Prepared by Sri Chaitanya Narayana IIT Academy, … by Sri Chaitanya Narayana IIT Academy,...

2013_JEE-ADVANCED_MODEL PAPER

PAPER-1 Max Marks :240

PHYSICS: Section Question Type +Ve

Marks - Ve

Marks No.of

Qs Total marks

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

Sec – II(Q.N : 9 – 12) Questions with Multiple Correct Choice 4 0 4 16

Sec – III(Q.N : 13 – 16) Comprehension Type Questions(2+2) 4 0 4 16

Sec – IV(Q.N : 17 – 22) Integer Type 4 0 6 24

Total 22 80

CHEMISTRY: Section Question Type +Ve

Marks - Ve

Marks No.of

Qs Total marks





Total 22 80 MATHEMATICS:

Section Question Type +Ve Marks

- Ve Marks

No.of Qs

Total marks





Total 22 80

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Prepared by Sri Chaitanya Narayana IIT Academy, Vijayawada

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2013_JEE-Advanced_ Model_Paper-1

Paper-1

PHYSICS: Max.Marks : 80 SECTION I

Single Correct Answer Type This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1. A steel bar of length ‘L’ is held between rigid supports and heated non uniformly in

such a manner that the temperature increases T at a distance x from one end is given

by 2

02

T xTL

as shown in figure. The stress in the bar is (Assume that modulus of

elasticity for steel is E and thermal expansion coefficient is )

x

L

T

A) 0E T3 B) 0E T

9 C) 03E T D) 09E T

2. Two thin convex lenses of focal lengths 1f and 2f are separated by a horizontal distance d (where 1d f and 2d f ) and their centres are displaced by a vertical separation as shown. Taking the origin of coordinates O at the centre of first lens, x and y coordinates of the focal point of this lens system, for a parallel beam of rays coming from the left, are given by: (Assume that f )

y

0

d

x

A) 1 2

1 2

,f fx yf f

B) 1 2

1 2 1 2

( ) ,f f dx yf f d f f

C) 1 2 1 1

1 2 1 2

( ) ( ),f f d f d f dx yf f d f f d

D). 1 2 1

1 2

( ) , 0f f d f dx yf f d


Paper-1

3. Two blocks Aand B , each of mass m are connected with two identical springs which

are initially unstretched, placed on a smooth horizontal surface as shown . Initially the

blocks touch each other. The spring connected with block A , is compressed by / 4A

and the other connected to B is compressed by / 2A along with their respective blocks.

Both blocks are released simultaneously to collide inelastically. Find the amplitude of

combined mass:

A BA/4 A/2

A) /12A B) / 6A C) /10A D) / 8A

4. Pressure p, volume V and temperature T for a certain gas are related by 2AT BTp

V

,

where A and B are constants. The work done by the gas as its temperature changes

from 1T to 2T while pressure remains constant is

A) 2 12BA T T B) 2 2

2 1 2 1A T T B T T

C) 2 2 3 32 1 2 13

A BT T T TT

D) 2 32 1 2 13

BA T T T T

5. Two thin rods of mass m and length l each are joined to form L shape as shown. The

moment of inertia of rods about an axis passing through free end O of a rod and

perpendicular to both the rod is

l

l

O A) 22

7ml B)

2

6ml C) 2ml D)

253

ml


Paper-1

6. Two sources 1 2S and S emitting coherent light waves of wavelength in the same

phase are situated as shown. The minimum distance OP, so that the light intensity

detected at P is equal to that at O is(D>> )

D

O

Screen

1S 2S

P2

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

7. At 0t the positions and velocities of the two particles are as shown in the figure. They

are kept on a smooth horizontal surface and being mutually attracted by gravitational

force. Then position of the center of mass at 2sect .

0x 10x m

1 kg 1 kgx

y

1 5 /m s 2 3 /m s

A) 5x m B) 7x m C) 3x m D) 2x m 8. A railway engine whistling at a constant frequency moves with a constant speed. It goes

past a stationary observer standing beside the railway track. The frequency (n) of the

sound heard by the observer is plotted against time (t). Which of the following best

represents the resulting curve?

n

t

a)n

t

b) n

t

c) n

t

d)


Paper-1

SECTION II Multiple Correct Answer(s) Type

This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. 9. Two blocks A and B, each of mass m, are connected by a massless spring of natural

length L and spring constant k. The blocks are initially resting on a smooth horizontal

floor with the spring at its natural length as shown in Fig. A third identical block C, also

of mass m moves on the floor with a speed v along the line joining A and B and collides

elastically with A, then :

vL

A BC

A) The KE of the AB system at maximum compression of the spring is zero

B) The KE of the AB system at maximum compression of the spring is 214

mv

C) The maximum compression of the spring is mvk

D) The maximum compression of the spring is 2mvk

10. In YDSE, the source is placed symmetrical to the slits. If a transparent slab is placed in

front of the upper slit, then (slab may absorb a fraction of light)

A) Intensity of central maxima may change

B) Intensity of central maxima may not change

C) Central maxima will be shifted up

D) Intensity of dark fringes will be always zero


Paper-1

11. Two parallel resistance less rails are connected by an inductor of self inductance L at

one end as shown in figure. A magnetic field B exists in the space which is

perpendicular to the plane of the rails inwards. Now a conductor of length ‘l’ and mass

‘m’ is placed transverse on the rails and given an impulse J towards the rightward

direction. Then select the correct option (s):

L l

A) Velocity of the conductor is half of the initial velocity after a displacement of the

conductor 2

2 2

34

J LisB l m

B) Velocity of the conductor is half of the initial velocity after a displacement of the

conductor 2

2 2

3J LisB l m

C) Current flowing through the inductor at the instant when velocity of conductor is

half of the initial velocity is 23

4JLm

D) Current flowing through the inductor at the instant when velocity of the conductor

is half of the initial velocity is 23J

mL


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12. There is a fixed semicircular ring of radius R, lying in y – z plane, with centre of arc at origin and it is uniformly charged with charge Q. There is a long hollow pipe of very small radius, inner surface of pipe is smooth and it is made of insulated material. Pipe is fixed along x – axis from origin. A small ball with charge q and mass m is projected into the pipe with negligible velocity. Ball can smoothly move in pipe. Whole arrangement lies in gravity free space. Assume that there is no effect of hollow pipe on the electrostatic interaction between the charges Q and q. Then,

A) The maximum acceleration of the ball in the pipe is 2

06 3Qq

mR

B) The maximum acceleration of the ball in the pipe is 2

03 3Qq

mR

C) The maximum electric field exists along the axis at a distance of 2

Rx .

D) The kinetic energy of the particle when its acceleration is maximum is

0

214 3

QqR

SECTION III Paragraph Type

This section contains 4 multiple choice questions relating to Two paragraphs with two questions on each paragraph. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Passage: - 1

One end of a light string ‘L’ is tied to a ball and the other end is connected to a fixed point O. The ball is released from rest with string horizontal and just taut. The ball then moves in a vertical circular path as shown in figure; let the velocity of ball at B and C be BV

and CV

respectively

C

B

A

O


Paper-1

13. If C BV 2 V

then the value of as shown is

A) 1 1cos4

B) 1 1sin4

C) 1 1cos2

D) 1 1sin2

14. If C B BV V V

, then the value of as shown is

A) 1/3

1 1cos4

B) 1/ 3

1 1sin4

C) 1/3

1 1cos2

D) 1/ 3

1 1sin2

Passage - II

In the Young’s double slit experiment a monochromatic light of wavelength is used. The

slits are (in air medium) separated by distance‘d’ as shown in the figure. The medium between the

plane of the slits and the screen is having a medium of refractive index which varies with time as

0n n kt

15. The y co-ordinate of central maxima at any time t is

A) 0

sinDn kt

B) 0

cosDn kt

C) 2

0

sinDn kt

D) 2

0

cosDn kt

16. The velocity of central maxima at any time‘t’ as a function of time‘t’ is

A) 2

0

2 sinkDn kt

B)

20

sinkDn kt

C) 0

2 sinkDn kt

D) 0

sinkDn kt


Paper-1

SECTION IV Integer Answer Type

This section contains 6 questions. The answer to each question is single digit integer, ranging from 0 to 9 (both inclusive). 17. A tank of cross sectional area 0A is filled with a liquid. A small orifice of area

0A A A is present at the bottom of tank. At a moment the height of liquid in the tank

is ‘H’, what is acceleration of top layer of liquid at this moment as a multiple of 2

0

AA

g

H

18. A bob of mass m = 4 kg is suspended from a massless string of length l. Other end of

the string is fixed from the ceiling. A horizontal force 34

F mg is applied on the bob

when it at rest at the lowest position. The maximum tension (in Newton) in the string during the motion. is 10x. Then the value of x is (Take 210 /g m s )

34mgF

19. The circuit was in the shown state for a long time. Now the switch S is closed. The

charge that flown through the switch is 10 x C then the value of x is


Paper-1

20. A particle of mass 4m at rest decays into two particles of masses m and 3m having

non-zero velocities. The de-Broglie wavelength of the particle of mass m is x times the

de-Broglie wavelengths of the particle of mass 2m. Then the value of x is

21. Two identical containers A and B with frictionless pistons contain the same ideal gas

at the same temperature and the same volume V. The mass of the gas in A is Am and

that in the B is Bm . The gas in each cylinder is now allowed to expand isothermally to

the same final volume 2V. The changes in the pressure in A and B are found to be P

and 1.5 P respectively. 3

A

B

m xm

.Then the value of x is

22. A slightly tapering wire of length ‘l’ and end radii ‘a’ and ‘b’ is subjected to stretching

forces F, F as shown in the Figure. If Y is its Young’s modulus, The extension

produced in the wire is 5K Fl

Yab . Then the value of k is


Paper-1

CHEMISTRY: Max.Marks: 80 SECTION I

Single Correct Answer Type This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 23. If P d Vs P (where P is pressure in atm and ‘d’ is density in gm/L) is plotted for

‘He’ gas (assume ideal) at a particular temperature. If P 8.21atm

d P d 5dP

,

then the temperature will be A) 160 K B) 320 K C) 80 K D) 240 K 24. A black, water insoluble powder (A) liberates yellowish green gas (B) on treatment

with conc. HCl and (A) dissolves to give a clear solution. Solid (A) when heated with PbO2 and HNO3 (or) sodium bismuthate & 2 4H SO gives a purple solution (C). The purple solution is due to the formation of

A) 4MnO B) 24MnO C) 4Mn D) 2 3Mn O

25. Two liquids A and B are mixed at temperature T in a certain ratio to form an ideal

solution. It is found that the partial pressure of A i.e., PA is equal to PB, the pressure of

B for liquid mixture. What is the total pressure of the liquid mixture in terms of 0AP and

0BP ?

A) 0 0A B

0 0A B

P PP P

B) 0 0A B

0 0A B

2P .PP P

C) 0A

0 0A B

2PP P

D) 0B

0 0A B

2PP P

26. Salt AB has zinc blende structure. The nearest distance between 2 2&A B ions is

2.5 0A .The edge length of AB unit cell is

A) 2.5 0A B) 03.5A C) 05.0A D) 05.77A

27. Which of the following has maximum vapour pressure at a given temperature?

A)

OHCHO

B)

OH

NO2 C)

OH

COOH D)

OH

CHO


Paper-1

28. Which of the following represents Freundlich adsorption isotherm ?

xm

1P

a)

xm

b)

P

xm

1P

c) log

xm

d)

P 29. The number of d-electrons in Fe2+ (Z = 26) is not equal to that of

A) p electrons in Ne B) s electrons in Mg

C) d electrons in Fe D) p electrons in Cl

30.

. ‘B’ is ethyl alcohol then ‘A’ is

A)

B)

C)

D)


Paper-1


This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.

31. Which of the following reactions are correctly given? A) 2 5 2 4 2

1N O N O O2

B) 2 3 2 2 2 4 2Na SO H O Na SO H O

C) 4 3 2 2NH NO N O 2H O

D) 2 2 2 2SO Cl SO Cl

32. Which of the following is the correct structure for aspartic acid

O

OHO

OH NH2

at the pH

indicated

A)

B)

C)

D)

33. Which of the following will produce acetone?

A) 2 4

43H SOHgSOCH C CH B)

2 6

23 /

i B Hii H O OHCH C CH

C)

CH3 C =C CH3KMnO4

KOH heat

CH3 CH3 D) 3CH CH CH OH

34. 100ml 0.1M HCl is mixed with 100ml 0.1M NaOH. Identify the correct statement (s)

A) 0.137 .H k Cal B) 0.573H kJ

C) 00.685T C D) 02.865T C


Paper-1


This section contains 4 multiple choice questions relating to Two paragraphs with two questions on each paragraph. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Passage-I:

One mole of hydrocarbon (A) reacts with 1 mole of bromine giving a dibromo compound 10 25 .C H Br (A) on treatment with cold dil. alkaline 4KMnO solution forms a compound 5 12 2 .C H O On ozonolysis gives equimolar amounts of propanone and ethanal. (A) on reduction gives alkane (B).

35. The compound A must be

A) 3 3CH CH CH CH B) 3 32CH C CHCH

C) 3 32 2CH C C CH D) 3 2 2CH CH CH CH

36. The compound B must be

A) 3 2 32CH CH CH CH B) 3 33

CH C CH

C) 3 2 2 3CH CH CH CH D) 3 2 33CH C CH CH

PASSAGE – 2

The cell potential cellE of a reaction is related as cellG nFE , where G represents

max. useful electrical work

n = no. of moles of electrons exchanged during the reaction for reversible cell reaction

r rd G V dp S .dT at constant pressure rd G S .dT

At constant pressure G H T. S …..1

p

d GG H

dT

…..2

cell

p

dEdT

is known as temperature coefficient of the e.m.f of the cell

37. The temperature coefficient of the e.m.f of cell, p

dEdT

is given

A) n FS

B) SnF C) S

nFT D) nFE


Paper-1

38. At 300 K, H for the reaction 2Zn s AgCl s ZnCl aq 2Ag s is 218kJ / mol while the e.m.f of the cell was 1.015 v.

p

dEdT

of the cell is

A) 4 14.2 10 VK B) 4 13.81 10 VK C) 10.11VK D) 4 17.62 10 VK


This section contains 6 questions. The answer to each question is single digit integer, ranging from 0 to 9 (both inclusive). 39. In a borax molecule the number of boron atoms having sp3 hybridised are 40. The concentration of R in the reaction, R P , was measured as a function of time and

the following data is obtained :

[R] (molar) 1.0 0.75 0.40 0.10

t (min.) 0.0 0.05 0.12 0.18

The order of the reaction is :

41. How many aliphatic saturated alcohols having five carbon atoms show optical

isomerism?

42. The no. of chlorine atoms that are directly bonded to ‘C’ in LEWISITE _______

43. The minimum HP required to prevent the precipitation of ZnS in a solution containing

0.01M 2ZnCl and saturated with 0.10 M H2S is____

(Given 1 2

21 20sp a a 2K ZnS 10 ; K K of H S 10 )

44. At STP the volume of nitrogen gas required to cover a sample of silica gel, assuming

Langmuir monolayer adsorption, is found to be 3 -11.33cm g of the gel. The area

occupied by each nitrogen molecule is 20.14nm . What is the surface area 2in m per gm

of silica gel ?


Paper-1

MATHEMATICS: Max.Marks : 80

SECTION I Single Correct Answer Type

This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

45. a and b

are non zero non–collinear vectors such that |a | = 2, a . b

= 1 and angle

between a and b

is 3 . If r is any vector satisfying r . a = 2, r . b

= 8, ( r + 2 a –

10 b

) . (a × b

) = 6 and r + 2 a – 10 b

= (a b ) then =

A) 12

B) 2 C) 43

D) 3

46. O is the circumcentre of ∆ABC and 1R , 2R and 3R are the radii of the circum circles of les OBC,OCA and OAB, respectively. Let a, b and c be the sides of le ABC. The value of

1 1 11 2 3aR bR cR is

A) 3abcR

B) 34abcR

C) 32abcR

D) abcR

47. The set of values of ‘ ’ for which three distinct chords drawn from ( , 0) to the ellipse 2 22 1x y are bisected by the parabola 2 4y x is

A) (8, ) B) 0, - 4+ 17 C) 0, 4+ 17 D) 8, 4+ 17 48. The area bounded by the curve 2 2 1y x x and tangent at (1, 4) and y-axis is

A) 2 sq. units B) 4 sq. units C) 43

sq. units D) 13

sq. units

49. The value of 0 0

0 0

3 cot 76 . cot16cot 76 cot16

is not equal to

A) Tan 046 B) Tan 0226 C) –cot 0134 D) –cot 0136 50. If A is a (3x3) skew symmetric matrix, formed by using the digits 0,1,-1, then the

number of such matrices is A) 10 B) 27 C) 8 D) 15

51. Total number of ways in which 2n number of identical balls can be put in n numbered boxes 1,2,3.....n such that thi box contains at least i number of balls is :

A) 21ncn

B) 2

11

ncn

C) 1

2 22

nC

n n

D) None

52. If 1f x x then the points where 1sin f x is non – differentiable, are

A) 0,1 B) 0, 1 C) 0,1, 1 D) 1,1


Paper-1


This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. 53. The length of the normal chord at 8,7 on 2 2 4 3 0y y x is

A) 3 107

B) 45 109

C) 37 511

D) 40 109

54. If 132 3 2 3 3 24 3 2 .

3 2 3 2x xx dx Cx x

( & are prime nos.) then

A) , , are in G.P B) , , are in H.P

C) ,2 , are in H.P D)

55. In ,ABC if 0c a bb c aa b c

then which of the following are correct.

A) tan tan 12 2A B

B) 2 2 3sin cos2 2A A

C) 2 9sin sin cos2 2AA B

D) 3 cot tanA A

56) Let : [0,1] [0,1]f be a function defined as ,( )

1 ,x x is rational

f xx x is irrational

.Then which of the

following is incorrect

(A) f is bijective, invertible but not monotonic function

(B) f is discontinuous at exactly one point

(C) f is continuous at exactly one point

(D) f is differentiable nowhere


This section contains 4 multiple choice questions relating to Two paragraphs with two questions on each paragraph. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Passage I Suppose 1 2,z z and 3z represent the vertices A, B and C of an equilateral triangle ABC

on the Argand plane. Then 2 1 3 2 1 3AB BC CA z z z z z z Also 3 1

2 1

arg3 3

z zCABz z


Paper-1

3 1 3 1

2 1 2 1

1 33 2 2

z z z z cis iz z z z

3 1 3 1 2

2 1 2 1

21 3 32 2 2 2

z z z z zi iz z z z

On squaring, we get 2 23 1 2 2 12 3 .z z z z z

1A z

2B z 3C z

57. If the complex number 1 2 3, ,z z z represent the vertices of an equilateral triangle such that

1 2 3 ,z z z then 1 2 3z z z is equal to :

A) 0 B) 3 C) D) 2

58. Let the complex numbers 1 2,z z and 3z be the vertices of an equilateral triangle. Let 0z

be the circumcentre of the triangle, then 2 2 21 2 3z z z is equal to :

A) 20z B) 2

03z C) 209z D) 0

Passage – II : If the squares of a 8 8 chess board are painted either red or black at random.

59. The probability that not all squares in any column are alternating in colour is

A) 8

7

112

B) 56

12

C) 7

112

D) 7

7

112

60. The probability that the chess board contains equal number of red and black squares is

A) 64

32642C B) 64

642 32

C) 32

64

2 12 D) 63

642 32


Paper-1


This section contains 6 questions. The answer to each question is single digit integer, ranging from 0 to 9 (both inclusive).

61. If 2 20, , 4sec 9cos2

and k ec

, then the number of solutions of the system of

equations 3 4 3, 2 3 2,6 5 3x y z x y z x y kz is

62. The shortest distance between the two opposite edges of a regular tetrahedron of edge

8 units is

63. The straight lines 3 2 1,3 13x y x y and 6 5x y form a triangle. Let the set

3 5 5 21 3 3 5 14 11 13, , , , ,2 2 2 5 2 2 2 5 4 2

s

then the number of points which lies in the

interior of the triangle is

64. The solution of the differential equation 33 1dy x x y x x ydx

is

2 2 1k xx y ce x then 3

4

2___

kk

65. A man starts from the point 3, 4P and reaches point 0,1Q touching x axis at

, 0R such that PR RQ is minimum, then 5

66. If d is the minimum distance between the curves logx xef x e and g x then the value

of 6d .

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