IIT-JEE Advanced 2016 Question Paper 1

IIT-JEE Advanced 2016 Question Paper 1

1. PART I : PHYSICS

SECTION 1 Maximum Marks: 15) |

‘This section contains FIVE questions,

Each question has FOUR options (A), (1, (C) and (D). ONLY ONE of these four options is |

For each question, darken the bubble corresponding to the correct option in the ORS.

For each question, marks vil be aware sof the following categories

Fall Marks +3. Ifonly the bubble corresponding to the correct option is darkened.
Zero Marks 0 Ifnone ofthe bubbles is darkened

Negative Marks : 1 In al other cases.

Q1 Im a historial experiment to detomine Planck constant, a mol surface was irradiated
wrth light of diferent wavelengths. The emitiodphotolectron energies were measured by
Srvlving a stoping potential Tho relevant date for the wavelongdh (2) finden Hight and
tho carrespending sopping potential Us) aro given blow

Tom, wan
a
01 10
os 04
Given that ¢ = 9 x 10*m 5% and e=16x100, Planck constant (in units of 5) ound
fron such an experiment le
(a) 60x10% (M) 64x10% (©) 66x10 (D) Bar“
Space Tor rough work
Answers for the above questions
Ans for Q1: (8)
am

“1

2. a2

A uniform wooden stick of mass 1.6 kg and length / rests in an inclined manner on a smooth,
vertical wall of I

ht A(</) such that a small portion of the stick extends beyond the wall
"The reaction force of the wall on the stick is perpendicular tothe stick. The stick makes an
angle of 30° with the wall and the bottom of the stick is on a rough floor. The reaction
wall on the stick is equal in masgnitu

the
de to the reaction ofthe floor on the stick. The ratio h/t

and the frietional force fat the bottom of the stick are

o

A 905 105

© 1
176 3

ae
=
Anewors tort abaya questions
[Ans for Q.2: (D) Ans for Q.
4

4136

3. Q4 A parallel beam of light is incident from air at an angle won the side PQ of a right angled
triangular prism of refractive index n°2. Light undorgoes total internal reflection in the
prism at th face PR when « has a minimum value of 45°, The angle 0 ofthe pri

y
xp
ar
wor B) 225 © 30° ©
Space for rough work
Answers for the above questions
Ans for Q.4: (A)
a

4. Q5 An infinite line charge of uniform eleetrie charge density 2 lies along the axis of an
clectrically conducting infinite cylindrical shell of radius R. At time ¢=0, the space inside
the cylinder is filled with a material of permittivity 2 and electrical conductivity 0. The

electrical conduction in the material follows Ohm's law. Which one of the following graphe
best describes the subsequent variation of the magnit

the material?

de of current density) at any point

a »
- . ‘
je jo
©) D) Mo
‘ st

0,9) 00

Space for rough work

Answers for the above questions
Ans for Q.5: (C)

“1 one

5. SECTION 2 (Maximum Marks: 82) ]

+ This section contains EIGHT questions
+ Fach question has FOUR options (A), (2), (C) and (D). ONE OR MORE THAN ONE of

these four option(s (are) correct.
+ For each question, darken the bubble(s) corresponding to all the correct option(s) in the
ORS.
For each question, marks will be awarded in one ofthe fllawing eategories
Full Marks +4. If only the bubble(s) corresponding to all the correct option(s)
istare) darkened.
Partial Marks; +) For darkening a bubble corresponding to each correct option,
provided NO incorrect option is darkened.
Zero Marks 0 If none of the bubbles is darkened
‘Negative Marks : -2 In all other cases.

+ For example, if (A), (C) and (D) are all the correct options for a question, darkening all
these three will result in +4 marks; darkening only (A) and (D) will result in +2 marks; and
darkening (A) and (B) will result in -2 marks, as a wrong option is also darkened.

Q6 Highly excited states for hydrogenlike atoms (also called Rydberg. states) with nuclear
charge Ze are defined by their principal quantum number 1, where n>>1. Which of the
following statements) (are) true?

(A) Relative change in the radii of two consecutivo orbitals does not depend on Z
(8) Relative change in the radii of two consecutive orbitals varies as Un

(€) Relative change in the energy of two consecutive orbitals varies as 1/n"

(D) Relative change in the angular momenta of two consecutive orbitals varies as Um

Space for rough work

Answers for the above questions
Ans for Q.6: (A), (B), and (D)

7136 “1

6. ar

‘Two loudspeakers M and N are located 20 m apart and emit sound at frequencies 118 Hz
and 121 Hz, respectively. A car is initially at a point P, 1800 m away from the midpoint @
of the lino MN and moves towards Q constantly at 60 kr along the perpendicular
bisector of MN. It crosses Q and eventually reaches a point R, 1800 m away from Q. Let
MO) represent the beat frequency measured by a person sitting in the car at time 1.
Let vp, Vg and v be the beat froquencios measured at locations P, @ and R, respectively

30 ms". Which of the following statement(s) stare) true

The speed of sound in air is

regarding the sound heard by the person?
A) Vet y= 2 Ya
(B) The rate of change in beat frequency is maximum when the car passes through Q

(©) The plot bolow represents schematically the variation of beat frequency with time

(D) The plot below represents schematically the variation of boat froqueney with time

Space for rough work

Answers for the above questions
Ans for Q.7: (A), (B), and (C)

sas

7. Qs

Qs

An incandescent bulb has a thin filament of tungsten that is heated to high temperature by
passing an electric current. The hot Glament emits black-body radiation, The filament is
Sbeerved to break up at random locations after a sufficiently long time of operation due to
fhomuniform evaporation of tungsten from the filament. Ifthe bulb is powered at constant
Voltage, which of the following statement(s) isare) true?

(A) The temperature distribution over the filament is uniform

(B) The resistance over small sections ofthe filament decreases with time

(©) The filament emits more light at higher band of frequencies before it breaks up

(D) ‘The filament consumes less electrical power towards the end of the life of the bulb

A plano-convex lens is made of material of refractive index n. When a small object is placed
30 cm away in front of the curved surface of the lens, an image of double the size ofthe abject
is produced, Due to reflection from the convex surface of the lens, another faint image is
Observed at a distance of 10 em away from the lens. Which of the following statement)
istare) true?

(A). The refractive index of the lens is 25
(B) The radius of curvature ofthe convex surface is 45 cm
(©) The faint image is erect and real

(D) The focal length ofthe lens is 20 em

Space for rough work

Answers for the above questions
[ans for Q.8: (C) and (D) | Ans for Q.9: (A) and (D)

“1

8. 10 A length-scale (1) depends on the permittivity (2) of a dieleetrie material, Boltzmann

constant (ip), the absolute temperature (7), the number per unit volume (n) of certain
charged particles, and the charge (9) carried by each ofthe particles. Which of the following
expression(s for 1 is(are) dimensionally correct?
a wi
hs
© D |
UT

Space for rough work

Answers for the above questions
Ans for Q.10: (B) and (D)

“1 1086

9. Qu

A conducting loop in the shape of a right angled isosceles triangle of height 10 em is kept
such that the 90° vertex is very close to an infinitely long conducting wire (see the figure)
‘The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to
the wire. The current in the triangular loop is in counterclockwise direction and increased at
a constant rate of 10 As". Which ofthe following statements) is(are) true?

(B) Ifthe loop is rotated at a constant angular speed about the wire, an additional emf of

(22) votes induced in the wire

‘The induced current in the wire is in opposite direction to the current along the
hypotenuse

(D) There is a repulsivo force between the wire and the loop

1136

Space for rough work

Answers for the above questions
Ans for Q.11: (A) and (D)

10. Q12 The position vector 7 of a particle of mass m is given by the following equation

FO=alispej

where a=10/9 ms, f= 5

(are) true about the partiels?
(4) The velocity & is given by U=(10/=10/) ms

um E with respect to the origin is given by L=~(

(8) The angular mome

(© Theforce F is given by F

(D) The torque 7 with respect to the origin is given by 7=-(20/DÉ Nm

5? and m=0.1 kg. At f=1 a, which of the following

6/2) Nms

Space for rough work

Answers for the above questions
Ans for Q.12: (A), (B) and (D)

19/36

11. Q13 A transparent slab ofthickness d has a refractive index n=) that increases with 2. Hk
from the top. The slab is placed between
à m3 (> 1), as shown in the figure. A ray of

is the vertical distance inside the slab, moasw
wo media with uniform refractive indices y

light is incident with angle @, from medium 1 and emerges in medium 2 with refraction

angle 0) with a lateral displacement 1

meconsta jr

0

Which ofthe following statement(s) is(are) true?

(A) msing =nysind, ®

(©) Lis independent of n (D) Lis dependent on n

Space for rough work

Answers for the above questions
Ans for Q.13: (A), (C) and (D)

19/86 1

12. SE

ks: 15)
+ This section contains FIVE qu
| + ‘The answer to each question is a SING
inclusive,
+ Forcach question, darken the bubble corresponding to the correct integer in the ORS.
+ Foreach question, marks will be awarded in one ofthe following categories
Full
Zero Marks: 0 In all other cases,

HER ranging from 0 to 9, both

Marks : +3. Ifonly the bubble exrrosponding to the correct answer is darkened.

Q14 A metal is hoated i
power radia

a furnace where a sensor is kept above the metal surface to read the
«4 (P) by the metal. The sensor has a scale that displays log,(P/P,), where Pa
ant, When the metal surface is at a temperature of 487 °C, the sensor shows a
value 1. Assume that the emissivity of the motallic surface remains constant. What is the
value displayed by the sensor when the temperature ofthe metal surface is raised to 2767 °C?

Q.15 The isotope "2B having a m

12.014 u undergoes f-decay to HO. HC has an excited state

of the nucleus (2C

) at 4041 MeV above ite ground state. If MB decays to ZC, the
maximum kinetic energy ofthe f-partiele in units of MeV is

1 u=931.5 MeV’, where cis the speed of light in vacuum).

Space for rough work

Answers for the above questions
Ans for Q.14: (9) [Ans for Q.15: (8) OR (9)

“41 1456

13. Q.16 A hydrogen atom in its ground state is irradiated by light of wavelength 970A. Taking
hele = 1.287 x 10% eV m and the ground

numberof lines present in the emission spectrum is

ate energy of hydrogen atom as 13.6 eV, the

Q.17 Consider two solid spheres P and Q each of density 8 gm em and diameters 1 em and
à into a liquid of density 0.8 gm em” and viscosity

to a liquid of density 1.6 gm em” and viscosity

0.5 em, respectively. Sphere P is droppe

n=3 poiseulles, Sphere Q is dropped

17=2 poiteulles. The ratio ofthe terminal velocities of P and Q is

ce 1 mH, internal resistance 3 ©) and L, (inductance 2 mil,
internal resistance 4 Q), and a resistor R (resistance 12 ©) are all connected in parallel
time £=0. The ratio of the maximum to

QS Two inductors L,(inducta

across a 5 V battery. The circuit is switched on
(he minimum current (Zas / La.) dawn from the battery is

END OF PART

pace for rough work

Answers for the above questions
Ans for Q.16: (6) | Ans for Q.17: (3) | Ans for Q.18: (8) |

15/36 “1

14. PART II : CHEMISTRY

SECTION 1 (Maximum Marks: 15)

+ This section contains FIVE 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 will be awarded in one ofthe following catego

Full Marks: #3 Tronly the buble corresponding tothe correct option is darkened. |
Zero Marks; 0 Home of he bubbles s darkened
| Negative Marke : 1 Ina other caves

Q19 P is the probability of finding the 1e electron of hydrogen atom in a spherical shell of
infinitesimal thickness, dr, at a distance 7 from the nucleus, The volume of this shell is
4 xrfdr. The qualitative sketch of the dependence of Pon ris,

r
Pp

A »

o 9 0

Space for rough wor

Answers for the above questions
[ Ans for Q.19: (D) ]

1636

15. Q20

One mole of an ideal gas at 300 K in thermal contact with surroundings expands
isothermally from 1.0 L to 2.0 L against a constant pressure of 3.0 atm. In this process, the
change in entropy of surroundings (AS) in JK is

A Latm = 101.83)

(a) 5168 @ 1018 (© -1013 Mm 5163
Q21 The increasing order of atomic radi of the following Group 13 elements is

(A) Al<Ga<In<M (5) Ga<Al<In<M

© Al<In<Ga<M (D) Al<Ga<Ticin
22 Among [Ni(CO),} [NCI], [ColNH,),C1,]O1, Nas(CoFa], Na,O, and Cs0,, the total

number of paramagnetic compounds is

w 2 os © 4 CE
223 On complete hydrogenation, natural rubber produces

(A) ethylene-propylene copolymer (E) vulcanised rubber

(©) polypropylene (D) polybutylene

Space for rough work

Answers for the above questions

Ans for @.20: (©) Ans for @21: (8) | Ans for 0.22: (B) [Ans for a23: (A)

1736

16. SECTION 2 (Maximum Marks: 32) 7

‘This section contains EIGHT questions,
FOUR options (A), (B), (C) and (D), ONE OR MORE THAN ONE of
these four option(s) is (are) correct.

For each question, darken the bubble(s) corresponding to all the correct option(s) in the
ons.

Each question has

+ For each question, marks will be awarded in one of the following categories:
Fall Marks :#4 K only the bubble(s) corresponding to all the correct option(s) itarc)
darkened
Partial Marks :+1 For darkening a bubble corresponding to each correct option,
provided NO incorrect option is darkened
Zero Marks: 0 Ifnone of the bubbles is darkened,
Negative Marks 1-2 In all other cases.

‘+ For example, if (A), (C) and (D) are all the correct options for a question, darkening all
these three will result in +4 marks; darkening only (A) and (D) will result in +2 marks, and
darkening (A) and (B) will result in -2 marks, as a wrong option is also darkened,

Q24 According to the Arrhenius equation,

(A) a high activation energy usually implies a fast reaction.

(B) rate constant increases with incroase in temperature. This is due to a greater number
of colisions whose energy exceeds the activation energy

(©) higher the magnitude of activation energy, atronger is the temperature dependence of
the rate constant

(D) the pre-exponential factor is a measure of the rate at which collisions occur,
irrespective oftheir energy

A plot of the number of neutrons (N) against the number of protons (P) of stable nuclei
exhibits upward deviation from linearity for atomic number, Z > 20. For an unstable nucleus
having N/P ratio less than 1, the possible mode(s) of decay islare)

(A) decay(P emission) (B) orbital or Kee

mn capture

(C) neutron emission (D) $ -decay (positron emission)

Space for rough work

Answers for the above questions
Ans for Q.24: (B), (C) and (D) | Ans for Q.25: (B) and (D)_|

186

17. az

The erystalline form of borax has

(A) tetranuclear {8,0,(011),}*

(B) all boron atoms in the same plane
(©) equal number of ep" and sp? hybridized boron atoms
(D) one terminal hydroxide per boron atom
‘The compound(s) with TWO lone pairs of electrons on the central atom is(are)
(A) BEF, CR CE D) SF,
Q28 The reagent(s) that can selectively precipitate S from a mixture of S” and 80," in
aqueous solution is(are)
A) CuCl, ®) Ball, (©) PBOOCCH;), (D) _Na,{Fe(CN),NO]
Q29 Positive Tollen’s testis observed for
Ho
w WA, D paro
on
O ar m o
"Y AA
o ep

Space for rough work

Answers for the above questions
Ans for Q.26: (A), (C) and (D) | Ans for Q.27: (B) and (C)
Ans for Q.28: (A) OR (A) and (C)|_Ans for Q.29: (A), (B) and (C)

19:56

18. 030. The product(s) ofthe following reaction sequence isare

D. Accticntydrido/pyridino
A io kaos

() mor har
NÓYEO, 273-2
mB

©

Space for rough work

Answers for the above questions
Ans for Q.30: (B)

“1 20/36

19. Q31 The correct statements) about the following reaction sequence stare)

0 CHCIyNaOH
»

Cumene Colt.)

Qmaior) + (minor)
ino

© Pom
A) Ris steam volatile
B) Q gives dark violet coloration with 1% aqueous FeCl, solution
(©) S gives yellow precipitate with 2, 4dinitrophenylhydr
©

S gives dark violet coloration with 1% aqueous FeCl, solution

Space for rough work

Answers for the above questions
Ans for Q.31: (B) and (C)

216

20. ‘The answer to each question is a SIA

STION 3 (Maximum Marks: 15)

E questions

LE DIGIT IN

'GER ranging from 0 to 9, both

inclusive.
+ For each question, darken the bubble corresponding to the correct integer in the ORS.
+ For each question, marks will be awarded in one ofthe following categories:
Full Marks: +3 only the bubble corresponding to the correct answer is darkened.
Zero Marks : 0 In all other cases.

Q.32 The mole fraction of a solute in a solution is 0.1. At 298 K, molarity of this solution is
same as its molality. Density of this solution at 208 K is 20 gem °. The ratio ofthe molecular

MW

Q33 The diffusion coefficient ofan ideal gas is proportional to its mean free path and mean speed
‘The absolute temperature of an ideal gas is increased 4 times and its pressure is increased
2 times. As a result, the diffusion coefficient ofthis gas increases x times. The value of ia

Space for rough work

Answers for the above questions
Ans for Q.32: (9) Ans for Q.3:

226

21. QM In neutral or faintly alkaline solution, $ moles of permanganate anion quantitatively oxidize
¡osulphato anions to produce X moles of a sulphur containing product, The magnitude of

x

35 The number of geometric isomers possible for the complex [CoL,C1,]” (L = H,NCH,CH,O")

Q.36 In the following monobromination reaction, the number of possible chiral products is

Homes
mer
Cu
(.0mole)

(enantomercaly pure)

END OF PART HL: CHEMISTRY

Space for rough wor

Answers for the above questions
Ans for Q.34: (6) | Ans for Q.35: (5) | Ans for Q.36: (5)|

23156 “1

22. PART III: MATHEMATICS

SECTION 1 (Maximum Marks: 15)

+ This section contains FIVE questions.
ch question has FOUR options (A), (B),
+ Foreach question, darken the bubble corresponding to the correct option in the ORS.
+ For each question, marks will be awarded in one ofthe following categories
Full Marks: +3 only the bubble corresponding to the correct option is darkened.
| Zero Marks 0. Ifnone of the bubbles is darkened,
egative Marks : -1 _Inall other cases |

2) and (D), ONLY ONE of these four options is

E<0<- E, Suppose a, and A are the roots of the equation 4? -2xsecO+1=0 and

a, and A, are the roots of the equation x +2xtand-1=0. If a> and a, >, then
a+ A equals

Q37 Let

(A) 26000 tan0) (B) 20000
(©) -2tano oo
Q.38 A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this

Club including the selection of a capt among these 4 members) for the team. If the
team has to include at most one boy number of ways of selecting the team is

(a) 380 CE) © 260 () 95

Qs Let S=(xe(-x,x):270,25}, The sum of all distinct solutions of the equation

is equal to

w 0) © 0 ©
ig ) ) D

Space for rough work

Answers for the above questions
Ans for Q.37: (C) | Ans for Q.38: (A) [Ans for Q.39: (C)

“1 24/36

23. Qo

A computer producing factory has only two plants 7, and 7. Plant 7, produces 20% and
plant 7, produces 80% of the total computers produced. 7% of computers produced in the
factory turn out to be defective. It is known that

P (computer turns out to be defective given that it is produced in plant 7)

10P (computer turns out to be defective given that

s produced in plant 73),

where P(E) denotes the probability of an event E. A computer produced in the factory is
randomly selected and it does not turn out to be defective. Then the probability that it is
produced in plant 7) is

a Y © & o %
79 E =

mi

eu all x 0, is
1 1 1
a CE CE D À
Space for rough work
Answers for the above questions
Ans for Q.40: (C) Ans for Q.41: (C) ]
2506 "1

24. Qe

ECTION 2 (Maximum Marks: 32)

This section contains EIGHT questions,
Each question has FOUR options (A), (B), (©) and (D). ONE OR MORE THAN ONE of
these four option(s stare) correct

For each question, darken the bubble(s) corresponding to all the correct option(s) in the
ons.
For each question, marks will be awarded in one of the following categories

Full Marks +4 If only the bubble(e) corresponding to all the correct option(s)
istare) darkened,

Partial Marks: +1 For darkening a bubble corresponding to each correct option,
provided NO incorrect option is darkened.

Zero Marks 0 none of the bubbles is darkened, |

Negativo Marks: -2 In al other eases.

For example, if (A), (©) and (D) are all the correct options for a question, darkening all
these three will result in +4 marks; darkening only (A) and (D) will result in +2 mar
darkening (A) and (B) will result in -2 marks, as a wrong option is also darkened.

Consider a pyramid OPQRS located in the first octant (x 20,920,220) with O as origin,
and OP and OR along the x-axis and the yraxis, respectively. The base OPQR of the pyramid
is a square with OP =3. The point S is directly above the mid-point T of diagonal OQ such
that TS 23, Then

(A) the acute angle between OQ and OS is

3
(B) the equation ofthe plane containing the triangle OQS is x - y- 0
(©) the length ofthe perpendicular from P to the plane containing the triangle OQS is 2
Y
(is
(D) the perpendicular distance from O to the straight line containing RS is [5

Space for rough work

Answers for the above questions

Ans for Q.42: (B), (C) and (D) |

25. 2-[ for all x (0,22) and

F:(0,2)>R be a differentiable function such that f'

Q4 La

F0)21. Then

B)

ma

© lim (mo (D) | Ax)]s2 forall x e(0,2

3-1-2)
Qué Lot P=[2 0 a | whore ae R. Suppose @ fr] is à matrix such that PQ=AL, whore
3-5 0

RER, 40 and io entity matrixof odor 3.1 qa = and detiQ)=

(A) a=0,k=8 (B) da-k+8=0

©) det(Padj(@)=2 D) deti@adi(P)) =2!

Space for rough work

Answers for the above questions
Ans for Q.43: (A) | Ans for Q.44: (B) and (C)

27136

“1

26. Q45 In a triangle XYZ, let x,3,2. be the lengths of sides opposite to the angles X.Y, Z,

respectively, and 2 = x + y +2. Ii and area of incirele of the triangle XYZ
then
(A) are ofthe triangle XYZ is 6/6

(8) the radius ofeireumeircle of the triangle XYZ is

(D) sin’

QA A solution curve of the differential equation (x? + a+ 4x +27) y*=0, x>0, passos

through the point (2,3). Then the solution curve

(A) intersects y = x +2 exactly at one point

(B) intersects y = x +2 exactly at two points

(©) intervocts y =( +2)

(D) does NOT intersect y = (x +8)

Space for rough work

Answers for the above questions
Ans for Q.45: (A), (C) and (D) | Ans for Q.46: (A) and (D)

“1 28136

27. QUT Let f:R9R, g:ROR and hRR bo differentia
Pa 22 43 +2, g(flx))=x and h(g(g(x)) =x forall xe R. Then

ble functions such

1

Mm cr B) WU) = 666

© AO=16 (D) hlg(3)=36
Q48 The circle C, :x° + y? 28, with contro at O, intersects the parabola x =2y at the point P in

the first quadrant. Lot the tangont to the circle C, at P touches other two circles C, and C,

at R, and R,, respectively. Suppose C, and C, have equal radii 2/3 and centres Q, and
Qu, respectively. If Q, and Q; lie on the y-axis, thon

a ee
B) RR
(©) area othe triangle OR, is 6/2
(D) arca ofthe triangle PQ, is 4/2
Q49 Lot RS be the diameter ofthe creo 3°.+9° 1, where S i the point (1,0) Lat P bo a
variable point (other than R and 5) onthe circle and tangonts to the circle at $ and P ment at

the point @. The normal to the circle at P intorseets a line drawn through Q parallel to RS
"Thon the locus of £ passes through the points)

Space for rough w

Answers for the above questions
Ans for Q.47: (B) and (C)_|Ans for Q.48: (A), (B) and (C)| Ans for Q.49: (A) and (C)

29188 "

28. SECTION 3 (Maximum Marks: 15)

+ ‘This section contains FIVE questions
+ ‘The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both
nelusive

+ For cach question, darken the bubble corresponding to the correct integer in the ORS.
+ Foreach question, marks will be awarded in one of the following categories
Full Marks: +3 Ifonly the bubble corresponding to the correct answer is darkened.
Zero Marks: 0 In all other cates

x # tex? |
Q50 The total number of distinct x e R for which |2x 43% 1480 |-10 is
sx où 1427s"

Q51 Let m be the smallest positive integer such that the coefficient of 2° in the expansion of
Dex)? (14x? + (Lx) + +x) is (in +1) IC, for some positive integer n, Then

the value of is

Space for rough work

Answers for the above questions
Ans for Q.50: (2) ] Ans for Q.51: (5) ]

“1 3036

29. 82 The total number ofditine x 60,1] for which |

Q53 be such that him (2x (a+ P) equals
Q54 Let 2 VFA, and recto, Let P=") and 1 be the

identity matrix of order 2, Then the total number of ordered pairs (r,s) for which P? =-1 is

END OF THE QUI

ION PAPER

Space for rough work

Answers for the above questions
Ans for Q.52: (1) | Ans for Q.53: (7) | Ans for Q.54: (1) |

sim “x