For a first order reaction A-P, the temperature (T) dependent rate
constant k was found to follow the equation logk=-2000
T
pre-exponential factor A and the activation energy Ea, respectively, are
A1.0 106s1and 9.2 kJ mol1
B6.0 s1
and 16.6 kJ mol1
(C
1.0 106 sand16.6 kJ mol1
1.0 106 s1and38.3 kJ mol1
Answer
)
The spin only magnetic moment value (in Bohr magneton units) of Cr(CO) is
In the following carbocation, H/CH that is most likely to migrate to the positively
charged carbon is
H3C
CH₃
HO
H
CH₃
A CH at C-4
BH at C-4
CCHat C-2
DH at C-2
Answer
000
The correct stability order of the following resonance structures is
HC=N=N
HC-N=N
HC-NEN
HC-N=N
(I)
(II)
(III)
(IV)
AI>II>IV>III
BI>III>II>IV)
For the reduction of NO ion in an aqueous solution, E is +0.96 V.Values of E for
some metal ions are given below
V2+aq+2eV
E=-1.19V
Fe+aq+3eFe
E=-0.04V
Au+aq+3e-Au
E=+1.40V
Hg+aq+2e-Hg
E=+0.86V
The pair(s) of metals that is(are) oxidized by NO in aqueous solution is(are)
- V and Hg
- Hg and Fe
- Fe and Au
- Fe and V
Among the following, the state function(s) is(are)
AInternal energy
In the reaction
2X+BHBHXBH]
the amine(s) X is(are
- NH
- CHNH
- CHNH
- CHN
The nitrogen oxide(s) that contain(s) N-N bond(s) is(are)
- NO
- NO3
- NO
- NO
The correct statement(s) about the following sugars X and Y is(are)
CHOH
CHOH
CHOH
HHO
HHOHC
O
OH
HO
OH H
HO
CHOH
HO
OH
H
OHH
H
HO
OHH
H
HO
X
(A
X is a reducing sugar and Y is a non-reducing sugar
Match each of the reactions given in Column I with the corresponding product(s)
given in Column II.
Column I
Column II
A
Cu + dil HNO₃
(d)
NO
Match each of the compounds given in Column I with the reaction(s) that they can
undergo, given in Column II.
Column I
Column II
Br
In a constant volume calorimeter, 3.5 g of a gas with molecular weight 28 was burnt
in excess oxygen at 298.0 K. The temperature of the calorimeter was found to
increase from 298.0 K to 298.45 K due to the combustion process.Given that the
heat capacity of the calorimeter is 2.5 kJ K~, the numerical value for the enthalpy
of combustion of the gas in kJ mol1 is
Answer
13.At 400 K, the root mean square rms speed of a gas X (molecular weight = 40) is
equal to the most probable speed of gas Y at 60 K. The molecular weight of the
gas Y is
The dissociation constant of a substituted benzoic acid at 25C is 1.0 104
The pH of a 0.01 M solution of its sodium salt is
Answer
15.The total number of
a
and
B
particles emitted in the nuclear reaction
92
The oxidation number of Mn in the product of alkaline oxidative fusion of MnO is
The number of water molecule(s) directly bonded to the metal centre in
CuSO5HO is
The coordination number of Al in the crystalline state of AlCl₃ is
The total number of cyclic structural as well as stereo isomers possible for a
compound with the molecular formula C,Ho is
Answer
PART II:MATHEMATICS
SECTION-1
Single Correct Choice Type
This section contains 4 multiple choice questions. Each question has 4 choices
If the sum of first n terms of an A.P.is cn, then the sum of squares of these
n terms is
A line with positive direction cosines passes through the point P(2,-1,2) and makes
equal angles with the coordinate axes.The line meets the plane
2x+y+2=9
at point Q. The length of the line segment PQ equals
- 1
- 2
- 3
- 2
The normal at a point P on the ellipse x+4y=16 meets the x-axis at Q.If M is
the mid point of the line segment PQ, then the locus of M intersects the latus
rectums of the given ellipse at the points
3519
The locus of the orthocentre of the triangle formed by the lines
1+px-py+p(1+p=0
1+qx-qy+q(1+q=0,
and y =0,where p+q,is
- a hyperbola
- a parabola
- an ellipse
- a straight line
If
sin nx
dxn=0,12
1+sinx
then
An ellipse intersects the hyperbola 2x-2y2 =1 orthogonally.The eccentricity of the
ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the
coordinate axes,then
For the function
x1
x
(Af
for at least one x in the interval 1,)fx+2-fx<2
The tangent PT and the normal PN to the parabola y =4ax at a point P on it meet
its axis at points T and N, respectively. The locus of the centroid of the triangle
PTN is a parabola whose
Avertex is
2a
0
Bdirectrix is x=0
3
2a
Match the statements/expressions given in Column I with the values given in
Column II.
Column I
Column II
ARoot(s of the equation
(d)
2sin0+sin20=2
6
Match the statements/expressions given in Column I with the values given in
Column II.
Column I
Column II
The maximum value of the function fx)=2x3-15x+36x-48 on the set
A={x|x+209x} is
Let (x, y,z) be points with integer coordinates satisfying the system of
homogeneous equations:
3x-y-z=0
-3x+2=0
3x+2y+ z= 0.
Then the number of such points for which x? + y2 + z? 100 is
Let ABC and ABC'be two non-congruent triangles with sides AB =4,
AC=AC'=22 and angle B =30.The absolute value of the difference between the
areas of these triangles is
Let p(x) be a polynomial of degree 4 having extremum at x =1,2 and
lim
1+P(x
=2.
Then the value of p(2) is
Let f:R->R be a continuous function which satisfies
f(x=f(tdt.
Then the value of f(ln 5) is
The centres of two circles C and C each of unit radius are at a distance of 6 units
from each other.Let P be the mid point of the line segment joining the centres of
Cand C and C be a circle touching circles Cand C externally.If a common
tangent to C and C passing through P is also a common tangent to C and C, then
the radius of the circle C is
The smallest value of k, for which both the roots of the equation
x2-8kx+16k2-k+1=0
are real, distinct and have values at least 4,is
Answer
If the function f(x) = x+ e2 and g(x) = f-1(x), then the value of g(1) is
Answer
PART II :PHYSICS
SECTION-I
Single Correct Choice Type
This section contains 4 multiple choice questions. Each question has 4 choices
The mass M shown in the figure oscillates in simple harmonic motion with
amplitude A.The amplitude of the point P is
k
k2
00000000
M
kA
kA
kA
kA
A piece of wire is bent in the shape of a parabola y = kx(y-axis vertical) with a bead
of mass m on it. The bead can slide on the wire without friction. It stays at the
lowest point of the parabola when the wire is at rest.The wire is now accelerated
parallel to the x-axis with a constant acceleration a.The distance of the new
equilibrium position of the bead, where the bead can stay at rest with respect to the
wire, from the y-axis is
Photoelectric effect experiments are performed using three different metal plates
Pq and r having work functions p=2.0 eV9q=2.5 eV and =3.0 eV
respectively.A light beam containing wavelengths of 550 nm,450 nm and 350 nm
with equal intensities illuminates each of the plates. The correct I-V graph for the
experiment isd
[Take hc=1240eV nm]
p
A uniform rod of length L and mass M is pivoted at the centre.Its two ends are
attached to two springs of equal spring constants k. The springs are fixed to rigid
supports as shown in the figure, and the rod is free to oscillate in the horizontal
plane. The rod is gently pushed through a small angle 0 in one direction and
released. The frequency of oscillation is
000000
000000
Two metallic rings A and B, identical in shape and size but having different
resistivities PA and PB are kept on top of two identical solenoids as shown in the
figure.When current I is switched on in both the solenoids in identical manner, the
rings A and B jump to heights h and hB,respectively, with hA >hg.The possible
relation(s) between their resistivities and their masses m and mg is(are)
- PA>PB and m=mB
- PA<PBand mA=mB
- PA>PB and mA>mB
- PA<PBand mA<mB
A student performed the experiment to measure the speed of sound in air using
resonance air-column method. Two resonances in the air-column were obtained by
lowering the water level. The resonance with the shorter air-column is the first
resonance and that with the longer air-column is the second resonance.Then,
A) the intensity of the sound heard at the first resonance was more than that at
the second resonance
B)
the prongs of the tuning fork were kept in a horizontal plane above the
resonance tube
The figure shows the P-V plot of an ideal gas taken through a cycle ABCDA. The part
ABC is a semi-circle and CDA is half of an ellipse. Then,
3
D
B
C
1
2
3V
- the process during the path A B is isothermal
- heat flows out of the gas during the path B-C-D
- work done during the path ABC is zero
- positive work is done by the gas in the cycle ABCDA
Under the influence of the Coulomb field of charge +Q,a charge -q is moving
around it in an elliptical orbit. Find out the correct statement(s).
A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure
A is the point of contact, B is the centre of the sphere and C is its topmost point.
Then,
B
A
Column II gives certain systems undergoing a process. Column I suggests changes
in some of the parameters related to the system.Match the statements in Column I
to the appropriate process(es) from Column II.
Column I
Column II
A The energy of the system is
(p System:A capacitorinitially
increased
uncharged
Process: It is connected to a
B
Mechanical energy is provided
battery
to the system, which is converted
into energy of random motion of
(q)
System: A gas in an adiabatic
its parts
container fitted with an
adiabatic piston
C
Internal energy of the system is
Process: The gas is compressed
converted into its mechanical
by pushing the piston
energy
(r)
SystemA gas in a rigid
Column I shows four situations of standard Young's double slit arrangement with
the screen placed far away from the slits S and S.In each of these cases
SP=SPoSP-SP=A/4 and SP-SP=A/3,whereis the wavelength
of the light used. In the cases B, C and D, a transparent sheet of refractive index
and thickness t is pasted on slit S.The thicknesses of the sheets are different in
different cases. The phase difference between the light waves reaching a point P on
the screen from the two slits is denoted by S(P) and the intensity by I(P).Match
each situation given in Column I with the statement(s) in Column II valid for that
situation.
Column I
Column II
Sa
(p)
8P=0
A metal rod AB of length 10x has its one end A in ice at OC and the other end B in
water at 100C. If a point P on the rod is maintained at 400C, then it is found that
equal amounts of water and ice evaporate and melt per unit time. The latent heat of
evaporation of water is 540 cal/g and latent heat of melting of ice is 80 cal/g.If the
point P is at a distance of A x from the ice end A, find the value of .
[Neglect any heat loss to the surrounding.]
A cylindrical vessel of height 500 mm has an orifice (small hole) at its bottom. The
orifice is initially closed and water is filled in it up to height H. Now the top is
completely sealed with a cap and the orifice at the bottom is opened. Some water
comes out from the orifice and the water level in the vessel becomes steady with
height of water column being 200 mm. Find the fall in height (in mm) of water level
due to opening of the orifice.
[Take atmospheric pressure =1.010N/m, density of water = 1000 kg/m and
g=10 m/s.Neglect any effect of surface tension.]
Two soap bubbles A and B are kept in a closed chamber where the air is maintained
at pressure 8 N/m. The radii of bubbles A and B are 2 cm and 4 cm, respectively.
Surface tension of the soap-water used to make bubbles is 0.04 N/m.Find the ratio
nB/nAwhere nA and ng are the number of moles of air in bubbles A and B,
respectively. [Neglect the effect of gravity.]
Three objects A, B and C are kept in a straight line on a frictionless horizontal
surface.These have masses m, 2m and m, respectively.The object A moves towards
B with a speed 9 m/s and makes an elastic collision with it. Thereafter, B makes
completely inelastic collision with C. All motions occur on the same straight line
Find the final speed (in m/s) of the object C.
m
2m
m
A
B
C
A steady current I goes through a wire loop PQR having shape of a right angle
triangle with PQ=3xPR =4x and QR=5x.If the magnitude of the magnetic field
HoI
at P due to this loop is k
find the value of k.
48x
A light inextensible string that goes over a smooth fixed pulley as shown in the figure
connects two blocks of masses 0.36 kg and 0.72 kg.Taking g =10 m/s,find the work
done (in joules by the string on the block of mass 0.36 kg during the first second
after the system is released from rest.
A solid sphere of radius R has a charge Q distributed in its volume with a charge
density p =kr,where K and a are constants and r is the distance from its centre.
R
If the electric field at r
times that at r = R, find the value of a
A 20 cm long string, having a mass of 1.0 g, is fixed at both the ends. The tension in
the string is 0.5 N. The string is set into vibrations using an external vibrator of
frequency 100 Hz.Find the separation (in cm) between the successive nodes on the
string.
