P.
F y4
qI 9 $
1.
cot (sin-'y) + tan (sin-' y) .
Q. qf cos x + cos y + cos z =0 = sin x + sin y + sin z q
V2
cOS
2
R. qf cos
t
x J cos 2x + sin x sin 2x sec x = cos x sin 2x sec x
3.
1
2
1
+ cos
+x
R Elh DRjltH Lcp x 3as pP xZ s0X
4
S. 4f cot (sin-'1-x2) = sin (tan' (x6)),x=0,
4.
1
dq x qT Ha HT
Codes :
P
Q
R
s
Conductivity increases and then
does not change much
x
Y
S. NaOH + HI
Conductivity does not change much
x
Y
and then increases
X h gdq fa4T nHRI: Y qT ud4 fd4T aR-aR 3dT GdT , d yaTI
fqRT RT $ 13 3fHfhy3i 3cq adhdT aT fHMdT ydTII # T n$ 1
ydtI nt ydt II # yARa aRy aT yRqf $ Aa fq T aIc nT yqNT n<q
: pUE ARa lH
yai I
ydt II
P. (C2Hs);N + CH;COOH
1.qdchdl qcdT 3iR acyqT qdt 1
x
Y
2.qldhd qcd 3 acy 3fgq
Q. KI (0.1M) + AgNO₃ (0.01M)
1 lPP lRE PPbdh
x
Y
R. CHCOOH + KOH
3. aldhdl aodt 3i acqq 3fgc
x
Y
1 lP RL PPbdh
S. NaOH + HI
4. qlaqn 3fgc qRqfa ei a\dt 3i
x
Y
Codes :
p
Q
R
s
Two bodies, each of mass M, are kept fixed with a separation 2L. A particle of mass
m is projected from the midpoint of the line joining their centres, perpendicular to the
line. The gravitational constant is G. The correct statement(s) is (are)
A particle of mass m is attached to one end of a mass-less spring of force constant k,.
Iying on a frictionless horizontal plane. The other end of the spring is fixed. The.
particle starts moving horizontally from its equilibrium position at time t = 0 with an.
initial velocity uo. When the speed of the particle is 0.5 uo, it collides elastically with a
rigid wall. Atter this coilision,.
A steady current I flows along an infinitely long hollow cylindrical conductor of radius
R. This cylinder is placed coaxially inside an infinite solenoid of radius 2R. The
solenoid has n turns per unit length and carries a steady current I. Consider a point
P at a distance r from the common axis. The correct statement(s) is (are)
Two vehicles, each moving with speed u on the same horizontal straight road, are
approaching each other. Wind blows along the road with velocity w. One of these
vehicles blows a whistle of frequency fi. An observer in the other vehicle hears the
frequency of the whistle to be f2. The speed of sound in still air is V. The correct
statement(s) is (are)
The magnitude of the induced electric field in the orbit at any instant of time during
the time interval of the magnetic field change is
jqqRq ax h qRqd h aRT qy # fh f9y quT yr dRa fy &r qT H
BR
BR
The change in the magnetic dipole moment associated with the orbit, at the end of
the time interval of the magnetic field change, is
3Tdgr h q4 Hdfa yqq|q fyq 3quf # qRqd1
BQR2
BQR2
The correct statement is
The speed of the block when it reaches the point Q is
uq ychT fargQyr ygadI , 3HqT R
The magnitude of the normal reaction that acts on the block at the point Q is.
f4gQq, JCh q a qId 3fHdq ad nT qRqI
If the direct transmission method with a cable of resistance 0.4 Q km-' is used, the
power dissipation (in %) during transmission is.
qf d ?fq qT 3ya\ fhyr uy fRqT yR`g 0.4 Q km'$ aq yry8T dqu1 ql
Ref f aTy (% )
In the method using the transformers, assume that the ratio of the number of turns in
the primary to that in the secondary in the step-up transformer is 1 : 10. If the power.
to the consumers has to be supplied at 200 V, the ratio of the number of turns in the.
primary to that in the secondary in the step-down transformer is
b ghJhIK df!hHI lhlh2a 4J Kh 3h k 3J Ib kdb IhK g df!hI2
fd4n adei aT ziT 3T 34 1:10 1 qf fag af, 3y4q3i q)
200 Vy at gdt $ at 3qqR 34i4 # yfAq q fadqh $ adcf at iT
2 PIhEte Lb
Match List I with List II and select the correct answer using the codes given below
the lists. :
List I
List II
P.
Boltzmann constant
1.
[MLT-]
Q.
Coefficient of viscosity.
2.
[MLT-]
R.
Planck constant
3.
[MLT~K~']
Thermal conductivity
4.
[MLT-2K-']
ydtI nT yat II yARa aRy 3iR yRqi $ Aa f4 T a\S hT ya n<
yat1
II pE
P.
q\cCH4R f4diqh
1.
[MLT-']
Q.
p!Inf IPEIha
2.
[ML'T-l]
R.
wiq fydih
3.
[MLT~K-']
S.
4.
[MLT-2K-']
Codes :
P
Q
R
s
A right angled prism of refractive index is placed in a rectangular block of
refractive index 2, which is surrounded by a medium of refractive index 3, as shown
in the figure. A ray of light 'e' enters the rectangular block at normal incidence.
Depending upon the relationships between 1, 2 and 3, it takes one of the four
' e, do, ye, ' &a, ' fo, suged aigassod.
yc j 3T9qdiq h HHq|or f9sq c\ 3Iyqdaicq $ 3T4d!cR sI5 3qr TRT $1
Lb Ial4K 1 2 5E l3J dlHFtc Al2 k ERJ hh3Ih b b!FPbhle r Ibh fnh
fhyuT 'e'3RdIhR cic qR 3fHciqqd 3qRa a\dt $ 11, 2 3iR 3 h qi qr
f s\dt g$ yor at fhxu qR iHq qf ef, 'eg, 'eh'qT ei'# gn ddl 1
45
g
H1
h
H₂
H3
Match the paths in List I with conditions of refractive indices in List II and select the
correct answer using the codes given below the lists:
ydtI# fq n qaf at yat II nT 3qqdia aT zdf yARa aRy 3 qRqi
hAa f4 a|g 3T y4 3xh HeT 3tR yA4 :
List I/qa1
List II / dt II
P.
e-f
1.u>V22
Q.
e->g
Match List I of the nuclear processes with List II containing parent nucleus and one
of the end products of each process and then select the correct answer using the
codes given below the lists :
yq 3iR4 nqq zjc fy Ty 1qRqi ? Aa f4 y nT hT yqNT n<h
HET 3tR yAy :
List I/ qat 1
List II/ qat II
P.
Alpha decay
O1'N+ ....
1.
dc4T-8T4
Q.
decay
2.
2381
234
hH+d
R.
Fission
3.
. + 9dT8<1g E8
185,
184
S.
Proton emission
239
140
4.
94 Pu > 57 La + ...
Codes :
P
Q
R
s
One mole of a monatomic ideal gas is taken along two cyclic processes.
Feaaeeead aee weaeep Ad aee e! eeeae ae HHe pue e
involved are purely isochoric, isobaric, isothermal or adiabatic..
ych yq-qHryh 3Hf R $ yq q\ cf, fy 3If PV 3Rq $ 3gHR at
qs|q ysh4f E-F-G-E q EFHE qRqT GdI 1iqId ygH ad:
P
F
32Po
Po
E1
H
Vo
Match the paths in List I with the magnitudes of the work done in List II and select
the correct answer using the codes given below the lists.
qaTI# f4 T qef at ydT II fhy Tt aRf $ qRqT $ HRT yHR aRy
1 hJE dH8 13H ydq hhK L 2p klt h2J PF fhRJF dltE
List I/ a 1
List II / 4dt II
P.
G->E
1.
160 PVo ln2
Q.
G->H
2.
36 PoVo
R.
F->H
3.
24 PoVo
S.
F->G
4.
31 PoVo
Codes :
P
Q
R
s
In the nuclear transmutation.
4Be + Y
(X, Y) is(are)
The carbon-based reduction method is NOT used for the extraction of
The thermal dissociation equilibrium of CaCO,(s) is studied under different
conditions.
CaCO₃(s) === CaO(s)+CO₂(g)
For this equilibrium, the correct statement(s) is(are).
In the following reaction, the product(s) formed is(are).
AfRq 3fHfhyT $ 3c93/3c4rci qT qaTS
OH
CHCI3
?
OH-
CH₃
OH
OH
OH
OHO
CHO
CHO
CH₃
H3C CHCl2
H3C^CHCI2
CH₃
P
Q
R
s
The major product(s) of the following reaction is(are)
OH
aqueous Br2 (3.0 equivalents)
SO?H
OH
OH
OH
OH
Br
Br
Br-
Br
Br
Br
Br
Br
BI
Br
SOzH
Br
Br
SOzH
P
Q
R
s
After completion of the reactions (I and II), the organic compound(s) in the reaction
mixtures is(are)
R4Rq 3fh4I3i (I 3iR II) $ y aH ? aTc RRRn fyoT # hTdAn
1 AIPk L 1bItJ(h) glj(h
0
Br2(1.0 mol)
Reaction I :
HzC
CH₃
3faT I :
(1.0 mol)
aqueous/ udlq NaOH
ReactionII: HgCCH3
Br2(1.0 mol)
: II h4tle
(1.0 mol)
CH?COOH
H3C
`CH2Br HzC
`CBr3
Br3C
CBr3BrHCCH2Br
H3C
`ONa
CHBr3
p
Q
R
s
T
n
The succeeding operations that enable this transformation of states are.
The pair of isochoric processes among the transformation of states is
P and Q, respectively, are the sodium salts of
The coloured solution S contains
Compounds formed from P and Q are, respectively.
In the following reaction sequences V and W are, respectively
f4RR 3ffh4I 3sh4i , V3R w39:
!N/2H
Q
V
A
AlCl₃ (anhydrous)
Match the chemical conversions in List I with the appropriate reagents in List II and
select the correct answer using the code given below the lists :.
ydT I# f4 T 2RR4Rn nyiaRui aT yaT II # fy T 3qyR 3fHq+qi h
HIR yARd aRy aT yfqf h A f2y TT nI cT yT qh HeT 3tR yA4 :
List I /gdt I
List II /yat II
P.
CI
The unbalanced chemical reactions given in List I show missing reagent or condition
(?) which are provided in List II. Match List I with List II and select the correct
answer using the code given below the lists :
yaTI# fRqd 3RigRa 3rffh43ii 3ycRI 3fq4g/3qe yat II # t T$
I:jhK Lb 2[p hlt dRJ RU 4IhRJE Ih Alb DRjtF I.p ip I pR 1 R
hrh HeT 3t yR4 :
List I /qat I
II p/ II Is!!
The standard reduction potential data at 25 C is given below.
qIq 3qqRq fqyq 25 C yr fRRqa 1
Eo(Fe3+, Fe2+) = + 0.77 V;
Eo(Fe2+, Fe) = - 0.44 V
E o(Cu2+, Cu) = + O.34 V;
Eo(Cu+, Cu) = + 0.52 V
A E+ = [OH< at + +H + (8)O]o]
A 0t0 += [-HOt< _a4 +OHZ+(8)O]oI
E(Cr3+, Cr) = -- 0.74 V;
Eo(Cr2+, Cr) = - 0.91 V
Match E of the redox pair in List I with the values given in List II and select the
correct answer using the code given below the lists :
PRJtA btJ chI2htE Rl bJ k II p Lb Ihrh HbI2? kl RDJ t I pR
: hUE AHa lH qa4 Ir[hK L 2[p hlt tRJ RlF 4 lhRJF ID AJle
List I /yat I
II p/ II Is!!
P.
E(Fe3+, Fe)
1.
-0.18 V
Q.
E(4H,O === 4H+ + 4OH)
2.
-0.4 V
R.
E(Cu2+ + Cu ->2Cu+)
3.
-0.04 V
S.
E(Cr3+, Cr2+)
4.
-0.83 V
Codes :
P
Q
R
s
An aqueous solution of X is added slowly to an aqueous solution of Y as shown in List I.
The variation in conductivity of these reactions is. given in List II. Match List I with List II
and select the correct answer using the code given below the lists :
List I
List II
P. (C2H5);N + CHCOOH
For a e R (the set of all real numbers), a -1,
lim
(1a+2a+...+ n)
1
[(u + ou) + " +(Z + ou) +(I + ou)] -p(I + u) o<u
60
Then a =
-15
-17
Circle(s) touching x -- axis at a distance 3 from the origin and having an intercept of
length 27 on y -- axis is (are)
In a triangle PQR, P is the largest angle and cos P =
. Further the incircle of the
triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the
the side(s) of the triangle is (are)
Area of S=
S cT &hd =
10
20
16
32
If 1 ball is drawn from each of the boxes Bj, B, and B3, the probability that all 3 drawn
balls are of the same colour is
qf qRqi Bj, B a2 B # ya 1 ja Rgd md , aq Pgd T H
: lPohIK I t ltd bA
82
90
558
566
If 2 balls are drawn (without replacement) from a randomly selected box and one of
the balls is white and the other ball is red, the probability that these 2 balls are drawn
from box B, is.
yf 2i2 yn ygf8n q4Aa dct (faT yfaryT h) fqId od ae yn
Lb FRb a Ph Lb IP! Z kE bP R lPWb DIR 2! lH3 e 24H Pf
: $ IP9bIK
116
126
65
55
Length of chord PQ is
: 5ltK g Od Iblf
A line L : y = mx + 3 meets y - axis at E(0, 3) and the arc of the parabola y2 = 16x,
0 y 6 at the point F(xo, Yo). The tangent to the parabola at F(xo, Yo) intersects the
y-axis at G(0, y). The slope m of the line L is chosen such that the area of the
triangle EFG has a local maximum.
Match List I with List II and select the correct answer using the code given below the
lists :
yq <TL:y=mx+3,y-3T h fag E(0,3) 3RT qRqdy $ qjq y2=16x,0y6
h fag F(xoyo) qr fAddt $ 1 qRqcR4 cT farg F(xoyo) 9r zqRff y-3RI cnt fqg
G(0,yi) q hTCdt 1qI L 3T yquRI m y uT f fyG EFG?
hc qT yq TTy 3fgqdH 1
yat Iht yat II yARa afy a yRi $ A fy y nT nT yqN chY4
: pUE dRe 1H
List I /yat I
II pI/ II I!!
P.
= u
1|2
Match List I with List II and select the correct answer using the code given below the lists :
List -1
List - II
) 1/2
Match List --I with List--II and select the correct answer using the code given below the lists :
List - 1
List II
P. Volume of parallelepiped determined by vectors , 3 and is 2.
1.100
Then the volume of the parallelepiped determined by vectors
2(d b), 3 (B ) and (c a) is
Q. Volume of parallelepiped determined by vectors a, 3 and is 5.
2.
30
Then the volume of the parallelepiped determined by vectors.
3 (a + b), (b + ) and 2(c + ) is
R. Area of a triangle with adjacent sides determined by vectors
3.
24
and b is 20. Then the area of the triangle with adjacent sides.
determined by vectors (2d + 3b) and (d - b) is
S. Area of a parallelogram with adjacent sides determined by
4.
60
vectors a and b is 30. Then the area of the parallelogram with.
adjacent sides determined by vectors (d + b) and 7 is
yat - I nT yt -II yAfa aRy aer qfqi h Aa fy Ty aT3 nT yqT
: pUE dRA H bAb
ya-1
II-1p
1. 100
P. Hfii d, B aT Z aRT faiR HHiaR yChdq hT 3dT 2
1aq Hfii 2(d x B), 3(B x ) ( x ) aRT faiR
R LPhlIE L gbWq2h dP!tId
Q.4fii a, b ar Z aRr fgfRa HHia ychdq nT 3lT 5 1
2.
30
dq afi 3 (a + b), (b + ) al 2(C + a) aRT fgfRa HHid
f EPhIIE Lb bWq2h
3. 24
R.yh fryg aT aahd, fRnt iat yony aRaii a ae b aRT
AqfRa ,20 1aq afi (2a+3b) a (d -B) aRI
fqiRa iT yo3i qId fyg aT &and
S. y HHiR agf aT aaba fRqt iaT yay aRii a ART
4.
60
lB p IhF (q+ p) yRE bP 1 0E R Pdfby IlB 9
AafRa iaT yo3f qd HHiR agfG hT aand
Codes :
P
R
s
