29 Qus
29 Qus
29 Qus
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FIITJEE
Paper 2
Time Allotted: 3 Hours
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 l l y. Yo u a r e a l l o t t ed 5 m i n ut 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.
Yo u a r e n o t a ll o wed t o l ea v e t h e E xa m i n at i o n Ha ll b ef o r e t h e en d o f
t h e t es t .
INSTRUCTIONS
A. General Instructions
1.
2.
3.
4.
5.
Attempt ALL the questions. Answers have to be marked on the OMR sheets.
This question paper contains Three Parts.
Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics.
Each part has only one section: Section-A.
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.
Section-A (01 to 08) contains 8 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 (09 to 14) contains 3 paragraphs with each having 2 questions. Each question carries
+3 marks for correct answer and 1 mark for wrong answer.
Section-A (15 to 20) contains 6 multiple choice questions which have more than one correct
answer. Each question carries +4 marks for correct answer. There is no negative marking.
Enrolment No.
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Useful Data
PHYSICS
Acceleration due to gravity
g = 10 m/s2
Planck constant
Charge of electron
e = 1.6 1019 C
Mass of electron
me = 9.1 1031 kg
Density of water
Atmospheric pressure
Pa = 105 N/m2
Gas constant
R = 8.314 J K1 mol1
CHEMISTRY
Gas Constant
Avogadro's Number Na
Plancks constant h
1 Faraday
1 calorie
1 amu
1 eV
=
=
=
=
=
=
=
=
=
=
8.314 J K1 mol1
0.0821 Lit atm K1 mol1
1.987 2 Cal K1 mol1
6.023 1023
6.625 1034 Js
6.625 1027 ergs
96500 coulomb
4.2 joule
1.66 1027 kg
1.6 1019 J
Atomic No:
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Physics
AIITS-PT-IV-(Paper-2)-PCM-JEE(Advanced)/15
PART I
SECTION A
Straight Objective Type
This section contains 8 multiple choice questions numbered 1 to 8. Each question has 4 choices (A),
(B), (C) and (D), out of which ONLY ONE is correct
1.
Two mirrors, one concave and the other convex, are placed 60 cm apart with their reflecting
surfaces facing each other. An object is placed 30 cm from the pole of either of them on their
axis. If the focal lengths of both the mirrors are 15cm, the position of the image formed by
reflection, first at the convex and then at the concave mirror, is
(A) 19.09 cm from the pole of the convex mirror
(B) 19.09 cm from the pole of the concave mirror
(C) 11.09 cm from the pole of the concave mirror
(D) 11.09 cm from the pole of the convex mirror
2.
An alternating voltage E = E0 sin t, is applied across a coil of inductor L. The current flowing
through the circuit at any instant t is
E
E
(A) 0 sin (t + /2)
(B) 0 sin (t - /2)
L
L
(C) E0 L sin (t - /2)
(D) E0 L sin (t + /2)
3.
1
2
1
2
(C) 1
S1
D
and
4d
D
y2 = +
equals 'n' times the intensity of maxima, then 'n' equals
4d
(A)
(B) 2 1
d
S2
D
1
2
(D) 1
2
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4.
One of the combination from the fundamental physical constants is hc/G. The unit of this
expression is
2
3
(A) kg
(B) m
(C) s1
(D) none of the above
5.
Let [0] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length,
T = time and I = electric current. Then
(A) [0 ] [M1L3 T 2I]
(B) [0 ] [M1L3 T 4I2 ]
(C) [0 ] [M1L2 T 1I2 ]
6.
A coil of resistance R and inductance L is connected across an a.c. power supply of r.m.s.
voltage V. The average power dissipated in the coil is,
V 2R
2
(A) V /R
(B)
(R2 2L2 )
(C)
7.
V2
(R2 2L2 )
(D) zero
8.
at t
at t1
P
x
Q
x
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Comprehension Type
This section contains 3 groups of questions. Each group has 2 multiple choice question based on a
paragraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE is
correct
Paragraph for Question Nos. 9 to 10
P
A metal wire PQ slides on parallel metallic rails having separation 0.25 m, each
having negligible resistance. There is a 2 resistor and 10 V battery as shown in
figure.
There is a uniform magnetic field directed into the plane of the paper of magnitude
0.5T. A force of 0.5 N to the left is required to move wire PQ with constant speed to
the right.
Then find the answer of following questions based on above paragraph.
9.
10.
10 V
0.25 m
2
Q
(B) 4 m/s
(D) 32 m/s
12.
C2
C1
L
(B) 152 A
(D) 20 A
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AIITS-PT-IV-(Paper-2)-PCM-JEE(Advanced)/15
Pole (P)
which is due to dependence of focal length f on Principle axis
angle of incidence as shown in figure is given by
C
F
f
R
f R sec
2
Where R is radius of curvature of mirror and is the angle of incidence. The rays which are closed to
principle axis are called paraxial rays and the rays far away from principal axis called marginal rays. As a
result of above dependence different rays are brought to focus at different points and the image of a point
object is not a point.
Then find the answer of following questions based on above paragraph.
13.
If f P and f m represent the focal length of paraxial and marginal rays respectively, then correct
relationship is:
(A) f p = f m
(B) f p > f m
(C) f p < f m
(D) none
14.
This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for
its answer, out which ONE OR MORE is/are correct
15.
Suppose the potential energy between electron and proton at a distance r is given by
Ke 2
.
2r 3
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16.
Let [o] denote the dimensional formula of the permittivity of the vacuum, and [o] that of the
permeability of the vacuum. If M = mass, L = length, T = time and I = electric current,
(A) [o] = M1L3T2I
(B) [o] = M1L3T4I2
(C) [o] = MLT2I2
(D) [o] = ML2T1I
17.
Which of the following (referred to a spherical mirror) do (does) not depend on whether the rays
are paraxial or not?
(A) Pole
(B) Focus
(C) Radius of curvature
(D) Principal axis
18.
A resistance-less rod of length ' ' and mass m can slide without
friction on long rails of zero resistance which are connected to
circuit element named X as shown. This arrangement is in the
horizontal plane in a uniform vertical magnetic field B as shown
below. Then match what happens to the rod
(A) X is resistor and rod is thrown with some velocity towards right
and it comes to rest
(B) X is a resistor and the rod is pulled to right with constant force
and it attains terminal velocity
B
X
2m
(C) X is resistor and rod is thrown with some velocity towards right and it never comes in rest
(D) X is a resistor and the rod is pulled to right with constant force and it never attains terminal
velocity
19.
A long wire carrying a steady current I lies in the plane of a circular conducting loop placed at a
certain distance from the wire. There will be an induced current in the loop if it is
(A) moved parallel to the wire
(B) rotated about an axis perpendicular to the plane of the loop, passing through the centre of the
loop
(C) rotated about an axis parallel to the wire passing through the centre of the loop
(D) moved away from the wire
20.
20 cm
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AIITS-PT-IV-(Paper-2)-PCM-JEE(Advanced)/15
Chemistry
PART II
SECTION A
Straight Objective Type
This section contains 8 multiple choice questions numbered 1 to 8. Each question has 4 choices (A),
(B), (C) and (D), out of which ONLY ONE is correct
1.
2.
Both [Ni(CO)4] and [Ni(CN)4]2 are diamagnetic. The hybridization of nickel in these complexes,
respectively, are
(A) sp3, sp3
(B) sp3, dsp2
2
3
(C) dsp , sp
(D) dsp2, dsp2
3.
At a certain temperature the dissociation constants of formic acid and acetic acid are 1.8 104
and 1.8 105 respectively. The concentration of acetic acid solution in which the hydrogen ion
has the same concentration as in 0.001 M formic acid solution is equal to
(A) 0.001 M
(B) 0.01 M
(C) 0.1 M
(D) none of these
4.
5.
Which one of the following pairs of ions have the same electronic configuration?
(A) Cr3+, Fe3+
(B) Fe3+, Mn2+
2+
2+
(C) Mn , Fe
(D) Sc3+, Cr3+
6.
A mono atomic gas is suddenly compressed to 1/8 of its volume adiabatically. The pressure of
gas will change to
(A) 24/5 times
(B) 8 times
(C) 40/3 times
(F) 32 times
7.
3+
3+
in group III?
(B) By increasing NH4 ion concentration
(D) Both (B) and (C)
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8.
AIITS-PT-IV-(Paper-2)-PCM-JEE(Advanced)/15
This section contains 3 groups of questions. Each group has 2 multiple choice question based on a
paragraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE is
correct
Paragraph for question Nos. 9 to 10
10.
When compound (B) and reacts with NH3 solution, the colour of the compound formed is
(A) black
(B) red
(C) yellow
(D) white
Paragraph for question Nos. 11 to 12
The binary compounds of oxygen with other elements are called oxides. They are classified either
depending upon their acid base characteristics or on the basis of oxygen content.
11.
12.
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AIITS-PT-IV-(Paper-2)-PCM-JEE(Advanced)/15
10
(1 atm) (1 M)
Read the above paragraph carefully and answer the questions given below:
13.
14.
The emf of the cell involving the reaction, 2Ag (aq) H2 (g)
2Ag(s) 2H (aq), is 0.80 V.
The standard oxidation potential of Ag electrode is
(A) 0.80 V
(B) 0.80 V
(C) 0.40 V
(D) 0.20 V
(B) AgCl
(D) ZnS
16.
A d-block element forms octahedral complex but its magnetic moment remains same either in
strong field or in a weak field ligand. Which of the following is/are correct?
(A) Element always form colourless compound
(B) Number of electrons in t2g orbitals are higher than in eg orbitals
(C) It can have either d3 configuration
(D) It can have either d7 configuration
17.
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18.
19.
20.
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Mathematics
12
PART III
SECTION A
Straight Objective Type
This section contains 8 multiple choice questions numbered 1 to 8. Each question has 4 choices (A),
(B), (C) and (D), out of which ONLY ONE is correct
1.
2.
Consider an invertible function f(x) with f(x) > 0 and f(x) < 0 x R. Also f (x) is the inverse
function of f(x). Let f(x) and f 1(x) intersect each other at x = 0 and x = ( > 0) only and if
2
1
f
dx
A
;
x
f x dx B and 2 C then
0
0
(A) A > B > C
(B) A > C > B
(C) A < B < C
(D) A < C < B
3.
4.
If Pth, qth, rth term of a GP are the positive numbers a, b, c then angle between the vectors
loga3 i logb3 j logc 3k and q r i r p j (p q) k is
5.
(A)
(B)
(C)
1
(D) sin1
2
2
2
a b c
If A is a square matrix of order n such that adj adjA A , then the value of n can be
(A) 1
(C) 3
(B) 2
(D) 4
Space for rough work
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13
6.
7.
8.
AIITS-PT-IV-(Paper-2)-PCM-JEE(Advanced)/15
1 0 0
Given that A 1 0 1 and A n An 2 A 3 A n 4 and A 3 A 2 A I 0 .
0 1 0
1 0 0
20
A k 1 1 0 . Then k is equal to
k 1 0 1
(A) 3
(B) 6
(C) 9
(D) none of these
vector is 6i j 3k.
(A) 24i 13j 4k
(B) 24i 13j 2k
(C) 24i 13j 4k
This section contains 3 groups of questions. Each group has 2 multiple choice question based on a
paragraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE is
correct
Paragraph for Question Nos. 9 to 10
Read the following write up carefully and answer the following questions:
3
3 4
x 4
2
Let M1
and M2
(x 0, 1, x R) are two matrices and let P
1
1 1
0 1
2 any matrix.
3
Trace (B + D) = 0 for
(A) x = 2
(C) more than 100 values of x
(B) x = 1
(D) no value of x
Space for rough work
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10.
Let matrix E (M1B1M2D1 )1 , then sum of all elements of second row of E is equal to
(A) 0
(B) 2012
(C) 2010
(D) none of these
Paragraph for Question Nos. 11 to 12
Read the following write up carefully and answer the following questions:
If P(A1 A 2 ) P(A1 ).P(A 2 ) then A1 , A 2 are called independent events for each pair is A1 , A 2 , A 3 if
(A i A j ) P(A i ).P(A j ) then A1 , A 2 , A 3 are called mutually pair-wise independent events
11.
An contains four tickets, each is marked as aab, aba, baa, bbb. And one ticket is drawn. Let
A i event that ith digit of the mark on ticket is a. Then
(A) A1 , A 2 , A 3 are pair-wise independent
(B) A1 , A 2 , A 3 are mutually independent
(C) A1 , A 2 , A 3 are need not be pair-wise independent
(D) none of these
12.
A and B are two independent events. The probability that both occur simultaneously is
probability the neither occurs is
1
and the
6
1
, then
3
1
1
, P(B)
2
3
1
1
(C) P(A) , P(B)
3
3
(A) P(A)
(B) P(A)
2
1
, P(B)
3
3
Read the following write up carefully and answer the following questions:
If P(x, yz) is varying such that ax by cz d 0 where a2 b2 c 2 0 then P traces a plane with
normal a i bj ck and a(x x ) b(y y ) c(z z ) 0 gives plane equation passing through
1
(a b c 2 0)
A variable plane with a constant distance d from origin cuts x, y, z axes at P, Q, R. Then locus of
centroid of triangle PQR is
1
1
1
1
1
1
1
9
(A) 2 2 2 2
(B) 3 3 3 3
x
y
z
d
x
y
z
d
1
1
1
9
1
1
1
1
(C)
(D) 2 2 2 2
x
y
z
d
|x|
|y|
|z|
| d|
Space for rough work
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15
14.
AIITS-PT-IV-(Paper-2)-PCM-JEE(Advanced)/15
A variable plane at a constant d from origin, intersects the axes at A, B, C. Planes are drawn to
the coordinate planes and passing through A, B, C. Then locus of point of intersection of all
planes is
1
1
1
1
1
1
1
2
(A) 2 2 2 2
(B) 2 2 2 2
x
y
z
p
x
y
z
p
1
1
1
3
(C) 2 2 2 2
(D) none of these
x
y
z
p
Multiple Correct Choice Type
This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for
its answer, out which ONE OR MORE is/are correct
p1 : ax by cz 1
15.
and
16.
17.
18.
sinB cosB
cos2 B 0 , then
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19.
i ( 1)j 2k,
3i 5j 2k.
Then
Let the vectors i 3j k,
(A) the number of planes determined above 3 vectors = 2
17
(B) angle between planes cos1
3 23
(C) angle between planes tan1
20.
f(t)dt
g(x)
3
1
(B) area bounded by y = f(x), y = g(x), x = 1 and y axis is 12(e1/ 4 1) sq. unit
(C) f(x) g(x) is decreasing in [1, 1]
x
(D) period of f is 8 ({.} denotes fractional part of x)
2
Space for rough work
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