jee-advanced paper-ii · the bead can freely move on smooth fixed ring placed on a smooth...

JEE-ADVANCED PAPER-II

Time: 2.00 PM to 5.00 PM IMPORTANT INSTRUCTIONS Max Marks: 180

PHYSICS: Section Question Type +Ve

Marks - Ve

Marks No.of

Qs Total marks

Sec – I(Q.N : 1 – 10) Questions with Single Correct Choice 3 -1 10 30

Sec – II(Q.N : 11 – 16) Questions with Comprehension Type

(3 Comprehensions – 2 +2+2 = 6Q) 3 -1 6 18

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

Total 20 60

CHEMISTRY:

Section Question Type +Ve Marks

- Ve Marks

No.of Qs

Total marks


Sec – II(Q.N : 31 – 36) Questions with Comprehension Type (3 Comprehensions – 2 +2+2 = 6Q) 3 -1 6 18


Total 20 60

MATHEMATICS:

Section Question Type +Ve

Marks

- Ve

Marks

No.of

Qs

Total

marks


Sec – II(Q.N : 51 – 56) Questions with Comprehension Type

(3 Comprehensions – 2 +2+2 = 6Q) 3 -1 6 18


Total 20 60

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PART-I_PHYSICS Max Marks : 60 Section-1

(Only one Option correct Type) This section contains 10 Multiple Choice questions. Each Question has Four choices (A), (B), (C) and (D). Out of Which Only One is correct

1. The length of a cylinder is measured with a metre rod having least count 0.1cm. Its

diameter is measured with vernier calipers having least count 0.01cm. Given that

length is 5.0 cm and radius is 2.0cm. The percentage error in the calculated value of

the volume will be

A) 1% B) 2% C) 3% D) 4%

2. A car is fitted with a device which transmits sound 60 times per minute. There is no wind

and speed of sound in still air is 345 m/s. If you hear the sound 68 times per minute,

when you are moving towards the car with a speed of 12m/s , the speed of the car must

be

A) 20.0 m/s towards you B) 30.0 m/s towards you

C)10.0 m/s away from you D) 10.0 m/s towards you

3. In a regular polygon with11 sides each cornet is at a distance ‘a’ from centre. Identical

charges are placed at 10 corners. At the centre the intensity is E and the potential is V.

The ratio of VE

has magnitude

A) 11a B) 10a

C) 1011

a D) 10a

4. A micrometer screw gauge with pitch of 0.5cm and 50 divisions on circular scale is used

to measure the diameter of a thin wire. Initially when the gap is closed the line of fourth

division coincides with the reference line. Three reading shows 46th, 48th and 44th

division coinciding with the reference line which is beyond 0.5 mm of the main scale.

The (best) measured value is

A) 0.46 mm B) 0.94 mm C) 0.92 mm D) 1.00 mm

5. How much heat must be supplied to convert 1 kg ice at 010 C to steam at 0100 C ( Take

specific heat of ice 00.5 /iS cal gm C )

A) 725 kcal B) 720 kcal C) 730 kcal D) 735 kcal

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6. The diagram shows a small bead carrying charge q. The bead can freely move on smooth

fixed ring placed on a smooth horizontal plane. Potential due to Q at P is V. If bead is

given a very small velocity tangential from Q. Velocity of bead when it reaches at P .

A) 6qVm

B) qVm

C) 3qVm

D) Zero

7. An electron (mass m, charge e) orbiting around a nucleus has angular momentum L.

the magnetic field produced by the electron at the centre of the orbit can be expressed

as

A) 30 / 8B e mr L B) 3

0 / 4B e mr L

C) 30 /B e mr L D) 3

0/ 4B e mr L

8. A bowl of water, initially at 010 C is brought to boiling after being 9 minutes at the

stove top. If it remains on the stove top, how long will it further take for all the water

to evaporate? Neglect heat losses and the heat capacity of the bowl.

A) 18 min B) 36 min C) 54 min D) 15 min

9. A skier plans to ski a hemisphere of radius R . He starts from rest a curve surface of

height (R/4) . The angle at which he leaves the hemisphere is

A) 1 2cos3

B) 1 5cos3

C) 1 5cos6

D) 1 1cos3

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10. A cylinder of mass 2kg is rolling up the place without slipping instantaneous velocity

of centre of gravity at point A is 110ms . The distance traveled by the cylinder before

coming to rest in metre is

A) 15 m B) 304

m C) 306

m D) 156

m

Section-2 (Paragraph Type)

This section contains 3 paragraphs each describing theory, experiment, data etc. Six questions relate

to three paragraphs with two questions on each paragraph. Each question pertaining to a particular

paragraph should have only one correct answer among the four choices A, B, C and D. Paragraph- I For Question No.s 11 to 12 :

Standing transverse waves can be set up in a string clamped at both ends and under

tension. For Example an arrangement such as one shown in the figure can set up such

standing waves. The weight W provides the necessary tension. In one such arrangement a

wire of length L , is in resonance in fundamental mode with a tuning fork.

11. If the weight is immersed in water and the length L is altered to L1 , there is again

resonance with the same tuning fork in fundamental mode. What can you say about L

and 1L ?

A) 1L L B) 1L L C) 1L L D) Data Insufficient

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12. Now the weight is immersed in a liquid and for length L , the wire in resonance with

the same tuning fork but in the first overtone. What is the ratio of densities of block

and liquid?

A) 4/3 B) 2/3 C) 5/3 D) 3/4

Paragraph- II For Question No.s 13 to 14 : A small disc and a thin uniform rod of length L , whose mass is times greater than

the mass of the disc, lie on a smooth horizontal plane. The disc is set in motion , in horizontal direction and perpendicular to the rod with velocity V , after which it elastically collides with the end of the rod.

L

m V

13. The velocity of the disc after collision is

A) 44

V

B) V C) 44

V

D) 2

V

14. Angular velocity of the rod after the collision is

A) 2VL

B) VL C) 4

4V

D)

12

4V

L

Paragraph -III For Question No.s 15 to 16:

A non-conducting disc of radius r and uniform positive surface charge density is placed on the ground, with its axis vertical. A Particle of mass m and charge q is dropped along the axis of the disc from a height h with zero initial velocity. The ratio of charge to

mass of the particle is given by 04 gqm

15. What is the value of h if the particle just reaches the disc?

A) 43r B) 2r C) 3

2r D) 2

5r

16. At what position z (from the ground) will the particle attain equilibrium position?

A) 3rz B)

3rz C)

2rz D)

2rz

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Section-3 (Matching List Type)

This section contains four questions, each having two matching lists (List-1 & List-II). The options for the correct match are provided as (A), (B),(C) and (D) out of which ONLY ONE is correct. 17. In the first column 1 2,m m and M and situation is indicated. Match the description in

column-II

List-I List-II

P) M=3 kg, 1 6m kg , 2 4m kg .

System is released from rest 1) Friction 1m is static

Q) M=3 kg, 1 2m kg , 2 6m kg .

System is released from rest 2) Friction 2m is static

R) M=3 kg, 1 7m kg , 2 3m kg .

System is released from rest 3) Friction 1m is kinetic

S) M=3 kg, 1 1m kg , 2 3m kg .

System is released from rest 4) Friction 2m is kinetic

P Q R S

A) 2,3 1,2 1,4 1,4

B) 1,2 2,3 1,4 2,3

C) 2,3 1,2 2,3 1,4

D) 1,2 2,3 2,4 1,2

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18. Match List(I) with List (II) and select the correct answer using given below the Lists .

List I List II

P)

1) 1 2

1 2

2m k k

Tk k

Q)

2) 1 2

2 mTk k

R)

3) 2 mTk

S)

4) 22mTk

Codes: P Q R S A) 3 2 1 4 B) 4 3 2 1 C) 2 1 4 3 D) 1 2 3 4

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19. Column-I shows certain situations and Column-II shows information about forces List-I List-II

P) Situation

Front view of a car rounding a curve with constant speed

1) 1 2 0F F

Q)

Passengers in a rotor not sliding relative to rotor wall cylindrical rotor is rotating with constant angular velocity about its symmetry axis

2) 1 2 3F F F

is centripetal force

R)

Particle kept on rough surface of a bowl , no relative motion of particle in bowl , bowl has constant angular velocity

3) 1F

is static friction

S)

Car parked on a banker road with no sideways skidding

4) 1 2 3 0F F F

Codes: P Q R S P Q R S A) 2,3 1,2,3 2,3 3,4 B) 1,2,3 2,3 2,3 3,4 C) 1,2 1,2 1,2,3 4 D) 1,2,3 1,2 2,3 2,3

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20. Match List (1) with List(II) and select the correct answer using codes given below the

lists. A proton and an -particle have their kinetic energies in ratio 1:8

List I List II

P) Ratio of their masses 1) 1/ 2

Q) Ratio of their velocities 2) (1/4)

R) Ratio of their charges 3) 1/2

S) Ratio of their De-Broglie

wavelength 4) 4 2

Codes :

P Q R S P Q R S

A) 2 4 3 1 B) 3 4 2 1

C) 3 1 2 4 D) 2 1 3 4

PART-II_CHEMISTRY Max Marks : 60

Section-1 (One or more options correct type)

This section contains 10 Multiple Choice questions. Each Question has Four choices (A), (B), (C) and (D). Out of Which Only One is correct

21. Phosphine gas is not prepared by

A) 3 2 .Ca P dil HCl B) 4 solnPH I KOH

C) Red phosphorus + NaOH soln D) 4 solnP NaOH

22. Given : 2 4 22N O g NO g

Degree of dissociation of 2 4N O

d = Vapour density of equilibrium mixture. Which is correct graph?

A)

1/ d B)

1/ d C)

1/ d D)

1/ d

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23. Potential difference of electrical double layer formed in a colloidal solution is called.

A) Zeta potential B) Brownian potential C) Dorn potential D) Nernst potential

24.

OH

||

3 32 2Oxidation

O

HNO CH C ClHNO HNi

products (x) is A) Aspirin B) Paracetamol C) Phenophthaline D) Phenylalanine

25. Which of the following co-ordination compound has three stereoisomers

A) 2 3Cd gly H O NH

B) 2 2 2Pt Br H O

C) 3

3Cr en

D) 2 2

Co Br NO en

26. What is the approximate average number of glucose units in an aqueous solution of

10 g/L of starch has an osmotic pressure 35 10 atm at 25 C ?

A) 300 units B) 100 units C) 450 units D) 1000 units

27. For the reaction A B following graph is given:

B

time The correct graph for the given reaction is

A)

0.5t

0A B)

rate

A C) 0A

0.5t

D) t

A

28. 5PCl g Ag x y

Where product x is water insoluble but y reacts with water, then product x is insoluble

in solution of :

A) KCN B) 2 2 3Na S O C) 3.dil HNO D) 3NH

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29. Which of the following co-ordination ion/compound does not exhibit structural isomerism.

A) 2 44PtBrCl H O SO B) 3 45

CoBr NH Cd CN

C) 2 4Co ox H O Br D) 23 3

Ir ONO H O

30. The energy of separation of an electron moving in He is 13.6 eV. Which is correct

statement?

A) kinetic energy associated with electron is 13.6 eV

B) Velocity associated with electron is 6 11.09 10 secm

C) orbit angular momentum of electron is 2h

D) none of these




paragraph should have only one correct answer among the four choices A, B, C and D.

Paragraph For Questions 31 & 32

XWatersoluble

salt

Excess KI Y Z Coloured(solution)

2 2 3 Colourless productsNa S O

whiteY

31. Salt ‘X’ is

A) 2 4 3Fe SO B) 4 2.5CuSO H O C) 2KNO D) 3 2

Hg NO

32. Salt ‘X’ does not produce precipitate with solution of

A) 4 6K Fe CN B) 2BaCl C)NaOH D) Excess 4NH OH


500 ml 0.2M XOH 710bK and 500 ml 60.16 10bM YOH K are mixed together.

Given: log 3 = 0.48 33. pH of final solution is A) 3.52 B) 6.52 C) 10.48 D) 7.48 34. The degree of dissociation of XOH in final solution is

A) 310

3

B) 410

3

C)

4102

D) 71.8 10

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The neutralization Equivalent is Eq.wt geq

of an acid as determined by titration with

standard NaOH . The number of ionisable H of an acid is the number of equivalents

per mole and is equal to mwNE

.

(Gemdicarboxyllic acids on heating loses 2CO 35. Which carboxylic acid (A) , NE=52g/eq , loses 2CO when heated to given an acid

, 60 /B NE g eq . Where mass

molecularNENumber of ionisable H

)

A) 2 32;A CH COOH B CH COOH

B) A 2CH COOH

2CH COOH3;B CH COOH

C) A

HOOC COOH

; B

OO

COOH

D) 3A CH CH COOH

COOH3 2; B CH CH COOH

36. Which of the following acid have higher pKa ?

A)

COOH

2NO

3CH B)

COOH

2NO

3CH C)

COOH

2NO

3CH D)

COOH

2NO

3CH

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Section-3

(Matching List Type) This section contains four questions, each having two matching lists (List-1 & List-II). The options for

the correct match are provided as (A), (B),(C) and (D) out of which ONLY ONE is correct.

37.

List-I (Conc.cell)

List-II (Condition for working of cell)

P) 2 2, | || | ,Pt H g H pH x H pH y H g Pt 1bar 1bar

1) y x

Q) 2 2, | | ,Pt H g HCl aq H g Pt

1P2P

2) 1 2P P

R) 1bar 1bar

2 2, | || | ,Pt Cl g Cl y Cl x Cl g Pt

3) x y

S) 1P

2P 2 2, | || ,Pt Cl g KCl aq Cl g Pt

4) 2 1P P

Codes :

P Q R S A) 2 3 1 4 B) 3 2 4 1 C) 3 2 1 4 D) 2 3 4 1

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38.

List--I List-II

P)

CHO

2CH OH

H OH

HOHH

HOD Xylose

1) On oxidation give meso

Q) D-Ribose

CHO

2CH OH

H OHH

OHHOH

2) Give the same osazone as D-arabinose

R) HO

CHO

2CH OH

HH OHD-Threose

3) Smallest aldose able to form cyclic hemiacetal

S) D-galactose

CHO

2CH OH

H OH

H

OHH

HOHHO

4) C-4 epimer of D-glucose

Codes : P Q R S A) 3 2 1 4 B) 4 3 2 1 C) 2 1 4 3 D) 1 2 3 4

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39.

List—I (Reactions )

List-II (One of the product)

P) ....3 2 32Co NO Al O 1) 3NH

Q) ....2coolNO g NO g 2) 2NO g

R) ....4 2 72NH Cr O s 3) 2N g

S) 4 4 4Na NH HPO CuSO 4) Coloured substance

Codes :

P Q R S A) 4 2 3 1 B) 4 1 3 2 C) 2 3 1 4 D) 2 4 3 1

40.

List--I List-II P) Pyruvic acid 1) 2,4 DNP Test

Q) Aspirine 2) Decolourises 2 4/Br CCl

R) Acrylic acid 3) Evolve 2H g with Na metal

S) Benzyl alcohol 4) Give 2CO g with 3NaHCO

Codes :

P Q R S A) 3 2 1 4 B) 4 3 2 1 C) 1 4 2 3 D) 1 2 3 4

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PART-III_MATHEMATICS Max Marks : 60 Section-1

(Only one Option correct Type) This section contains 10 Multiple Choice questions. Each Question has Four choices (A), (B), (C) and

(D). Out of Which Only One is correct

41. Let 1 1 32 3 2

x y z and 1

1 5 1x k y z

be two lines intersect at , , then

k equals

A) 1 B)4 C)6 D)9

42. Let 1, 2,3, 4,5,6,7,8A be a set Let :f A A be a function such that

, ,f X X X A f X is even when ever X is even and f X is odd when ever X is

odd. Then total number of on-to functions satisfying these conditions will be

A)36 B) 49 C) 64 D) 81

43. Let A be square matrix of order n and nI be an identity matrix of order . 0n A and

3 0A . Let 212 nM A A I and 21

2 nN A A I be two matrices . Then which of the

following must be correct ?

A) 1M N B) det 0M C) TM N D) det 1MN

44.

1

1

3 23 3 3 sin 1lim

30 sin .sin 2

x

x

t t t t dt

x x x x

equals :

A) 110

B) 15

C) 25

D) None of these

45. Let ,Z x iy x y R be a complex number such that 2 3 2Z i and 5 3Z i

then Z is equal to

A) 31 B) 615

C) 315

D) 5

46. Let

24 42 33 31 1 1 1

n kSn k k k k

then 2 / 3

SnLimn n

equals

A) 0 B) 14

C) 12

D) 1

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47. 2

21

11

xln dxx x

equals

A) 0 B)1 C) 2 D) None of these

48. The line 1y mx cuts the parabola 2 4y ax at two points P and Q if equation of circle

with one diameter PQ is 2 2 18 4 5 0x y x y then a m equals

A) 0 B) 3 C) 5 D) None of these

49. Let A,B,C and D be four points in space satisfying 4 4 4 1 4x y z xyz then the volume

of tetrahedron A BCD is

A) 16 B) 163

C) 83

D) None of these

50. Let 0,0 be the focus of a parabola which is passing through the point 1,1 . If the line

2 3x y is tangent to the parabola at 1,1 then the length of latus-rectum of the

parabola is

A) 36 25

B) 18 25

C) 9 25

D) 9 2




paragraph should have only one correct answer among the four choices A, B, C and D.

Paragraph for Questions 51 & 52

Let ,a b and c be three non-negative numbers such that

3 2

3 2

3 2

a a a bb b b cc c c a

51. Number of possible triplets of type , ,a b c is /are A) 0 B)1 C)2 D) More than 2

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52. If at least one among ,a b and c is different from other two then number of possible

triples of type , ,a b c is /are

A)0 B)1 C)2 D) More than 2


In ,ABC AB AC . Points D and E lie on BC such that BD DC and BE CE .

tan EAC , tan EAD and tan EAB are in G.P.

53. EAD is equal to

A) 6 B)

4 C)

3 D) 1 3tan

4

54. If 10AE then AD equals

A) 5 2 B) 5 3 C) 5 D) 6


Let y f x be a polynomial such that 5

2

, 0x

x

f x dx ax b x R a

and ,a b R

0 3f and 1 5f

55. The function y f x is

A) one-one and on-to B) on-to but not one-one

C) one-one but on-to D) Neither one-one nor on-to

56. Area bounded by the curve y f x , between the ordinates 0x and 2x and the x-

axis is

A) 3 B) 7 C) 9 D) 10

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Section-3 (Matching List Type)

This section contains four questions, each having two matching lists (List-1 & List-II). The options for the correct match are provided as (A), (B),(C) and (D) out of which ONLY ONE is correct. 57.

List--I List-II P) Number of real roots of

2013 2014 2015x x x 1) 1

Q) If 4 3 210 26 10 1 0x x x x has n

distinct real roots than n 2) 2

R) Let a,b,c and d be four positive real

numbers such that 1abcd . If n is

the least value of

1 1 1 1a b c d then

positive integral factors of n which

are not a perfect square are

3) 3

S) 2

20

sin cos sinx

xLim

x

equals

. GIF

4) 4

Codes :

P Q R S

A) 3 2 1 4

B) 4 3 2 1

C) 2 1 4 3

D) 1 4 2 3

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58. Let 2 10y x be a parabola, From 15 ,02

three normals are drawn to the parabola . ,A B

and C are co-normal points .

List--I List-II

P) Area of ABC is 1) 252

Q) Radius of circumcircle of ABC 2) 254

R) Centroid of ABC 3) 5 ,03

S) Circumcentre of ABC 4) 25 ,04

Codes: P Q R S A) 3 2 1 4 B) 4 3 2 1 C) 2 1 4 3 D) 1 2 3 4

59. Let ,a b and c be three distinct real numbers such that 3 3 32 2 2 3a b c

a b c

List--I List-II P) a b c 1) 6 Q) 3 3 3a b c 2) 12 R) ab bc ca 3) 0 S) 2 2 22 a b c 4) -3

Codes: P Q R S A) 3 1 4 2 B) 4 3 2 1 C) 2 1 4 3 D) 1 2 3 4

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60.

List--I List-II

P) 0

2

1 1 2 3x x x x x dx

is equal to 1) 1

Q) If 5 4 3 2 0x ax bx cx dx e has exactly 3 distinct

real root, then minimum number of points where

5 4 3 2f x x ax bx cx dx e is not

differentiable is , , , ,a b c d e R

2) 0

R) 8 41

8 41 1x

Limx x

equals 3) 3

S) If the roots of the equation 4 3 2 60 0x ax bx cx are natural numbers other

than 1. If 61 2na b c then n equals

, ,a b c R

4) 2

Codes:

P Q R S

A) 3 2 1 4

B) 4 3 2 1

C) 2 1 4 3

D) 1 2 3 4

VARSITY EDUCATION MANAGEMENT LIMITED

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Solutions

PHYSICS

Single correct choice Type 1. (C) Sol: 5 0.1l cm 2 0.01r cm 2V r l

% error in volume= 2 2 0.01 0.1100 100 3%2 5

r lr l

2. (B)

Sol: 00

0

,appV Vf fV V

assuming car moving towards us .

345 1268 60 30 /345 C

c

V m sV

3. (D) Sol: 2

10,kq kqE Va a

10V aE

4. (C) Sol: 0.5. 0.01

. . 50PitchL C mmC S D

Zero error is positive Reading . . . . . .X M S R C S R Zero Error L C

1 0.5 46 4 0.01 0.92X mm 2 0.5 48 4 0.01 0.94X mm 3 0.5 44 4 0.01 0.90X mm

Best reading= 0.92meanX mm 5. (A) Sol: 10 100total i f w vQ mS mL mS mL Putting 11 , 0.5, 1, 540, 80w V fm kg S S L L 6. (A) Sol: 21. . 0

4 4 2i i f fkQq kQqU K E U K E mv

a a

Given 64kQ qVV v

a m

7. (B) Sol: 0 .... 1

2iB

r

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Where 2

e eiT

.

Also 2L I mr 2

Lmr

Putting values in (1) , 034

eB Lmr

8. (C) Sol: Let rate of heat supply = P Heat to boil 1Q P (9 min) = 100 10 90wmS m Heat to evaporate 2 540vQ Pt mL m

540 54min9 90t t

9. (C) Sol: At point of leaving contact

2 2 2 1 cos4Rv gh g R

And 2

cos 0mvMg NR

2 5cos cos

6vRg

10. (A) Sol:

/v r

V

Rest

hl

2 21 1

2 2MV I Mgh

2 2

22

1 sin2 2 2

MR vMV MglR

Putting 030 and 10 /v m s 15l m Section-II

Comprehension Type Paragraph for Questions No.s 11 to 12 11. (B) 12. (A) Sol: 3;

2 4 4new New bV T TV T F plVg

0T Vg

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0

0

3 44 3

ll

Paragraph for Questions No.s 13 to 14 13. (C) 14. (D )

CM

2V

V1V

CM

Sol: i fL L about CM of rod

2

1 ...... 12 2 12L L MLmV mV

1 2 ...... 2i f mV mV mV

2

2 2 2 21 2

1 1 1 1 ...... 32 2 2 2 12i f

mLE E mV mV mV

Solving the equations

144

V V

and

124

VL

15. (A) 16. (B) Sol: 2 2 2 2

0 0 0

; 0 ;2 2 2c hV R X X X V R V R h h

2 2

0 0 0 0

0; 4 22 2 2q q q qmgh R h h R mg mg

2 2 2 22 2 ; 2 2mgh mg R h h mgR h R h h R

2 2 2 2 2 2 2 2 2 42 2 ;4 4 4 ;4 4 ;3 43RR h R h R h R h Rh h h Rh h Rh h

For equilibrium 0NetF 2 2 2 2

0

1 ; 2 12q x xmg mg mg

R X R X

2 2

1 12

xR X

2 2 2 2 2

2 2

1 4 ;32 3

x RX R X X R XR X

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Section-III

17. (B)

1m

2m

Sol :

1maxsf 1kf

2maxsf 2kf

1 6m kg 18 12 16 12 2 4m 1 2m kg 6 4 24 18 2 6m 1 7m kg 21 14 12 9 2 3m 1 1m kg 3 2

If all three stationary T=15N

2T

30

For Case –I : In

1 2max max& 15s sP F f Both static : 1,2P In 1R f static 2f kinetic : 1,4R In 2Q f static , 1f kinetic : 2,3Q (Check option) 18. (C) 19. A

(P) speed constant & moving in circle 2

1 2 3 3 2& 0cmvF F F f F FR

(for equilibrium in vertical) & 1F

must be static friction. (Q) 1 2&F F will cancel each other.

1F friction (static) & 1 2 3 cF F F F

(as circular motion)

(R) 1 2 3 cF F F F

1F static friction (S) Car at rest 1 2 3 0F F F 20. D

18

p

K

2P

2 2 2

22 21 1 1 1 1; ;8 4 8 82 2

2

p p p p

p

V V V PmPPm V V V mm

1/22 1 1 1 1; ; ; 4 2

8 4 8 4 2p p p p p

p

P m P PP m P P

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CHEMISTRY 21. C

3 2 2 36 3 2Ca P HCl CaCl PH

4 3 2PH I KOH PH KI H O

4 2 3 2 23 3 3P NaOH H O PH NaH PO

Red phosphorus + NaOH soln. no reaction

22. D

1 2 1Dd

46 1d

23. A

Potential difference of electrical double layer formed in a colloidal solution is called

Zeta potential.

24. B

25. D

Complexes Hyd. Of central

Metal cation

No. of

stereoisomers

(A) 2 3Cd gly H O NH

3sp 2

(B) 2 2 2Pt Br H O 2dsp 2

(C) 3

3Cr en

2 3d sp 2

(D) 2 2Co Br NO en

2 3d sp 3

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26. A

mRT (m = molarity, R = 0.082 L atm/mol. K, 25 298T C K )

3

45 10 2 100.082 298

M mRT

wMm V

wmM V

44

10 5 102 10

m

Each glucose unit (mw = 180)

Bonded to the starch chain with bss of 21 18H O mm giving a effective molecular

mass 180 18 162

So approximate average number of glucose 45 10 309 300

162

27. D

t

AReaction is zero order

28. C

5 3PCl Ag AgCl PCl

3PCl is water soluble while AgCl is insoluble in dil 3HNO .

29. C

A) Ionization isomerism B) Co-ordination isomerism

C) No isomerism D) Linkage isomerism

30. A

2

2

13.6 13.6sepzE

n 2 2n z

2

213.6 2 13.6

2nKE E eV

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8 622.18 10 2.18 10 /2

V m s

22 2h h hJ n

31. B

2Cu give ppt with excess of KI

23excess brownCu KI CuI KI

32. D

2Cu gives deep blue colour solution in excess of 3NH .

33. C

7 60.1 10 0.08 10OH

7 70.1 10 0.08 10

89 10

43 10

4 log3pOH

34. A

7 3

4

10 0.1 100.1 3 10 3XOH

35. A

+mol.massNE=

H

Assume B is monocarboxylic aid and NE = MW the –COOH accounts for 45 g/ml of

molecular wt, leav 60 45 15 /g mol for the remainder 3due to CH so “b” is

3CH COOH

“A” has a second COOH replacing an H of 3CH COOH , it is malonic acid

2CHCOOH

COOH104 52 /

2g mol

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36. A

Due to H-bonding it is weak acid & have higher pKa.

37. C

P: 0.05911cell anode cathodeE pH pH

0.059cellE x y

;cellE ve x y

Q: 1

2

0.0591 log2cell

PEP

cellE ve 1 2P P

R: 0.0591 log1cell

yEx

,cellE ve y x

S: 2

1

0.0591 log2cell

PEP

2 1cellE ve P P

38. D

(P) D-xylose

OH

OHHO H

H

HCHO

2CH OH

OxidationOH

OHHO H

H

H

COOH

P.O.S

COOH MESO

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(Q) D-Ribose

OH

OHH

HCHO

2CH OH

OHH 2 epimer of D-Arabinose, give same osazone as D-arabinoseC

(R) D-threose

OH

OHH

HCHO

2CH OH

OH

OHH

H

H C OH

2CH

: :O

Smallest aldose (4C) able to form cyclic hemiacetal.

(S) D-galactose = it is C-4 epimer of D-glucose

OHH

CHO

2CH OH

OHH

OHH

OHH

5

6

1

234

4EpimerC

OH H

CHO

2CH OH

OH H

OHH

OHH

5

1

234

(D-glucose) (D-galactose) 39. (D) 3 2 3 2 22

Co NO Al O CoO NO g O g

Cool2 2 3NO g NO g N O s

4 2 7 2 2 3 22NH Cr O s N g Cr O s H O g

4 4 4 3 3 2Na NH HPO CuSO NaPO NH g H O g

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40. C

(P) Pyrcuric acid ||

3

O

CH C COOH

have carbonyl group i.e. show 2, 4 DNP

test.

(Q) Aspirine is

COOH3OCOCH

& give 2CO gas with 3NaHCO

(R) Acrylic acid 3CH CH CH COOH

Due to bond , it declourise 2 4/Br CCl (Unsaturation test).

(S) Benzyl alcohol is

OH

& react with Na metal evolve 2H gas.

MATHEMATICS Single correct choice Type

41. (B)

Sol: Let 1 2 ,1 3 , 3 2p p p be a point on the first line and , 1 5 ,k q q q be a point on

the line. If they are co-ordinates of point of intersection then

3 2 p q and 1 3 1 5p q

1 2 p k q

1p q and 2k

Point of intersection will be 3, 4, 1

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42. (D)

Sol: From given condition odd elements of the domain can associate with unequal odd

elements of the co-domain and even elements of the domain can associate with

unequal even number of the co-domain

Number of ways if X is odd = 1 1 1 14! 1 91! 2! 3! 4!

Number of ways if X is even = 1 1 1 14! 1 91! 2! 3! 4!

43. (A)

Sol: 212 nM A A I ; 21

2 nN A A I

4 31 1.4 4n nM N A I A A I

nI 3 0A

1M N

44. (B)

Sol: 1 1

33 2 3 3

1 1 0

3 3 3 sin 1 1 4 sin 1 4 sin 2 sinx x x

x x x

t t t t dt t t dt t tdt t tdt

13 2

130

3 3 3 sin 1lim

sin sin 2

x

xx

t t t t dt

x x x

33

040 0

2 sinsin 2 1lim . . lim . .

sin sin 2 5 sin sin 2 5

x

x x

t tdtx x x x x x

x x x x x x

45. (B)

Sol: 2 3 2z i is a circle and 5 3z i is another circle

The distance between their centres is equal to sum of their radii that’s why ‘Z’ will be

their point of contact .

16 7 615 5 5

Z i Z

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46. (C)

Sol:

4 2 2 43 3 3 31 1 . 1 1

kkT

k k k k

2 23 3

2 23 3

3 32 23 3

1 11 1 14

1 1

k k kk k

k k

2 22 23 33 3

1 11 1 0 1 14 4nS n n n n

23

22/3 2/33

1 1 1 11 14 2

n n

x

S SLimn n nn

47. (C)

Sol: 21

1Ix

ln 2

1x dx

x

Put 1xt

2

dtdxt

0 1 1 1 1

1 0 0 0 0

1 1 1 2 21

I ln dt lnt t dt lntdt ln t dt lntdtt t

48. (A)

Sol: Let 1 1,P x y & 2 2,Q x y then the roots of the equation 21 4 0mx ax

22 2

2 4 1 0m ax xm m

are 1x and 2x

And the roots of the equation 2 21 4 44 0y a ay a y ym m m

and 1y and 2y

Required circle is

2 22 2

2 4 4 1 4 0m a a ax y X ym m m m

………(1)

2 2 18 4 5 0x y x y ……………………………………………..(2)

From (1) and (2)

2

4 1 44, 5a am m m

and 2

2 4 10m am

13

m and 13

a

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49. (C)

Sol: 4 4 4 1 4 0x y z xyz

4 4 2 2 4 2 2 2 22 1 2 2 2 4 0x y x y z z x y z xyz

2 2 22 2 2 1 2 0x y z xy z

2 1z xy z and 2 2x y

1z 1x 1y

1x 1y

1 1 1z x y

1 1x y

1,1,1 1, 1,1 1,1, 1 1, 1, 1A B C and D

2 2AB i j 2 2AC i k

2 2AD j k

2 2 0

1 1 82 0 2 8 86 6 3

0 2 2Volume

50. (B)

Sol:

0,0S

1,1P

Q

R

From properties of parabola

RS PS and RQ PR

: 2 3PR x y

0 3, 3RS x y R

Now: : 2 9

9, 9RQ x yPQ x y Q

1 2PS l

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2 9 2QS l

Length of latus-rectum= 1 2

1 2

4 4 9 2 2 36 2 18 210 59 2 2

l ll l

Section-II

Comprehension Type

Paragraph for question Nos : 51-52

51. (C)

52. (A)

Sol: Consider the function 3 2f x x x x

f x is an increasing function such that

0 0,1f x x x

And 0 1f x x x

Now , if , , 0,1a b c

,b a c b and a c (not possible)

If , , 1,a b c

,b a c b and a c (not possible)

1a b c ir 0a b c


53. (B)

54. (A)

A

B D C E Sol: EAD and CAD

tan , tan and tan are in GP ,

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2 22

2 2

sin sin sin sintancos cos cos sin

2 2 2 2 2 2 2 2sin cos sin sin cos sin cos sin

2sin 0 or 2tan 1

04

cos 5 24

AD AE


55. (A)

56. (D)

Sol: 5

2

x

x

f x dx ax b x R

5 2f x f x a x R

' '5 2f x f x a x R

'f x is a periodic function but f x is polynomial 'f x is a polynomial

'f x k (a constant)

'f x kx c

Now 0 3f and 1 5f

2 3f x x

Section-III

Matching List Type

57. (D)

58. (D)

Sol: The co-normal points will be 0,0 5 ,52

and 5 , 52

centroid 5 ,03

Circumcenter 25 ,0 ;4

Radius = 254

; Area of 252

ABC

59. (A)

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Sol: 3 3 32 2 2 3a b c

a b c

Let 32 3x

x

, ,x a b c

3 3 2 0x x

0, 3a b c ab bc ca and 2abc 3 3 3 3 3 33 0 6a b c abc a b c

2 2 2 2 6a b c ab bc ca

60. (C)

Sol: (A) 0 1

2 1

1 1 2 3 2 1 1 2 0x x x x x dx x x x x x dx

(B) If 0f x has two pairs of equal roots than y f x has 1 point where it is not

differentiable .

(C) 8 41

8 4lim ....... 11 1x

Lx x

8 4

8 41

8 4lim ....... 21 1x

x xLx x

1 2

2 8 4 4 2L L

(D) 4 3 260 2.2.3.5 60 2 2 3 5x ax bx cx x x x x

31 60 8 2a b c

VARSITY EDUCATION MANAGEMENT LIMITED

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JEE-ADVANCED : KEY : PAPER-II

PHYSICS KEY CHEMISTRY KEY MATHEMATICS KEY

1 C 21 C 41 B

2 B 22 D 42 D

3 D 23 A 43 A

4 C 24 B 44 B

5 A 25 D 45 B

6 A 26 A 46 C

7 B 27 D 47 C

8 C 28 C 48 A

9 C 29 C 49 C

10 A 30 A 50 B

11 B 31 B 51 C

12 A 32 D 52 A

13 C 33 C 53 B

14 D 34 A 54 A

15 A 35 A 55 A

16 B 36 A 56 D

17 B 37 C 57 D

18 C 38 D 58 D

19 A 39 D 59 A

20 D 40 C 60 C

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