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CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA


ANDHERI / BORIVALI / DADAR / CHEMBUR / THANE / MULUND/ NERUL / POWAI
IIT – JEE - 2013 FULL TEST – 3 MARKS: 226
PAPER – I (ADVANCED PATTERN)

SECTION - I PHYSICS

PART I: Single Correct Answer Type

This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C)
and (D) out of which ONLY ONE is correct. (+3, –1)


1. Block A is placed on block B, whose mass is greater than that of
A. There is friction between the blocks, while the ground is
smooth. A horizontal force P, increasing linearly with time, begins
to act on A. The accelerations
1
a and
2
a of A and B respectively
are plotted against time (t). Choose the correct graph



(a) (b)






(c) (d)







2. A force
( )
F k yi xj = ÷ +

 
, where k is a positive constant, acts on a particle moving in the xy plane.
Starting from the origin, the particle is taken along the positive x – axis to the point (a, 0) and then
parallel to the y – axis to the point (a, a). The total work done by the force on the particle is
(a)
2
2ka ÷ (b)
2
2ka (c)
2
ka ÷ (d)
2
ka

3. A rectangular block has a square base measuring a a × , and its height is h. It moves with a speed v
on smooth horizontal surface
(a) It will topple if v 2gh > . (b) It will topple if v 2ga >
(c) It will topple if
2
v 2ga h > (d) It will not topple for any value of v

1
a
2
a
t
1
a
2
a
t
2
a
1
a
1
a
2
a
t
2
a
1
a
1
a
2
a
t
2
a
1
a
B
A P
4.




A cyclic process ABCD is shown in the p-V diagram. Which of the following curves represent the same
process?

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

5. A short linear object of length b lies along the axis of a concave mirror of focal length f, at a distance
u from the mirror. The size of the image is approximately
(a)
1
2
u f
b
f
÷ | |
|
\ .
(b)
f
b
u f
| |
|
÷
\ .
(c)
u f
b
f
÷ | |
|
\ .
(d)
2
f
b
u f
| |
|
÷
\ .


6. In region of space, the electric field is in the x-direction and proportional to x, i.e.,
0
ˆ
E E xi =

.
Consider an imaginary cubical volume of edge a, with its edges parallel to the axes of coordinates.
The charge inside this volume is
(a) zero (b)
3
0 0
E a c (c)
3
0
0
1
E a
c
(d)
2
0 0
1
E a
6
c

7. In a parallel-plate capacitor, the region between the plates is filled by a dielectric slab. The capacitor
is connected to a cell and the slab is taken out.
(a) Some charge is drawn from the cell.
(b) Some charge is returned to the cell.
(c) The potential difference across the capacitor is reduced.
(d) No work is done by an external agent in taking the slab out.

8. Sound of wavelength ì passes through a Quincke’s tube, which is adjusted to give a maximum
intensity
0
I . Through what distance should the sliding tube be moved to give an intensity
0
I / 2?
(a) /2 ì (b) /3 ì (c) /4 ì (d) /8 ì




PART II: Multiple Correct Answer(s) Type

This section contains 4 multiple choice questions. Each question has four choices (A),
(B), (C) or (D) out of which ONE or MORE are correct. (+4, –1)


9. A thin uniformrod of mass mand length l is free to rotate about its upper end. When it is at rest, it receives
an impulse J at its lowest point, normal to its length. Immediately after impact,
(a) the angular momentumof the rod is Jl
(b) the angular velocity of the rod is 3J ml
(c) the kinetic energy of the rod is 3 2 J m
2

(d) the linear velocity of the midpoint of the rod is 3 2 J m



CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA
10. The magnetic field perpendicular to the plane of a conducting ring of radius r changes at the rate
dB
dt

(a) The emf induced in the ring is
2
dB
r
dt
t
(b) The emf induced in the ring is
dB
2 r
dt
t
(c) The potential difference between diametrically opposite points on the ring is half of the induced emf.
(d) All points on the ring area at the same potential

11. Two long, thin, parallel conductors are kept very close to each other, without touching. One carries a current
i
, and the other has charge ì per unit length. An electron moving parallel to the conductors with velocity v is
undeflected. Let c=velocity of light.
(a)
2
c
v
i
ì
=
(b)
i
v=
ì

(c)
i
c=
ì

(d) The electron may be at any distance fromthe conductor.

12. A charged particle is fired at an angle uto a uniformmagnetic field directed along the x÷axis. During its
motion along a helical path, the particle will
(a) never move parallel to the x÷ axis
(b) move parallel to the x÷axis once during every rotation for all values of u
(c) move parallel to the x÷axis at least once during every rotation if 45
°
u =
(d) never move perpendicular to the x÷direction


PART III: PARAGRAPH TYPE

This section contains 3 multiple choice questions relating to ONE paragraph. Each question
has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. (+3,–1)

PARAGRAPH – I

A biconvex lens is made of material with refractive index
2
n . The radii of curvatures of its left surface and
right surface are
1
R and
2
R . The media on its left and right have refractive indices
1
n and
3
n respectively.
The first and second focal lengths of the lens are respectively
1
f and
2
f

13. The ratio,
1 2
f f of the two focal lengths is equal to
(a)
1 3
n n (b) ( ) ( )
1 3
n 1 n 1 ÷ ÷ (c) ( ) ( )
3 3
n 1 n 1 + + (d) ( ) ( )
2 3 2 1
n n n n ÷ ÷

14. Assume that
1 3
n n = .Which of the following statements is not correct?
(a)
1 2
f f =
(b)
2
f is inversely proportional to
3
n 1 ÷
(c) If
1
R and
2
R are unequal , the focal length would depend on the direction in which light travels through
the lens
(d)
1
f may be negative if
1 2
n n >


CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA
15. Assume that
1 2 1 3
R R ,n n = = . The ratio,
1 2
f f of the two focal lengths is equal to
(a) 1 (b)
1 3
n n (c)
3 1
n n (d) ( ) ( )
3 1
n 1 n 1 ÷ ÷


PART IV: Integer Answer Type

This section contains 4 questions. The answer to each question is a single/ two digit
integer, ranging from 0 to 99 (both inclusive) (+4,0)

16. A sphere of mass m is given some angular velocity about a horizontal axis through its centre and
gently placed on a plank of mass m. the coefficient of friction between the two is 0.3. The plank rests
on a smooth horizontal surface. Find the initial acceleration of sphere relative to the plank
(Take g =10
2
m/s )
m
m


17. A satellite can be in a geostationary orbit around a planet at a distance
1
3
32 km from the centre of the
planet. If the angular velocity of planet about its axis doubles, a satellite can now be in a
geostationary orbit around the planet if its distance from the centre of planet is x km. Find x.

18. A wheel of radius 10 m rolls without slipping on the ground with speed of its center 1m/s. When its
bottommost point is at point P, a piece of mud flies off tangentially from its highest point and lands
on the ground at point Q. The distance PQ is x metres. Find x (g =lom/s
2
)

19. 2 identical sounds A and B reach a point in the same phase. The resultant sound is C. The loudness
of C is n dB higher than loundness of A. Find value of n. (
10
log 2 0.3 = )


PART V: Matrix Match Type

T hissection contains1 questi on. Each question containsstatementsgi ven in two columns, which have
to be matched. T he statements in Column-I are labelled A, B, C and D, while the statements in
Column - I I are labelled p, q, r, sand t. Any gi ven statement in Column-I can have correct matchi ng
with ONE OR MORE statement( s) in Column- I I . T he appropri ate bubbles corresponding to the
answers to these questions have to be darkened as illustrated in the followi ng example: I f the correct
matchesare A - p , sand t ; B - q and r ; C - p and q ; and D - sand t. (+ 8, 0)

20. In fig, shown, when the persons A and B exchange their positions, then match Columns I and II. There is no
friction between plank and ground.


1 2
m 50kg,m 70kg,M 80kg = = =

COLUMN A COLUMN B
(p) The displacement of the plank is (a) 20 cm
(q) The displacement of A with respect to ground is (b) 180 cmor 220 cm
(r) The displacement of B with respect to ground is (c) Towards right
(s) The displacement of center of mass of (A +B)
systemwith respect to ground is
(d) Towards left

PAPER – I (SOLUTION)
1. (c)
The two blocks will move together with the same acceleration as long as the force of friction between themis
less than the limiting friction, as the only force on the lower block B is the force of friction. Once limiting
friction is reached, the acceleration of B becomes constant
lim
F
massof B
| |
=
|
\ .
, and the acceleration of A
continues to increase at a faster rate.

2. (c)
For the first displacement , y 0 = . Hence
x
F 0 = and no work is done. For the second displacement,
y
F ka = ÷ and
2
y ka A = ÷ .

3. (d)
A body topples due to an unbalanced torque about its centre of mass. Hence, the two forces acting on the
block, viz; mgand N, both pass through the centre of mass and hence produced no torque.

4. (b)
(a) AB÷ constant p, increasing V; increasing T (b) BC÷constant T, increasing V , decreasing p
(c) CD÷constant V , decreasing V , decreasing p (d) DA ÷ constant T, decreasing V , increasing P
Also, BC is at a higher temperature than AD


5. (d)







For the image of
A
1 1 1
A,
u f
+ =
u ÷ ÷

For the image of
( )
B
1 1 1
B,
u b f
+ =
u ÷ + ÷

The image size is
A B
u ÷ u

6. (b)











The field at the face ABCD
0 0
ˆ
E x i =
flux over the face ( )
2
0 0
ABCD E x a = ÷
The negative sign arises as the field is directed into the cube. The field at the face EFGH ( )
0 0
ˆ
E x a i = +
The flux over the other four faces is zero as the field is parallel to the surfaces.
total flux over the cube
3
0
0
1
E a q = =
c
,
where q is the total charge inside the cube.

3
0 0
q E a = ÷c

7. (b)
When a capacitor remains connected to a cell, its potential difference remains constant and is equal to the emf
of the cell. Any change in the capacitor may change its capacitance, its charge and the energy stored in it.
When the dielectric slab is taken out, the capacitance decreases. Hence charge decreases, and the difference in
charge is returned to the cell.

8. (d)
Let a= amplitude due to each wave
( )
2 2
0
I k 2a 4ka = =
Let | =phase difference to obtain the intensity
0
I 2
Amplitude ( )
2 2 2
a' a a 2a cos 2acos 2 = = + + | = |

( ) ( )
2 2 2
0 0
I 2 k 4a cos 2 I cos 2
(
= | = |
¸ ¸

or ( ) cos 2 | 1 2 = or 2 4 | = t
or
2
2
t t
| = =
ì
A, where A = path difference
4 2x A = ì = , where x=displacement of the sliding tube.
x 8 = ì


9. (a,b,c,d)
Angular momentum=linear momentum× perpendicular distance fromthe point of rotation
or = L J l
Also,
2
3 I ml =
3 L I J ml e = =
Kinetic energy
( )
2 2 2 2
2
3
2 2
2 3
L J l J
I m
ml
= = =


3
.
2 2
C
l J
m
u = e =


10. (a,d)

2
r B | = t
2
dB
e r
dt
= | = t
Let R = resistance of the ring
the current in the ring i e R = =
Consider a small element dl on the ring
Emf induced in the element
2
e
de dl
r
| |
= =
|
t
\ .
. Resistance of the element
2
R
dR dl
r
| |
= =
|
t
\ .
.
p.d. across the element 0
2 2
e R e
idR de dl dl
R r r
| || | | |
= + = ÷ + =
| | |
t t
\ .\ . \ .

all points on the ring are at the same potential.

11. (a,d)







At P, electric field
0
E
2 x
ì
= =
tc
(to the right) and magnetic field
0
i
B
2 x
µ
= =
t
(into the paper)
For no deflection , E B = u or
E
B
u =
or
2
0 0 0 0
2 x 1 c
.
2 x i i i
ì t ì ì
u = × = =
tc µ c µ


12. (a,d)
Let d=distance of the target T fromthe point of projection. P will strike T if d is an integral multiple of the
pitch.
Pitch
m
2 cos
QB
| |
= t u u
|
\ .

Here, m,Q and u are constant
pitch k
B
u | |
=
|
\ .
, where k= constant
Initially,
0
0
d k
B
| | u
=
|
\ .


13. (a) 14. (c) 15. (b)

16. (6)
The only horizontal forces acting on the two bodies are these due to friction of magnitude µmg each,
in opposite directions. Hence they have accelerations g µ each, in opposite directions.

17. (2)

2 3
T r · . Also when angular velocity doubles, time period becomes half.

18. (4)

4r r
t 2
g g
= =

r
PQ 2vt 4v
g
= ÷ .

19. (6)
Loudness due to A =I Loudness due to A +B =4I
N =10
4
10 10
4I
log 10log 6
I
(
= =
(
¸ ¸


20. (i) ÷ (a)
(ii) ÷
(iii) ÷ (b)
(iv) ÷(c)
2v
v
2r
P Q
SECTION - II CHEMISTRY

PART I: Single Correct Answer Type

This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C)
and (D) out of which ONLY ONE is correct. (+3, –1)

1. The minimum mass of mixture of A
2
and B
4
required to produce at least 1 kg of each product is :
(Given At. mass of 'A' =10 ; At. mass of 'B' =120)
5A
2
+2B
4
 2AB
2
+4A
2
B
(A) 2120 gm (B) 1060 gm (C) 560 gm (D) 1660 gm

2. Calculate the heat capacity of the monoatomic gas undergoing the process, as shown in the P-V
graph:


(A)
3
2
R (B)
5
2
R (C)
7
2
R (D)
8
6
R

3.

A solid has a structure in which W atoms are located at the corners of a cubic lattice, O atom at the
centre of the edges and Na atom at centre of the cubic. The formula for the compound is
(A) NaWO
2
(B) NaWO
3
(C) Na
2
WO
3
(D) NaWO
4

4. How many geometrical isomers are possible for :



(a) 0 (b) 1 (c) 2 (d) 3

 
3
H O /
A ;


 product (A) of the reaction is : 5.





(a) (b)



(c) (d)



V(ltr.)
P
(
a
t
m
)
45°
4
2
Cl Cl
Cl
O
O
O
O
O
O
CO
2
H
CO
2
H
O
O
O
CN
CN
CN
CN
PART II: Multiple Correct Answer(s) Type

This section contains 5 multiple choice questions. Each question has four choices (A),
(B), (C) or (D) out of which ONE or MORE are correct. (+4, –1)

6. The energy levels of hypothetical one electron atom are shown below.

0 eV ——— n =∞
– 0.50 eV ——— n =5
– 1.45eV ——— n =4
– 3.08 eV ——— n =3
– 5.3 eV——— n =2
– 15.6 eV ——— n =1
Select correct statements

(A) ionisation potential of atom is 15.6 eV
(B) short wavelength limit of the series terminating at n =2 is 233.9 nm
(C) wave no. of photon emitted for the transition made by the electron from third orbit to first orbit
is1.009 ×10
7
m
–1
(D)ionisation potential of electron in 1
st
excited state is 5.3 eV.

7. Which is/are correct statements:
(A) In any strong acid’s solution, the concentration of [OH

] will be zero.
(B) If Gº of a reaction is positive, then the reaction will not proceed at all, in the forward direction
for any concentrations of reactants and products.
(C) [H
+
] =[OH

] =
w
K for a neutral solution at all temperatures.
(D) When titration curves are drawn for
(i) 1M HCl (50 mL) with 1 M NaOH and
(ii) 0.01 M HCl (50 mL) with 0.01 M NaOH on the same graph paper they look like:



8. An unsaturated hydrocarbon on complete hydrogenation gives 1-isopropyl-3 methylcyclohexane
after ozonolysis it gives one mole of formaldehyde one mole of acetone and one mole of 2,4-
Dioxohexanedial. The possible structure/s of the hydrocarbon may be
(a) (b) (c) (d)


9. Which of the following are pair of antiaromatic species.
(a) (b) (c) (d)


B
H
10. Iron salts cannot form complexes with ammonia because
A) In alkaline solutions iron salts are precipitated as their hydroxides which are insoluble in excess of
alkali
B) In acid solutions NH
3
cannot form complex because of protanation it changes to ion which have
no donor site
C) In the presence of ammonia iron nitrides are formed
D) In solution aqua complexes of iron salts are produced which protects the ions of iron


PART III: PARAGRAPH TYPE

This section contains 2 multiple choice questions relating to three paragraphs with two
questions on each paragraph. Each question has four choices (A), (B), (C) and (D) out of which
ONLY ONE is correct. (+4, –1)

PARAGRAPH FOR QUESTION NOS. 11 TO 12

The thermal decomposition of N
2
O
5
occurs as : 2N
2
O
5
 4NO
2
+O
2

Experimental studies suggest that rate of decomposition of N
2
O
5
, rate of formation of NO
2
or rate of
formation of O
2
all becomes double if concentration of N
2
O
5
is doubled.

11. The correct mechanism for decomposition of N
2
O
5
is :
(A) N
2
O
5
Slow
 NO
2
+NO
3
; N
2
O
5
+NO
3
Fast
 2NO
2
+O
2

(B) N
2
O
5
Fast
 NO
2
+NO
3
; N
2
O
5
+NO
3
Slow
3NO
2
+O
2

(C) N
2
O
5
Fast
 2NO
2
+O
2

(D) N
2
O
5
Slow
 NO +NO
2
+2O
2
; N
2
O
5
+NO
2
Fast
3NO
2
+O
2


12. The container of 2 litre contains 4 mole of N
2
O
5
. On heating to 100°C, N
2
O
5
undergoes complete
dissociation to NO
2
and O
2
. Select the correct answers if rate constant for decomposition of N
2
O
5
is
6.2 ×10
–4
sec
–1
.
1. The mole ratio before and after dissociation is 4 : 2.
2. Half life of N
2
O
5
is 1117 sec and it is independent of temperature.
3. Time required to complete 40% of reaction is 824 sec.
4. If volume of container is doubled, the rate of decomposition becomes half of the initial rate
(A) 1, 3, 4 (B) 1, 2, 3, 4 (C) 3, 4 (D) 2, 3, 4

PARAGRAPH FOR QUESTION NOS. 13 TO 14

I
II.
III.
IV.
13. Compound (A) and (B) are.
A) B)
C) D)

14. (X) and (Y) are
A) C and Al B) Al and C C) C in both D) Al in both

( )
2 4 2 3
FeCr O NaOH air A Fe O ÷ ÷ ÷÷÷ ÷
( ) ( )
2 2 7
A B Na Cr O ÷ ÷÷÷
2 2 7 2 3
Na Cr O X Cr O
^
÷ ÷ ÷÷
2 3
Cr O Y Cr
^
÷ ÷÷÷
2 4 2 4
, Na CrO H SO
2 2 7
, Na Cr O HCl
2 5 2 4
, Na CrO H SO ( )
4 2 4 6
, Na Fe OH H SO
l
l
l
CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA
PART IV: Integer Answer Type

This section contains 4 questions. The answer to each question is a single digit
integer, ranging from 0 to 9 (both inclusive) (+4, 0)

15. A current of 2 ampere is passed for 5 hrs through the molten metal salt and it causes deposition of
22.2 g of metal (atomic weight 177). The oxidation state of the metal in salt is +x, then value of x
is______

16. One mole of (C
6
H
5
)
3
C.OH dissolved in 1000 g of 100% pure sulphuric acid lowers the freezing point
of sulphuric acid twice as one mole of CH
3
OH shows in 1000 g of 100% pure sulphuric acid.
Calculate the Van’t Hoff factor of Ph
3
COH assuming that CH
3
OH is neither dissociated nor
associated in 100% pure sulphuric acid.

17. (a)



(b)



(c)


(d)


Sum of X +Y +Z +P =

18. How many different Grignard reagents when react with EtOH, give n-butane as product
(excluding stereoisomerism).

19. InCuSO
4
. 5H
2
O, the no. of oxygen atoms surrounding each Cu
+2
ion is

 
alc.KOH
X products 
Br
 
alc.KOH
Y 
Br
 
alc.KOH
Z 
Br
 
alc.KOH
P 
Br
H
3
CH
3
CH
3
CH
CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA

PART V: Matrix Match Type

T hissection contains1 questi on. Each questi on contai nsstatementsgi ven in two columns, which have
to be matched. T he statements i n Column-I are labelled A, B, C and D, while the statements in
Column - I I are labelled p, q, r, sand t. Any gi ven statement in Column-I can have correct matching
with ONE OR MORE statement( s) in Column- I I . T he appropriate bubbles corresponding to the
answers to these questions have to be darkened as illustrated i n the followi ng example: I f the correct
matchesare A - p , sand t ; B - q and r ; C - p and q ; and D - sand t. (+ 8, 0)

20. Column-I Column-II
(A) If SOP of substance is exist between (p) Oxidation of substance is not possible
– 1.23 to – 0.81 V
(B) If SOP of substance is exist between (q) Possible only in acidic medium
– 0.81 V to – 0.40 V
(C) If SOP is less than – 1.23 V (r) Possible in any medium
(D) If SOP is greater than – 0.40 V (s) Oxidation easily takes place

SOP (Standard Oxidation Potential) of water is – 1.23 V







CENTERS : MUMBAI / AKOLA / NASHIK / PUNE / DELHI / KOLKATA / LUCKNOW / GOA
1 Point P is moving along the circumference of the circle
( ) ( )
2 2
x 4 y 8 16. ÷ + ÷ = Then it
breaks away from it and moving along a tangent to the circle, cuts the x-axis at the point
(8,0). The coordinates of the points on the circle at which the moving point broke away
can be :
(A) (8,8) (B) (0,8) (C) (4,4) (D) none of these
2 If
2
2
mx 3x 4
7
x 3x 4
÷ +
s
+ +
, x R ¬ e , then the value of m is
(A) m 7 s (B) m 1 > (C) | ) m 1, 7 e (D) ( | m ,1 e ÷·
3 a,b,c,d are in increasing G.P. If the AM between a and b is 6 and the AM between c and d
is 54, then the AM of a and d is
(A) 15 (B) 48 (C) 44 (D) 42
4 The primitive of the differential equation
( ) ( )
4 y 3 2 4 y 2 2
2xy e 2xy y dx x y e x y 3x dy 0 + + + ÷ ÷ = is
(A)
2
2 y
3
x x
x e c
y y
+ + = (B)
2
2 y
3
x x
x e c
y y
÷ + =
(C)
2
2 y
3
x x
x e c
y y
+ ÷ = (D)
2
2 y
3
x x
x e c
y y
÷ ÷ =
5 Let
1
3
0
dx
1 x
ì =
+
}
,
( )
1
2 2
n
n
2
n
r 1
n r
lim L
n
÷·
=
( +
= (
(
¸ ¸
[ , then
(A)
e
3 log L 1
2
t
ì + = +
(B) e
3 log L 1
3
t
ì ÷ = ÷
(C)
e
3 log L 1
2
t
ì + = ÷
(D) e
1 1
3 log L 2
2 3
| |
ì ÷ = ÷ t +
|
\ .
6 If ( ) ( ) f 4 x f 4 x ÷ = + and ( ) ( ) f 8 x f x 8 ÷ = + and f(x) is a function for which
( )
8
0
f x dx 5 =
}
then ( )
200
0
f x dx
}
is
(A) 100 (B)
( )
46
8
2 f x dx
÷
}
(C)
( )
104
4
f x dx
}
(D) none of these
SECTI ON I I I : MATHEMATI CS
PART I : Single Correct Answer 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. (+3, –1)
CENTERS : MUMBAI / AKOLA / NASHIK / PUNE / DELHI / KOLKATA / LUCKNOW / GOA
PART II : Multiple Correct Answer(s) Type
This section contains 4 multiple choice questions. Each question has four choices (A),
(B), (C) and (D) out of which ONE or MORE are correct. (+4, –1)
7 If Rolle’s theorem is applicable to the function f defined by ( )
2
ax b, x 1
f x 1, x 1
, x 1
x
¦
¦
+ <
¦
¦
= =
´
¦
ì
¦ >
¦
¹
for | | x 2, 2 e ÷ then
(A)
a b 1 + =
(B)
a b ì = +
(C)
3
b
2
= (D)
3a b 0 + =
8 If
( )
2 2
2sin cos x 1 cos sin2x
2
t | |
= ÷ t
|
\ .
, then
(A)
( ) x 2n 1 , n I
2
t
= + e (B)
1
tanx
2
=
(C)
1
tanx
2
= ÷ (D)
n
x , n I
2
t
= e
9 Which of the following function is periodic?
(A)
( ) ( )
x
f x sgn e
÷
= where sgn x denotes signumfunction of x.
(B)
( ) f x sinx sinx = +
(C)
( ) ( )
f x min. sinx, x =
(D)
( ) | |
1 1
f x x x 2 x
2 2
( (
= + + ÷ + ÷
( (
¸ ¸ ¸ ¸
where | | x denotes greatest integer less than or equal to x.
10 The line 3x 6y k + = intersect the curve
2 3
2x 2xy 3y 1 + + = at points A and B. The circle on
AB as diameter passes through the origin. The possible value of k is
(A) 3 (B) 4 (C) – 4 (D) – 3
PART III : Paragraph Type
This section contains 4 multiple choice questions relating to two paragraphs with two
questions on each paragraph. Each question has four choices (A), (B), (C) and (D) out of
which ONLY ONE is correct. (+3, –1)
PASSAGE 1
If a b c, b c a, c a b × = × = × =
  
     
. If vectors a,bandc
  
are forming a right handed system.
11 If x a b c, y a b 2c, z a 2b c = + ÷ = ÷ + ÷ = ÷ + ÷
  
        
, then a vector normal to the vector x y +
 
and y z +
 
is
(A)
3a 6b 4c ÷ + +

 
(B)
3a 6b 4c + +

 
(C)
3a 6b 4c ÷ +

 
(D)
3a 6b 4c + ÷

 
CENTERS : MUMBAI / AKOLA / NASHIK / PUNE / DELHI / KOLKATA / LUCKNOW / GOA
12 Let x a b, y 2a b = + = ÷
 
   
, then the point of intersection of straight lines
r x y x, r y x y × = × × = ×
       
is
(A)
2b

(B)
3b

(C)
3a

(D)
2a

PASSAGE 2
There are four boxes
1 2 3
A ,A ,A and
4
A .Box
i
A has i balls and on each ball a number is
printed, the numbers are from 1 to i. A box is selected randomly, the probability of
selection of box
i
A is
i
10
and then a ball is drawn. Let
i
E represents the event that a
ball with number ‘i’ is drawn.
13 The value of ( )
4
i i
i 1
P E A
=
·
¿
is
(A)
1
5
(B)
1
10
(C)
2
5
(D)
1
4
14 ( )
3 2
P A /E is equal to
(A)
1
4
(B)
1
3
(C)
2
3
(D)
1
2
PART IV : Integer Answer Type
This section contains 5 questions. The answer to each question is a single digit integer,
ranging from 0 to 9 (both inclusive). (+4, 0)
15 If x,y,zare 3 numbers in GP such that 4 is the AM between x and y and 9 is the HM between y and z, then
y is_____________
16 If ( ) f x is a polynomial of degree 4 with leading coefficient one satisfying ( ) ( ) ( ) f 1 1,f 2 2,f 3 3 = = = then
( ) ( )
( ) ( )
f 1 f 5
f 0 f 4
( ÷ +
(
+
¸ ¸
(where [ .] represents the greatest integer function) is equal to__________
17 If z 3 Rez, w 3 Rew ÷ = ÷ = and ( ) arg z w
4
t
÷ =
, then the ( ) Im z w + equals______
18 The volume of tetrahedron AKHI is
3
1
unit
6
, KIH
4
t
Z = and
( ) 2 AK HI KI 3 2 + + = ,
AK 1 = , then 3AI is equal to
19 Let A and B be two non-singular square matrices such that B I = and
2
AB BA = . If
3 1 3 n
A B A B
÷
= , then
value of
n
is_________
CENTERS : MUMBAI / AKOLA / NASHIK / PUNE / DELHI / KOLKATA / LUCKNOW / GOA
PART V: Matrix Match Type
T hissection contains1 question. Each question containsstatementsgiven in two columns, which have to
be matched. T he statementsin Column-I are labelled A, B, C and D, while the statementsin Column -
I I are labelled p, q, r, sand t. Any given statement in Column-I can have correct matching with ONE OR
MORE statement( s) in Column- I I . T he appropriate bubblescorresponding to the answers to these
questionshave to be darkened asillustrated in the following example: I f the correct matchesare A - p , s
and t ; B - q and r ; C - p and q ; and D - sand t. (+ 8, 0)
20 If
1 2 3 4
z ,z ,z ,z are the roots of the equation
4 3 2
z z z z 1 0 + + + + = then
Column I Column II
(A)
4
4
i
i 1
z
=
¿ is equal to (P) 0
(B)
4
5
i
i 1
z
=
¿ is equal to (Q) 4
(C) ( )
4
i
i 1
z 2
=
+
[
is equal to (R) 1
(D) Least value of
1 2
z z + (
¸ ¸
is (where [ ] stands for G.I.F) (S) 11
CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA



ANDHERI / BORIVALI / DADAR / CHEMBUR / THANE / MULUND/ NERUL / POWAI
FULL TEST – 3
PAPER – I (ANSWER KEY)

PHYSICS

1. (B) 2. (C) 3. (D) 4. (B) 5. (D)

6. (B) 7. (B) 8. (D) 9. (A, B, C, D) 10. (A, D)

11. (A, D) 12. (A, D) 13. (A) 14. (C) 15. (B)

16. (6) 17. (2) 18. (4) 19. (6)

20. p a,c;q b,c;r b,d;s d    


CHEMISTRY


1. (A) 2. (C) 3 (B) 4. (C) 5. (D)

6. (A, B, C, D) 7. (C, D) 8. (A,C) 9. (B, D) 10. (A.B)

11. (B) 12. (C) 13. (A) 14. (A) 15. (4)

16. (2) 17. (8) 18. (2) 19. (6)

20. Aq ; Br ; Cp ; Ds

MATHS

1. A 2. D 3. D 4. A 5. D

6. D 7. ABCD 8. ABC 9. ABCD 10. AD

11. B 12. C 13. C 14. D 15. 6

16. 5 17. 6 18. 03 19. 6

20. A – R, B – Q, C – S, D – P
CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA
PAPER – II

PHYSICS
1. (c) 2. (a) 3. (b) 4. (b) 5. (b)

6. (b) 7. (c) 8. (c) 9. (a, b, c) 10. (b, d)

11. (d) 12. (c) 13. (d) 14. (d) 15. (a)

16. (2) 17. (3) 18. (2) 19. (4)

20. i – b; ii – c; iii – d; iv – d


CHEMISTRY

1. (B) 2. (C) 3. (C) 4. (B) 5. (C)

6. (A, B, C, D) 7. (A, B, C, D) 8. (B, D) 9. (B,C, D) 10. (B,C)

11. (C) 12. (B) 13. (B) 14. (C) 15. (2)

16. (3) 17. (1) 18. (6) 19. (3)

20. a – p; b – s, c – q; d - r
MATHS

1. D 2. C 3. A 4. C 5. B

6. C 7. ABCD 8. AC 9. BD 10. ABC

11. BCD 12. B 13. D 14. D 15. B

16. 4 17. 5 18. 8 19. 2

20. A – PQRS, B – R, C – RS

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