HzOt,
2. 03
O
A ray of light travelling in the direction -.
1(i + 3j) is incident on a plane mirror. After
1(i - 3j). The angle of incidence is
reflection, it travels along the direction -'
H2O₂
AnsweR : 2
Two non-reactive monoatomic ideal gases have their atomic masses in the ratio
constant temperature, is 4 : 3. The ratio of their densities is
Two rectangular blocks, having identical dimensions, can be arranged either in.
configuration I or in configuration II as shown in the figure. One of the blocks has.
thermal conductivity k and the other 2k. The temperature difference between the.
ends along the x-axis is the same in both the configurations. It takes 9 s to transport.
a certain amount of heat from the hot end to the cold end in the configuration I. The
time to transport the same amount of heat in the configuration II is
at HHyT 34aIoR ycqi nT 3R fagHR 3t fq4Ri I 3i II aqRd
fl2 4 HlE-x k lHh lF2 1 yZ b X lPbPIh ln4 Lb lb2f 1 IhIt Ih4J
8Ri q aI94I qT 3R 34 $ 1 fa2R I #, 3HT qT yq fRqa HII TRH
8R j oR aq 3f 9 s dd 1fq4RII, HH H q3 h
3f44 ? fy a4y :
Configuration II
Configuration I
fqrqR II
fqrR I
2K
K
2k
K
A pulse of light of duration 100 ns is absorbed completely by a small object initially at
rest. Power of the pulse is 30 mW and the speed of light is 3 108 ms⁻¹. The final.
momentum of the object is
A particle of mass m is projected from the ground with an initial speed u, at an angle
a with the horizontal. At the highest point of its trajectory, it makes a completely.
inelastic collision with another identical particle, which was thrown vertically upward
from the ground with the same initial speed uo. The angle that the composite system
makes with the horizontal immediately after the collision is.
The work done on a particle of mass m by a force,.
A
(K being a constant of appropriate dimensions), when the particle is taken from the
point (a, 0) to the point (0, a) along a circular path of radius a about the origin in the.
x-y plane is
2K
Kt
One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an
end of another horizontal thin copper wire of length L and radius R. When the
arrangement is stretched by applying forces at two ends, the ratio of the elongation in
the thin wire to that in the thick wire is.
The image of an object, formed by a plano-convex lens at a distance of 8 m behind
the lens, is real and is one-third the size of the object. The wavelength of light inside
2
the lens is
3
times the wavelength in free space. The radius of the curved surface.
of the lens is
A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic
according to the equation, y(x, t) = (0.01 m) sin [(62.8 m-l) x] cos [(628 s⁻¹)t]
Assuming = 3.14, the correct statement(s) is (are).
A solid sphere of radius R and density pis attached to one end of a mass-less spring
of force constant k. The other end of the spring is connected to another solid sphere
of radius R and density 3p. The complete arrangement is placed in a liquid of density
2p and is allowed to reach equilibrium. The correct statement(s) is (are).
4n R pg
A particle of mass M and positive charge Q, moving with a constant velocity.
u, -- 4i ms', enters a region of uniform static magnetic field normal to the x-y plane.
The region of the magnetic field extends from x = 0 to x = L for all values of y. After
passing through this region, the particle emerges on the other side after 10
milliseconds with a velocity u, = 2(3i + j) ms-' . The correct statement(s) is (are)
Two non-conducting solid spheres of radii R and 2R, having uniform volume charge
densities p1 and p2 respectively, touch each other. The net electric field at a distance
2R from the centre of the smaller sphere, along the line joining the centres of the
P1
spheres, is zero. The ratio.
can be
32
In the circuit shown in the figure, there are two parallel plate capacitors each of
capacitance C. The switch S, is pressed first to fully charge the capacitor C, and.
then released. The switch S, is then pressed to charge the capacitor C,. After some.
time, S, is released and then S, is pressed. After some time,.
The work functions of Silver and Sodium are 4.6 and 2.3 eV, respectively. The ratio of
the slope of the stopping potential versus frequency plot for Silver to that of Sodium
is
qicT yq aRyq $ qRf qdT 3HI: 4.6 q 2.3 eV 1aicT q alRyq ? f\f
fqHq gq 3TqR h aq y1qi $ ?Td bT 3y4Id
AnswER : 1
A freshly prepared sample of a radioisotope of half-life 1386 s has activity 103
disintegrations per second. Given that ln 2 = 0.693, the fraction of the initial number
of nuclei (expressed in nearest integer percentage) that will decay in the first 80 s
after preparation of the sample is.
yq gia dqR fhy1 g3n <Rqt 354clq yRqf, fRHqT 3rf-3ry 1386 s $, q]
Hfh4l 103 fqqc7 yR dcg 1 qf ln 2=0.693 ,aq yH 80 s fqqfCd
aHqi q yRPq afHni aT i3i qT 3g4I (9R fncd4 yuniq A)
AnswER : 4
PHYSICS
A particle of mass 0.2 kg is moving in one dimension under a force that delivers a
constant power 0.5 W to the particle. If the initial speed (in ms⁻¹) of the particle is
zero, the speed (in ms⁻¹) after 5 s is
yq 0.2 kg 3QHIT qhT quI yq ac ? 3Ia, of f yqn f4d 2IRT 0.5 W quT
qt 3I , yq f nRNa 1 qR qu aT yRfn nR yy aq 5s qI
HqT R (ms⁻¹) a\ :
AnSWER : 5
A uniform circular disc of mass 50 kg and radius 0.4 m is rotating with an angular
velocity of 10 rad s-' about its own axis, which is vertical. Two uniform circular rings,
each of mass 6.25 kg and radius 0.2 m, are gently placed symmetrically on the disc
in such a manner that they are touching each other along the axis of the disc and are
horizontal. Assume that the friction is large enough such that the rings are at rest
relative to the disc and the system rotates about the original axis. The new angular
velocity (in rad s-') of the system is
yc 50 kg T 0.4 m fwyI qT yqHHI f3xq 3q 3eqfr 3TT $ fd 10 rad s⁻¹h
Lb HlE 4 c>J R 4J R Dln bd dh WP g>RJ dLbK H5 AS p3 Lb AH3 eA H
f rqf nf 1 yrq 8c nT 3QHI 6.25 kg q fywT 0.2 m $ 1 3H fqR qhT
InhB blp 4 K3 hbA b>J J hU ElH) l(E kY(-s pnu) le hYn(p IhB
$dI $ fh Rxh q 8c ? aq Hda aR yy $ 3 AoR yc 3T q yof
qT 8T &) :
AnsweR : 8
PHYSICS
A bob of mass m, suspended by a string of length l,. is given a minimum velocity
required to complete a full circle in the vertical plane. At the highest point, it collides
elastically with another bob of mass m suspended by a string of length l,, which is
initially at rest. Both the strings are mass-less and inextensible. If the second bob,
after collision acquires the minimum speed required to complete a full circle in the
vertical plane, the ratio ,
Ih2J lR bA HE1 U83 Lb2K llE Lb flbK 1 gWlr Ip Flhh5 u bd
HPh2E FhIE 1 R hPLh dRJ dla4 lh aB qd lt kP dRjb4 J l R IPln
fg q ye nan g4 m 3QH $ na5 yR HgE hdI 13HRT
M l,a$ qT 3R ach g3 a yRiy faRHqT y 1
3\Rqi 3QH fa q 3aIy 1 qR xaE $ qT g man at d nR
yI a\d t fh 3qfr a # yof y yT h fy ydH , dq
hT
: DIhEte
ANSWER : 5
PART II : CHEMISTRY
SECTION -- 1 : (Only One option correct Type)
qug -1 : (hq yc A faqcy ycR)
This section contains 10 multiple choice questions. Each question has four choices
The compound that does NOT liberate CO,, on treatment with aqueous sodium
bicarbonate solution, is
Concentrated nitric acid, upon long standing, turns yellow-brown due to the formation of
Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at
25 C. For this process, the correct statement is
Sulfide ores are common for the metals
The arrangement of X- ions around A* ion in solid AX is given in the figure (not
drawn to scale). If the radius of X- is 250 pm, the radius of A* is
Upon treatment with ammoniacal H,S, the metal ion that precipitates as a sulfide is
Consider the following complex ions, P, Q and R..
P = [FeF]~. Q=[V(H,O)]* and R =[Fe(H,O)6]2+.
The correct order of the complex ions, according to their spin-only magnetic moment
values (in B.M.) is.
In the reaction,
P+Q-
R+S
The concentration of Q varies with reaction time as shown in the figure. The overall
order of the reaction is
KI in acetone, undergoes S,2 reaction with each of P, Q, R and S. The rates of the
reaction vary as
HzC-CI
C
CI
P
R
S
The pair(s) of coordination complexes/ions exhibiting the same kind of isomerism
is(are)
Among P, Q, R and S, the aromatic compound(s) is/are
The hyperconjugative stabilities of tert-butyl cation and 2-butene, respectively, are
due to
Benzene and naphthalene form an ideal solution at room temperature. For this
process, the true statement(s) is(are)
The initial rate of hydrolysis of methyl acetate (1M) by a weak acid (HA, 1M) is
The total number of carboxylic acid groups in the product P is.
A tetrapeptide has -COOH group on alanine. This produces glycine (Gly), valine
(Val), phenyl alanine (Phe) and alanine (Ala), on complete hydrolysis. For this
tetrapeptide, the number of possible sequences (primary structures) with --NH, group
attached to a chiral center is.
yq 2grqeI$c # yaIA qr -COOH yq feH 13Hh ziyof gd 3IqgCT aRT TdIsR
(Gly), dd (Val), hRa >af (Phe) aa taf (AIa) y atd 1 3 2gqec q)
HHfa aa3i (9aHn ia3i) nt c ad f -NH yy fh\c ha h H
1 $ PRJpE
AnsweR : 4
CHEMISTRY
EDTA4- is ethylenediaminetetraacetate ion. The total number of N-Co-O bond
angles in [Co(EDTA)]'- complex ion is
EDTA4- yfd 3IsA gryCc 3n4 1 ig 3T4 [Co(EDTA)]l- N-Co-O
The total number of lone-pairs of electrons in melamine is.
AdH qt 3yd&T 3d4i ? ycqt yqi qT gd icyI
AnSWER : 6
The atomic masses of He and Ne are 4 and 20 a.m.u., respectively. The value of the
de Broglie wavelength of He gas at -73 C is "M" times that of the de Broglie
wavelength of Ne at 727 C. M is
He 3i Ne yy aH 34: 4 3i 20 a.m.u. 1 He at -73 C y aie
au a$ Ne qt 727C q aidt a aq$ "M" y 1MhT y
AnSWER : 5
PART III : MATHEMATICS
SECTION - 1 : (Only One option correct Type)
qu3 -1 : (hqc yc et faccy yqR)
This section contains 10 multiple choice questions. Each question has four choices
Let complex numbers and
18
1
lie on circles (x - xo)2 + (y - yo)2 = r2 and
(x - xo)2 + (y - yo)2 = 4r?, respectively. If zo = xo + iyo satisfies the equation.
2 |zgI2 = r2 + 2, then|a| =
Four persons independently solve a certain problem correctly with probabilities
1311
. Then the probability that the problem is solved correctly by at least one
2'4'4'8'
of them is
The area enclosed by the curves y = sin x + cos x and y = Icos x - sin x| over the
is
The value of cot.
cot'
1 +
E
2k
is
n=1
k=1
23
25
For a > b > c > 0, the distance between (1, 1) and the point of intersection of the
lines ax + by + c = 0 and bx + ay + c = 0 is less than 22 . Then
Perpendiculars are drawn from points on the line
to the plane
2
-1
x + y + z =- 3. The feet of perpendiculars lie on the line.
r_y-1_z-2
x12
y-1
z-2
Let PR=3i +j -2k and SQ= i -3j -4k determine diagonals of a parallelogram
PQRS
and PT=i+2j+3k be another vector. Then the volume of the.
parallelepiped determined by the vectors PT, PQ and PS is.
LetS, =(-1)
2
k2. Then S, can take value(s)
k=1
For 3 x 3 matrices M and N, which of the following statement(s) is (are) NOT correct ?
A rectangular sheet of fixed perimeter with sides having their lengths in the ratio
8 : 15 is converted into an open rectangular box by folding after removing squares of
equal area from all four corners. If the total area of removed squares is 100, the
resulting box has maximum volume. Then the lengths of the sides of the rectangular
sheet are
A line I passing through the origin is perpendicular to the lines
l: (3+t)i+(-1+2t)j+(4+2t)k,-<t<00
l: (3+2s)i+(3+2s)+(2+s)k,-c0<s<00
Then, the coordinate(s) of the point(s) on l, at a distance of 17 from the point of
intersection of I and I, is (are)
(7 7 5)
(Z 7 8)
A pack contains n cards numbered from 1 to n. Two consecutive numbered cards are
removed from the pack and the sum of the numbers on the remaining cards is 1224.
If the smaller of the numbers on the removed cards is k, then k -- 20 =
yq n q i3i 1 n aRT fP 1a Hr Hi3 qld
qTC T fgI f d 3i 3qRIe qTcf qt zi3i qT qF 1224 1
yf Aqd Ty aTcf qT fPa i3i ayd i k , aq k-20=
AnsWER : 5
MATHEMATICS
Of the three independent events Ej, E, and E3, the probability that only E, occurs is.
a, only E, occurs is and only E, occurs is y. Let the probability p that none of
All the given probabilities are assumed to lie in the interval (0, 1)..
Probability of occurrence of E1.
Then
Probability of occurrence of E3
d rqda qc43ii E1,E2 a2T Ez # hqd E, h qc nT unRodI a $,hqc E2
h qc qT yRndI $ aeT hqd E $ qc qT yIRqdI y $ 1HT fh qc43i
Ej, E qT E fh h t act at yrRndI p, HHnxui (a-2) p=a
3RT (-3y) p =2y ct Hg n<dt 1 t yIRcdI 3dRId (0, 1) # RaTd
pP 2 lPI flh
JpotJIK ge k2B y '3
ANSWER : 6
MATHEMATICS
A vertical line passing through the point (h, 0) intersects the ellipse
1 at
3
the points P and Q. Let the tangents to the ellipse at P and Q meet at the point R.
max
8
541-84=
x+
f+g (h, 0) ygR qIdt yqn 3tfgr {qI aEqH
=1 nt farg3i P aRI Q
4
3
q qTcdT 1 HTT fh fag3i P ae Q qr agg aT rqgRaIj fag R q fdd
8
AnSWER : 9
Consider the set of eight vectors V= {ai + bj + ck : a, b, c c {-1, 1}}. Three non-
coplanar vectors can be chosen from Vin 2' ways. Then p is.
3TC 4fsi cT H#cqq V={ai+bj+ck:a,b,cE{-1,1}} dRRt 1 V A d
3RHddq AfI 2P ycR y gI Hnd 13d p qT HI $:
AnsWER : 5
