bansal paper 2
TRANSCRIPT
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IIT JEE-2010 Paper-2 (Chemistry)
Useful dataAtomic Numbers : B = 5; C = 6; N = 7; O = 8; F = 9 ; Na = 11; Si = 14; P =15; S = 16; Cl = 17;
Ti = 22; V = 23; Cr = 24; Ni = 28; Cu = 29; Br = 35; Rh = 45; Sn = 50;
Xe = 54; Tl = 81
1 amu = 1.66 1027 kg e = 1.6 1019 C
R = 0.082 L-atm K1 mol1 c = 3.0 108 m s1
h = 6.626 1034 J s F = 96500 C mol1
NA = 6.022 1023 RH = 2.18 10
18 Jm
e= 9.1 1031 kg 4
0= 1.11 1010 J1 C2 m1
PART-I
SECTION-ISingle Correct Choice Type
This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D),
out of which ONLY ONE is correct.
Q.1 The packing efficiency of the two-dimensional square unit cell shown below is
L
(A) 39.27 % (B) 68.02 % (C) 74.05 % (D) 78.54 %
Ans. [D]
Q.2 Assuming that Hunds rule is violated, the bond order and magnetic nature of the diatomic molecule B2
is
(A) 1 and diamagnetic (B) 0 and diamagnetic
(C) 1 and paramagnetic (D) 0 and paramagnetic
Ans. [A]
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Q.3 The compounds P, Q and S
HO
COOH
P
H C3
OCH3
QS
CO
were separately subjected to nitration using HNO3
/ H2SO
4mixture. The major product formed in each
case respectively, is
(A) HO H C3
CO
O
NO2 NO2
COOH OCH3
O2N
(B) HO H C3
C
O
O
NO2
NO2
NO2
COOH OCH3
(C)HO H C3
CO
O
NO2
NO2
NO2
COOH OCH3
(D)HO H C3
CO
O
NO2
NO2
NO2
COOH OCH3
Ans. [C]
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Q.4 In the reaction C
C
O
O
NH2Cl
H C3
(1) NaOH/Br2
(2)
T the structure of the Product T is
(A) C
O
O
OC
H C3 (B) NH
O
C CH3
(C) NH
O
C
H C3 (D)
C
O
O
NHC
H C3
Ans. [C]
Q.5 The complex showing a spin-only magnetic moment of 2.82 B.M.is
(A) Ni(CO)4
(B) [NiCl4]2 (C) Ni(PPh
3)4
(D) [Ni(CN)4]2
Ans. [B]
Q.6 The species having pyramidal shape is
(A) SO3
(B) BrF3
(C) SiO32 (D) OSF
2
Ans. [D]
SECTION-II(Integer Type)
This Section contains a group of5 questions. The answer to each questions is a single digit integer
ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled.
Q.7 One mole of an ideal gas is taken from a to b along two paths denoted by the solid and the dashed lines
as shown in the graph below. If the work done along the solid line path is wsand that along the dotted line
path is wd, then the integer closet to the ratio w
d/ w
sis
0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
P
V
(atm)
(lit.)
a
b
Ans. [2]
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Paragraph for Questions 15 to 17
Two aliphatic aldehydes P and Q react in the presence of aqueous K2CO
3to give compound R, which
upon treatment with HCN provides compound S. On acidification and heating, S gives the product
shown below:
O
H C3
H C3
OH
OQ.15 The compounds P and Q respectively are
(A) H C3
H C3CH
C C
H H
CH3
O O
and
(B)H C3
HCH
C C
H H
CH3
O O
and
(C)
H C3 H C3CH C C
H H
CH3
CH2
O O
and
(D)
H C3CH C C
H HH
CH3
CH2
O O
and
Ans. [B]
Q.16 The compound R is
(A)H C3
H C3CH
C
CH2
O
OH
H (B)H C3
H C3
H C3C
C
CH
O
OH
H
(C)
H C3
CH3
CH
CCH
CH2
O
OH
H
(D)
H C3
H C3
CH3
CH
CCH
CH
O
OH
H
Ans. [A]
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Q.19 Match the reactions in Column I with appropriate options inColumn II.
Column I Column II
(A) N Cl +2 OH OHN=NNaOH/H O
2
0C (p) Racemic mixture
(B)
H S2
O4
H CCCCH
3 3 H C3 CH3
CH3
CH3OH OH
CH3 CH3
C
C
O
(q) Addition reaction
(C) C CH1. LiAlH
4
2. H3O
+
O
CH3 CH3
OH
(r) Substitution reaction
(D)Base
HS ClS
(s) Coupling reaction
(t) Carbocation
intermediate
Ans. [(A) r,s,t (B) t, (C) p, q, (D) r ]
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IIT JEE-2010 Paper-2 (Mathematics)
PART-II (MATHEMATICS)
SECTION-I
(Single Correct Choice Type)
This Section contains 6 multiple choice questions.Each question has 4 choices A), B). C) and D) out
of which ONLY ONE is correct.
Q.20 Two adjacent sides of a parallelogram ABCD are given by
k2j2iADandk11j10i2AB The side AD is rotated by an acute angle in the plane of the parallelogram so that AD becomes AD.If ADmakes a right angle with the side AB, then the cosine of the angle is given by
(A)9
8(B)
9
17(C)
9
1(D)
9
54
Ans. [B]
Q.21 A signal which can be green or red with probability 5
4
and 5
1
respectively, is received by station A and
then transmitted to station B. The probability of each station receiving the signal correctly is4
3. If the
signal received at station B is green, then the probability that the original signal was green is
(A)5
3(B)
7
6(C)
23
20(D)
20
9
Ans. [C]
Q.22 If the distance of the point P(l, -2, 1) from the plane x + 2y - 2z = , where> 0. is 5, then the foot
of the perpendicular from P to the plane is
(A)
3
7,
3
4,
3
8(B)
3
1,
3
4,
3
4(C)
3
10,
3
2,
3
1(D)
2
5,
3
1,
3
2
Ans. [A]
Q.23 Let f be a real-valued function defined on the interval (1, 1) such that x
0
4x dt1t2xfe ,
for all x(-1,1), and let f1 be the inverse function of f.Then (f1) (2) is equal to
(A) 1 (B)31 (C)
21 (D)
e1
Ans. [B]
Q.24 For r = 0, 1, .... 10, let Ar, B
rand C
rdenote, respectively, the coefficient of xr in the expansions of
(1+x)10, (1+x)20 and (1+x)30. Then
10
1r
r10r10r ACBBA is equal to
(A)B10C
10(B) 101021010 ACBA
(C) 0 (D) C10B
10
Ans. [D]
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Q.25 Let S = {1, 2, 3, 4). The total number of unordered pairs of disjoint subsets of S is equal to
(A) 25 (B) 34 (C) 42 (D) 41
Ans. [A]
Section-II (Integer Type)
This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to
9. The correct digit below the question no. in the ORS is to be bubbled.
Q.26 Let k be a positive real number and let
1k2k2
k21k2
k2k21k2
A and
0k2k
k20k21
k1k20
B
If det (adj A) + det(adj B) =106, then [k] is equal to
[Note : adj M denotes the adjoint of a square matrix M and [k] denotes the largest integer less than or
equal to k].
Ans. [4]
Q.27 Two parallel chords of a circle of radius 2 are at a distance 13 apart. If the chords subtend at the
center, angles ofk
2and
k
where k > 0, then the value of [k] is
[Note : [k] denotes the largest integer less than or equal to k]
Ans. [3]
Q.28 Consider a triangle ABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and
C respectively. Suppose a = 6, b = 10 and the area of the triangle is 315 . IfACB is obtuse and if r
denotes the radius of the incircle of the triangle, then r2 is equal toAns. [3]
Q.29 Let f be a function defined on R (the set of all real numbers) such that
f(x) = 2010(x - 2009)(x - 2010)2(x - 2011)3 (x - 2012)4, for all x R.If g is a function defined on R with values in the interval (0,) such that
f(x) = ln (g (x)), for all x R,then the number of points in R at which g has a local maximum is
Ans. [1]
Q.30 Let a1, a
2, a
3.....a
11be real numbers satisfying
a1
= 15, 27 - 2a2
> 0 and ak
= 2ak_
1ak2 for k = 3, 4..... 11.
If 9011
a.........aa 2112
2
2
1
, then the value of11
a......aa 1121 is equal to
Ans. [0]
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SECTION - III (Paragraph Type)
This Section contains 2 paragraphs. Based upon each of the paragraphs3 multiple choice questions
have to be answered. Each of these question has four choices A). B). C) and D) out of which ONLY
ONE is correct.
Paragraph for questions 31 to 33.
Tangents are drawn from the point P(3, 4) to the ellipse 14
y
9
x 22 touching the ellipse at points AA
and B.
Q.31 The coordinates of A and B are
(A) (3. 0) and (0. 2) (B)
5
8,
5
9and
15
1612,
5
8
(C) )2,0(and15
1612,
5
8
(D)
5
8,
5
9and0,3
Ans. [D]
Q.32 The orthocenter of the triangle PAB is
(A)
7
8,5 (B)
8
25,
5
7(C)
5
8,
5
11(D)
25
7,
25
8
Ans. [C]
Q.33 The equation of the locus of the point whose distances from the point P and the line AB are equal, is
(A) 9x2 + y26xy54x62y + 241 = 0
(B) x2 + 9y2 + 6xy54x + 62y241 = 0
(C) 9x2 + 9y26xy54x62y241 = 0
(D) x2 + y22xy + 27x + 31y120 = 0
Ans. [A]
Paragraph for questions 34 to 36.
Consider the polynomial
f(x) = l + 2x + 3x2 + 4x3. Let s be the sum of all distinct real roots of f(x) and let t = | s |.
Q.34 The real number s lies in the interval
(A)
0,4
1(B)
4
3,11 (C)
2
1,
4
3(D)
4
1,0
Ans. [C]
Q.35 The area bounded by the curve y = f(x) and the lines x = 0, y = 0 and x = t, lies in the interval
(A)
3,
4
3(B)
16
11,
64
21(C) (9, 10) (D)
64
21,0
Ans. [A]
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Q.38 Match the statements inColumn I with those in Column-II
[Note : Here z takes values in the complex plane and Im z and Re z denote, respectively, the
imaginary part and the real part of z.]
Column I Column II
(A) The set of points z satisfying (p) an ellipse with eccentricity5
4
|zi| z || = | z + i | z ||
is contained in or equal to
(B) The set of points z satisfying (q) the set of points z satisfying Im z = 0|z + 4| + |z4| = 10
is contained in or equal to
C) If | w | = 2, then the set of points (r) the set of points z satisfying | Im z | 1
z = ww
1 is contained in or
equal to
D) If | w | = 1, then the set of points s) the set of points z satisfying |Re z| 2
z =
w
1w is contained in or
equal to
(t) the set of points z satisfying |z|3
Ans. [(A) q,r (B) p (C) p,s,t (D) q,r,s,t ]
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PART III: PHYSICS
SECTION -I
Single Correct Choice TypeThis section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and
(D) out of which ONLY ONE is correct.
Q.39 A tiny spherical oil drop carrying a net charge q is balanced in still aire with a vertical uniform electric field
of strength 7
81
105
Vm1
. When the field is switched off, the drop is observed to fall with terminal
velocity 2 103 m s1. Given g = 9.8 ms2, viscosity of the air = 1.8 105 Ns m2 and the density of oil
= 900 kg m3, the magnitude of q is
(A) 1.6 1019C (B) 3.2 1019C (C) 4.8 1019C (D) 8.0 1019C
Ans. [D]
Q.40 A uniformly charged thin spherical shell of radius R carries uniform surface charge density of per unit
area. It is made of two hemispherical shells, held together by pressing them with force F (See figure). F
is proportional to
FF
(A)22
0
1R
(B) R
2
0
1
(C)
R
2
0
1
(D) 2
2
0
1
R
Ans. [A]
Q.41 A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards it is subjected
to a time-dependent force F(t) in the x direction. The force F(t) varies with t as shown in the figure. Thekinetic energy of the block after 4.5 seconds is
4.5s
3s
4N
F(t)
O t
(A) 4.50J (B) 7.50J (C) 5.06J (D) 14.06JAns. [C]
Q.42 A biconvex lens of focal length 15cm is in front of a plane mirror. The distance between the lens and the
mirror is 10cm. A small object is kept at a distance of 30 cm from the lens. The final image is
(A) virtual and at a distance of 16 cm from the mirror
(B) real and at a distance of 16 cm from the mirror
(C) virtual and at a distance of 20 cm from the mirror
(D) real and at a distance of 20 cm from the mirror
Ans. [B]
PAPER-2
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Q.43 A Vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which
match with 16 main scale divisions. For this Vernier caplipers, the least count is
(A) 0.02 mm (B) 0.05 mm (C) 0.1 mm (D) 0.2 mm
Ans. [D]
Q.44 A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long uniform string is vibrating
in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the
wire is 50N and the speed of sound is 320 ms1, the mass of the string is
(A) 5 grams (B) 10 grams (C) 20 grams (D) 40 grams
Ans. [B]
SECTION - II
Integer TypeThis section contains 5 questions. The answer to each question is a single-digit integer, ranging
from 0 to 9. The correct digit below the question number in the ORS is to be bubbled.
Q.45 To determine the half life of the radioactive element, a student plots a graph ofdt
tdN )(ln versus t. Here
dt
tdN )(is the rate of radioactive decay at time t. If the number of radioactive nuclei of this element
decreases by a factor ofp after 4.16 years, the value ofp is
87654321
2
3
4
5
6
Years
dt
)t(dNn
Ans. [8]
Q.46 A diatomic ideal gas is compressed adiabatically to32
1of its initial volume. In the initial temperature of
gas is Ti(in Kelvin) and the final temperature isT
i, the value of is
Ans. [4]
Q.47 At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitorshave no charge initially, at what time (in seconds) does the voltage across them become 4 V?
[Take : ln 5 = 1.6, ln 3 = 1.1]
2F
2F
BA
2M
2M
Ans. [2]
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Q.48 Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is
observed to move from3
25m to
7
50m in 30 seconds. What is the speed of the object in km per hour?
Ans. [3]
Q.49 A large glass slab ( = 5/3) of thickness 8 cm is placed over a point source of light on a plane surface.
It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What
is the value of R?
Ans. [6]
SECTION - III
Paragraph TypeThis Section contains 2 paragraphs. Based upon each of the paragraphs 3 multiple choice
questions have to be answered. Each of these questions had four choice (A), (B), (C) and (D)
out of which ONLY ONE is correct.
Paragraph for Questions 50 to 52The key feature of Bohrs theory of spectrum of hydrogen atom is the quantization of angular momentum
when an electron is revolving around a proton. We will extend this to a general rotational motion to find
quantized rotational energy of a diatomic molecule assuning it to be rigid. The rule to be applied is Bohrsquantization condition.
Q.50 A diatomic molecule has moment of inertia I. By Bohrs quantization condition its rotational energy in the
nth level (n = 0 is not allowed) is
(A)
I8
h
n
122 (B)
I8
h
n
12 (C)
I8
hn
2 (D)
I8
hn
2
2
Ans. [D]
Q.51 It is found that the excitation frequency from ground to the first excited state of rotation for the CO
molecule is close11
1041 Hz. Then the moment of inertia of CO molecule about its center of mass is
close to (Take h = 2 10-34 J s)
(A) 2.75 10-46 Kg m2 (B) 1.87 10-46 Kg m2
(C) 4.67 10-47 Kg m2 (D) 1.17 10-47 Kg m2
Ans. [B]
Q.52 In a CO molecule, the distance between C (mass = 12 a.m.u.) and O (mass = 16 am.u.), where 1 a.m.u.
2710
3
5 Kg, is close to
(A) 2.4 10-10 m (B) 1.9 10-10 m (C) 1.3 10-10 m (D) 4.4 10-10 mAns. [C]
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Paragraph for Questions 53 to 55When liquid medicine of density is to be put in the eye, it is done with the help of a dropper. As the bulb
on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the
size of the drop. We first assume that the drop formed at the opening is spherical because that requires
a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to
the surface tension T when the radius of the drop is R. When this force becomes smaller than the weight
of the drop, the drop gets detached from the dropper.
Q.53 If the radius of the opening of the dropper is r, the vertical force due to the surface tension on the drop ofradius R (assuming r
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SECTION - IV
(Matrix Type)This section contains 2 questions. Each questions has four statements (A, B, C and D) given
in Column I and five statements (p, q, r, s & t) in Column II. any given statement is Column I
can have correct matching with one or more statement(s) given in Column II. For example, if
for a given questions, statement B matches with the statements given in q and r, then for that
particular question, against statement B, darken the bubbles corresponding to q and r in the
ORS.
Q.56 You are given many resistances, capacitors and inductors. These are connected to a variable DC voltage
source (the first two circuits) or an AC voltage source of 50 Hz freqeuncy (the next three circuits) in
different ways as shown in Column II. When a current I (steady state for DC rms for AC) flows through
the circuit, then corresponding voltage V1and V
2. (indicated in circuits) are related as shown in Column
I. Match th two
Column-I Column-II
(A) I 0, V1
is proportional to I (p)6mH 3F
V1 V2
V
(B) I 0, V2
> V1
(q)6mH 2
V1 V2
V
(C) V1
= 0, V2
= V (r)6mH 2
V1 V2
~ V
(D) I 0, V2
is proportional to I (s)6mH 3F
V1 V2
~V
(t)
1k 3F
V1 V2
~V
Ans. [(A) r,s,t (B) q,r,s,t (C) p,q (D) q,r,s,t ]
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Q.57 Two transparent media of refractive indices1and
3have a solid lens shaped tanparent material refractive
index2between them as shown in figures in Column II. A ray traversing these media is also shown in the
figures. In Column I different relationships between 1,
2are given. Match them to the ray diagrams
shown in Column II.
Column-I Column-II
(A) 1<
2(p) 3 2 1
(B) 1>
2(q) 3
21
(C) 2=
3(r) 3 12
(D) 2>
3(s) 3 12
(t) 3 12
Ans. [(A) p,r (B) q,s,t (C) p,r,t (D) q,s ]