PART A -
PHYSICS
1. A body of mass m = 3.513 kg …….
Ans :
3
Sol: min
(4, 3)
=
3
2. Consider a uniform square plate of side …….
Ans :
Sol: I
= I
cm + md2
=
=
3. The speed of sound in oxygen ……..
*Ans : 1419 m/s
Sol:
=
v
He
=
=
1419 m/s
* None of the given answers matches
with our answer.
4. A thin spherical shell of radius R has ……..
Ans :
Sol: E = 0, r < R
E =
r > R
5. Relative permittivity and permeability of a
……
Ans : e
r
= 1.5, m
r =
0.5
Sol: m
r < 1 for diamagnetic
e
r > 1 for all materials
6. Suppose an
electron is attracted towards the …..
Ans : Tn independent of n, rn µ
n
Sol:
Ž
independent of n
mvr =
Ž
r µ
n
7. A block of
mass 0.50 kg is moving with a speed…
Ans : 0.67 J
Sol:
=
8. A wave
traveling along the x-axis is …..
Ans : a
= 25.00
p
, b
= p
Sol: a
=
b
= w
=
Ž
a
= 25.00
p
, b
= p
9. A working
transistor with its three legs….
Ans : it
is npn transistor with R as base.
Sol: Emitter to collector will always be non conducting.
10. A jar is filled
with two non-mixing …….
Ans : r
1 < r
3 < r
2
Sol: r
3 floats in r
2 and sinks in r
1
=
r
1
< r
3
< r
2
11. An athlete in
the Olympic games…….
Ans : 2000
J – 5000 J
Sol: v
is of the order of 10 ms-
1 and mass is around
50 kg Ž
2000 J – 5000 J
12. A parallel
plate capacitor with air between……
Ans : 40.5
pF
Sol: C
1
= 9 ´
3 ´
3 = 81
C
2
=
C
=
= 40.5 pF
13. The dimension
of magnetic field in …….
Ans : MT-
1C-
1
Sol: F = Bqv
[B] =
= MT-
1C-
1
14. A body is at rest at x = 0. At t = 0 …….
Ans :
Sol: x
1
-
x2 =
15. In the circuit below, A and B represent …..
Ans : OR
gate
Sol: Either
A or B is high, it pulls C high
Ž
OR gate
16. While measuring the speed of sound ……
Ans : x
> 54
Sol: Speed
increases slightly with
temperature
Ž
l
increases Ž
for
second resonance x > 54
17. Shown in the figure below is a meter-bridge…..
Ans : 220
W
Sol:
R
= 220 W
18. A spherical solid ball of volume V is …….
Ans :
Sol: Kv
2 = mg -
FB
= (r
1-
r
2) Vg
v =
19. A thin rod of length ‘L’ is lying along ……
Ans :
Sol: x
cm
=
=
20. A planet in a distant solar system is ……
Ans
: 110 km s-
1
Sol: v
esc =
=
Ž
v2
= 110 km/s
21. An insulated container of gas has two……
Ans :
Sol: n
1 CV T1 +
n2 CV T2 = (n1 + n2) CV T
T =
22. Two full turns of the circular scale …..
Ans : 3.38
mm
Sol: 3
+
=
3.38 mm
23. A horizontal overhead powerline is ……
Ans : 5
´
10-
6 T southward
Sol:
B
=
= 5 ´
10-
6 T
24. An experiment is performed to find …..
Ans : a
vernier scale provided on the
microscope
Sol: Vernier
scale on the microscope
25. A 5 V
battery with internal resistance …..
Ans : 0.03
A P2 to P1
Sol: E
eff
=
Ž
I
=
0.03 A P2 to P1
26. A capillary tube (A) ……
Ans :
Sol: Surface tension is lowered.
27. Two coaxial solenoids are made ……
Ans : 2.4
p
´
10-
4 H
Sol: M
=
= 2.4 p
´
10-
4 H
28. A student measures the focal ….
Ans :
Sol: u
< 0, v > 0
29. This question contains statement – 1
Ans : Statement
– 1 is true, Statement – 2 is
true;
Statement – 2 is a correct
explanation
for Statement -1
Sol: Gauss
law for gravitation
30. This question contains statement -
1
Ans : Statement
– 1 is true, Statement – 2 is
false’
Sol: BE
per nucleon increases for lighter
nuclei and decreases for heavy nuclei.
31. For current entering ….
Ans :
Sol: j
´
2p
r2 = I
E
= r
j =
32.
D
V measured between B and C is
Ans :
Sol: D
V =
=
33. If a strong diffraction peak is observed when
electrons
are incident at an angle `i’ -
Ans: 2d
cos i = n l
dB
Sol: 2d
cos i = n l
dB
34. Electrons accelerated by potential V are
diffracted
from a crystal. -
Ans: 50
V
Sol:
=
50 V
35. In an experiment, electrons are made to pass through a narrow slit of
Ans:
PART B -
CHEMISTRY
36. The ionization enthalpy of hydrogen …….
Ans: 9.84 x 10
5 J mol–1
Sol :
= 1.312 ´
106
= 1.312 ´
´
106
= 9.84 ´
105 J mol–1
37. ….. pairs of
species have the same bond order?
Ans: CN
‑ and NO+
Sol : Both CN
‑ and NO+
contain 14 electrons each and hence they have the same bond order.
38. …….. a group of the isoelectronic species?
Ans: NO
+ , C22–,
CN–, N2
Sol : Total no. of electrons in NO
+ = 14
(7+8–1), C22– = 14 (6+6+2), CN– = 14 (6+7+1)
and
N2 = 14 (7+7).
39. Four species are…….
i. ii. iii. iv.
…… the correct
sequence of their acid strength?
Ans: i < iii < ii < iv
Sol : Fluoro sulphonic acid is the strongest,
followed by H3O+,
and
.
i
< iii < ii < iv
40. The pKa of a weak acid, HA is ………………
Ans: 7.01
Sol : pH =
[pKw + pKa – pKb]
=
[14 + 4.8 – 4.78] =
7.01
41. …… decreasing order of priority for the functional groups of
…….
Ans: -
COOH, -
SO3H, -
CONH2,
-
CHO
Sol : Priority order is
-
COOH
> -
SO3H > -
CONH2 > -
CHO
42. ……. CH3MgX with CH3C
C–H …….
Ans: CH
4
Sol : CH
3-
C ŗ
C-
H + CH3MgX ®
CH
3-
C ŗ
CMgX +
CH4
43. …….can react with sodium in liquid ammonia
Ans: CH
3-
CH2-
C ŗ
CH
Sol : CH
3-
CH2-
C ŗ
CH is a
terminal alkyne containing acidic hydrogen. So it reacts with sodium in liquid
ammonia forming the corresponding sodium derivative.
44. The vapour pressure of water at 200C is ………
Ans: 17.325 mm Hg
Sol :
=
=
17.5
– p = 0.175
P =
17.325
45. Gold numbers of protective colloids A, B, C and D …….…
Ans: A < C < B < D.
Sol : Lesser the gold number greater is the
protective action. Protective action follows the order A < C < B < D.
46. ……. atoms of element Y form ccp …….
Ans: X
4Y3
Sol :
= X4Y3
47. …… the industrial preparation of hydrogen from water gas
……..
Ans: CO is oxidized to CO
2 with steam
in the presence of a catalyst followed by absorption of CO2 in
alkali.
Sol : From water gas (CO + H
2), CO is
oxidized to CO2 with steam and which is then absorbed in alkali.
48. …… substituted silane the one ……… to cross linked silicone
……..
Ans: RSiCl
3
Sol : Among the substituted silanes, RSiCl
3
on hydrolysis give rise to cross linked silicone polymers.
49. Amount of oxalic acid present in a solution can ….
Ans: reduces permanganate to Mn
2+ .
Sol : Mn
+7 oxidises both
and Cl‑.
50. Given
= –0.72 V
= –0.42 V. The potential for the cell ………..
Ans: 0.26 V
Sol : Cell reaction is 3Fe
2+ + 2Cr ®
2Cr3+
+ 3Fe
E
cell
=
= (0.72 -
0.42) +
= 0.3 -
0.04
= 0.26 V
51. …… the correct statement?
Ans: Chlorides
of both beryllium and aluminium have bridged chloride structures in solid
phase.
Sol : Beryllium and aluminium chlorides have
bridged structures in solid phase.
52. Identify the wrong statement ………
Ans: Ozone
layer does not permit infrared radiation from the sun to reach the earth.
Sol : The incorrect statement is “Ozone layer does
not permit I
.R radiation from the sun to reach the earth”. Actualy ozone
layer prevents u.v. radiation from the sun to reach the earth.
53. The coordination number and the oxidation state of the
element ……..
Ans: 6 and 3
Sol : en and
are bidendate ligands.
\
Coordination
number of E is 6 and oxidation state of E is 3 (en is neutral and
)
54. ……. Octahedral complexes of Co ….
Ans: [Co(CN)
6]3‑
Sol : The strongest ligand is CN
‑
and hence D
0
will be the highest for [Co(CN)6]3‑.
55. Larger number of oxidation states are exhibited …..
Ans: lesser
energy difference between 5f and 6d than between 4f and 5d orbitals.
Sol : The energy difference between 5f and 6d
(actinoids) is less than between 4f and 5d (lanthanoids) and hence actinoids
exhibit larger number of oxidation states.
56. ……. no significance for roasting sulphide ores to ……
Ans: CO
2 is more volatile than CS2
Sol : The insignificant statement is ‘CO
2
is more volatile than CS2’.
The reduction
process is based on the thermodynamic stability of the products and not on
their volatility.
57. Oxidising power of chlorine in aqueous solution ….
Cl2(g) ……………………Cl–(aq)
The energy
involved in the conversion of ………
Ans: -
610 kJ mol‑1
Sol : Energy involved the conversion of
Cl2(g) ®
=
-
349 -
381
=
-
610 kJ mol‑1
58. …… the alkene affords the compound ….
Ans: CH
3CHO
Sol : CH
3-
CH=CH-
CH3
2CH3CHO.
59. Phenol, when it first reacts with concentrated sulphuric
acid …..
Ans:
*2,4,6-trinitrophenol.
Sol: :
* None of
the given answers matches with our
answer.
60. Toluene is nitrated and the resulting ……
Ans: mixture of o-
and p-
bromotoluenes
Sol :
61. The organic chloro compound, which …..
Ans: CH
3Cl
Sol : Primary alkyl halides undergo S
N2
reaction with inversion of configuration.
62. The absolute configuration of ………
Ans: R, R
Sol : The absolute configuration of both the
carbons are ‘R’.
63.
-D-(+)-glucose and
-D-(+)-glucose are
Ans: anomers
Sol : a
-D(+)glucose and b
-D(+)glucose
are anomers.
64. The electrophile,
attacks …….
Ans:
Sol :
group is a deactivating group.
Hence the
intermediate formed from benzene will have lower energy than that formed from
nitro benzene.
65. Standard entropy of X2, Y2 and XY3
…….
Ans: 750K
Sol
: T =
D
S = -
40 J
\
T =
=
750K
66. For the following three reactions a, b and c, …..
Ans
: K3 = K1 K2.
Sol : The
first two reactions are added to get the third reaction, hence K3 =
K1 ´
K2.
67. Bakelite is obtained from phenol …..
Ans: HCHO
Sol : Bakelite is a polymer of phenol and
formaldehyde.
68. The equilibrium constant
and
for ……
Ans: 1 : 36
Sol : X
2Y, Equilibrium constant =
Z
P + Q, Equilibrium constant =
When the degree
of dissociation is the same for the two reactions, then
=
and
= p2.
i.e.,
;
69. For a reaction
A
2B, rate of ………
Ans:
Sol : For the give reaction,
2 X
=
or
70. At 800C, the vapour pressure of pure liquid ‘A’
is 520 mm Hg and that of ……..
Ans: 50 mol percent
Sol :
= 760
520X
A
+ 1000(1 -
XA) = 760
x
A
=
Mole
percent = 50
PART C -
MATHEMATICS
71. Let f : N ®
Y be a
function defined as ……….
Ans: g(y) =
Sol:y
= 4x + 3
x
=
g(y) =
72. Let R be the real line. Consider the
following…..
Ans: T is an equivalence relation on R but S is not
Sol:S = {(x, y): y = x + 1 0 < x < 2
(x,
x) ®
x = x + 1 ®
not reflexive
(x,
y) ¹
(y, x) ®
not symmetric
73. The conjugate of a complex number is
…….
Ans:
Sol:
Conjugate
number =
=
74. The quadratic equations x2
-
6x + a = 0 and ……
Ans: 2
Sol:Let a
, b
be the roots of x2 -
6x + a
= 0 and a
, g
be the roots of x2 -
cx + 6
= 0
Ž
a
+ b
= 6 a
+ g
=
c
and
a
b
=
a a
g
=
6
and
\
a
\
The
first equation is x2 -
6x + 8 = 0
Ž
2 and 4 are the roots.
If
b
= 2, then g
=
Ž
Not
possible, since roots are integers
If
b
= 4 Ž
g
= 3 Ž
possible
\
The
common root is 2
75. Let A be a square matrix all of whose
entries……
Ans: If det A = ±
1, then
A-
1 exists and all its
entries are integers
Sol:If det A ¹
±
1, then det A may be zero Ž
A-
1 does not
exist.
When
det A = ±
1, then A is orthogonal
Ž
A-
1 =
AT Ž
A-
1 will have all enteries as integers
76. Let a, b, c be any real numbers.
Suppose…….
Ans: 1
Sol: x -
cy -
bz = 0
-
cx + y -
az = 0
-
bx -
ay + z = 0
Given
that x, y, z not all zero.
Ž
The given
homogeneous system has non-trivial
solutions.
Ž
= 0
Ž
1(1 -
a2)
+ c(-
c -
ab) -
b(ac + b) =
0
Ž
-
a2
-
b2
-
c2
-
2abc + 1 =
0
Ž
a2
+ b2 + c2 + 2abc = 1
77. How many different words can be
formed by ……
Ans: 7.6C4.8C4
Sol: 4I, 2p, 4s and 1 M are there
in MISSISSIPPI
.
Arrange
the remaining 7 letters ®
*
-
* -
* -
* -
* -
* -
* -
*
In the eight places in
between (marked as *) we can arrange the 4s’s in 8C4.wsays
\
Total
number of words =
=
7.6C4.8C4
78. The first two terms of a geometric
progression….
Ans : -
12
Sol: a + ar = 12
ar
2
+ ar3 = 48
r
2
(a + ar) = 48
r
2
= 4
r
= ±
2
r = -
2, since terms are alternately
positive and negative
a
=
79. Let f(x) =
……..
Ans : f is differentiable at x = 0
but not at x = 1
Sol :
f(x) =
=
=
f’(1) =
=
=
does
not exist
80. How many real solutions does the
equation……..
Ans: 1
Sol:f(x)
= x7 + 14x5 + 16x3 + 36x -
560
f'(x) =
7x6 + 70x6 + 48x2 + 30
>
0 for all x Ī
R
f(x)
is monotonic increasing
f(x)
= 0 has only one real solution
81. Suppose the cubic x3 -
px + q
has three distinct..
Ans: The cubic has minima at
and maxima
at -
Sol:f(x)
= x3 -
px + q
f'(x) =
3x2 -
p
f”(x) =
6x
3x
2
= p Ž
x = ±
f(x)
is minimum at x =
and
maximum at x = -
82. The value of
is ………..
Ans: x + log
Sol:
=
=
= x + log
83. The area of the plane region bounded
by the …..
Ans:
Sol:x
+ 2y2 = 0 Ž
x = -
2y2
x + 3y
2 = 1 Ž
x = 1 -
3y2
Shaded
portion is the required area
Required
area =
=
=
84. Let I
=
and J =
…….
Ans : I
<
Sol : I
=
<
< 2
J =
<
< 2
In (0, 1) Ž
sin x
< x
I
<
85. The differential equation of the
family of circles…
Ans: (y -
2)2
y’2 = 25 -
(y -
2)2
Sol : (x -
h)2
+ (y -
2)2 = 25
2(x
-
h) + 2(y -
2)
= 0
(x
-
h) = -
(y -
2)
Differential
equation is
(y
-
2)2
= 25
86. The solution of the differential
equation
……
Ans: y = x ln x + x
Sol:Put y = Vx
\
V +
V
+
= 1 + V
x
\
V = log
x + C
y(1)
= 1 Ž
C = 1
\
= log x + 1
y
= xlogx + x
87. The perpendicular bisector of the
line segment ...
Ans: -
4
Sol : Slope of the line =
= k -
1
Passes
through
Perpendicular
bisector is
y
-
= (k -
1)
2y
-
7 = 2x(k -
1) -
(k2 -
1)
2x(k
-
1) -
2y = k2 -
8
= -
4
k
2
-
8 = 8
Ž
k = ±
4
88. The point diametrically opposite to
the point
P(1, 0) on the circle……..
Ans: (-
3, -
4)
Sol:Centre (-
1, -
2) .
P(1, 0)
\
opposite point Q(x, y)
\
mid
point of PQ = Centre
\
x
= -
3, y = -
4
\
Point (