NaOH(aq)
produ
Y
Zn,HO
2. heat
ANSWER: 1
The synthesis of 3-octyne is achieved by adding a bromoalkane into a mixture of
sodium amide and an alkyne. The bromoalkane and alkyne respectively are
A) BrCH,CH,CH,CH,CH, and CH,CH,C=CH
B) BrCH,CH,CH, and CH,CH,CH,C=CH
C) BrCH,CH,CH,CH,CH, and CH,C=CH
D) BrCH,CH,CH,CH, and CH,CH,C=CH
ANSWER:
D
The correct statement about the following disaccharide is
CHOH
H
H
CHOH
H
H
(a)
H
(b)
HO
OH
H
HO
OCHCH
COHH
H
HO
HO
H
A) Ring (a) is pyranose with a-glycosidic link
B) Ring (a) is furanose with a-glycosidic link
C) Ring (b) is furanose with -glycosidic link.
D) Ring (b) is pyranose with -glycosidic link
ANSWER: A
In the reaction
OCH3
HBr
the products are
A)Br
OCH and H
BJ
Br and CHBr
Br and CH,OH
D
-0ll and CH,Br
ANSWER: D
Plots showing the variation of the rate constant (k) with temperature (T) are
given below. The plot that follows Arrhenius equation is.
A)
k
B)
K
k
C)
D)
K
ANSWER:A
The species which by definition has ZERO standard molar enthalpy of formation
at 298 K is
A) Br, (g)
B) Cl, (g)
C) H,O (g)
D) CH₄ (g)
ANSWER:B
The bond energy (in kcal mol-t) of a C-C single bond is approximately.
A) 1
B) 10
C) 100
D) 1000
ANSWER:C
SECTION - II(Multiple Correct Choice Type)
The reagent(s) used for softening the temporary hardness of water is(are)
A) Ca,(PO)2
B) Ca(OH),
C) Na,CO3
D) NaOCl
ANSWER: B
HO
In the reaction
NaOH(aq)/Br.
the intermediate(s) is(are)
O
Br
A)
B)
D
Br
Br
Br
Br
Br
ANSWER: A and C
In the Newman projection for 2,2-dimethylbutane
x
H3C
CH₃
X and Y can respectively be
H
H
Y
A) H and H
B) H and C,H5
C) C,H, and H
D) CH, and CHg
ANSWER: B and D
Among the following, the intensive property is (properties are).
A) molar conductivity
B) electromotive force.
C) resistance
D) heat capacity
ANSWER: A and B
Aqueous solutions of HNO,, KOH, CH,COOH, and CH,COONa of identical.
concentrations are provided. The pair(s) of solutions which form a buffer upon
mixing is(are)
A) HNO, and CH,COOH
B) KOH and CH,COONa
C) HNO,and CH,COONa
D) CH,COOH and CH,COONa
ANSWER: C and D
SECTION - III
(Paragraph Type)
Paragraph for Questions 14 to 16
Copper is the most noble of the first row transition metals and occurs in small deposits in
several countries. Ores of copper include chalcanthite (CuSO,-5H,O), atacamite (Cu,Cl(OH),),
cuprite (Cu,O), copper glance (Cu,S) and malachite (Cu,(OH),CO.). However, 80% of the.
world copper production comes from the ore chalcopyrite (CuFeS,). The extraction of copper.
from chalcopyrite involves partial roasting, removal of iron and self-reduction..
Partial roasting of chalcopyrite produces
A) Cu,S and FeO
B) Cu,O and FeO
C) CuS and Fe,O3
D) Cu,O and Fe,O3
ANSWER: A
Iron is removed from chalcopyrite as
A) FeO
B) FeS
C) Fe,O3
D) FeSiO3
ANSWER: D
In self-reduction, the reducing species is.
A) S
B) O₂-
C) S2-
D) SO,
ANSWER: C
Paragraph for Questions 17 to 18
The concentration of potassium ions inside a biological cell is at least twenty times
higher than the outside. The resulting potential difference across the cell is important
in several processes such as transmission of nerve impulses and maintaining the ion
balance. A simple model for such a concentration cell involving a metal M is:
(s)n(en 1 be)n(eno goo be)n(s)
For the above cell
AJ Ecen<O; G>O
B) Ece>0; G <0
C) Ecel < O; G > O
D) Ece> O; G <0
ANSWER: B
If the O.05 molar solution of M+ is replaced by a O.o025 molar M+ solution, then
the magnitude of the cell potential would be
A) 35 mV
B) 7O mV
C) 14O mV
D) 700 mV
ANSWER: C
SECTION - IV
(Integer Type)
The total number of basic groups in the following form of lysine is.
HN--CH-CH-CH-CH
CH-
ANSWER: 2
formula C4H. is
ANSWER: 5
In the
ecular aldol condensation
1. 03
Amongst the following, the total number of compounds soluble in aqueous NaOH is
HgC~NCHg
COOH
OCH,CH₃
OH
CHOH
OH
NO₂
CHCH3
COOH
CHCH
HgC
CH
ANSWER: 4
Amongst the following, the total number of compounds whose aqueous solution.
turns red litmus paper blue is
KCN
K,SO4
(NH4)C,O4
NaC1
Zn(NO3)2
FeC1
K,CO3
NH,NO3
LiCN
ANSWER: 3
Based on VSEPR theory, the number of 9O degree F-Br-F angles in BrF is
ANSwER: either 0 or 8.
The value of n in the molecular formula Be.Al,Si.O is.
18
ANSWER:3
A student performs a titration with different burettes and finds titre values of
25.2 mL, 25.25 mL, and 25.0 mL. The number of significant figures in the average.
titre value is
ANSWER: 3
The concentration of R in the reaction R -) P was measured as a function of
time and the following data is obtained:
[R] (molar)
1.0
0.75
0.40
0.10
t(min.)
0.0
0.05
0.12
0.18
The order of the reaction is.
ANSWER: 0
ANSWER: 4
PART - II : MATHEMATICS
SECTION - I
(Single Correct Choice Type)
If the angles A, B and C of a triangle are in an arithmetic progression and if a, b.
and c denote the lengths of the sides opposite to A, B and C respectively, then.
the value of the expression
sin2C+=sin2A is
C
a
A)
2
1
B)
3
2
C) 1
D) 3
ANSWER: D
x
y
Z
Equation of the plane containing the straight line
2
3
4
and perpendicular to
x_y_z
x
y
Z
the plane containing the straight lines.
and
is
3
4
2
4
2
3
C) x-2y + z = 0
D) 5x + 2y - 4z = 0
ANSWER: C
Let be a complex cube root of unity with 1.A fair die is thrown three times.
If r,, r, and r, are the numbers obtained on the die, then the probability that.
o1 +oI2 +oFs =0 is
1
1
2|
1
A)
B)
C)
D)
18
9
9
36
ANSWER: C
Let P, 9, R and S be the points on the plane with position vectors
-2i - j, 4i, 3i+3j and -3i +2j respectively. The quadrilateral PgRS must be a
A) parallelogram, which is neither a rhombus nor a rectangle.
B) square
C) rectangle, but not a square.
D) rhombus, but not a square.
ANSWER: A
The number of 3x3 matrices A whose entries are either O or 1 and for which the system
[x]
[1]
Ay
=
0
has exactly two distinct solutions, is.
[o]
A) 0
B) 29 - 1
C) 168
D) 2
ANSWER: A
X t ln (1+t)
1
The value of lim
t4+4
dt is
x->0
0
1
1
1
A) 0
B)
C)
D)
12
24
64
ANSWER: B
Let p and q be real numbers such that p = 0,p3 = q and p3 =-q. If and are
nonzero complex numbers satisfying + = - p and 3 + 3 = q . then a quadratic
as its roots is
a.
A) (p3+q)x2-(p+2q)x+(p3+q)=0
B) (p+q) x2-(p-2q)x+(p+q)=0
C) (p3-q)x2-(5p3-2q)x+(p3-q)=0 D)(p3-q)x2-(5p+2q)x+(p3-q)=0
ANSWER: B
Let f, g and h be real-valued functions defined on the interval [0, 1] by
f(x)=e+e
-x2
g(x)=xe+ e
X
and h(x) =x'e* + e
x2ex2
-X
. If a, b and c denote,
respectively, the absolute maximum of f, g and h on [0, 1], then
A) a=bandcb
B)a=candab
C)abandcb D)a=b=c
ANSWER: D
SECTION - II |(Multiple Correct Choice Type)
Let A and B be two distinct points on the parabola y2 = 4x. If the axis of the
parabola touches a circle of radius r having AB as its diameter, then the slope of
the line joining A and B can be.
1
1
2
2
A)
B)
C)
D)
r
r
r
ANSWER: C and D
T
and let a, b and c denote the lengths of
6
the sides opposite to A, B and C respectively. The value(s) of x for which.
a = x2 + x + 1, b = x2 - 1 and c = 2x + 1 is (are)
A) -(2+3)
B) 1+3
C) 2+3
D) 43
ANSWER: B
Let z, and z, be two distinct complex numbers and let z = (1 - t) z, + tz, for some
real number t with O < t < 1. If Arg(w) denotes the principal argument of a
nonzero complex number w, then
A) |z-z|+|z-z|=|z-z|
B) Arg (z - z) = Arg (z - z)
Z-Z1 Z-Z
=0
C)
D) Arg (z - z) = Arg(z - Z)
Z2-Z1 Z2-Z1|
ANSWER: A and C and D
Let f be a real-valued function defined on the interval (O, ) by
X
f(x) = en x+ j 1+sint dt. Then which of the following statement(s) is (are) true ?
0
A) f"(x) exists for all xe(0,)
B) f'(x) exists for all xe(0,) and f' is continuous on (O,), but not
differentiable on (O, )
D) there exists > 0 such thatf(x)+f'(x) for all xe(0, )
ANSWER:B and C
f x*(1-x)4
The value(s) of
dx is (are)
1+x2
22
0
2
71
3t
A)
B)
C) 0
D)
15
7
105
2
ANSWER: A
SECTION - III
(Paragraph Type)
Paragraph for Questions 42 to 44
Let p be an odd prime number and T, be the following set of 2x2 matrices :
ab
: a,b,c e {0, 1, 2, ..,p-1}
The number of A in T. such that A is either symmetric or skew-symmetric or
both, and det
The number of A in T such that the trace of A is not divisible by p but det
The number of A in T. such that det
Equation of a common tangent with positive slope to the circle as well as to the
hyperbola is
A) 2x-5y-20=0
B) 2x-5y+4=0
C) 3x-4y + 8 =0 D) 4x-3y + 4 =0
ANSWER:B
Equation of the circle with AB as its diameter is.
A) x2 + y2 - 12x + 24 = O
B) x2 + y2 + 12x + 24 = O
C) x2 + y2 + 24x - 12 = 0
D) x2 + y2 -24x - 12 = 0
ANSWER: A
SECTION -IV
(Integer Type)
n n
The number of values of 0 in the interval.
2'2
such that 0
for
5
n=0,1,2 and tane =cot 50
ANSWER: 3
1
The maximum value of the expression
is
sin? 0 + 3 sin 0 cos0 + 5cos2 e
ANSWER: 2
i-2j
and b=2i+j+3k
then the
5
14
value of 2a+ b
axba-2b
is
ANSWER: 5
The line 2x + y = 1 is tangent to the hyperbola
=1. If this line passes
a2
b2
through the point of intersection of the nearest directrix and the x-axis, then the
eccentricity of the hyperbola is
ANSWER: 2
If the distance between the plane Ax - 2y + z = d and the plane containing the lines
x-1_y-2
z-3
x-2
y-3
z-4
and
is 6, then |d| is
2
3
4
3
4
5
ANSWER: 6
For any real number x, let [x] denote the largest integer less than or equal to x.
Let f be a real valued function defined on the interval [10, 10] by
x-[x]if[x]isodd,
f(x)=
[1+[x]-x if[x] is even
Then the value of
10-10
f(x) cos nx dx is
ANSWER: 4
Let obe the complex number cos
2
+i sin
2nt
Then the number of distinct
3
3
z+1
o2
complex numbers z satisfying
Z+w2
1
=Ois equal to
02
1
Z +@
ANSWER: 1
Let S. k = 1, 2, .., 100, denote the sum of the infinite geometric series whose first
term is
k-1
and the common ratio is
1
. Then the value of
1002
100
|(k2 -3k +1)Sk
k!
k
100!
k =1
is
ANSWER: 3
The number of all possible values of 0 , where O <0 < , for which the system of
equations
(y + z) cos 30= (xyz) sin 30
2 cos 30 2 sin30
x sin 30 = 3
y
z
(xyz) sin 30 = (y + 2z) cos 30 + y sin 30
have a solution (x. yo, z.) withyoZo = 0, is
ANSWER: 3
Let f be a real-valued differentiable function on R (the set of all real numbers) such
that f(1) = 1. If the y-intercept of the tangent at any point P(x, y) on the curve y = f(x)
is equal to the cube of the abscissa of P, then the value of f(-3) is equal to
ANSWER: 9
PART - III : PHYSICS
SECTION - I
(Single Correct Choice Type).
Consider a thin square sheet of side L and.
thickness t, made of a material of resistivity p.
The resistance between two opposite faces,
shown by the shaded areas in the figure is
<L
A) directly proportional to L.
B) directly proportional to t.
C) independent of L
D) independent of t
ANSWER: C
A real gas behaves like an ideal gas if its
A) pressure and temperature are both high
B) pressure and temperature are both low
C) pressure is high and temperature is low
D) pressure is low and temperature is high
ANSWER: D
Incandescent bulbs are designed by keeping in mind that the resistance of their.
filament increases with the increase in temperature. If at room temperature,
100 W, 60 w and 40 w bulbs have filament resistances R.oo, R6o and R4o'.
respectively, the relation between these resistances is
1
1
1
B) R100 = R4 + R60
1
1
1
C) R1o0> R6o > R40
D) R100
R60
R40
ANSWER: D
To verify Ohm's law, a student is provided with a test resistor R., a high resistance
R, a small resistance R, two identical galvanometers G, and G,, and a variable
voltage source V. The correct circuit to carry out the experiment is
www
R2
R1
WW
G]w
G
Www
RT
RI
RT
R2
A)
B)
R1
R
Gw
M
Rr
WW
G
R2
Rr
www
R
D)
ANSWER:C
An AC voltage source of variable angular frequency and fixed amplitude V.is
connected in series with a capacitance C and an electric bulb of resistance R
(inductance zero).when @ is increased
A) the bulb glows dimmer
B) the bulb glows brighter
C) total impedance of the circuit is unchanged
D) total impedance of the circuit increases
ANSWER: B
A thin flexible wire of length L is connected to two adjacent fixed points and
carries a current I in the clockwise direction, as shown in the figure. When the
system is put in a uniform magnetic field of strength B going into the plane of the
paper, the wire takes the shape of a circle. The tension in the wire is.
XX
X
XXXX
X
X
X
X
XXXX
X
XXXXXX
X
X
X
X
X
X
X
X
X
X
X
X
XXX
IBL
IBL
IBL
A) IBL
B)
Tt
C)
2t
D)
4
ANSWER:C
A block of mass m is on an inclined plane of angle 0.The coefficient
block is held stationary by applying a force P parallel to the plane..
The direction of force pointing up the plane is taken to be positive..
As P is varied from P,= mg(sin0 - cos) to P,= mg(sin0 + cos0).
the frictional force f versus P graph will look like
P2
A)
P1
B)
P1
P2
P
P1
P1
P2
C)
P2
D)
P
ANSWER:A
A thin uniform annular disc (see
figure of mass M has outer
4R
radius 4R and inner radius 3R.
The work required to take a unit.
mass from point P on its axis to.
3R
infinity is
4R
2GM(42-5)
2GM(42 -5)
GM
2GM(J2-1)
A)
7R
B)
7R
C)
4R
D)
5R
ANSWER:A
SECTION - II|(Multiple Correct Choice Type)
A few electric field lines for a system of two charges.
9, and g, fixed at two different points on the x-axis
are shown in the figure. These lines suggest that
A) |9|>|9|
B) l9l<|9|
C) at a finite distance to the left of 9, the electric field is zero.
D) at a finite distance to the right of 9, the electric field is zero
ANSWER:A and D
A student uses a simple pendulum of exactly 1m length to determine g, the
acceleration due to gravity. He uses a stop watch with the least count of 1 sec
for this and records 40 seconds for 20 oscillations.For this observation, which of
the following statement(s) is (are) true ?.
A) Error AT in measuring T, the time period, is O.05 seconds
B) Error AT in measuring T, the time period, is 1 second.
C) Percentage error in the determination of g is 5%.
D) Percentage error in the determination of g is 2.5%.
ANSWER:A and C
A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After
their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms⁻¹.
Which of the following statement(s) is (are) correct for the system of these two
masses ?
A) Total momentum of the system is 3 kg ms⁻¹.
B) Momentum of 5 kg mass after collision is 4 kg ms⁻¹
C) Kinetic energy of the centre of mass is O.75 J
D) Total kinetic energy of the system is 4 J
ANSWER: A and C
B
60
C
angle of 60o (see figure). If the refractive index of the
P*
135
material of the prism is 3, which of the following is
(are) correct ?
A) The ray gets totally internally reflected at face CD
90
75
B) The ray comes out through face AD.
A
D
D) The angle between the incident ray and the emergent ray is 120
ANSWER: A and B and C
One mole of an ideal gas in initial state A undergoes
A
a cyclic process ABCA, as shown in the figure. Its
pressure at A is P.. Choose the correct option(s) from.
B
4Vo
the following.
A) Internal energies at A and B are the same
B) Work done by the gas in process AB is P.V. ln 4
A
A
Po
C
C) Pressure at C is
4
To
To
D) Temperature at C is
4
ANSWER: A and B and C and D
SECTION - III
(Paragraph Type)
Paragraph for Questions 70 to 72
When a particle of mass m moves on the x-axis in a
potential of the form V(x) = kx2, it performs simple
V(x
harmonic motion. The corresponding time period is
m
Vo
dimensional analysis. However, the motion of a particle
can be periodic even when its potential energy increases
Xo
on both sides of x = O in a way different from kx and its
total energy is such that the particle does not escape to
infinity. Consider a particle of mass m moving on the
x-axis.Its potential energy is V(x) = ax (a>O) for |x
near the origin and becomes a constant equal to V for
Ix| X, (see figure).
If the total energy of the particle is E, it will perform periodic motion only if
A) E<0
B) E>0
C) V>E>O
D) E>V
ANSWER: B or C or (B and C)
Option C implies option B.
proportional to
A) A
m
B)
ATa
1
m
C
m
a
D)
AVm
1
ANSWER: B
The acceleration of this particle for |x|>X, is
Vo
B) proportional to
mXg
A) proportional to V.
C) proportional to mX,
Vo
D) zero
ANSWER: D
Paragraph for Questions 73 to 74.
Electrical resistance of certain materials, known as
superconductors, changes abruptly from a nonzero value to
TcB
zero as their temperature is lowered below a critical Tc(0) -
is that their critical temperature becomes smaller than T. (O).
if they are placed in a magnetic field, i.e., the critical
temperature T
In the graphs below, the resistance R of a superconductor is shown as a function
of its temperature T for two different magnetic fields B, (solid line) and B, (dashed
line). If B, is larger than B,, which of the following graphs shows the correct
variation of R with T in these fields ?
R
R
A)
B1
B)
B1
B2
o
R
R
B
C)
B1
:
B2
D)
B2
0
ANSWER:A
A superconductor has T. (0) = 100 K. When a magnetic field of 7.5 Tesla is applied,
its T decreases to 75 K. For this material one can definitely say that when
A) B = 5 Tesla, T
The focal length of a thin biconvex lens is 2Ocm. When an object is moved from a
distance of 25cm in front of it to 5Ocm, the magnification of its image changes
m²5
from m,, to m5o. The ratio
m50
is
ANSWER: 6
An a-particle and a proton are accelerated from rest by a potential difference of
1oov. After this, their de Broglie wavelengths are aand prespectively. The
Np
ratio
.to the nearest integer, is
ANSWER: 3
77. when two identical batteries of internal resistance 1 each are connected in series
across a resistor R, the rate of heat produced in R is J,. When the same batteries are
connected in parallel across R, the rate is J,. If J, = 2.25 J, then the value of R in is
ANSWER: 4
Two spherical bodies A (radius 6 cm) and B (radius 18 cm) are at temperatures T,
and T,, respectively. The maximum intensity in the emission spectrum of A is at
500 nm and in that of B is at 1500 nm. Considering them to be black bodies, what
will be the ratio of the rate of total energy radiated by A to that of B ?
ANSWER: 9
are
superimposed, the amplitude of the resultant wave is
ANSWER: 5
A O.1 kg mass is suspended from a wire of negligible mass. The length of the wire
is 1m and its cross-sectional area is 4.9x10-m². If the mass is pulled a little in
the vertically downward direction and released, it performs simple harmonic
motion of angular frequency 14O rad s-'. If the Young's modulus of the material
of the wire is nx10Nm-2, the value of n is
ANSWER: 4
A binary star consists of two stars A (mass 2.2M) and B (mass 11M), where M is
the mass of the sun. They are separated by distance d and are rotating about
their centre of mass, which is stationary. The ratio of the total angular momentum
of the binary star to the angular momentum of star B about the centre of mass is
ANSWER:6
6
Gravitational acceleration on the surface of a planet is
gravitational acceleration on the surface of the earth. The average mass density of.
2
the planet is
times that of the earth. If the escape speed on the surface of the earth.
3
is taken to be 11 kms-l. the escape speed on the surface of the planet in kms-' will be
ANSWER: 3
A piece of ice (heat capacity = 2100 J kg⁻¹ C-1 and latent heat = 3.36 10 J kgl) of
mass m grams is at -5C at atmospheric pressure. It is given 420 J of heat so that
the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is
found that 1 gm of ice has melted. Assuming there is no other heat exchange in
the process, the value of m is
ANSWER:8
A stationary source is emitting sound at a fixed frequency f, which is reflected
by two cars approaching the source. The difference between the frequencies of
sound reflected from the cars is 1.2% of f,. what is the difference in the speeds
of the cars (in km per hour) to the nearest integer ? The cars are moving at
constant speeds much smaller than the speed of sound which is 330 ms1.
ANSWER:7
********************************************
