[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.
1. The correct structure of ethylenedialninetetraacetic acid (EDTA) is
COON
HOOC`.."CHZ CH2"COOH
\I
C)/N-CH2-CH2-N\
HOOC-CH2\N_CCH~_CH___N/H
D)
HOOC""CH2 CH2-COOH
Ml
`
|`
\
' ' CH2 CH2 -COOH
HOOC'
ANSWER: C
[CI`(H2O)4C1(NO2)]CI
is
C)[CI`O)4C1(ONO)]CI
ANSWER: B
of
3.
B)BrCH~CH2CH3 mld CH3CCII2C -=CH
D ) BrCH2CH2C H2CH3 and CH3C fI2C @ CH
ANSWER: D
4) The correct statement about the following disaccharide is
o H cHzOH O H
/CI|20 OH fB)
ANSWER: A
D) OH and CH3Br
ANSWER: D
6.
Plots showing the variation of the rate constant Ck) with temperature CT) are
en below. e plot that follows Arrhenius equation is
1
A)
k
D)
1
C)
ANSWER:
A
7. The species which by definition has ZERO standard mo enpy of formation
at 298 K is
k
A} Br!2 (gJ
B} C(7 (g)
C) H2O lg)
D) CH4 (gJ
ANSWER: B
8. The bond energy (In kea1 mol-IJ of a C-C slngle bond Is approtely
A) 1
B) 10
C) 100
D) 1000
ANSWER: C
9. The reagent(s) used for softening the tempor hardness of water is(are)
A) Ca3(PO4)2
B) Ca(OH)2
C) Na2CO3
ANSWER: B
11. In the Newman projection for 2.2-dimethv.Ibutane
X and Y can respectively be
A) H and H
B) H and C2H5
C) C2H5 d H
D) CH3 mld CH3
ANSWER: B and D
12) Among the following, the intensive property is (properties are)
A) molar conductivity
B) electromotive force
C) resistance
D) heat capacity
ANSWER: A and B
D) NaOCI
13.
Aqueous solutions of HNO3 , KOH. C H3 C O O H, and C H3C O ONa of identical
concentrations are provided. The pair(s) of solutions which form a buffer upon
g is(are)
A)HNO3 and CH3COOH
B) KOH and CH3COONa
B)HNO3 and CH3COONa
D) CHsCOOH and CH3COONa
ANSWER: C and D
SECTION II- PARAGRAPH TYPE
14. Partial roasting of chalcopyrite produces
B)CuQ{O and FeO
ANSWER: A
15.Iron is removed from chalcopyrite
A)FeO
B)Fe2O3
ANSWER: D
B) FeS
C)FeSiO3
16.In self-reduction, the reducing species is
A )S
B)O 2-
ANSWER: C
Paragraph for guestions 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:
M(s) |M+ aq: 0.05 molar) ||M- aq: 1 molar) IM(s)
For the above electrolytic cell the magnitude of the cell potential IE ] = 70 mV.
17.FOl` file above cell
A)E < 0: D G > 0
B) E < 0: D Go > 0
B) E > 0: DG < 0
D) E > 0: DGo < 0
ANSWER: B
18. If the 0.05 molar solution of M+ is replaced by a 0.0025 molar M+ solution. then
the tude of the cell potential would be
A)35 mV
B)140 mV
ANSWER: C
B) 70 mV
D) 700 mV
SECTION- IV(INTEGER TYPE)
ANSWER: 2
19.
ANSWER: 5
20.
ANSWER: 1
22. Amongst the following the total number of compounds soluble in aqueous NaOH is
ANSWER: 4
23. Amongst the following, the total number of compounds whose aqueous solutlon
turns red litmus paper blue is
ANSWER: 3
24) Based on VSEPR theoly. the number of 90 degree F-Br-F anes in BrF5 is
ANSWER: either 0 or 8
25.The value of n in the molecular formula Be 3Si6Ol3 Is
ANSWER: 3
26. A student performs a titration with different burettes and finds titre values of
25.2 Inf. 25.25
and 25.0 inf. e number of
ant figures in the e
titre value is
ANSWER: 3
27 . The concentration of R In the reaction R P was measured as a function of
time and the following data is obtained:
[RI (molm`) 1 .O
t(n.) O . O
O. 7 5 0.40
0.05
0.10
0.12 0.18
ANSWER: o
28. The number of neutrons emitted when 2U undergoes controlled nuclear fission
ANSWER: 4
| SECTION -I| (Single Correct Choice Type)
29.
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 1`espectively, then
a
c
the value of the expression a/c sin2C+ c/a sin2A is
c
/3
1
Al
B)
a
C)1
ANSWER: D
x y"Z
30. Bquation of the plane containing the straight line == and perpendicular to
xVz
the plane containing the straight lines =-=-2 and ==-3
A)
x + 2y ~- 2z=0
B) 3x+ 2y
2z=o
C) x
-
xyz
is
+ z=0
D) 5X+ 2y - 4z=0
ANSWER: C
31. Let wbe a complex cube root of uni~ with w=l. A fan` die is tllrowll three tilnes.
If rl , r2 and r3 are the numbers obtained on the die. then the probabih mat
I
1
2
C)
B)
I
D)
Al I
ANSWER: C
A)parallelogram, which Is neither a rhombus nor a rectangle
B)square
C)rectangle, but not a square
DJ rhombus, but not a square
ANSWER: A
33. The number of 3x3 matrices A entries are either O or 1 and for the
Ix| II|
A|y|=|o| has exactlv two distinct solutions, is
Izl
IO|
A)0
B)28 ` 1
C) 168
D) 2
ANSWER: A
A)0
1
B)-' 12
1
C)
'24
I
D)
' 64
--
ANSWER: B
35. Let p and q be real numbers such that p = 0 p 3 # q and p 3 # - q . If a and b are
nonzero complex number sans a + b = - p and a3 + b3 = q , then a quadratic
a
equation ha-b and as Its roots is
A)(p3 + q) x 2 - (p 3 + 2q)x + (p3 + q) = 0
B) (p3 + q) x 2 - (p 3 - 2q)x + (p3 + q) = 0
B)(p 3 - q ) x2 - (5p 3 - 2q) x + (p 3 - q) = 0
D) (p 3 - q) x 2 - (5p 3 + 2q) x + (p 3 - q) = 0
ANSWER: B
36. Let f, g and 11 be real-valued functions deflned on the Interval lo, ll by
f (x) = ex2 + e-x2 , g(x) = Xex2 + e-x2 and h(x) = X2ex2 + e-x2 . If a. b and c denote.
respe ely. the absolute um of f, g and h on IO, 11, then
ANSWER: D
| SECTION - II | Multiple Correct Choice Type)
37. let A and B be o distinct points on the parabola y2 - 4x. If the axis of the
parabola touches a circle of radl'us r ha AB as its diameter, then the slope of
the line joining A and B can be
1
1
A) - -
B)
ANSWER: C and D
38.
2
C)-
DJ
r
2
1
1. r
Let ABC be a triangle such that ACE= and let a, b and c denote the lengths of
<
6
the sides opposite to A. B and C respe
.e
s) of x for ch
a=
x2 + x + 1. b = X2 - 1 and c = 2x + 1 is (are)
ANSWER: B
39. Let 21 and Z2 be tw"o mstmct complex numbers and let z = (1 - t) 21 + tZ2 for some
real number t th O < t < 1. If Arg(w) denotes the principal argument of a
nonzero complex number w. then
A)
|z ` Ell
C}
Z ` 21
Z
+
|z - 22| = |21 - 22|
Z-z
2 ` zl
=O
22 ` 21
ANSWER: A and C and D
Bl Arg (z - zl) =Arg (z ~- 22)
D) Arg (z ~- zl) - Arg(22 - Zl)
40. Let f be a real-valued function defined on the interval (0. ) by
x
f(x) = In x+ "l t dt , Then which of the renewing statement(s) is (are) true ?
AJ f _(x) exists for all xe (O . )
B) f '(x) exists for an xe (O ) and f' is continuous on (O.). but not
differentiable on (O. )
C)dlere exlsts a > 1 such that
DJ there exists
b
/f' (x)I<If(xJ/
> o such that
for all Xe (a . )
If(xJ/+If'(x)/ b
for aH x CO )
ANSWER: B and C
C)O
ANSWER: A
Paragraph for Questions 42 to 44
p be
odd
prime ntmlber and
Tp
be the foHowing set of 2x2 matrices
~ A~ ~ : a,b,c E lo. L 2. ,...p-1}}
42.
The number of A in Tp such that A is either symmetric or skew-symmetric or
both. and det (A) dl
A)(p ~- 1)2
-1
Bible by p is
8) 2 (p - 1)
C) (p - IJ2 + 1
DJ 2p
ANSWER: D
43.
The number of A HI Tp such that the trace of A is not divisible by p but det (A) is
divisible by p is
(Note : The trace of a matrix is the sum of its dl Dual entries.)
A) (p - 1) (p2 - p + 1)
ANSWER: C
B) p3 - (p - 1)2
C) (p - 1)2
D) (p - 1) (p2 - 2)
44) The number of A in Tp such that det CA) is not divisible by p is
A) 2p2
B) p3 5p
C) p3 - 3p
D) p3 - p2
ANSWER: D
Paragraph for questions 45 to 46
22
Xv
e
circle X2 + y2 - ax = O and hyperbola -- w`
^
^
= I intersect at the points A and B.
9
4
45.
~tion of a coroman ~ ent wl'tll positive slope to the circle as wen as to the
hyperbola is
A) 2x-y-20 = O B) 2x-y + 4 = O
ANSWER: C
46. Equation of the circle with AB as its diameter is
A) x2 + y2 - l2x + 24 = O
ANSWER: A
ANSWER: 3
B) x3 + y2 + l2x + 24 = O
ANSWER: 2
X2 y2
1
- 2 = 1 . If this line passes
ao
through the point of intersection of the nearest directrix and the x-axis. then the
0. The line 2x + y
=
1 is tangent to the herbola
ANSWER: 2
ANSWER: 6
to X.
ANSWER: 4
53.
Let wbe the complex number cos
+ i sin -2p . Then the number of distinct
^33
z+1
w
w2
complex numbers z satisg
w
z + w2
I
= D is equal to
w2
1
z+w
ANSWER: 1
ANSWER: 3
55. The number of all possible ues of 0 , where O < 0 < p . for which the system of
equations
+ z) cos 3 o=
) sin 3 0
2cos30
2sin30
xsin3O=--+-y
z
sin 30
=
+ ) cos 3 0 + y sin 30
is equal to the cube of the abscissa of P, then the value of f(-3) is equal to
ANSWER: 9
| SECTION -I | (Single CoHect Choice e)
57 . Consider a thin square sheet of side L and
thickness t. made of a material of resistivity p . ~
The
resistance
between
two
opposite
faces.
v
shown b the shaded areas in the figure Is
A) directlv ProPortional to L B) directly proportional to t
C) indePendent of L DJ independent of t
ANSWER: C
58.A real gas behaves like an ideal gas if its
AJ pressure and temperature are both high
BJ pressure and temperature are both low
CJ pressure Is high and temperature is low
DJ pressure is low and temperature is high
ANSWER: D
59. Incandescent bulbs are des~ed 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 re sistance s Rloo . R6o and R4OI ,
respectively. the relation between these resistances is
1
A)
Rl =
1
1
R+
C) Bl00 > R6o >
ANSWER: D
B) Rloo
D)
111
>
>
=
R4o
+ R6o
60. To ~ Ohm's law, a student is provided with a test~ resistor RF. a Iligfl resistance
R], a small resistance R2, two identical galvanometers Gl and G2, and a variable
voltage source V. The correct circuit to out the experiment is
A)
B)
C)
DJ
ANSWER: C
61.
w and fixed amphtude VD ls
An AC voltage source of ~
le
frequen
electric
bulb of resistance R
comlected in series wl'th a capacl~tance C and an
(inductance zero). en w is increased
A)tlle bulb glows
B) tlle bulb glows brigflter
C) total impedance of tlle circuit is unchanged
DJ total impedance of tlle circuit illcreases
ANSWER: B
62.
A thin flexible wire of lengtfl L is connected to two adjacent fixed points and
carries a current I in the cl e direction, as sho in the figtlre. en the
stem is put in a uniform magnetic field of strength B going into the plane of the
paper the e kes the shape of a ch`cle. The tension m the e I`s
IBL
B)
-p
A)IBL
C)
ANSWER: C
63. A block of mass m is on an inclined plane of ar!gle 0 . The coefficient
of friction between the block and the plane is and tanq >m . The
block is held statio by app 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 I= l1lg(sin O - m cos 0 ) to P2= mg(sinO + m cosq ),
the frictional force f versus P graph look like
f
I
J
B)
DJ
ANSWER: A
IBL
IBL
DJ
64. A thin uniform annular disc (see
figure) of mass M has outer
radius 4R and inner radius SR.
The work required to take a unit
mass from point P on its axis to
'lllfini 'IS
ANSWER: A
| SECTION - II|(Multiple Correct Choice Type)
65.
A few electric field lines for a stem of two charges
91 and 92 fixed at two different points on the x-axis
are shown in the . These lines suggest that
Al |91| > |92|
Bl | 91 | < |92 |
CI at a finite distance to the left~ of 91 the electric field~ is zero
D) at a ~finite distance to the ~t of g the electn'c field is zero
ANSWER: A and D
66.
A student uses a simple pendulum of exactly Iln length to deterlnine 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
A) En`o1` DT in meas T, the time perl`od is 0.05 seconds
BI En`or DT In meas T, the tlme period is 1 second
DJ Percentage elTor in the detel`lnination of g is 2.5%
ANSWER: A and C
67 . A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After
their co~ the 1 kg mass leverses its direction and moves with a speed of 2 ms-I.
Wln'ch 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-l
B)Momentum of 5 kg mass after collision is 4 kg ms-1
C)
etic energy of the centre of mass is O75 J
D)Total kinetic energy of the system Is 4 J
ANSWER: A and C
68. A ray OP of monochromatic light is lucident on the
o
face AB of prism ABCD near vertex B at an incident
angle of Goo (see figure). If the refractive it1dex of the
material of the prism is which of the following is
(are) correct ?
A)The ray gets totally intel'nafly reflected at face CD
B)The ray comes out through face AD
C)The angle between the incident ray and the emergent ray is goo
ANSWER: A and B and C
69. One mole of an ideal gas in initial state A undergoes
a cyclic process ABCA, as shown in the figure.
Its
pressure at A is Po. Choose the correct op6on(s) from
the following
A) Internal enel'gles at A and B are the same
B) Work done by the gas in process AB is PoVo en 4
Po
CJ Pressnre at C is
To
D) Temperature at C ~Is
ANSWER: A and B and C and D
aph for Questions 70 to 72
When a particle of mass m moves on the x-axis in a
potential of the form V(xJ = kX2 , it performs simple
harmonic motion~ e corresponding time period is
Jul
proportional to \i -k . as can be seen easily using
dimensional analysis. However. the motion of a particle
can be periodic even when its potential energy increases
on both sides of x = 0 in a way different from
total energy is such that the particle does not escape to
infinity. Consider a particle of mass m moving on the
and its
x-axis. Its potential energy is V(xJ - a Ca >OJ for [x[
near the origin and becomes a constant equal to Vo for
[x[ (see figurel.
70. If the total enc
Al E < 0
of the parUcle is E it `vifl perform periodic motion olllv if
B) E > 0
C) Vo > E > 0
D) E > Va
ANSWER: B or C or (B and C)
Option C implies option B.
71. For periodic motion of small amplitude A, the time pteriod T of this particle is
propol'tional to
ANSWER: B
72. The acceleration of this particle for |x| > is
bJ proportional to
/ Va
C) proportional to --InXa
ANSWER: D
Al proportional to Va
DJ zero
Pph for Questions 73 to 74
Electrical resistance of certain materials, known as
superconductors.
s abruptly from a nonzero value to
zero as their temperature is lowered below a critical
temperature Tc(0). An interestin g property of superconductors
Is that their critical temperature becomes smafler than Tc (OJ
if they are placed in a magnetic field , i. e . , the critical
temperature Tc (B) is a
of the ~ field strength B.
The dependence of Tc (B) on B is shown in the figure.
73.In the graphs below, the resistance R of a superconductor is shown as a function
of its temperature T for two different magnetic flelds Bl (sohd line) and 82 (dashed
lineJ. If 82 is larger than Bl, which of the following graphs shows the correct
variation of R with T in these fields ?
ANSWER: A
74. A superconductor has Tc (O) = 100 K Wllen a maglleUc field of 7.5 Tesla is apphed.
its Tc decreases to 75 K For this material one can defmitely say that when
A) B =
5 Tesla. Tc (B) = 80 K B) B = 5 Tesla, 75 K < Tc (B) < 100 K
~C) B = 10 Tesla. 75 K < ~ (B) < 100 K DJ B = 10 Tesla, Tr (B) = 70 K
ANSWER: B
75.The focal lengtfl of a thin biconvex lens is 2Ocm. When an object is moved from a
distance of 25cm in~ front of it to 5Ocm. the cation of its image changes
from n-125 to mso" The ratio ~ is
ANSWER: 6
76.An a ~particle and a proton are accelerated from rest by a potential diff~ erence of
IOOV. After this, their de Broglie wavelengths are laand IprespecUvely. The
I
"p
.
ratlo
. to the nearest Integer, Is
ANSWER: 3
77 . \\Ilen two 'Identical battenes of internal resistance 1 each are connected In sen'es
across a resisWr R. the rate of heat produced in R is Jl. When the same batteries are
comlected in parallel across R the rate is J2. If Jl =
2.25 J2 then the value of R in W Is
ANSWER: 4
78. Two spherical bodl~es A (radius 6 cm) and B (radius 18 cm) are at temperatures ~
and T2, respectively. The maximum intensi in the emission spectrum of A is at
500 nm and in that of B is at 1500 mu. Considering them to be black bodies, what
will be the ratio of the rate of total~ enc radiated by A to that of B ?
ANSWER: 9
When two progressive waves
yl - 4
sin(2x - 6t) and y2
superimposed, the amplitude of the resultant wave is
ANSWER: 5
=
3
sill(2x-6t
-
-2)p
80. A 0.1 kg mass I_s suspended from a of negligftlle mass. The lengtfl of the w1re
is Im and It,s cross-sectional~ area is 4.9xlO-7m2. If the mass is pulled a little in
the vertl~cally downward direction and released. it performs simple Ilarmonl_c
of the wire is nxlO9 Nm-2, the value of n is
ANSWER: 4
8 1 . A bHlaly star
consists of two stars A (mass 2.2Ms) and B (mass IlMs), where Ms is
the ma~ss of the sun. They are separated by dl_stance d and are rotating about
their centre of mass. which is statio . e ratio of the total angular momentum
of the b_~ star to the anglllar momentum of star B about the centre of mass is
ANSWER: 6
82. Gravitational acceleration on the surface of a planet is \/g , where g is the
11 .-.
gravitational acceleration on the surface of the earth. e average mass densi of
2
the planet is -3 times that of the eal If the escape speed on the surface of the earth
3 kmS-l. the
Is ANSWER:
taken to be 11
escape speed on the surface of the planet in kms-I will be
83. A piece of ice (heat capaci~ = 2100 J kgl oC-I and latent heat =
3.36 x 105 J kgll of
mass m grams is at C at atmospheric pressure. It is given 420 J of heat so that
the ice starts melting. when tlle l~ce-water mixfure is in equilibrl_um, it is
found that 1 gm of ice has melted. Assuming there is no other heat exchange m
the process. the value of m is
ANSWER: 8
A statio source is emittlllg sound at a flXed frequency fa, which is reflected
by two cars approaching the source. The difference between the frequencies of
sound reflected from the cars is 1.2% of ~. 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 ms-.1
ANSWER: 7