’
(C) Electric field around A in air = Electric field around B’ in liquid.
(D) Electric field around B in liquid = Electric field around B’ in liquid.

9. Two identical solenoids each of self inductance

L are joined and placed coaxially and
overlapping in such a way that they carry equal
and opposite currents. This arrangement is
joined to a resistance R and battery of emf .
Switch is closed at t = 0. Identify the correct
statements: R
(A) Energy stored in the magnetic field increases
with time.  S
2L
(B) Time constant of the circuit is .
R
(C) Time constant of the circuit is zero.
(D) Power delivered by battery remains constant.

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
Review Test-11-(Paper-1)-PCM-JEE(Advanced)

Comprehension type (Only One Option Correct)

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. 10 and 11

A particle of mass m is fixed on a massless ring which rests

on a sufficiently rough surface so as to prevent slipping. The
system is released from the shown configuration. Then: R
m 

10. Immediately after releasing from the shown configuration what is the angular acceleration
of the ring?
gsin  gsin 
(A) (B)
 2R
4R sin2  
2
 
gsin  gsin 
(C) (D)
R R(1  cos )

11. If  be the  anticlockwise angular acceleration immediately after release from the shown
position, then what is the normal reaction immediately after release:
(A) N = mg – mRcosθ (B) N = mg
(C) N = m[g – Rsinθ] (D) None of these

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
Review Test-11-(Paper-1)-PCM-JEE(Advanced)

Paragraph for Question Nos. 12 and 14

A large cylindrical chamber has a massless piston fitted at the top. An acoustic source is situated
at the centre of the bottom of the cylinder, while an observer is situated at the bottom
circumference (inside the chamber). The observer is moving directly towards the source with
constant velocity and hears a frequency f.

12. If the chamber were to be isobarically heated then the observed frequency will be
(A) same as f (B) higher than f
(C) lower than f (D) data insufficient

13. If the chamber were to be isochorically cooled then the observed frequency will be:
(A) same as f (B) higher than f
(C) lower than f (D) Date insufficient

14. If the chamber were to be isothermally heated then, the observed frequency will be:
(A) same as f (B) higher than f
(C) lower than f (D) Data insufficient

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
Review Test-11-(Paper-1)-PCM-JEE(Advanced)

SECTION - B
Matrix – Match Type
This section contains 2 questions. Each question contains p q r s t
statements given in two columns, which have to be matched. The
A p q r s t
statements in Column I are labelled A, B, C and D, while the
statements in Column II are labelled p, q, r, s and t. Any given B p q r s t
statement in Column I can have correct matching with ONE OR
MORE statement(s) in Column II. The appropriate bubbles C p q r s t
corresponding to the answers to these questions have to be
darkened as 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. Initially there are N0 number of radioactive nuclei of species A while zero nuclei of
species B and C. A decays to B with a decay constant 1 and B decays to C with a decay
2. C is not radioactive. Then match the column:
Column I Column II
(A) NB + NC (p) Continuously increases.
(B) NB (q) Continuously decreases.
(C) NA + NC (r) First increases then decreases.
(D) NA + NB (s) First decreases then increases.
(t) Remains constant.

2. A black box having 6 points (A, B, D, F, G, A i H

H) contains a network of capacitors, real R1 R
inductors (with resistance) and resistors. E1 Black Box
There is no battery inside the black box. E1 B L G
and E2 are the EMFs of ideal batteries. If we
choose E1 = E2 = 1 volt, then steady state R2
current i is 5A. If we choose E1 = 2 volt and D F
E2
E2 = 1 volt, the steady state current i = 7A.
Now match the column:
Column I Column II
(A) E1 = 3 volt, E2 = 1 volt (p) i = 10A
(B) E1 = 1 volt, E2 = 2 volt (q) i = 11A
(C) E1 = 1 volt, E2 = 3 volt (r) i = 8A
(D) E1 = 4 volt, E2 = 1 volt (s) i = 9A
(t) i = 20 A

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
Review Test-11-(Paper-1)-PCM-JEE(Advanced)

SECTION – C
(One Integer Value Correct Type)
This section contains 5 questions. Each question, when worked out will result in one integer
from 0 to 9 (both inclusive).

1. A hydrogen atom in ground state absorbs a photon of energy corresponding to energy

difference of first orbit and fourth orbit. After this, electron de-excite from excited state. As
a result what maximum number of photons may be obtained?

2. A capillary tube is a glass cylinder of radius r. It is dipped vertically in a liquid of surface

tension T, T = 80 × 10–3 N/M, and angle of contact θ = 60°, liquid has normal capillary
rise in the tube [mass of the tube and its material volume is negligible. Then force
required to hold the tube is P × 10–3 N. Calculate P.

3. Two bodies A and B are joined through a conducting rod of high thermal conductivity with
insulated cover. A and B are thermally insulated from surrounding. Initial temperature of
A and B is 100°C and 20°C respectively. After one hour temperature of A is 80°C and B
is 40°C. After further one hour temperature of B is x × 10°C, calculate x?

4. A ring of radius (R = 10 cm) is fixed in a horizontal (Top view)

plane. A sleeve of mass m = 300 gm can move on
circumference of ring without friction. Sleeve is joined
to a spring of spring constant K and natural length R, C
 3  3
other end is fixed at P CP  R  . Sleeve is R
 4  4
released from rest. Calculate the net normal force (in
N) exerted by ring on sleeve just after releasing. [g = P
10 m/s2]

5. A ball is thrown form ground towards a vertical

wall in such a way that motion plane of ball
makes an angle of 30 with normal to wall.
Distance of point of projection form wall is
4 3 m. Collision between ball and wall is elastic. P
Had wall not been there range would have been
16 m. At what distance (in metre) from point of
projection ball falls. Q
A
O

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
Review Test-11-(Paper-1)-PCM-JEE(Advanced)

Chemistry PART – II

SECTION – A
(One or More than One Options Correct Type)
This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C)
and (D) out of which ONLY ONE is correct.

1. The major product formed in the following reaction:

H3C CH3
C C  : CH2  singlet  
H H
(A) (B)
H3C CH3 H3C H

H H H CH3
(C) 50 : 50 mixture of above two compounds (D) H3C CH2 CH3
C C
H H

2. O

MeI excess

KH excess
 81% yield, product of the reaction is

(A) O (B) O

(C) O (D) O

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
Review Test-11-(Paper-1)-PCM-JEE(Advanced)

3. Which of the following exhibits aromaticity?

(A) Cyclopentadienyl cation (B) Cyclopentadienyl radical
(C) Cycloheptatrienyl radical (D) Cycloheptatrienyl cation

4. H < E for the reaction:

(A) N2(g) + 3H2(g)  3H2(g) (B) Ag2O(s)  2Ag(s) + ½ O2(g)
(C) C (s) + ½ O2 (g)  CO (g) (D) C (s) + O2 (g)  CO2 (g)

5. Which of the following is isoelectronic and isostructural?

NO3 , CO32 , ClO3 , SO3
(A) NO3 , CO32 (B) SO3 , NO3
(C) ClO3 , CO32  (D) CO23  , ClO3

6. A particular 100-octane aviation gasoline used 1.00 cm3 of tetraethyl lead (C2H5)4Pb of
density 1.66g/cc, per litre of product. This compound is made as follows.
4C2H5Cl + 4NaPb  (C2H5)4Pb + 4NaCl + 3Pb. How many gram of ethyl chloride is
needed to make enough tetraethyl lead for 1 L of gasoline.
(A) 1.33g (B) 2.66 g
(C) 9.2g (D) 0.33g

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
Review Test-11-(Paper-1)-PCM-JEE(Advanced)

Multi Correct Choice Type

This section contains 3 multiple choice questions. Each question has four choices (A), (B), (C)
and (D) out of which ONE or MORE THAN ONE are correct.
3 2 2 3
7. The d-orbitals involved in sp d or d sp hybridisation of the central metal ion are:
(A) dx 2 – y2 (B) dxy
(C) dyz (D) dz2

8. Which of the following statement(s) is/are correct when a soid mixture of NaCl and K2Cr2-
O7 is gently warmed with conc. H2SO4?
(A) A deep red vapour is evolved
(B) The vapour when passed into NaOH solution gives a yellow soluton of Na2CrO4
(C) Chlorine gas is evolved
(D) Chromyl chloride is formed

9. Which of the following compound/s shall undergo condensation by reacting with

NaOEt/EtOH.
(A) O (B) O

O O
(C) O (D) O

O O

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
Review Test-11-(Paper-1)-PCM-JEE(Advanced)

Comprehension type (Only One Option Correct)

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. 10 and 11

Variation of equilibrium constant K with temperature is given by Van’t Hoff equation

Sro Hor
lnK  
R RT
From this equation, Hor can be calculated if equilibrium constant K1 and K2 at two temperature
T1 and T2 are known.
K  Hro  1 1
log  2     
 K1  2.303R  T1 T2 

10. 

For an isomerization X (g) 
 Y (g), the temperature dependency of equilibrium
constant is given by
1000
lnK  2 
T
the value of Sor at 300 K is
(A) 2R (B) 2/R
(C) 1000 R (D) None of these

11. Select the correct statement

(A) value of Kc always increases with increasing temperature
(B) for exothermic reaction value of Kc increase with decreasing in temperature
(C) for endothermic reaction value of Kc increases with decreasing in temperature
 1
(D) for exothermic reaction slope is  log K vs  negative
 T

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
 14
Review Test-11-(Paper-1)-PCM-JEE(Advanced)

Paragraph for Question Nos. 12 to 14

Consider the following reaction

light
 X2   mono halogenated product

12. Which halogen will give the best yield of a single mono halogenation products
(A) F2 (B) Cl2
(C) Br2 (D) I2

13. How many mono halo derivatives are possible (excluding stereo-isomers)?
(A) 3 (B) 4
(C) 5 (D) 6

14. Among the following halogens which one is least reactive towards halogenation reaction?
(A) F2 (B) Cl2
(B) Br2 (D) I2

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
 15
Review Test-11-(Paper-1)-PCM-JEE(Advanced)

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

(A) Chalcopyrite → copper (pure) (p) Froth floatation

(B) Zinc blende → zinc (pure) (q) Hall process

(C) Bauxite → aluminium (pure) (r) Roasting

(D) Galena → lead (pure) (s) Self reduction

(t) Basemerisation
2. Match the following:
Column – I Column – II
(A) KP > Q p (p) Non-spontaneous
(B) Go  RTloge Qp (q) Equilibrium
(C) KP = Q p (r) Spontaneous and endothermic
H
(D) T (s) Spontaneous
S
(t) Spontaneous and exothermic

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
 16
Review Test-11-(Paper-1)-PCM-JEE(Advanced)

SECTION – C
(One Integer Value Correct Type)
This section contains 5 questions. Each question, when worked out will result in one integer
from 0 to 9 (both inclusive).

1. Number of stereo centres in a given molecule?

CH3
H3C
C C
H
H H

2. Number of stereoisomers in given molecules [Ma3b2C].

3. Number of possible products formed in given reaction

H3C
CCl2
C CH C2H5  Br2   Pr oduct
H

4. The conductivity of 0.001 M Na2SO4 solution is 2.6  10–4 S cm–1 and increases to 7.0 
10–4 S cm–1 and increases to 7  10–4 S cm–1, when the solution is saturated with CaSO4.
The molar conductivity of Na+ and Ca2+ are 50 and 120 S cm 2 mol–1, respectively.
Neglect conductivity of used water the solubility product of CaSO4 is y  10–x M2. What is
the value of x.

234
5. 90 Th disintegrate to give 82 Pb206 as the final product. Total number of  particles
emitted out during this process are:

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
 17
Review Test-11-(Paper-1)-PCM-JEE(Advanced)

Mathematics PART – III

SECTION – A
(One or More than One Options Correct Type)
This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C)
and (D) out of which ONLY ONE is correct.

1. The locus of a point which moves so that the distance between the feet of perpendiculars
drawn from it to the lines 3x2 – 6xy + y2 = 0 is 3 3 is a circle with radius
(A) 2 15 (B) 15
(C) 6 5 (D) none of these

n  n  1
2. The sum to (n + 1) terms of the series cos   ncos 2  cos3  ..... is
2!
   
(A) 2n sinn cos  2  n  (B) 2n cosn cos  2  n 
2 2 2 2
n 
(C) 2 cos  2  n  (D) none of these
2

3. A tangent is drawn to the curve x2 + 2x – 4ky + 3 = 0 at a point whose abscissa is 3. The

tangent is perpendicular to the line x – 2y + 3 = 0. Then the area bounded by the curve,
this tangent, the x-axis and the ordinate x = –1, is
108 109
(A) sq. units (B) sq. units
47 48
111 104
(C) sq. units (D) sq. units
47 40

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
 18
Review Test-11-(Paper-1)-PCM-JEE(Advanced)

x2 y2
4. Given an ellipse   1 (a > b). A circle is drawn which passes through the foci and
a2 b2
the extremities of the minor axis of this ellipse and let this circle be the auxiliary circle for
a second ellipse whose vertices are the foci of the given ellipse. If any tangent to the
second ellipse meets its auxiliary circle at two points such that it subtends a right angle at
the origin, then the locus of the point of tangency, is (if eccentricity of both the ellipse are
same)
(A) x2 + 2y2 = a2 (B) 2x2 + y2 = a2
2 2 2 2 2 2
(C) 2x + y = a (D) x + y = 2a

1/2 1/3 1/4 1/n

2 x  3 x  4x  .....  n  x 
5. The value of lim 1/2 1/3 1/n
is
x 
 2x  3    2x  3   .....   2x  3 
(A) 0 (B) 2
1
(C) 2 (D)
3

4 2

 e  x  x  2x  e dx
x 3 5 x
6. is equal to
1 x2 x4 1 2 x4
(A) xe e  c (B) x e c
2 2
1 2 4 1 2 4
(C) e x e x  c (D) x 2 e x ex  c
2 2

Multi Correct Choice Type

This section contains 3 multiple choice questions. Each question has four choices (A), (B), (C)
and (D) out of which ONE or MORE THAN ONE are correct.

a b
1  x  1  x  1
a b
7. If f  x   1 1  x  1  x  , then
b a
1  x  1 1  x 
(A) constant term of f(x) = a + b (B) constant term of f(x) = 0
(C) coefficient of x in f(x) is zero (D) none of these

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
 19
Review Test-11-(Paper-1)-PCM-JEE(Advanced)

1
x cos a  1
8. If f  a    dx , ‘a’ being a real number other than an odd multiple of , then
0
ln x
(A) f(a) = ln(cos a) (B) f(a) = ln(1 + cos a)
a a
(C) f(a) = tan (D) f(a) =  tan
2 2

9. If f(x) = x3 – x2 + 100x + 2002, then

 1   1 
(A) f(1000) > f(1001) (B) f    f 
 2000   2001 
(C) f(x – 1) > f(x – 2) (D) f(2x – 3) > f(x)

Comprehension type (Only One Option Correct)

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. 10 and 11

Read the following write up carefully and answer the following questions:
Consider a triangle ABC, where x, y, z are the length of perpendicular drawn from the vertices of
the triangle to the opposite sides a, b, c respectively. Let the letters R, r, s,  denote the
circumradius, in-radius, semi-perimeter and area of the triangle respectively

bx cy az a2  b2  c 2
10. If    , then the value of k is
c a b k
(A) R (B) s
3
(C) 2R (D) R
2

 1 1 1
11. If cot A + cot B + cot C = k  2  2  2  , then the value of k is
x y z 
2
(A) R (B) rR
(C)  (D) a2 + b2 + c2

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
 20
Review Test-11-(Paper-1)-PCM-JEE(Advanced)

Paragraph for Question Nos. 12 and 14

Read the following write up carefully and answer the following questions:
If the locus of the circumcentre of variable triangle having sides x-axis, x = 3 and px + qy = 4,
where (p, q) lies on the parabola x2 = 4ay is a curve C, then

12. Co-ordinates of the vertex of this curve C is

 9 81   9 81 
(A)  ,  a  (B)   ,  a 
4 8   4 8 
9 9   9 81 
(C)  ,  a  (D)   , a 
4 8   4 8 

13. The curve C is symmetric about the line

9 9
(A) x   (B) x 
4 4
9 9
(C) y   (D) y 
4 4

14. The length of smallest focal chord of this curve C is

1 1
(A) (B)
2a 4a
1 1
(C) (D)
12a 16a

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
 21
Review Test-11-(Paper-1)-PCM-JEE(Advanced)

SECTION - B
Matrix – Match Type
This section contains 2 questions. Each question contains p q r s t
statements given in two columns, which have to be matched. The
A p q r s t
statements in Column I are labelled A, B, C and D, while the
statements in Column II are labelled p, q, r, s and t. Any given B p q r s t
statement in Column I can have correct matching with ONE OR
MORE statement(s) in Column II. The appropriate bubbles C p q r s t
corresponding to the answers to these questions have to be
darkened as 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) If A is an idempotent matrix and I is an identity matrix of the
(p) 9
same order, then the value of n, such that (A + I)n = I + 127A is
(B) If (I – A)–1 = I + A + A2 + ….. + A7, then An = O where n is (q) 10
(C) If A is a matrix such that aij = (i + j) (i – j) then A is singular if
(r) 7
order of matrix is
(D) If a non-singular matrix A is symmetric and A–1 is also
(s) 8
symmetric, then order of A can be
(t) 6

2. ‘n’ whole numbers are randomly chosen and multiplied then match the following Column-I
with Column-II
ColumnI ColumnII
8n  4n
(A) The probability that the last digit is 1, 3, 7 or 9 is (p)
10n
5  4n
n
(B) The probability that the last digit is 2, 4, 6 or 8 is (q)
10n
4n
(C) The probability that the last digit is 5 is (r)
10n
10n  8n  5n  4n
(D) The probability that the last digit is zero is (s)
10n
n n
8 4
(t)
10n

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
 22
Review Test-11-(Paper-1)-PCM-JEE(Advanced)

SECTION – C
(One Integer Value Correct Type)
This section contains 5 questions. Each question, when worked out will result in one integer
from 0 to 9 (both inclusive).
2 2
1. Let the circle (x – 1) + (y – 2) = 25 cuts a rectangular hyperbola with transverse axis
along y = x at four point A, B, C and D having coordinates (x i, yi), (where i = 1, 2, 3, 4)
respectively, O being the centre of the hyperbola. If  = x1 + x2 + x3 + x4, m =
x12  x 22  x32  x24 , n = y12  y 22  y32  y24 , then find value of n – m – 4  _____

2. If x  [0, 2] for which 2cos x  1  sin2x  1  sin 2x  2 has solution set
   
x   ,  , then  –  is _____
4 4

2 3 n 2
3. Given (1 – 2x + 5x + 10x )(1 + x) = 1 + a1x + a2x + ….. and that a12  2a2 , then the
value of n is _____

f  x
4. If f(x) = a0 + a1x + a2x2 + ….. + anxn + ….. and = b0 + b1x + b2x2 + ….. + bnxn + ….. If
1 x
a0 = 1 and b1 = 3 and b10 = k11 – 1, then k is _____ (Given that a0, a1, a2, ….. are in G.P.)

 cos 2 sec 2  cos2 sec 2 

5. For tan1 
 
1 2
2 1
  tan tan      tan       tan 1

 the

value of  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