PART SECTION
. .
I
: PHYSICS
I (Maximum Marks:
28)
This section contains SEVEN questions Each question has FOUR options these four options is(are) correct
[A], [S], [C] and [D]. ONE OR MORE THAN ONE of
.
For each question, darken the bubble(s) conesponding to all the conect option(s) in the oRS
.
For each question, marks ..
Full Marks Parlial
kro
Marlcs
:+l
:0
Marks
Negative Marks
.
+4
._1
will be awarded in one of the followins cateqories:
If only
the bubble(s) corresponding to all the conect option(s)
is(are) darkened For darkening a bubble corresponding to each correct option, provided NO inconect option is darkened Ifnone ofthe bubbles is darkened
In all other cases
and [D] are all the conect options for a question, darkening all these +4 marks; darkening only [A] and [D] witl get +2 marks; and darkening [A] tkee wili get and [B] will get -2 marks, as a wrong option is also darkened
For example,
if tA], tcl
Space for rough work
3136
Q.l
A block M hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to a fxed rigid support at O. A transverse wave pulse (Pulse l) of wavelength,T,a is produced at point O on the rope. The pulse takes time Tq to reach point ,4 If the wave pulse of wavelength la is produced at point A (Pulse 2) without disturbing the position of M it takes ttme Tp to reach point O. Which of the following options is/are conect?
o
Pulse L
Pulse 2
A
[A]
,(y
The time T,to = Tot The velocities of the t'wo pulses (Pulse rope
I
and Pulse 2) are the same at the midpoint
[C]
The wavelength of Pulse
[D]
The velocity of any pulse along the rope is independent of its frequency
I
becomes longer when it reaches point
of
,4
and
wavelength Space for rough work
4136
*9
body has a surface area of approximately 1 m2. The normal body temperature is 10 K above the sunounding room temperatwe 16. Take the room temperature to be Io = 300 K. For T6 = 300 K, the value of oT{ 460 Wm-z (where o is the StefanBoltzmann constant). Which ofthe following options is/are correct?
Q.2 A human
-
[A]
The amount of energy radiated by the body in 1 second is close to 60 foules
[B] If
the surrounding temperature reduces by a small amount Afg << Io, then to maintain the same body temperature the same (living) human being needs to radiate LW = 4oT; LTo more energy per unit time
[C]
Reducing the exposed surface area of the body (e.g. by curling up) allows humans to maintain the same body temperature while reducing the energy lost by radiation
[D] If
the body temperahrre rises significantly then the peak in the spectrum of
electromagnetic radiation emitted by the body would shift to longer wavelengths
Q.3 A block of mass Mhas a circular cut with a frictionless
surface as shown. The block rests on the horizontal frictionless surface ofa fued table. Initially the right edge of the block is at r = 0, in a co-ordinale system faed to the table. A point mass ,n is released from rest at the topmost point of the path as shown and it slides down. Wlen the mass loses contact with the block, its position is x and the velocity is v. At that instant, which of the following options is/are correct? R
l-:
v
R
x
ir= 0
-fr\ y
Th",
"o^oonent
of displacement of the center of mass of the block M is:
[B]
The position of the point mass is:
x=
-A#
tcl
The velocity ofthe point mass
ir, u
= rlm
tDl
The vetocity of the
^
blockMis: V =
'*E
-#
.yY\
A7
(A-r)
)-
l,^4
l\:,
Mx
'-t
"
() o
\a K
d1.1
1''^
(
r ;-l )
(
J
) x
l
wt1 nu.f4
M\
(R-Y)
L
5136
ff|
.l z I 6l\
L,
JTSR
Space for rough work
w^.
o
-
"n1 + L
0
*9
f-1
Q.4 A circulr
insulated copper wire loop is twisted to form two loops of area A and 2A as shown in the figure. Al the point of crossing the wires remain electrically insulated from
each olher. The entire loop lies in the plane (of the paper). A uniform magnetic field B poinS into the plane of the paper. At t = 0, the loop starts rotating about the common diameter as axis with a constant angular velocity ar in the magnetic field. Which of the following options iVare conect? X
x
x
X
X
X
x
x
X
x
B
area A X
X
X
x
x
X
x
X
area 2A x
X
x
x x
o [A]
The rate of change of the flux is maximum when the plane of the loops is perpendicular to plane ofthe paper
tBl
The nel emf induced due to both the loops is proportional to co.r al,
tcl
The emf induced in the loop is proportional to the sum ofthe areas of the two loops
tDl
The amplitude of the maximum net em/induced due to both the loops is equal to the amplitude of maximum arz/induced in the smaller loop alone Space for rough work
t
6136
- 6td "L-r
*9
prism of angle ,4 and refractive index p, it is found that the angle of minimum deviation 6- = ,4. Which of the following options iVare conect?
Q.5 For an isosceles
v [B]
At minimum deviation, the incident angle d, and the refracting refracting surface are related by rr - (ql4 1
frst
as
-'g)
For this prism, the emergent ray at the second surface will be tangential to the
surface when t1
"v
at the
For this prism, the refractive index p and the angle of prism z{ are related A = - cos 2
[C]
t
atrgle
=sln'
sin
the angle of
incidence
at the first surface is
/ 4cos24-1-cos/ 2
For the angle ofincidence i1 the prism
- /, the ray inside the prism is parallel to the base of
Space for rough work
L
t
1A
n!
A
<.:
0
5--A 6
4
t
o
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I
A
L
>B !
; 66.1
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(,
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,
e.s4 : s
fsl
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-f
tr)
- lr'n
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1{ >.
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9rn O: J.t 9irl
a.A
-t >**1
A
"v
It t-
U (\ 1136
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A
L t cf1 '' -/r-, *9
Q.6 In the circuit
shown,
an a.c. soruce V
-
L=
Vo sin
7 pH,C
at
= IUF andR = 1kO.
They are connected in series with following options is/are correct? C=1pF R=1kQ
as shown. Which of the
i=1pH Yosinot
The frequency at which the curent
will
be in phase with the voltage is independent
ofR At ar-0 the current flowing through the circuit becomes nearly zero
tBl
tcI At ar >> L06 rad. s- 1, the circuit behaves like a capacitor
yl'l
The cunent
will be
Q.7 A flat plate is moving
rn phase with the voltage
if
ar
=
104 rad. s-1
normal to its plane through a gas under the action of a constant force
F. The gas is kept at a very low pressure. The speed of the plate v is much less than the average speed r of the gas molecules. Which of the following options is/are tme?
[A]
The resistive force experienced by the plate is proportional to v
[B]
The pressure difference between the leading and trailing faces
of the plate
proportional to zu
[C]
The plate
[D]
At a later time the extemal force F balances the resistive force
will continue to move with constant non-zero acceleration,
Space for rough work
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Jc
L
IL ,./
'1 \\)
\4
I
o
.,,tr'
I
rQ-'
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8136
at all times
('
l-
is
SECTION 2 (Maximum Marks: 15)
. This sectiou contains FIVE questions . The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive
. .
For each question, darken the bubble conesponding to the corect integer in the ORS For each question, marks
Full
be awarded in one
Marks : +3 Ifonly the bubble
kro Marlcs : 0
e.8
will
ofthe following categories:
conesponding to the conect answer is darkened
In all other cases
91 y111-r divides itself A drop of tiquid of radius R = 10-2 m having surface tension 5 = into K identicat drops. In this process the total change in the surface energy AU = 10-3 J' If K = 10" then the value of a is is un isotope of Iodine that p decays to.an isotope of Xenon with a half-life of 8 days l3rl is injected into the blood of a person The A small amount of a ser,.rm labetled with r3rl inlccted was 2.4 x10s Becquerel (Bq). It is known that the activity of the amount of injected serum will get distributed uniformty in the blood sFeam in less than half an hour. Aher 11.5 hours, 2.5 ml ofblood is drawn from the person'.s bodv, and gives an activity of ximately 115 Bq. The total volume ofblood in the person's body, in liters ts a x 2 0.7) and ln ! + r for lrl << 1 (you may use e' ^'
'''I
Q.e
-,\ /r/ .1
a
/y
l,/
ff
L ,1J
U
f'
for rough work
sP a
d2
&"4.
'2q
q
&
.D
(\
"k
*
Y
@$*
t4 {t
P
k
->/
"t+
L
I
-Fr a-
)
6
V] "^pvB
A"
,,.'/
9
')*
t
;Y
\r/" 1, ,@
9136
q
L
IA
\+, )
.-4-r+) *9
from an orbit with quanum number Q.l0 An electron in a hy&ogen atom undergoes a transition respectively the initial and fina VS are fli to another with quantum number n1. Vi and potential energies of the electron rc
fi=
e 'zs tbenthe smallest possiblenJ is '
light is travetling in a medium of refractive index n = 1.6. It enters a of the glass stack of glass layers from the bottom side at an angle I = 30o. The interfaces layers ar-e puroil.l to each other. The refractive indices of different glass tuy.:,r L. the rz" slab monotonicaily decreasing as nn= n - mL'n, where n' is the refractive index of the between to the interface and An = 0.1 (see the figure). The ray is refiacted out parallel (m - l)'h and m'h slabs from the right side of the stack' What is the value of rz?
Q.ll A monochromatic
n-m n n- m-1 An
m
'm-
n-3An n-2An n-An
:3
,.J \c
4
ci..
.\
2 L
n
l tr
J Space for rough work 0
J
(/
.
^A ,II
9)
J \\
1kil, 4 -c.
\
.O
q'
.\)
.(^\
qo d
<"
s$ \t
"C(.
$\$
I
\
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4
"r\ *'a.Q
r,
//
(
.C'
f\ @
)
F.
Y
w
-.s. C^' r0136
I
*9
492 Hz. The sovnd is reflected bY a Q.12 A stationary source emits sound of frequency /s 1. received large car approac fting the source with a sPeed of 2 ms- The reflected signal is of the frequency the beat will be What by the source and superposed with the original. the car resulting signal in Hz? (Given that the speed of sound in air is 330 ms-1 and reflects the sound at the frequency i, has received)
Space for rough work
)-
0
o
I /.lo\
I
t
>\ \
?t "2:o 9jD' 1j0
1-t\
)/r *:y )+L,.
<\
q
t,
\E
\q ")
Y
tt-t+j
n
j*$
r
r 3i{ Yrv >-+6
1-3
*9 11/36
SECTION 3 (Maximum Marks: 18)
. . . .
This section contains SIX questions of matching type This section contains TWO tables (each having 3 columns and 4 rows) Based on each table, there are
THREE questions
Each question has FOUR options is conect
[A], [B], [C], and [D]. ONLY ONE of these four options
.
For each question, darken the bubble conesponding to the conect opticn in the ORS
.
For each question, marks
Marlc : +3 kro Marks : 0 Full Ne.
live
Marh: -l
wil[
be awarded in one of the followinq categories
Ifonly the bubble conesponding to the conect option If none of the bubbles is darkened
is darkened
In all other cases Space for rough work
12136
*9
given in the three Ansrver Q.13, Q.14 and Q.15 by appropriately matching the information columns of the following table.
A charg ed partl c
e (e ectro n o r
proto n)
s
tn trod u c ed at th e o rrg rn (x
0
0
v
0)
th a
ty v A uru form e c tfl Ir e d E an d a u nl form ma8 n tl fi d B ex rs 1 d T he ve lo c ly v ectn c fi e d E and magn ti c fi e d B are grven m co runn s 2 an
en nl tial YE lo c
eryw he IC
(r)
B afe
T h u an trtl CS E Column I
tl
3 re
r7
(r) t
(III)
Proton with r7 = 0
(lV)
pro16n y116
Q.l3 In which
fAl
f
case
(rD (iiD
toi
=
=
will
n ma
tud
Column 3
=
(P) d =
Loz
Bo
-B6i
(ii) 7 = -Eo!
(e) d = Boi
(iii)
G) d=Boi
E=
-E6i
(iv)t=Ei
E.^
2
tl
Column 2
Electronwithi=2 Bo
(II) Electron with
S
(s) d =
Bqz
the particle move in a straight line with co'?s'an' velocity?
(s)
$Bl
(IV) (r)
(s)
tcl
(IID (iD
(R) y1
Qtr)(ti1)(P)
helical path with axis along the positive z Q.l4 In which case will the particle describe a direction?
Ant
trrl tiil
W
/uu)
(ii) (R)
(IV) (i)
Xl
(s) I
0rr) (iiD (P)
Q.l5Inwhichcasewouldtheparticlemoveinasfiaightlinealongthenegativedirectionofyaxis (i.e., move along - f)?
tAl 0v) (iD (s)
tBl
(IID (iD (P)
I
(D(iii)(Q)
CID (ii) (R)
Space for rough work
J
*9 13136
matching the information given in the three Answer Q.16, Q.17 and Q.18 by appropriately columns of the following table' n the th EIIN odynam c p roce s s n di ffer en t ays as s hown An de al gas ts un derg o ng a c v t o state p from ath v diagrams m c o umn J o f the tab Co ns d er on v the c OITE sponding P rk d o ne o n th e Sv s m Th e eq u a ti ons and p o ts ln the sta te 2 W d eno te S the c orr ES p onding tlo o f he a ITN o dy na ml c proce s ses H ere v ls the ra tab 1e ha e s tandard notati o ns as used 1n th s n o f m o e s m the s sure and c ons ant o ume The number ties al c onsta n c Column 3 Column 2 Column I (P)
(D
(D
\^2
Wt-z
1
y-l
(P2V2
-
2
L
Isothermal
hvL) (a)
(ii)
(r)
8zo Wp2= -PV2*
Isochoric
PV1
2
(ii,)
(ID Wp2=
u -,, f,V
(iv)
1,
wr-r-- -nntn(f,)
(R) 1 2
Isobaric
0
(IV)
1
.rt
(S)
Adiabatic
2
{
Space for rough work
t-o
Pv
{ .(
P' flt -Pv
*9 14136
*\v
{
Q.
l6
representation of a process in which Which of the following options is the only correct
AU= AQ- PAV?
f
(r)
tel (tD (iv) (R)
Q.l7 Which
dAl
(iiD
e)
h
tct
(D (iii)
(s)
tDl
(llD (iiD G)
combination? one of the foltowing options is the conect
flIXiD(s)
(I)(iv)(R)
1l
fcl
(r)(iv)(P)
,!Dl
(IV)(ii)(s)
process that is options correctly represents a thermodynamic Q.18 Which one of the following gas? the speed of sound in an ideal used as a correction in the d-etermination of
tnl (Itt)(iv)(R)
iBl
(I) (ii)
(Q) tcl (IV) (iD G)
(l) (iv) (Q)
END OF PART I : PHYSICS Space for rough work
6
b
?e
v
\
@
*9 15136
PART
II : CHEMISTRY
SECTION 1 (Maximum Marks:28)
. This section contains SEVEN questions . Each question has FOUR options [A], [B]' [C] and [D] ONE OR MORE THAN ONE of these four options is(are) correct
.Foreachquestion,darkenthebubbte(s)conespondingtoalltheconectoption(s)intheoRS
.
For each question, marks
Full Marks Partial Marks
kro
Marks
Negative Marl
will be awarded in o ne of the follo wtng categorles
+4 +1 0 -Z
If only
option(s) the bubble(s) conesponding to all the conect
is(are) darkened fJ. autt.niog a bubble conesponding to each correct option' provided NO inconect option is darkened ifnone ofthe bubbles ls darkened
In all other cases
.Forexample,iftA]'tcland[Dlarealltheconectoptionsforaouestion.darkeningallthese toi *,r get +i mark; and darkening [A] ttuee will get +4 marks; a"*Ll;"g ""iv fnf
'J
is also darkened and [B] wil-l get -2 marks' as a wrong option
of the following compound is(are) Q.19 The IUPAC name(s) CI
Hrc
YAr
rt
r6136
4-methYlchlorobenzene 1
-chloro-4-methYlbenzene
[B]
4-chlorotoluene
[D]
1-methYl-4-chlorobenzene
Space for rough work
-_ addition reactions is(are) correct statement(s) for the fottowing The Q.20
H.C (D
(ii)
H
H
CH:
HrC.
,cH:
Br2 / CHCI3
MandN
Br2 / CHCI3
OandP
HH (M
pairs ofdiastereomers and O) and (N and P) are two
in both the reactions Bromination proceeds through /rars-addition
F;
O and P are identical molecules
(M and O) and (N and P)
tDl
are two pairs of enantiomers
aoueous solution of MCh'6HuO aqueous ammonia to a pink coloured excess of Addition Q.2l in the presence of air' In aqueous solution' (X) and NHrCI gi"' un ot"ui"-aoi tornpft* Y X with excess HCI at room ihe reaction complex Y behaves as complex Z' The calculated spin a blue coloured'of tht in results temperature Y' N'{'' *tttteas it is zero for complex : mornt"
;il;;;G ;;;;;;; o'i"#i?l' iig
only magnetic which statement(s) is(are) correct? Among the followlng optrons'
f
I
#
tDl
metal ion in Y is d2sp3 The hybridization of the central
Z is a tetrahedral comPler' chloride gives only two equivalents ofsilver Addition ofsilver nitrate to Y is pink 0oC' the colour ofthe solution When X and Z are in equilibrium at
o{1 v1 f
tr
afU
lj+
0
\(
Space for rough work
L+!
tab
?'8
n,
1
q
,1
'(J 4
\
"P
\
Nt
11136
o P
/'.r
"l)
vt rn =,)
.f,{ *9
L plotted against the mole fraction of Ni in rolrtion is shown in the following figure. Here:1 and:1,a represent mole fractions of L and M, respectively, in the solution. The correct statement(s)
L and M, the vapour pressure of Q.22 For a solution formed by mixing liquids applicabte to this system is(are)
'Z 1
Pg
I
.ry
0
in pure liquid L and M-M in tAl Attractive intermolecular interactions between L-L pure liquid M are stronger than those between L-M when mixed in solution
t p1
rne point Z when
]
rr )
represents vapour pressure of pure
liquid M and Raoult's law is obeyed
0
The point Z represents vapour pressure of pure liquid I when rr
L
and Raoult's law is obeyed
)
[D]ThepointZrepresentsVapourpressureofpureliquidMandRaoult'slawisobeyed
fromrr:0toxr.=
1
Space for rough work
\
18/36
\
J
t
+h {+l
*9
(pz,Yz,Tz) under different conditions. The Q.23 An ideal gas is expanded from (pr, V1, T1) to is(are) correct statement(s) among the following
it is
compressed irreversibly from
[A]
The work done on the gas is maximum when (p2, V2) to (pr, V1) against constant pressure pr
[B]
The work done by the gas is less when it is expanded reversibly from Vr to V2 under adiabatic conditions as compared to that when expanded reversibly from Vr to V: under isothermal conditions The change in intemal energy of the gas is (i) zero, if it is expanded reversibly with Tr = Tz, and (ii) positive, if it is expanded reversibly under adiabatic conditions with
Tr*Tz
[D]
If
the expansion is carried out freely, adiabatic
it is simultaneously both isothermal
Space for rough ,,nJ
-,\:
19V
work
(
?
v
as
well
as
D
-M4
t9136
b1
*9
Q.24 The conect statemcnt(s) about the oxoacids, HCIOr and HCIO, is(are)
[A] [B]
rl
-1 I
HCIOa is more acidic than HCIO because of the resonance stabilization of its anion
HCIO4 is formed in the reaction between Ch and HzO
Jf,J The central atom in both HClO.r and HCIO is sp3 hybridized - [Dl The conjugate base of HC1O.1 is weaker base than H2O Q.25 The colour of the X2 molecules of group 17 elements changes gradually from yellow to violet down the group. This is due to
[A]
the physical state of X2 at room temperature changes from gas to solid down the
goup
tBl
decrease in HOMO-LUMO gap down the group
tcl
decrease in
iDl
decrease in ionization energy down the group
l-o+
gap down the group
Space for rough work t-,\
{w
20136
'@
o\^'
*9
SECTION 2 (Maximum Marks: 15)
.
.
This section contains FIVE questions The answer to each question is a SINGLE inclusive
DIGIT INTEGER ranging from 0 to 9,
.
For each question, darken the bubble corresponding to the conect integer in the ORS
.
For each question, marls
Full
Marl
Zero
Marl
+3
:
0
will
both
be awarded in one of the followine catesories:
If only the bubble conesponding to the correct answer
is darkened
In alI other cases
j
iei,Lrr,Bez,Il2, €z,Nrdi, ana r:, ttre number of diamagnetic species is (Atomic numbers: H= 1, He=2, Li=3,8e= 4,8 =5, C =6,N=7, O= 8,F:9)
Q.26 Among H:,
Q.27 Among the following, the number of aromatic compound(s) is
o
J.
F
t
@
@
.1
a
o
@
J}
I
Space for rough work
r
+
lq
{
.1
L
lt
o- 79
rL
d
4
,L 1-.
t
a-
T
i
n1' v
!
I lg
21136
*9
",
.1'r
JF
I:-
+ \o
1q
\52
+\ il^
-Lo
\
q
0.0015 M aqueous solution of a weak monobasic acid was determined by using a conductiviry cell consisting of platinized Pt electrodes. The distance between the ilectrodes is 120 cm with an area ofcross section of I cm2. The conductance of this solution was found to be 5x10-7S. The pH of the solution is 4. The value of
Q.28 The conductance
of a
limiting molar conductivity (A', ) or trris weak Zx102S cm-rmol-r. The value of
monobasip{in
Z is
h 1J,
Q.29 The sum of the number of lone pairs of electrons
r0
species is
v
[TeB16]2-,
(Atomicnumbers:
N=7,
F
=9,
Qq each
central atom in the foll owrng
€
[BrFr*,
S:
aqueous solution is
16,
SNF3, and
[XeF]]-
Br=35,Te= 52,Xe=
54)
A crystalline solid ofa pure substance has a face-centred cubic structure with a cell edge of e.30 - a00 pm. If the density of the substance in the crystal is 8 g cm-3, then the number of atoms present in 256 g of the crystal is Nx 102a. The value of N is fa
\I
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+
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+
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rg X(,
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,.
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vr q D
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\^a
tou
* ,ot{
tt' b.uv\l
* F+r
bt -\1 * o
'r
*t '{ tu
r\
{"
f
,d.4 qb
-,9
Nr
U
<
f I.x )t
l6
lt * H
Y ro -i
,/ ,\
d,,o' 1
g
*}.
t)
./)
Space for rough work
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't M
16*6 I l0
t- \,
+1
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/i
22136
*9
Ll
SECTION 3 (Maximum Marks: 18)
. This section contains SIX questions of matching type . This section contains TWO tables (each havtng 3 columns and 4 rows) . Based on each table, there are THREE questions . Each question has FOUR options tAl, tBl, [C], and [D] ONLY ONE of these four options is correct
. For each question, darken the bubble corresponding to the correct option in the ORS cateqones . For each question, marks will be awarded in one of the foll +3 Ifonly the bubble conesponding to the conect option is darkened Full Marl
)t9 23136
information given in the three Answer Q.31, Q.32 and Q.33 by appropriately matching the columns of the followitrg table' depends upon spherical The wave function, l) ,,t.^,is a mathematica I function whose value the quantum numbers n' / and polar coordinates (r,0,0) of lhe electron and characterized by
-m,.Hererisdistancefromnucleus,discolatitudeand/isazimuthlnthemathematical functions gi ven in the Table,
Column (l) ls orbital
Z
is atomic numb er ar.id
I
Column l (t)
"
{.t.",
a" is Bohr radius Column 3
2
(P)
(z\1
\i)'
I \
\v/-
0
r (ll)
2s orbital
loo+
(Q) Probabiliry density at nucleus
(ii) One radia[ node
c(
I
-T ao
(lII) 2p, orbital (tn) q^.,,,,
c(
Z
(R) Probability density is maximum
lL\
at nucleus
re lz." / cosd
ao
(rv)
3dz orbital
needed to excite electron fiom n=2stateto n= )1 4 state is 1 times the energy
(S) Energy
(iv) ry-plane is a nodal Plane
32
needed to excite electron from
/,=2statcton=6state
l, the only GoRRECT combination for any hydrogenJike Q.31 For the given orbital in column specles ls
lAl
(lv) (iv) (R)
P
GD(ii)(P)
ff
€*XrnfGF tDl O(il)(s)
combination is Q.32 For He* ion, the only INCORRECT
tAl
(ID (ii)
(Q
tBl
(I) (i)
(s)
tcl
0) (i) (R)
tDl (D(ii')(R)
combination is Q.33 For hydrogen atom, the only CORRECT
tel 0 (iv) (R)
tel-tltxff
tcl
0D (') (Q)
Space for rough work
24136
tDl (I) (') (s)
^t/
I
.t)
!
F:
Answer Q.34, Q.35 and Q.36 by appropriately matching the information given in the three columns of the following tableColumns
1,2
and
3 contain starting materia ls, reaction conditions, and type of
reactions,
respectivelY
Column
I
Column 3
Column 2
(l) Toluene
(i) NaOtV Brz
(P) Condensation
(ll)
(ii) Bal hv
(Q) Carboxylation
Acetophenone
(lll)
Benzaldehyde
(lV) Phenol
(iii) (CHTCO)rOI CH:COO
) Substitution
(iv) NaOtU COz
) Haloform
combination is Q.34 For the synthesis ofbenzoic acid, the only CORRECT
t.ql 0D
f Q.35
(iv)
G)
tBl (lv)
s
(iD
(P) tcl (t) (iv) (Q)
-raf
uu t,l
ttl
The onty GoRRECT combination in whicli the reaction proceeds through radical mechanism is
tAl
0) (ii)
(R)
tBl
(ll) (iir)
(R) tcl 0lD (iD (P)
(i) (a) JDI 0v)
carboxylic acids is Q.36 The only CORRECT combination that gives two different
tAl v
(rv) (iiD (Q)
u;y'Orrl tii,l
el fcl (tt) (iv) (n)
tDl
19 (D (s)
0 END OF PART II : CHEMISTRY Space for rough work
2st36
*9
=-
PART
III : MATHEMATICS
SECTION 1(M aximum Marks: 28)
.
This section contains SEVEN questions
.
Each question has FOUR options these four oPtions is(are) conect
. .
in the ORS conesponding to all the conect option(s) For each question, darken the bubble(s) For each question, marks
Full
.
Marks
'.
[A], [B], [c]
and
will be awarded in one of
+4
lf
of [D] oNE oR MORE THAN ONE
the
followins categories:
conect opfion(s) only the bubble(s) corresponding to all the
is(are) darkened
Partial Marlcs
ri. Jl*""rg a bubble conesponding : +1
Zero Marlts Negative Marks
: 0 : -2
For example,
provided NO inconect option is 'larkened
if tAl, tcl
,trrJ;iis; -i and [B]
will
to each correct oPtion'
none of the bubbles is darkened In all other cases
if
for a question, darkening all these
[Dl are all the correct options and darkening [A] ou'itnlng onlv [A] and [D] wilt get +i marks;
and
'nuiti; get -2 marks, as a wrong option is also darkeneo
with real entries? is(are) NOT the square of a 3x3 matrix Q.37 Which of the following
11
0 0l
ts
ril
v [: l -l] { Q.38 If
f,I
has the equation 2x + y - p' l' !:. h and k? *f'l""f' of tf't following is(are) possible value($ ofp'
the.parabola a chord, which is not a tangent'-of
and midpoint (h,
It ,(ct
k), then
*tBl P= -1,h=L'k--3 .P' p=2,h=3,k=-4
P=5,h=4,k--3
p=-2,n=z,k=-4
,Sw .t +
P
-l 0 0 0-1 0 00-7 00 1 0 -L0 0 -1 0
)
J
space for rough work
v'.r-
16,
r
7
9.
.A
.t
.tC
F.
L \
\
ro
1
n'v
26136
)
rb
tv.
\
14
r.tt
\ ! i..
)qf
\
q\
*9
a,b,x
Q.39 Let
z=x
y
and
a- b - I and y + 0. If the complex number
be real numbers such that
r t! satisfies /z(4J
of
= y, then which of the fotlowing is(are) possibte vatue(s)
x?
tBl 1+.ra + I
-1-JT=F
W1
tcl 1- .lTl7 Q.40 Let X and Y be two events such that P(X) =
Jp
=i
I
i,r
y)
t
tN P(x'tD=: P(xvv)
-r+,h-yi
161
lDt
P(x
and P ( Y
2
n
? Then 5
nD =:
P(D =
*
Q.4l Let [x] be the greatest integer less than or equals to r. Then, at which of the following point(s) the tunction f(x) = r cos(n(r * [x])) is discontinuous?
{Bl x= o
r=-t
/
y)
v
x=2
Space for rough work
l ,/
Ir
.-i
P
r)
q '/,i
€s
r('
rnvl.
l0
f+Yb,'r) r r-
\1-
0v
x
27136
',
/t'
h.)
r
r
lrv
r'\
d
t
t-'-
r$A
u^)A
ao
ilv
rL)
t{r(
n.nln* {r \^,o) (I^, \^
-,
7n
1\a
(
J'
J
$
i\
,t\
\
r(
1
I
q
v
.
-ih - u>
l
'o
"(nx Yq
eJ+-t
(
,/ r.
r
1-1.r^.ye>a-'
)
nY
t{
r}
I
,
OLr, . lt' : - rr
-)
5
\r'{
Y
_h
o
Itt
)-r
-tt
L/
,r
)
r
:4r
lo
%
(lr-
*rL\b
'T-^rY V\
t
rCg tg/Q-r-q,
/\
1
.J PI r ) o
.r
x=7
h
t-o'\
tt (r)
+h
re4
r
(
.'^i2t)
lfzx-
Q.42
y+l=0isatangenttothehyperbola *-';=1'thenwhichofthefollowing
CANNOT be sides of a right angled triangle?
za,a,l
lA) Q.43 Let
f:
R.
-+ (0,
[B]
24,8,
I
lCl
a,a't
lDl
a,4,2
1) be a continuous function. Then, which of the following
function(s)
has(have) the vatue zero at some point in the intewal (0, 1)?
lAl
e,
- Ii f G) sint at 1n
lcl f(x)
+
li
fG) sint
[B]
dt
x'- /(x)
[D] x - I;-' !(t) rott at Space for rough work
7
\L \
.I
,
I
,il.')
f
,
cr
a\
J
o
.,0
s
-s
o
\
,d
\t
I
\
-r
\,
(
s
@!
?
.t
+
\
{\
\
v I \+
$'
,v^ \h
bc'.
v
v \
19
\r
\
q\ ./(-c..
\s
28136
a'
\
\
{
\
\
o..' {l
\
c'
c'
t'
\)*
I \h
.t
+
+ (/
,//
o..
-!'SECTION 2 (Maximum Marks: 15)
.
This section contains FIVE questions
.
0 to 9, both The answer to each question is a sINGLE DIGIT INTEGER ranging from inclusive
.
in the oRS For each question, darken the bubble corresponding to the correct integer
.
For each question, marks
Futt Marks Zero Marks
will
be awarded in one
ofthe followins cateqories:
: +3 lf only the bubble corresponding
: 0
to the correct answer is darkened
In all other cases
are in arithmetic progression. If the triangle has area 24, Q.44 The sides of a right angted triangle th"n what is the iength of its smal[est
-
side?
LD
a 45 For how many values of p, the circle
xz + yz + 2x + 4y
- P = 0 and the coordinate axes &"tl
have exactly three common Points?
Space for rough work
,tr rfr -- vb
t f )t lt\
I
r
>
)
"r4
+5
) t
[,' ---1
\
l.! +
fr
\\i2
#
tt -Cl
o
,11'", .\ I )-
w*l (
t: I o(
rlc tvE
--
$
l!
a
t"y$
Ptl'\-
')
v
s 1)
w
uf
J,
,
.\
-1,
<6 o
!.
d"
.ail'
,"J
-.,
i0
C:
-t
)a
I dv8. 1,
n>
%
*9 29136
6
0^
)s
DL ,
,l
r\^r{
,Y 7[
,c
Q.46 For a real number a, if the system
ln: ;lEr tilI
of linear equations, has infrnitely many solutions, then L
a
*
qz =
a) :
the letters A, B, C, D, E, F, G, H,l' J Let be the Q.47 Words of length 10 are formed using number of suc-h words where no letter is repeated; and let y be the number of such where exactly one letter is repeated twice and no other lettcr is repeated Then,,l =
Q.48 Let
/:
R -r
R.
be a differentiable function such that
/(0) =
O,f
lt 1 o (x)
I [/'(t)
cosec
t
e) = 3 and /'(0) = 1. If
- cott cosec t /(t)] dt
x
for
r e (0,|], then lim,-o g (x ) )rt a
Space for rough work
, l-o
\
.A
I -a
q
tDr
x
I o
J
wa-t tt ' 1
cth o* ( t uet
t
/w-%
cltl=
t D >t
7\/
.l
30135
x
D
t
N
I
lo q
\.,t
>l rrl
f
| -- \o
). )
t
a
b
*9
SECTION 3 (Maximum Marks: lE)
. This section contains SIX questions of matching type . This section contains TWO tables (each having 3 columns and 4 rows) . Based on each table, there are THREE questions . Each question has FOUR options [A], [B], [C], and [D]. ONLY ONE of these four options is correct
. .
For each question, darken the bubble corresponding to the correct option in the ORS For each question, marks
Marl
Full
live Marl$'. -1
will
be awarded in one
Ifonly
ofthe following cateqories:
the bubble coresPonding to the correct option is darkened
Ifnone ofthe bubbles is darkened In all other cases Space for rough work
3r136
*9
$
\r
tr $t'
-1
tss#
9
v
Answer Q.49, Q.50 and Q.5l by appropriately matching the information given in the three columns of the following table. Columns
l,
2 and 3 contain conics, equations of tangents to the conics and points of contact,
respectrvely.
I
Column
(D
Column 2
x2+Y2 =42
I
,(1) mY = m2x
Column 3 (P)
a
-)
(ID
x2 + a2y2 =
a2
-(ii)y=4a1o
/
0D !2 = 4ax
azmz
.,-..\ t)
m2+7
(lii)y=7niaa
a2a
(m2 'm )
r(Q)
-|
(R)
\}t.
-m@ (,'lm2+t'.'lm2+t ) a
-a2m (.@;?n' Va\n4J
.\
x' - a'y'
(rv)
a
2
(iv) y =7n74
a2m2
+
-),
(s)
-azm
(
azmz
1
-7
a2m2
-
Q.49 The tangent to a suitable conic (Column l) at (f3, ]) is founa to be r/-3x + 2y which of the following options is the only CORRECT combination?
tAl
(lD (iii)
(R)
[n]
(lv) (iv)
(s) tcl (lv) (iiD (s)
v
-
4, then
(lI) (iv) (R)
Q.50 Ifa tangent to a suitable conic (Column l) is found to be y = x * 8 and its point ofcontact is (8, 16), then which of the following options is the only CORRECT combination?
Jd
ruuttlt.r
,.t"
I (IIt)(iD(O tcl (r)(iv)(R) b
tDl
(r) (iD
(a)
- r11, if u tangent is drawn to a suitable conic (Column 1) at the point of contact (-1, 1), then which of the following options is the only CORRECT combination for
Q.5'l For a
obtaining its equation?
tAl
rl
* Dr'
(rr) (ii)
I
t
tBl
l5c^
.,
0) (ii) (a)
(J
?)
-
).r
!e
t" +
\IJ \
'r..[ $A Y
J4,n l6
L
rn
a
I
{
1
ll9
a
I
-1 rb)
g
r'
k-.
\l'la'r'
1 .i-"" ,ll
\
^Yr,ft
-tlJZv
') fa +
., v tlriajj
.r(\
32t36
b
I 'l/
tr'
"l.t&nE \nt
(p) F tct (r) (D G)
(rrD (i)
Space for rough work
\
u
'/ ,1" ,,P
(Q)
aA,+ .-r
B
I$v
.r
0 -u-
eo
L,
Answer Q.52, Q.53 and Q.54 by appropriatety matching the information given in the three columns of the following table.
f(x) = r + Iogex - xlog"x, r E (0,co). . Column t contains in fo rm tion about zeros of / (r), f' (x) and f " (x). . Cotumn 2 contains informatioD about the limiting behavior of /(r), /' (x) and f " (x) at infinity . Column 3 contains information about increasing/decreasing nature of f (x) ail f'(x).
Let
a
I
Column (I)
/(r)
=
x e (7, e2)
o for some
/'(x) = o for some x € (1, e)
(u)
Column 3
Column 2
z € (0, 1)
(i) lim,-- /(x) = 0
(P)
f
is increasing in (0,
(ii) lim,-- f (x) = -co
(Q)
/
is decreasin
(iii) Iim,-- f'(x) = -o
(R)
/'
is increasing in (0, 1)
(S)
f
is decreasin g in (e, e2)
(llt)
/'(r)
(IV)
f"(x) = 0 for some x E (1, e) (iv) lim,-- /"(x) = 0
=
o for some
Q.52 Which of the following options is the only CORRECT combination?
\f
IAI
t
(tvl til
tst
XtBl
(R)
(l) (ii)
(lll) (iv)
[c]
(P)
Ff
1
gh (e, e2)
f
\r ,G{, (ID (iiD (S) .tr .i
Q.53 Which of the following options is the only CoRRECT combination?
tt
tAl
DF
(IID (iiD
(R)
tBl
(l) (i)
(P)
(lv) (iv) (s)
tcl
,^ B!','
\+
tDl (rD (ii) (Q)
combination? Q.54 Which of the following options is the only INCORRECT
tAl r \,r
tBl
(ID (iii) (P)
p\sv-
(lD (iv)
(Q) tcl (D (iii) (P)
rfGrtltiltnl ) '
END OFTHE QUESTION PAPER
-t
,r Space for rough work
!A )
Y+
J
-l
'1 1
.f
r^
l
l-e-)/ '
.t
v-'
(t-, r 1 tn r
9
o
:8('r
.,
e-
,(
- t L-t*
I
o
L
I
w
) +'l >0
I v-l ]i t
a
0
p-l c>
(
4 33136
*9
0
t-
f I
u1 a
l+ Lu>
(
q\r^ 1
3
i
f Ira )'
t-'t ^
\
