The complex showing a spin-only magnetic moment of 2.82 B.M. is
A) Ni(CO)4
B) [NiC14]2-
C) Ni(PPhg)4
D) [Ni(CN)4]2-
ANSWER: B
The species having pyramidal shape is.
A) SO₃
B) BrF3
C) SiO,2-
D) OSF2
ANSWER: D
(1)NaOH/Br2
In the reaction HC
T
the structure of the
NH2
Product T is
B)
NH
A)
HC
CH₃
D)
HC
C)
HC
NH
ANSWER: C
The compounds P, and S
COOH
OCH,
HO
HC
P
Q
S
were separately subjected to nitration using.
HNO/H,SO4 mixture. The major
product formed in each case respectively, is.
COOH
OCH
A)
HO
HC
NO₂
NO₂
ON
OCH3
COOH
HC
B)
HO
NO₂
NO₂
NO₂
COOH
OCH
NO
C)
HO
NO
HC
NO₂
COOH
OCH
D)
HO
NO
NO₂
HC
NO
ANSWER: C
The packing efficiency of the two-dimensional square unit cell shown below is
----
A) 39.27%
B) 68.02%
C) 74.05%
D) 78.54%
ANSWER: D
Assuming that Hund's rule is violated, the bond order and magnetic nature of
the diatomic molecule B, is
A) 1 and diamagnetic
C) 1 and paramagnetic
B) O and diamagnetic
D) O and paramagnetic
ANSWER: A
SECTION - II (Integer Type)
The total number of diprotic acids among the following is.
HgPO4
HSO4
HgPO3
H2CO3
H2S2O7
HgBO3
HgPO2
H2CrO4
H,SO₃
ANSWER: 6
Total number of geometrical isomers for the complex [RhCl(CO)(PPhg)(NHg)] is
ANSWER: 3
Among the following, the number of elements showing only one non-zero oxidation
state is
O,
C1,
F.
N,
P.
Sn,
T1.
Na,
Ti
ANSWER: 2
Silver (atomic weight = 108 g mol-l) has a density of 10.5 g cm-3. The number of.
silver atoms on a surface of area 10-12 m² can be expressed in scientific notation
as y 10x. The value of x is
ANSWER: 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 w, and that along the dotted line path is wg, then the integer
closest to the ratio wa/ws is
4.5
4.0
a
3.5
P
3.0
(atm.)
2.5
2.0
1.5
1.0
0.5
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
V (lit.)
ANSWER:2
SECTION - III
(Paragraph Type)
Paragraph for guestions 12 to 14.
Two aliphatic aldehydes P and Q react in the presence of aqueous KCO3 to give
compound R, which upon treatment with HCN provides compound S. On acidification
and heating, S gives the product shown below :
HC
HO
HC
The compounds P and g respectively are
CH₃
CH₃
HzC.
-
H
and
CH
and
A)
B)
HzC
0
O
O
H3C
CH
HzC
HzC.
CH
H-
C)
CH
and
D)
CH
and
CH₃
O
CH₃
O
1
O
ANSWER: B
The compound R is
HC
HC
A)
B)
HC
H3C
CH2.
H3C
OH
OH
CH₃
CH₃
O
C)
H3
CH2.
OH
ANSWER: A
The compound S is
CH₃
H3C
A)
HC
B)HC
CH2
CH2
N
CN
CH₃
CN
CN
HC
CH
D) HC
OH
CH2
CH2.
OH
OH
ANSWER: D
Paragraph for guestions 15 to 17.
The hydrogen-like species Li2+ is in a spherically symmetric state S with one radial
node. Upon absorbing light the ion undergoes transition to a state S,. The state S, has
one radial node and its energy is equal to the ground state energy of the hydrogen atom.
The state S, is
A) 1s
B) 2s
C) 2p
D) 3s
ANSWER: B
Energy of the state S in units of the hydrogen atom ground state energy is
A) 0.75
B) 1.50
C) 2.25
D) 4.50
ANSWER: C
The orbital angular momentum quantum number of the state S, is
A) o
B) 1
C) 2
D) 3
ANSWER: B
SECTION - IV
(Matrix Type)
Match the reactions in Column I with appropriate options in Column II.
Column 1
Column II
NaOH/HO
A)
NCI+
HO
0C
N=N-
-OH
p) Racemic mixture
B)HC-CC-CH
CHCH
HO HO
HSO
HC
O-
CH₃
-CH
q) Addition reaction
C)
1.LiAIH
H.
HO
r) Substitution reaction
CH,
2.HO
CHy
D)
HS
CI
Base
s) Coupling reaction
t) Carbocation intermediate
ANSWER:
A:
r and s
B:
t
C:
p and q
D:
r
All the compounds listed in Column I react with water. Match the result of the
respective reactions with the appropriate options listed in Column II.
Column 1
Column II
A) (CH),SiCl
p) Hydrogen halide formation
B) XeF4
q) Redox reaction
C) C1,
r) Reacts with glass
DJ VC15
s) Polymerization
t) O, formation
ANSWER:
A:
p and s
B:
p and q and r and t
C:
p and q
D:
p
PART - II : MATHEMATICS
SECTION - 1
(Single Correct Choice Type)
For r = O, 1, ..., 10, let Ar, B, and C. denote, respectively, the coefficient of x in
the expansions of (1+x)10, (1+x)20 and (1+x)30. Then
10
Ar (B1oB, -C10Ar)
r=1
is equal to
A) B10-C10
B) A
C) 0
D) C1o-B10
10
10
1010
ANSWER: D
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
ANSWER: D
Let f be a real-valued function defined on the interval (-1, 1) such that
X
e- f(x)=2+ [t4 +1 dt, for all xe (-1,1), and let f1 be the inverse function of f.
0
Then (f-1)' (2) is equal to
1
1
1
A) 1
B)
3
C)
2
D)
e
ANSWER: B
23.If the distance of the point P(1,-2, 1) from the plane x + 2y-2z = where
> O, is 5, then the foot of the perpendicular from P to the plane is.
(847
(441
(12 10
215
A)
B)
C)
D) 3~3'2
ANSWER: A
Two adjacent sides of a parallelogram ABcD are given by.
AB =2i+10j+11k andAD =-i+2j+2k
The side AD is rotated by an acute angle a in the plane of the parallelogram so
that AD becomes AD'.If AD' makes a right angle with the side AB, then the.
cosine of the angle a is given by.
18
v17
45
A)
19
B)
C)
D)
9
9
6
ANSWER: B
4
A signal which can be green or red with probability
5
and
5
respectively, is received
by station A and then transmitted to station B. The probability of each station
3
receiving the signal correctly is.
then the probability that the original signal was green is.
m|5
6
20
9
A)
B)
7
C)
23
D)
20
ANSWER: C
SECTION - II
(Integer Type)
Two parallel chords of a circle of radius 2 are at a distance 3+1 apart. If the chords.
T
2nt
subtend at the center, angles of
and
, where k > O, then the value of [k] is
k
k
[Note : [k] denotes the largest integer less than or equal to k]
ANSWER: 3
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 15/3. If AcB is obtuse and if r denotes the radius of the incircle.
of the triangle, then r2 is equal to.
ANSWER: 3
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) (x-2012), for all x e R.)
If g is a function defined on R with values in the interval (O, o) such that.
f(x) = ln (g (x)),for all x e R,
then the number of points in R at which g has a local maximum is.
ANSWER: 1
a = 15, 27 - 2a > 0 and ak = 2ak-1 - ak-2 for k = 3, 4, .., 11.
a+a+...+a1
If
is equal to
11
11
ANSWER: 0
Let k be a positive real number and let.
[2k-1 2vk 2vk
0
2k-1 vk
A=2k1 -2k
and B=|1-2k
O 2k
-2/k 2k -1
-k -2k O
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].
ANSWER: 4
SECTiON - III] (Paragraph Type)
Paragraph for questions 31 to 33.
Consider the polynomial
f(x)=1+ 2x + 3x2 + 4x3.
Let s be the sum of all distinct real roots of f(x) and let t = |s|..
The real number s lies in the interval
3
1
D) (0.1)
A)
4
B)
-11
C
4
2
ANSWER: C
The area bounded by the curve y = f(x) and the lines x = 0, y = O and x = t, lies in
the interval
D) (0.21
(21 11)
A)
3
3
BJ
64'16
C) (9,10)
4
ANSWER: A
The function f(x) is
(-4.t)
A) increasing in
and decreasing in
B) decreasing in
and increasing in
4
C) increasing in (-t, t)
D) decreasing in (-t, t)
ANSWER:B
Paragraph for guestions 34 to 36.
Tangents are drawn from the point P(3, 4) to the ellipse
42
=1
6
4
touching the ellipse at points A and B.
The coordinates of A and B are
8
2161
9
A) (3,O) and (O,2)
B)
5
and
15
8 2v161
9
C)
5
15
and (0, 2)
D) (3,O) and
5'
ANSWER: D
The orthocenter of the triangle PAB is.
7
25
7
A)
BJ
5'
8
C)
5'5
D)
8
25'
ANSWER: C
The equation of the locus of the point whose distances from the point P and the
line AB are equal, is
A) 9x2 + y2- 6xy - 54x - 62y + 241 = 0
B) x2 + 9y2 + 6xy - 54x + 62y - 241 = 0
C) 9x2 + 9y2 - 6xy - 54x - 62y - 241 = 0
D) x2 + y2 - 2xy + 27x + 31y - 120 = 0
ANSWER: A
SECTION - IV]
(Matrix Type)
Match the statements in Column-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
4
A) The set of points z satisfying.
p) an ellipse with eccentricity
5
l-i|zl=k+i|z1
is contained in or equal to
q) the set of points z satisfying Im z = 0
B) The set of points z satisfying.
|z+ 4| + |z-4|=10
r) the set of points z satisfying |Im z|1
is contained in or equal to
C) If |w] = 2, then the set of points
s) the set of points z satisfying |Re z| 2
1
Z=W
is contained in or equal to
W
D) If |w] = 1, then the set of points
t) the set of points z satisfying |z|3
1
Z=W+
is contained in or equal to
W
ANSWER:
A:
q and r
B:
p
C:
p and s and t.
D:
q and r and s and t
Match the statements in Column-I with the values in Column-II
Column I
Column II
A) A line from the origin meets the lines
p) - 4
8
x-2_y-1_z+1
X-
3_y+3_z-1at P and g
and -
1
-2
1
2
-1
1
respectively. If length Pg = d, then d2 is
B) The values of x satisfying
3
tan' (x + 3) - tan- (x - 3) = sin-'
are
q) o
C) Non-zero vectors a,bandc satisfy a.b=0,
(b-a).(b+c)=Oand2|b+c|=|b-a|.
If a =b+4c, then the possible values of are
r) 4
D) Let f be the function on [-n,n] given by
(y/()
f(O) = 9 and f(x) = sin
for x=0.
s) 5
2
J f(x) dx is
The value of
T
-
t) 6
ANSWER:
A:
t
B:
p and r
C:
either q or (q and s)
D:
r
PART - II : PHYSICS
SECTION - I
(Single Correct Choice Type).
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
calipers, the least count is
A) 0.02 mm
B) 0.05mm
C)0.1mm
D) 0.2 mm
ANSWER: D
A hollow pipe of length O.8 m is closed at one end. At its open end a O.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 50 N and the speed of
sound is 320 ms⁻¹, the mass of the string is.
A) 5 grams
B) 10 grams
C) 20 grams
D) 40 grams
ANSWER: B
A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance
between the lens and the mirror is 10 cm. 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
ANSWER: B
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. The kinetic energy of the block
after 4.5 seconds is
F(1
4N
4.55
3s
A) 4.50 J
B) 7.50 J
C) 5.06 J
D) 14.06 J
ANSWER: C
A tiny spherical oil drop carrying a net charge q is balanced in still air with a
vertical uniform electric field of strength
81
-x10 Vm-l.When the field is
5
7
switched off, the drop is observed to fall with terminal velocity 2 10-3 m s⁻¹.
Given g = 9.8 m s-2, viscosity of the air = 1.8 10-5 Ns m-2 and the density of
oil = 900 kg m-3, the magnitude of q is
A) 1.6 x 10-19 C
B) 3.2 10-19 C
C) 4.8 x 10-19 C
D) 8.0 x 10-19 C
ANSWER: D
A uniformly charged thin spherical shell of radius R carries uniform surface
charge density of oper unit area. It is made of two hemispherical shells, held
together by pressing them with force F (see figure). F is proportional to
1o2R2
Lo2R
1 o2
1 02
A)
03
B)
03
C)
Eo R
D)
Eo R2
ANSWER: A
SECTION - II
(Integer Type)
A diatomic ideal gas is compressed adiabatically to
of its initial volume. In the
32
initial temperature of the gas is T, (in Kelvin) and the final temperature is aT,, the
value of a is
ANSWER: 4
2F
At time t = O,a battery of 10 V is connected across
2M2
points A and B in the given circuit. If the capacitors
have no charge initially, at what time (in seconds) does
the voltage across them become 4 V ?
11
B
[Take : ln 5 = 1.6, ln 3 = 1.1]
2M
2F
ANSWER: 2
Image of an object approaching a convex mirror of radius of curvature 20 m along
25
50
its optical axis is observed to move from
m to
m in 30 seconds.What is
3
7
the speed of the object in km per hour ?
ANSWER: 3
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?
ANSWER:6
To determine the half life of a radioactive
element, a student plots a graph of
NP
5
dN(t)
dN (t)
en
versus t. Here.
is the rate
3
1p
dt
2
of radioactive decay at time t. If the number
of radioactive nuclei of this element
decreases by a factor of p after 4.16 years,
2
3
4
5
6
7
8
the value of p is.
Years
ANSWER: 8
SECTION - III
(Paragraph Type)
Paragraph for questions 50 to 52.
When liquid medicine of density 0 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..
If the radius of the opening of the dropper is r, the vertical force due to the
surface tension on the drop of radius R (assuming r <<R) is
2nrT
2nRT
A) 2rT
BJ 2tRT
C)
D)
R
r
ANSWER: C
detaches from the dropper is approximately
A) 1.4x10-3m
B) 3.3x10-3m
C) 2.0x10-3m
D) 4.1x10-2m
ANSWER:A
After the drop detaches, its surface energy is.
A) 1.4x10-6J
B) 2.7x10-6J
C) 5.4x10-6J
D) 8.1x10-6J
ANSWER:B
Paragraph for guestions 53 to 55.
The key feature of Bohr's 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 assuming it to be rigid. The rule to be applied is Bohr's quantization.
condition.
A diatomic molecule has moment of inertia I. By Bohr's quantization condition its
rotational energy in the nth level (n = O is not allowed) is
A) n2[8n1
h2
B) n[8n1
h2
C) n[8nI
h2
D) nsn21]
h2
ANSWER: D
It is found that the excitation frequency from ground to the first excited state of
x1ol'Hz. Then the moment of inertia of
4
rotation for the CO molecule is close to
TC
CO molecule about its center of mass is close to (Take h = 2 10-34 J s)
A) 2.76x10-46 kg m²
B) 1.87x10-46 kg m²
C) 4.67x10-47 kg m²
D) 1.17x10-47 kg m²
ANSWER: B
In a CO molecule, the distance between C (mass = 12 a.m.u.) and O (mass = 16 a.m.u.),
5
27
where 1 a.m.u.
=-x10 kg, is close to
3
AJ 2.4x10-10 m
B) 1.9x10-l0m
C) 1.3x10-l0 m
D) 4.4x10-l1 m
ANSWER: C
SECTION - IV
(Matrix Type)
Two transparent media of refractive indices 1 and 3 have a solid lens shaped transpar.
material of refractive index 2 between them as shown in figures in Column II. A :
traversing these media is also shown in the figures. In Column I different relationsh
between 1 H₂ and 3 are given. Match them to the ray diagrams shown in Column.
Column I
Column II
A) D<H₂
p) s
B) D1>H₂
q)
3
C) H₂=H3
r)
H3
D) l2>H3
s)
t)
ANSWER:
A:
p and r
B:
ann s aud b
C:
p and r and t
D:
q and s
You are given many resistances, capacitors and inductors. These are connected to
variable DC voltage source (the first two circuits) or an AC voltage source of 50 Hz frequenc
(the next three circuits) in different ways as shown in Column II. When a curent
(steady state for DC or ims for AC) flows through the circuit, the corresponding voltage I
and V,. (indicated in circuits) are related as shown in column I. Match the two
Column I
Column II
A) I =0,V, is proportional to I
p)
8880
6mH
3 F
B) I=0,V>Vi
b
MW
HW9
202
C) Vj=0,V=V
r)
HW9
wWW
2
D) I 0, V, is proportional to I
sJ
8806
6 mH
3 F
1k
3 F
ANSWER:
A:
r and s and t.
B:
1 aan d ann n and b
C:
p and q
D:
q and r and s and t
********************************************
