JEE-ADVANCED PAPER-II -...

JEE-ADVANCED_PAPER-II Time: 3:Hrs IMPORTANT INSTRUCTIONS Max Marks: 180

PHYSICS:

Section Question Type +Ve Marks

- Ve Marks

No.of Qs

Total marks

Sec – I(Q.N : 1 – 8) Questions with Multiple Correct Choice 3 -1 8 24

Sec – II(Q.N : 9 – 16) Questions with Comprehension Type (4 Comprehensions – 2 +2+2+2 = 8Q) 3 -1 8 24

Sec – III(Q.N : 17 – 20) Matrix Matching Type 3 -1 4 12

Total 20 60 CHEMISTRY:


- Ve Marks

No.of Qs

Total marks

Sec – I(Q.N : 21 –28) Questions with Multiple Correct Choice 3 -1 8 24



Total 20 60 MATHEMATICS:


- Ve Marks

No.of Qs

Total marks

Sec – I(Q.N : 41 – 48) Questions with Multiple Correct Choice 3 -1 8 24



Total 20 60

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JEE-Advanced_Paper-2_Q’Paper

PHYSICS Max Marks : 60

Section-I (One or more options correct type)

This section contains 8 Multiple Choice questions. Each Question has Four choices (A), (B), (C) and (D). Out of Which One or MORE are correct 1. Two spherical black bodies A and B, having radii rA and rB where rB = 2rA emit

radiation with peak intensities at wavelength 400 nm and 800 nm respectively. If their

temperatures are TA and TB respectively in Kelvin scale, their emissive powers are EA

and EB and energies emitted per second PA and PB then

A) 2A

B

T

T=

B) 4A

B

P

P=

C) 8A

B

E

E=

D) A

B

E16

E=

2. Force acting on a particle is given by F a p= ×

, where , a is a constant vector and P

is linear momentum of the particle. Choose the correct option(s):

A) speed of the particle remain same

B) If F

is constant and a p⊥ path described by the particle is a circle

C) Linear momentum of the particle is conserved

D) Kinetic energy of the particle is conserved

JEE-Advanced Space for rough work Page 2

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JEE-Advanced_Paper-2_Q’Paper 3. A particle of mass m is doing horizontal circular motion with the help of a string

(conical pendulum) as shown in the figure. If speed of the particle is constant then,

(point O is point of suspension).

Z(vertical)

Y

gθX

O

A) the angular momentum of the particle about O is changing

B) magnitude of angular momentum about O remains constant

C) Z component of the angular momentum about ‘O’ remains conserved

D) Z component of torque about ‘O’ is always zero


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JEE-Advanced_Paper-2_Q’Paper 4. A particle of mass m moves on the x – axis as follows: it starts from rest at t = 0 from

the point x = 0, and comes to rest at t = 1 at the point x = 1. No other information is

available about its motion at intermediate times (0 < t < 1). If α denotes the

instantaneous acceleration of the particle, then

A) α can not remain positive for all t in the interval of (0 < t < 1)

B) |α | cannot exceed 2 at any point in its path

C) |α | must be ≥ 4 at some point or points in its path

D) α must change sign during the motion, but no other assertion can be made with the

information given


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JEE-Advanced_Paper-2_Q’Paper 5. The figure shows a potentiometer arrangement. D is the driving cell and C is the cell

whose emf is to be determined. AB is the uniform potentiometer wire and G is

galvanometer. J is sliding contact which can touch any point on AB. Which of the

following are essential conditions for obtaining balance ?

JA B

D

CG

A) the emf of D must be greater than the emf of C

B) either the positive terminals of both C and D or the negative terminals of

both C and D be joined to A

C) the positive terminals of D and C must be joined

D) the resistance of G must be less than resistance of AB.


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JEE-Advanced_Paper-2_Q’Paper 6. The temperature drop through a two layer furnace wall is 900°C. Each layer is of

equal area of cross section. Which of the following actions will definitely result in

lowering the temperature θ of the interface?

Inner layer

Outer layer

1000°C 100°C

θ

A) by increasing the thermal conductivity of outer layer

B) by increasing the thermal conductivity of inner layer

C) by increasing thickness of outer layer

D) by increasing thickness of inner layer

7. Just after a K shell capture, which of the following come out from the atom ?

A) Neutrino

B) Antineutrino

C) x – Ray photon

D) Electron


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8. A parallel glass slab of refractive index 3 is placed in contact with an equilateral

prism of refractive index 2 . A ray is incident on left surface of slab as shown. The

slab and prism combination is surrounding by air. The magnitude of minimum

possible deviation of this ray by slab-prism combination is

2

3

A) 30º

B) 45º

C) 60º

D) 1 260º sin

3−−


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JEE-Advanced_Paper-2_Q’Paper Section-2

(Paragraph Type) This section contains 4 paragraphs each describing theory, experiment, data etc. Eight questions relate to four paragraphs with two questions on each paragraph. Each question of a paragraph has only one correct answer among the four choices A,B,C and D. Passage-I:

A very small circular loop of radius a is concentric with a much larger circular loop of

radius b (>>a). A constant current I is passed in the large loop which is kept fixed in

space & the small loop is being rotated with constant angular velocity ω about a

diameter as shown. The resistance of the small loop is R & its self inductance is

negligible. The current in the larger loop is clockwise. At t = 0 smaller loop lies in

plane of large loop.

ωa b

axis

I


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JEE-Advanced_Paper-2_Q’Paper 9. Calculate external torque required to rotate smaller loop with constant angular speed

A) 22

0 sin

2

b I t

R b

π µ ωω

B) 22

0 sin cos2

b It t

R b

π µω ω ω

C) 22

0 sin

2

a I t

R b

π µ ωω

D) 22

0 sin cos2

a It t

R b

π µω ω ω

10. At the moment both the loops are in the same plane

A) the induced current in small loop is zero

B) the induced current in small loop is clockwise

C) the induced current in small loop is in anticlockwise direction

D) can’t be determined


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JEE-Advanced_Paper-2_Q’Paper Passage-II:

The planet Venus has following characteristics

Time period of spin motion 220 days

Radius 6000 km

Mass 4 × 1024 kg

Orbital period 220 days

Orbital radius 108km

Venus

Sun

Orbital Path

Spin

The spin is in sense opposite to orbital motion as shown. The planet is spherical in

shape and uniformly dense. It’s orbit is essentially a circle.


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11. If we assume spin angular velocity to be perpendicular to the plane of orbit,

A) It’s total angular momentum about centre of Sun has same direction as orbital

angular momentum but is lesser in magnitude

B) It’s total angular momentum about centre of Sun has same direction as orbital

angular momentum but is more in magnitude

C) It’s total angular momentum about centre of Sun has opposite direction as orbital

angular momentum but is lesser in magnitude

D) It’s total angular momentum about centre of Sun has opposite direction as orbital

angular momentum but is more in magnitude


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JEE-Advanced_Paper-2_Q’Paper 12. If the axis of rotation is nearly perpendicular to the plane of its orbit. (The angle

between axis and a line perpendicular to orbit is 4°). As venus moves to the diametrically opposite point in it’s orbit the axis of rotation will be tilted in which manner

4°

Sun

A)

4°

Sun

B)

4°

Sun

C)

4°

Sun

D)

4°

Sun


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JEE-Advanced_Paper-2_Q’Paper Passage-III:

Three identical metal plates of area S are at equal distances b as shown. Initially metal

plate A is uncharged, while metal plates B and C have respective charges +Q0 and –

Q0 initially as shown. Metal plates A and C are connected by switch K through a

resistor of resistance R. The key K is closed at time t = 0

+Q0

- Q0

b

b

R

A

B

C

K

13. Then the magnitude of current in amperes through the resistor at any later time t is :

A) 00

0

btRSQ b

eRS

ε

ε

−

B) 0

2

0

0

btRSQ b

eRS

ε

ε

−

C) 0

2

0

02

btRSQ b

eRS

ε

ε

−

D) 00

02

btRSQ b

eRS

ε

ε

−


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JEE-Advanced_Paper-2_Q’Paper 14. The total heat dissipated through resistor of resistance R is:

A) 20

04Q b

Sε

B) 20

08Q b

Sε

C) 20

02Q b

Sε

D) 20

0

34Q b

Sε

Passage-IV:

Figure shows a convex lens of focal length 12cm lying in a uniform magnetic field of

B of magnitude is 1.2 T parallel to its principle axis. A particle having a charge 32 10 C−× and mass 52 10−× kg is projected perpendicular to the plane of the diagram with

a speed of 14.8ms− . The particle moves along a circle with its centre on the principal

axis at a distance of 18cm from the lens.

P

B


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15. The radius of the circular path of the particle is

A) 2 cm

B) 24 10 cm−×

C) 4cm

D) 8cm

16. The distance of the image point on the axis of the particle from the lens.

A) 36cm

B) 18cm

C) 7.2cm

D) None of these


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JEE-Advanced_Paper-2_Q’Paper Section-III

(Matching List Type) This section contains 4 multiple choice questions. Each question has matching lists. The codes for lists have

choices A,B,C and D out of which ONLY ONE is correct. 17. An ideal monatomic gas undergoes different types of processes which are described in

Column – I match the corresponding effects in column – II. The letters have usual meaning.

Column – I Column – II

a)PV-2 = constant P) If volume increases then temperature

will also increase

b) PV2 = constant q) If volume increases then temperature

will decrease

c) C = Cv + 2R r) For expansion, heat will have to be

supplied to the gas

d) C = Cv – 2R s) If temperature increases then work

done by gas is positive

t) If pressure increases the work done by

gas is negative

A) a-p,s;b-q,t;c-r,s,t;d-qt

B) a-q,t;b-p,r,s;c-p,q,r,s;d-q,t

C) a-p,r,s;b-q,t;c-p,r,s,t;d-q,t

D) a-p,r,s;b-p,s;d-r,s,t;d-p,s


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18. A square loop is placed near a long straight current carrying wire as shown.

+∞

−∞ Match the following

Column – I Column – II

a) If current is increased P) Induced current in loop is clockwise

b) If current is decreased q) Induced current in loop is anticlockwise

c) If loop is moved away from the wire r) wire will attract the loop

d) If loop is moved toward the wire s) wire will repel the loop

A) a-q,s;b-p,r;c-q,s;d-p,r

B) a-q,s;b-p,r;c-p,r;d-q,s

C) a-p,r;b-q,s;c-q,s;d-p,r

D) a-p,r;b-q,s;c-p,r;d-q,s


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19. Match the following

a) Boltzmann constant p) 2 1ML T

b) Coefficient of viscosity q) 1 1ML T

c) Plank constant r) 3 1MLT K

d) Thermal conductivity s) 2 2 1ML T K

A) a-q;b-s;c-p;d-r

B) a-s;b-q;c-p;d-r

C) a-p;b-q;c-s;d-r

D) a-r;b-q;c-p;d-s


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JEE-Advanced_Paper-2_Q’Paper 20. 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 :

List-I List-II

a) Alpha decay p) 15 15

.....8 7

O N

b) decay q) 238 234

.....92 90

U Th

c) Fission r) 185 184

.....83 82

Bi Pb

d) Proton emission s) 239 140

.....94 57

Pu La

A) a-q;b-p;c-s;d-r

B) a-p;b-q;c-s;d-r

C) a-r;b-p;c-s;d-p

D) a-s;b-r;c-q;d-p


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CHEMISTRY Max Marks : 60

Section-1 (One or more options correct type)

This section contains 8 Multiple Choice questions. Each Question has Four choices (A), (B), (C) and (D). Out of Which One or MORE are correct 21. Which of the following is true for a CsCl type crystal

A) Cs forms a simple cubic lattice, Cl forms a simple cubic lattice.

B) Cl occupies body centre of Cs

C) Csoccupies body centre of Cl

D) It is impossible for Cl to occupy body centre of Cs because the body centre void

of Cs is smaller than the Cl ion size.

22. Decrease in atomic number is observed during

A) alpha emission

B) Beta emission

C) Positron emission

D) Electron capture


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23. Which of the following heterocyclic compound/s might be aromatic?

A) NH

B) BH

C) O

D) B H

24.

3 2 2 2 5 3( ) ( )CH CH CH CH C C H− − − −

3CH

3 2( )CH CH The correct statements about this compound

A) The IUPAC name is 3, 3 – diethyl -5 (1- methyl ethyl ) – 4 – methyl octane

B) Number of primary carbon atoms, primary hydrogens are 7, 21

respectively

C) The number of Neo carbons are two

D) All carbons do not use 3sp hybrid orbitals.


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JEE-Advanced_Paper-2_Q’Paper 25. The suitable reagents for the following reaction are :

3COCH

3CH 3CH

2NH

A) 5PCl NaOH ∆→ → →

B) +

32 2NHI +NaOH BrHKOH∆→ → → →

C) 5 32 PCl N HH NOH dil.NaOH∆ ∆→ → → →

D) 2H NOH ∆→ →

26. Among the following the correct statements is/are

A) Asbestos and beryl are silicate minerals

B) Anglesite and barytes are sulphate minerals

C) Sylvine and fluorspar are halide minerals

D) Calamine and calcite are minerals of calcium


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JEE-Advanced_Paper-2_Q’Paper 27. Correct statements among the following are

A) 2CaF is insoluble in water.

B) When 2

Mn OH is exposed to air hydrated manganese (IV) oxide is formed

C) Ammonia gives black precipitate with 2 2Hg Cl but white precipitate with 2HgCl

D) MnS dissolves in hot dilute HCl because 2MnCl and 2H S are formed and HCl

suppresses the dissociation of 2H S and there by prevents 2MnCl from reacting with

2H S

28. In all the following molecules the central atom is having two bond pairs and two lone

pairs. The smallest bond angle is present in

A) HOF

B) 2OF

C) 2H O

D) 2SI


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JEE-Advanced_Paper-2_Q’Paper Section-II


The decomposition of 3NH as follows 3 2 22 3NH N H of the rate obeys

1 33

2 31

K NHdNH

dt K NH

than 1 2,K K are constants

29. If 3NH is very very less then order of reaction is

A) 1

B) 0

C) 2

D) 3

30. If 3NH is very very high then order of reaction is

A) 1

B) 0

C) 2

D) 3


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Br

Br

i) Alc.KOH

ii)2A

0210 C

A

2

3

1. 2

2. 2

NH moles

CH I moles

B 4 2 4

2

,HgSO H SOH O

C .dil OH

D[Mixture]

31. “A” gives

A) Lucas test

B) Silver mirror test

C) White precipitate with ammoniacal 3AgNO

D) Yellow precipitate with ammoniacal cuprous chloride

32. How many isomeric products are existed in the mixture “D”

A) 2

B) 4

C) 6

D) 8


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Sulphur forms large number of Oxoacids. The oxoacids in lower oxidation state are

called ‘ous’ acids while in higher oxidation state are called ‘ic’ acids Oxoacids of

sulphur containing S-S bond are called thioacids and those containing O-O bond are

called peroxoacids

33. The oxoacids containing both sulphur atoms in the same oxidation state.

A) 2 2 2H S O

B) 2 2 3H S O

C) 2 2 4H S O

D) 2 2 5H S O

34. Which of the following statement is/are false for polythionic acid series

A) The average oxidation state of S-atom increases with decreases in number of S-

atoms

B) The absolute oxidation state S-atom increases with decrease in number of S-atoms

C) The average oxidation state of S-atom decreases with increase in number of atoms

D) The absolute oxidation state of S-atom remain constant with increase or decrease in

number S-atoms


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JEE-Advanced_Paper-2_Q’Paper Passage-IV:

The standard cell potential 0cellE of a reaction is related as 0 0

cellG nFE where 0G equals

maximum electrical work.

n = number of moles of electrons exchanged as per the balanced chemical equation.

0 0 0r r rG H T S ………..(1)

and also

0

0r

r

GS

T

……………(2)

35. The temperature coefficient of the emf of cell0dE

dT

is given by.

A) 0r

nF

S

B) 0rS

nF

C) 0rS

nFT

D) 0nFE


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JEE-Advanced_Paper-2_Q’Paper 36. At 300K, 0H for the reaction. 22 2Zn s A Zg nCl aq gl s sC A is -218 kJ while the

E0 of the cell was 1.015V.0

p

dE

dT

of the cell is.

A) 44.2 10 VK

B) 4 13.81 10 VK

C) 10.11VK

D) 4 17.62 10 VK

Section-III This section contains 4 multiple choice questions. Each question has matching lists. The codes for lists have choices A,B,C and D out of which ONLY ONE is correct. 37. a) bPK for X ( aK of HX= 610 ) p) 6.9

b) PH of 810 M HCl q) 8

c) PH of 210 M acetic acid 51.6 10aK r) 3.3

d) PH of the solution obtained by mixing initially equal s) 3.4

volumes of PH=3 and PH=5.

A) a-q;b-p;c-s;d-r

B) a-s;b-r;c-p;d-q

C) a-p;b-q;c-s;d-r

D) a-r;b-s;c-p;d-q JEE-Advanced Space for rough work Page 28

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JEE-Advanced_Paper-2_Q’Paper 38. Column-I Column-II

a)

O

2NH OHconc

A B 2 4H SO p) Final product is ketone

(or) , -unsaturated ketone

b) O

O

OH

Major

q) Formation of six membered ring occurs

c)

O

2/ NaNOKCN H LAHHCl

A B C

r) Formation of product

involves crabanion

d)

Ph

OH3CH

OH

H

Major

s) Formation of product involves carbocation A) a-p,q,s;b-p,q,r;c-p,q,s;d-p,q,s

B) a-p,r;b-p,q,r;c-p,s;d-p,q,s

C) a-p,r;b-p,s;c-p,s;d-p,r

D) a-q,s;b-p,q,r;c-p,q,s;d-p,q,s


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39. Matching

a)

C3CH

2CH HBr Major

p) More than one racemate

b)

2CH CH

3CH 2 2

HBrH O

Major q) Freidel-Craft’s alkylation

c)

H

(Major)

r) Ring expansion does not occur

d)

C CH

2 4 4,H SO HgSO Major

s) Product gives iodoform test

A) a-p,r;b-p,r;c-q;d-r,s

B) a-p;b-r;c-q;d-r,s

C) a-r;b-r;c-q;d-r,s

D) a-p;b-r;c-q;d-r


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40. Matching the following given in column-I with the properly given in column-II

Column-I Column-II

a) NO p) Can act as oxidising agent

b) 2 3N O q) Can act as reducing agent

c) 2NO

r) Paramagnetic

d) 3NO

s) Gives brown ring test

A) a- pqs;b- pqrs;c-pqr;d-pr

B) a- pr;b-pqs;c-pqr;d-pqrs

C) a-pqrs;b-pqs;c-pqs;d-ps

D) a- pqr;b-pqs;c-pqrs;d-pr


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MATHEMATICS Max Marks : 60 Section-I

(One or more options correct type) This section contains 8 Multiple Choice questions. Each Question has Four choices (A), (B), (C) and (D). Out of Which One or MORE are correct

41. Family of curves which makes an angle of 4

π with the family of hyperbola xy = a, is

(a >0 , and a is a parameter)

A) 2 22x xy y A− − =

B) 2 22y xy x A− − =

C) 2 23x xy y A+ − =

D) 2 24y xy x A+ − =

42. Let position vector of the orthocenter of ABC∆ be r . Then, which of the following

statement(s) is/are correct (Given position vector of points A, B, C are ˆˆ ˆ, ,ai bj ck and 0abc ≠ )

A) 2 2 2

ˆ.1 1 1

ar i

a b c

=+ +

B)

2 2 2

1ˆ.1 1 1

r ia

a b c

= + +

C) ˆˆ ˆ. . .

ˆ ˆ ˆ. ..

r i r j r k a b c

b c ar j r ir k+ + = + +

D) ˆˆ ˆ. . .

ˆ ˆ ˆ. ..

r i r j r k b c a

a b cr j r ir k+ + = + +


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JEE-Advanced_Paper-2_Q’Paper 43. Let ( ) 3 22 1f x x x x= + − + , then which of the following statement(s) is/are correct

A) [ ]( )( ) [ ]( )( )1 1sin sin cos cos 6α α π− −+ = − (where α is real root of ( ) 0f x = and [.]

denotes the G. I.F.)

B) f(x) = 0 has three distinct real roots

C) y=f(x) is increasing function

D) [ ]( )( ) [ ]( )( )1 1sin sin cos cos 5 2α α π− −+ = − (where α is real root of ( ) 0f x = and [.]

denotes the G.I.F.)

44. Let 2 2

lim1n

b

ndxI

n x

∞

→∞=

+∫ , where b R∈ . The value of ‘I’ can be

A) π

B) 2

π

C) 0

D) 3

4

π


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JEE-Advanced_Paper-2_Q’Paper 45. The equations of AB, BC, AC, the three sides of ABC∆ are 1 0, 1 0x y x y− + − = + − = and

4.x = − If ( ),0α and ( )0, β lie inside the triangle where , ,Zα β ∈ then

A) 3, 2,α β φ= − − ∈

B) 3, 2, 1α β= − − =

C) orthocenter of triangle ABC is at (0,1)

D) The circumcentre of the triangle will lie on the line y =1

46. ,a b I∈ satisfies equation ( ) 21 3a b b b− = + − , then a b+ is equal to

A) 2

B) 3

C) 1

D) -1


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JEE-Advanced_Paper-2_Q’Paper 47. Let ( )1nS n ≥ be a sequence of sets defined by

{ }1 2 3 4

3 5 8 11 14 15 19 23 270 , , , , , , , , , ,....,

2 2 3 3 3 4 4 4 4S S S S = = = =

then

A) third element in 20S is 439

20

B) third element in 20S is 431

20

C) sum of elements in 20S is 589

D) sum of elements in 20S is 609

48. A right angle triangle ABC, right angle at A is inscribed in hyperbola ( )2 0xy c c= >

such that slope of BC is 2. If distance of point A from centre of 2xy c= is 10 , then

which of the following is/are correct for 2xy c=

A) the value of c is 2

B) the value of c is 4

C) the equation of normal at point A can be 2 3 2y x= −

D) the equation of normal at point A can be 3 8 2y x= +


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JEE-Advanced_Paper-2_Q’Paper Section-II


Let P(a, b) be a variable point satisfying 2 24 a b 9≤ + ≤ and 2 2b 4ab a 0− + ≤ . Let R be

the complete region represented in x-y plane in which P can lie.

49. Area of region R is

A) 2

3

π

B) 5

6

π

C) 4

3

π

D) 5

3

π

50. Let A & B be two points lying in region R, then maximum possible distance between

them is

A) 2

B) 3

C) 7

D) 6


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Two lines whose equations are 3 2 1

2 3

x y z

λ− − −= = and 2 3 2

3 2 3

x y z− − −= = lie in the

same plane, then

51. The value of 1sin− sin λ is equal to

A) 3

B) 3π −

C) 4

D) 4π −

52. Point of intersection of the lines lies on

A) 3 20x y z+ + =

B) 3 25x y z+ + =

C) 3 2 24x y z+ + =

D) 3 2 10x y z+ − =


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A JEE aspirant estimates that she will be successful with an 80% chance if she studies

10 hours per day, with a 60% chance if she studies 7 hours per day and with a 40%

chance if she studies 4 hours per day. She further believes that she will study 10 hours,

7 hours and 4 hours per day with probabilities 0.1, 0.2 and 0.7, respectively.

53. The chance that she will be successful, is

A) 0.28

B) 0.38

C) 0.48

D) 0.58

54. Given that she is successful, the chance she studied for 4 hours, is

A) 6

12

B. 7

12

C. 8

12

D. 9

12


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JEE-Advanced_Paper-2_Q’Paper Passage-IV:

Consider a polynomial ( )f x , which satisfies the following conditions

(i) ( ) ( ){ }2' ,f x f x x= ∀

(ii) ( )1

0

19

12f x dx =∫

(iii) ( )' 0 0f >

55. The function ( )f x can be

A) a linear function

B) a quadratic function

C) a cubic function

D) any polynomial of even degree

56. The value of ( )' 0f is

A) 0

B) 1

4

C) 1

2

D) 1


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JEE-Advanced_Paper-2_Q’Paper Section-III

This section contains 4 multiple choice questions. Each question has matching lists. The codes for lists have choices A,B,C and D out of which ONLY ONE is correct. 57. Match the following

Column I Column II (a) If 2 ,z i a− = ( )max Arg zθ = ( )min ,Arg z− 0

3

πθ< ≤

then the range of a is

(p) [0,10]

(b) If 0,

2

πθ ∈ , the range of

1 3cos 1

sin 1 3cos

1 sin 1

θθ θ

θ is

(q) (0,1]

(c) If 66

12sinx

xθ+ = and x is positive, then the range

of 1x

x+ is

(r) {2}

(d) Let : 0,2

f Rπ →

defined by

( ) ( )1 2tanf x x x λ−= + + then the range of values of λ

for which f is onto is

(s) 1

4

A) a-q;b-s;c-r;d-p

B) a-q;b-r;c-p;d-s

C) a-q;b-p;c-r;d-s

D) a-p;b-q;c-r;d-s


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JEE-Advanced_Paper-2_Q’Paper 58. Match the following

Column I Column II (a) Two adjacent sides of a triangle are

represented by the vectors 2 3 2 3 3i j k− +

and 2 2i j k+ − then the angles of the triangle

are

(p) 2

π

(b) If 3

0

sin 4x xdx kπ

=∫ , then k= (q) 2

3

π

(c) [ ]0

2sin x dxπ

∫ is (r)

6

π

(d) If 1 2z and z satisfy 3 4 5z i− − = and

3 3 4 5 2z i− − = then 1 3

2 3

z zArg

z z

− −

is

(s) 3

π

A) a-prs;b-q;c-r;d-prs

B) a-prs;b-q;c-q;d-prs

C) a-r;b-prs;c-q;d-prs

D) a-q;b-r;c-prs;d-prs


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Column-I Column-II

a) If 2

3xlog 1y

=

and ( )2 3log x y = 7 then ( )log xy is equal

to

p) 0

b) { }2f(x) min. x ,x ,2 , x [ 5, 5]= ∈ − number of points where

f(x) is not derivable, is

q) 3/2

c) 2 3 2

20

2x 6x 9x 5 dxx 2x 5− + −

− +∫ = r) 3

d) If the range of the function ( )2 2x (x 1)2f(x) log 4 4 −= + is

[a, ∞) then the value of ‘a’ equals

s) 4

A) a-r;b-s;c-p;d-q

B) a-r;b-p;c-s;d-q

C) a-s;b-r;c-p;d-q

D) a-s;b-p;c-q;d-r


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Column-I Column-II

A Total number of positive integral solution of the equation

1 2 3. . 60x x x = is 18k, then k is equal to P) 1

b A bag contains 5 balls of either white or black .

Two balls are drawn and found to be white. Then

the probability that another ball drawn (without

replacing the earlier two balls) is white is m

n where

gcd (m, n) = 1 then n – m equals

Q) 2

C The two curves y2 = 4x and x2 = 12y intersect at O

and A, then OA divides the area enclosed by the

curves in the ratio m : n where gcd (m, n) = 1 then

m + n equals

R) 3

d One of the values of x satisfying

tan-1 (x+3) – tan-1 (x-3) = sin-1 3

5

is / are S) 4

A) a-r;b-p;c-q;d-s

B) a-r;b-q;c-p;d-s

C) a-s;b-r;c-p;d-q

D) a-s;b-p;c-q;d-r


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