Iit 2011 FST2 QNS P1
Iit 2011 FST2 QNS P1
Iit 2011 FST2 QNS P1
BMAT2/CPM/P(I)/Qns
19.12.2010
Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.
A. General
1. This booklet is your Question Paper containing 84 questions. The booklet has 29 pages.
2. This question paper CODE is printed on the right hand top corner of this sheet and on the back page
(page no. 29) of this booklet.
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6. The answer sheet, a machine-readable Objective Response Sheet (ORS), is provided separately, in which
appropriate bubble for each question must be darkened with HB pencil.
SEAL
3. This question paper contains 2 blank pages for your rough work. No additional sheets will be provided for
rough work.
Name: .
Enrollment No.:
IIT/B.MAT2/CPM/P(I) - 1
SEAL
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INSTRUCTIONS:
TEST-I
CHEMISTRY
PART-I
SECTIONI
Single Correct Choice Type
This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C)
and (D), out of which ONLY ONE is correct.
1.
A mixture of H2SO4 and H2C2O4 (oxalic acid) and some inert impurity weighing 3185 g was
dissolved in water and solution made upto 1 L . 10 mL of this solution required 3 mL of
0.1 N NaOH solution for complete neutralization. In another experiment 100 mL of the same
solution in hot condition required 4 mL of 0.02 M KMnO4 solution for complete reaction.
The weight % of H2SO4 in the mixture was:
(A) 80 %
(B) 60 %
(C) 40 %
(D) 20 %
2.
Calculate the ratio of F and HCOO in a mixture of 0.1 M HF (Ka = 6.6 104) and
0.2 M HCOOH (Ka = 2 104).
(A) 3.3 : 2
(B) 2 : 3.3
(C) 1 : 6.6
(D) 1: 3.3
3.
One gram of activated carbon has a surface area 100 m 2 . Considering complete coverage as
well as monomolecular adsorption, how much NH3 at STP would be adsorbed on the surface
of 88 g carbon if radius of NH3 molecule is 108 cm and N A = 6 10 23 .
(A) 11.20 L
(C) 10.45 L
(B) 1.045 L
(D) 44.80 L
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4.
Product (P)
(A)
5.
(B)
(C)
(D)
OH
OH
H
(I)
(II)
(III)
OH
OH
H
(IV)
(A) (I)
(C) (III)
6.
(B) (II)
(D) (IV)
0001 mole of octahedral complex Cr (NH 3 )5 (NO3 )SO 4 was passed through cation exchanger
and the acid coming out of it required 20 mL of 0.1N NaOH for neutralization. Hence the
complex is
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7.
O (ii) H3O
(A)
H2SO4
(B)
18
(A)
(B)
O
Ph
Ph
Ph
(C)
Ph
18
(D)
O
Ph
Ph
18
8.
What is the hybridization state of central atom in the cationic part of the solid form of XeF6?
(A) sp3
(B) sp3d2
3
(C) sp d
(D) dsp2
SECTIONII
Multiple Correct Choice Type
This section contains 5 multiple correct questions. Each question has 4 choices: (A), (B),
(C) and (D) for its answer, out of which ONE OR MORE may be correct.
9.
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10.
Which of the following statement(s) is/are correct about the solution containing chloroform
and acetone?
(A) Solution shows + ve deviation from Raoult's law.
(B) The enthalpy change is ve.
(C) Pure chloroform can be separated by the fractional distillation of a solution having any
composition of both the components.
(D) The forces of attraction acting between molecules of acetone and chloroform in solution
are greater than those acting between molecules of pure component.
OMe
11.
AlCl3
ZnHg/HCl
(A)
(B)
C
O
Which of the following statement(s) is/are correct regarding the above reaction?
OMe
O
(A) Compound (A) is
COOH
COOH
C
COOH
CH2
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12.
CH2OH
(A)
13.
(B)
(C)
CH2
(D)
(D) In two dimensional sheet silicates (Si 2 O 5 )2n n , four oxygen atoms of each tetrahedron are
shared with neighbouring tetrahedra.
SECTIONIII
Paragraph Type
This section contains 2 paragraphs. Based upon the first paragraph 3 multiple choice
questions and based upon the second paragraph 2 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. 14 to 16
Nucleophiles such as ammonia and its derivatives H 2 N Z add to the carbonyl group of
aldehydes and ketones. The reaction is reversible and catalysed by acid. The equilibrium favours
the product formation due to rapid dehydration of the intermediate to form C = N Z
R1
R2
R1
R2
C = O + NH2 Z
OH
C
NHZ
H+
R2
OH
H+
NHZ
R1
H
H2O, H
R1
R2
C = NZ
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14.
If the medium of reaction is fairly alkaline in the beginning of the reaction and pH of the
solution is made to decrease gradually.
(A) The rate of reaction decreases throughout.
(B) The rate of reaction increases throughout.
(C) The rate of reaction reaches maximum at a particular pH, and then decreases.
(D) The rate of reaction reaches minimum at a particular pH and then increases.
R1
15.
Product (P)
R2
Which of the following types of isomerism are possible in the product (P)?
(I) Optical
(II) Tautomerism
(III)Geometrical
(IV) Metamerism
(A) (I) and (II)
(B) (I) and (III)
(C) (II) and (III)
(D) (I), (II), (III) and (IV)
16.
C = O + H2N.NH2
(A) Me
(B) OH
(C) NH2
(D)
O
||
C NH 2
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is also based on a regular tetrahedron. The phosphorus atoms remain at the vertices but are no
longer bonded to each other. Instead the P atoms are joined by bridging oxygens.
Phosphorus(V) oxide has a further oxygen atom bonded to each phosphorus atom at the
vertex of the tetrahedron.
Each oxide reacts with water to form an acid. Phosphorus(V) oxide forms phosphorus(V)
acid, H3PO4.
17.
18.
SECTIONIV
Integer Type
This section contains TEN 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.
19.
OH
H
H
H
Br
C=C
H
Br
H
20.
H
C=C
H
C=C
Br
H
A gas at 350 K and 15 atm has a molar volume 12 percent smaller than that calculated from
the perfect gas law. Compressibility factor under these conditions can be expressed in
scientific notation as 88 10 x . The value of x is ________ .
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21.
3Cr2+. How many cells with different E cell and different values of n but
= 091 V)
E Cr
2+
/ Cr
22.
Two first order reactions A and B have the same frequency factor and activation energy of
A exceeds that of B by 1046 kJ mol1. If A is 30% complete in 60 min. at 100C, how long
will the B take for 70 % decomposition. [Given: log 3 = 0.4771, log 7 = 0.845, antilog
0.4633 = 2.9]
23.
A current of 10.0 A flows for 2hr through an electrolytic cell containing a molten salt of metal
X and results in the deposition of 0.25 moles of metal X at the cathode. The oxidation state of
X in the electrolysed salt is
24.
The given compound exists in polar form in which there is a close loop of Huckels number
of electrons. The value of n in (4n + 2)-electrons which are present on outer peripheral part
of the polar structure of given organic compound is _________ .
25.
26.
90
120
60
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10
27.
Ar and He are both gases at room temperature. The average molecular velocity of He atoms is
x times of the average molecular velocity of Ar atoms at this temperature. The numerical
value of x is ________ .
28.
The standard electromotive force of the rechargeable lithium ion battery is 3.70 volt. Assume
that half-reaction at the cathode is
CoO2 + Li+ + e LiCoO2
and the half-reaction at the anode is
LiC6 6C + Li+ + e
The value of the standard Gibbs energy of the cell reaction is y 10x J/mol. If the value of
y is less than ten, the numerical value of x is ________ .
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11
PHYSICS
PART II
SECTION I
Single Correct Choice 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.
29.
30.
31.
F = 10 t
In a certain hypothetical radioactive decay process, species A decays into species B and
species B decays into species C according to the reactions
A 2B + particles + energy:
B 3C + particles + energy
The decay constant for the species A is 1 = 1 sec1 and that for the species B is
2 = 100 sec 1 . Initially 104 moles of the species of A were present while there was none of
B and C. It was found that species B reaches its maximum number at a time
t0 = 2 ln(10)sec. Then value of the maximum number of moles of B is (e2.303 = 10)
(A) 2
(B) 3
(C) 4
(D) 6
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12
32.
33.
34.
35.
x
x
2R
2R
+++++ +++++
2l
O
l
v
q0
(D)
4.2 gl
(D) 75
v0
B
A
l
(D)
3gl
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13
36.
eB
eB
mv
mv
m
2m
mv
mv
(C)
(D)
tan 1
tan 1
eB
eB
eBR
eBR
SECTION II
Multiple Correct Choice Type
This section contains 5 multiple choice questions. Each question has four choices (A), (B),
(C) and (D) out of which ONE OR MORE may be correct.
37.
(A) The particle executes SHM in the ground frame about the mean position 1, , 3t .
2
(B) The particle executes SHM in a frame S moving along the positive zaxis with a velocity of 3 m/s.
5
(C) The amplitude of the SHM of the particle in frame S is m .
2
3
4
(D) The line of the SHM of the particle is parallel to the vector i j .
5
5
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14
38.
39.
A solid cone is placed on a horizontal surface with height h and radius R. Its apex angle
is . To change the position of the cone from fig. (A) to fig. (B), no work is required, then
R
Fig. (A)
1
(A) = sin1 3
40.
(B) =
Fig. (B)
(C)
h
=1
R
(D)
h
=2 2
R
(A) the sum of total energy per unit length at nodes and antinodes is constant
(B) the total energy of a point midway between a node and an adjacent antinode is constant
(C) if the string has a standing wave and a component of traveling wave, then the kinetic
energy of the points of minimum amplitude is non-zero at some instant of time.
(D) if the string has a standing wave and a component of traveling wave, then the potential
energy of the points of maximum amplitude is non zero at some instant of time.
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15
41.
Nucleus A decays to B with decay constant 1 and B decays to C with decay constant 2.
Initially at t = 0, number of nuclei of A and B are 2N0 and N0 respectively. At t = t0, number
3N 0
of nuclei of B stop changing. If at this instant number of nuclei of B are
.
2
1 4 1
1
4 1
(A) the value of t 0 is
(B) the value of t 0 is
ln
ln
1 3 2
2 3 2
3N 0 2
2N 0 2
(C) the value of NA at t 0 is
(D) the value of NA at t 0 is
2 1
3 1
SECTION III
Paragraph Type
This section contains 2 paragraphs. Based upon the first paragraph 3 multiple choice
questions and based upon the second paragraph 2 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.
R 2 = 12
i2
R 3 = 12 C = 125F
L = 18mH
30mH
S2
R1 = 8
~
E = (500 V) sin (500 s1)t
S1
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16
42.
The difference in phases of the currents i 1 and i 2 , when switch S 1 and S 2 are closed is
(A) 37
(B) 53
(C) 90
(D) 60
43.
44.
If S 1 and S 2 both are opened, then the average power consumed in the circuit will be
(A) 1 KW
(B) 3.125 KW
(C) 2 KW
(D) 5 KW
v0
2
45.
46.
A
i0
v0
R 3
R
The current through the rod when it is at a distance from the point A of the loop will
2
be
v i
16v0 0i0
9v0 0i0
ln3
ln3
(A) 0 0 0 2 ln3
(B)
(C)
(D) zero.
2
16 R
R
16 R 2
Force required to maintain the uniform velocity of the rod at this instant is
9 02 i02 v0 (ln 3)
9 02i02 v0 (ln 3)
(B)
16
R 3
R 3
2
(A)
02i02 v0 (ln 3)
32 R 3
(C)
9 02i02 v0 (ln 3)
32 R 3
(D)
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17
SECTION IV
Integer Type
This section contains TEN 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.
47.
48.
O2
He
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18
49.
A copper plate of length 1 m is riveted to two steel plates of same length and same crosssection area at 0C. The tension (in kilo newton) generated in copper plate when heated to
20C is 56n. Find the value of n.
1
Ycopper = Ysteel = 2 1011 N/m2
Y = Youngs modulus
2
copper = 18 106 K1
steel = 11 106 K1
= coefficient of linear expansion
2
Area of each plate = 50 cm
50.
v0
a
B
51.
In a vertical cylindrical vessel of base area A = 60 cm2 water is filled to a height h = 10 cm.
If density and Bulk Modulus of water are = 1000 kg m3 and B = 2 109 Nm2
respectively, the elastic deformation energy of water in the vessel is found to be n 107 J.
Find n.
52.
A particle is projected from a point O with an initial speed of 30 m/s to pass through a point
which is 40m from O horizontally and 10m above O. There are two angles of projection for
which this is possible. If these angles are and then find the value of tan[( + )] .
53.
The electric potential V in volt in a region of space is given by V = ax2 + ay2 + 2az2, where a
is a constant given by a = 1.25 103 V/m2. What is the radius (in m) of the circle of the
equipotential line corresponding to V = 6250V and z = 2 m
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19
54.
n =1
40cm
3
2
n=2
9cm
10cm
n=
55.
When the voltage applied to an X-ray tube is increased from V1 = 10 KV to V2 = 20 KV, the
wavelength interval of K line and cut-off wavelength of the continuous X-ray spectrum
increases by a factor . If the atomic number of the element of which the tubes anode is
made is 29, then find .
56.
given as
1+ n .
30
Find n. (m = 2kg, l = 1m, k = 40 N/m)
l/2
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20
MATHEMATICS
PART-III
SECTION - I
Single Correct Choice 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.
57.
58.
zz
If arg(z) < 0, then arg
is equal to
2
(A) 0
(B)
2
(C)
(D)
1
1
1
+
+ ... +
= 10 and
a1 a 2 a 2 a 3
a 4000 a 4001
(A) 20
59.
(B) 30
For 0 < < 2 , sin1 (sin ) > cos1 (sin ) is true when
(A) ,
4
3
(B) ,
60.
(C) 40
3
(C) ,
4 4
(D) , 2
4
(A) 16
(B) 25
(C) 8
(D)
35
2
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21
61.
If the curves x y = 4 and xy = 5 intersect at points A and B, then the possible number
2
(A) 0
(C) 2
62.
(B) 1
(D) 4
If A and B are two events such that P(A B) = 0.3 and P ( A'B ' ) = 0.6 , then the value of
P ( A B ' or A' B ) is equal to
(A) 0.9
(C) 0.3
(B) 0.7
(D) 0.1
63.
The number of values of k for which the equation x 3 3 x + k = 0 has two distinct roots
lying in the interval (0, 1) are
(A) three
(B) two
(C) infinitely many
(D) no value of k satisfies the requirement
64.
If
dy
= f ( x) + f ( x) dx, then the equation of the curve y = f (x) passing through (0, 1) is
dx
0
(A) f ( x) =
2e x e + 1
3e
(B) f ( x) =
3e x 2e + 1
2( 2 e )
(C) f ( x) =
e x 2e + 1
e +1
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22
SECTION - II
Multiple Correct Choice Type
This section contains 5 multiple choice questions. Each question has four choices (A), (B),
(C) and (D) out of which ONE OR MORE may be correct.
65.
(B) lim[ f (x )] does not exist (where [.] denotes greatest integer function)
x 0
(C) f
(x ) = ln
(D) f ( x ) < e x
4 x
x , x > 0
has infinite solution in (0, 6)
x+a
If a, b, c, d are in A.P. and f ( x) dx = 4 where f ( x) = x + b
0
x+c
common difference of the A.P. may be
(A) 1
(B) 1
(C) 2
(D) 4
2
67.
x+b
x+c
x+d
x+ac
x 1 , then the
xb+d
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23
68.
Let z1 and z 2 be two complex numbers such that z12 4 z 2 = 16 + 20i . If and are roots
of x 2 + z1 x + z 2 + M = 0 (where M is complex number) and
69.
( )2
= 28 , then
SECTION - III
Paragraph Type
This section contains 2 paragraphs. Based upon the first paragraph 3 multiple choice
questions and based upon the second paragraph 2 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. 70 to 72
A curve x = f(y) passing through origin is such that slope of tangent at any point is
reciprocal of sum of co-ordinates of the point of tangency.
70.
(D) 2
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24
1
71.
x dy
is equal to
1
2
5
(C) e
2
(A) e
72.
1 xe
(B) e
3
2
(D) e + 1
d (e y ) is equal to
(A) e e 1
(C) e
1
3
(B) e e1 2
1
e
(D) e + e 1 +
1
3
A = f ( x)i + g ( x) j , B = g ( x)i + f ( x) j make an obtuse angle with each other x 0 then
73.
(A) f(x) < 0, g(x) > 0 (B) f(x) > 0, g(x) > 0
74.
lim f ( x) g ( x) is
x
(A) +
(B)
(C) 0
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25
SECTION IV
Integer Type
This section contains TEN 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.
75.
76.
a+b c+b
If a, b, c are in H.P. and
+
...... , then find the least value of
2 a b 2c b
. (where a, b, c are positive).
If e be the eccentricity of a hyperbola and f (e) be the eccentricity of its conjugate
3
77.
78.
is (n is even)
n times
A staircase has 10 steps. A person can go up the steps one at a time, two at a time, or any
combination of 1s and 2s. If the number of ways in which the person can go up the stairs
p
is p, then find
.
89
If the normals to curve y = x 2 at the points P, Q & R pass through the point 0,
3
, find
2
e x / a eb / x
a x dx
b
79.
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26
80.
Let
'f'
be
function
such
that
f (1 + x) = 1 + x(1 + ( g ( x ))),
where
f ( x)
and
f ' ( x) .1 + x
dx
is
1
a
log e where a & b are co-prime. Find a + b .
2
b
81.
If A, B, C are vectors such that | B |=| C |, then find (( A + B ) ( A + C )) ( B C ).( B + C )
82.
If
83.
If line y = x + 2 does not intersect any member of family of parabolas y2 = ax, (aR+) at two
distinct point, then find the maximum value of latus rectum of parabola.
84.
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29
Name: .
Enrollment No.:
Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.
IIT/B.MAT2/CPM/P(I) - 29