P1-QP

NARAYANA IIT ACADEMY INDIA

Sec: Sr.IIT-IZ3-CO-SPARK PTA-3 Dt: 02-11-14

JEE-ADVANCE-2013-P1-Model Time: 3:00 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 2 0 10 20

Sec – II(Q.N : 11 – 15) Questions with Multiple Correct Choice 4 -1 5 20

Sec – III(Q.N : 16 – 20) Questions with Integer Answer Type 4 -1 5 20

Total 20 60

CHEMISTRY: Section Question Type +Ve

Marks - Ve

Marks No.of

Qs Total marks




Total 20 60

MATHEMATICS:

Section Question Type +Ve Marks

- Ve Marks

No.of Qs

Total marks




Total 20 60

PAPER SETTERS : HYD-DNM VEDAVYAS

MATHEMATICS: SANTHOSH G (9396714888) PHYSICS :ADITYA SACHAN ((9885774968) CHEMISTRY : D SRINIVAS RAJU(9490231058)

Narayana IIT Academy 02-11-14_Sr.IIT-IZ3-CO-SPARK_JEE-ADV_(2013_P1)_ PTA-3

Sr.IIT (IZ3)_P1_Advanced space for rough work

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. Three blocks are initially placed as shown in the figure. Block A has mass m and initial

velocity v to the right. Block B with mass m and block C with mass 4m are both initially at

rest. Neglect friction. All collision are elastic. The final velocity of block A is

A) 0.6v to the left B) 1.4v to the left C) v to the left D) 0.4v to the right

2 In the arrangements shown in figure masses of each ball 1 kg and mass of trolley is 4 kg. In

the figures shell of mass 1 kg moving horizontally with velocity v=6 m/sec collides with

the ball and get stuck to it then its maximum deflection of the thread (length 1.5 m) with

vertical is

A) 053 B) 037 C) 030 D) 060

3 A body of mass 1 kg starts moving from rest at t = 0, in a circular path of radius 8 m. Its

kinetic energy varies as a function of time as : KE = 22t joules, where t is in seconds. Then:

A) tangential acceleration 24 /m s B) power of all forces at t 2 sec is 8 watt

C) first round is completed in 2 sec D) tangential force at t = 2 sec is 4 newton



4 A ball is held at rest in position A by two light cords. The horizontal cords is now cut and

the ball swings to the position B. What is the ratio of the tension in the cord in position B to

that in position A ?

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

5 Figure shows the overhead view of a disk rotating counter clockwise. The angular speed of the disk is decreasing. Which of the vector correctly represents total acceleration of a point on the rim of the disk

A)1 B)2 C)3 D) 4 6 A sphere of mass M and radius R is rolling on a horizontal surface with a velocity v and

then climbs up on a smooth inclined plane up to a height h. The height up to which its rises will be

A) directly proportional to the square of the velocity and inversely proportional to the

angle of the inclination B)directly proportional to the velocity and inversely proportional to its mass C) directly proportional to the square of the velocity and independent of mass and the

angle of the inclination D) directly proportional to its velocity and inversely proportional to the angle of the

inclination



7 A hemispherical shell of mass m and radius R is hinged at point O and placed on a horizontal surface. A ball of mass m moving with a velocity u inclined at an angle

1tan 1/ 2 strikes the shell at point A (as shown in the figure) and stops . What is the minimum speed u given to the ball so that the hemispherical shell can reach the horizontal surface OP?

A) Zero B) 2

3gR

C) 5

gR D) It cannot come on the surface for any value of u

8 A straight uniform metal rod of length 3l is bent through angle as shown. The bent rod is

then placed on a rough horizontal table. A light string is attached to the vertex of the right angle . The string is then pulled horizontally so that the rod translates at constant velocity. Then the angle which the side 2l makes with string is

A) 1 1tan

2 B) 1 1tan

4 C) 1 1sin

2 D) 1 1sin

4



9 A particle of mass is attached to a disc of equal mass m by means of a slack string as shown. The disc is hinged about its centre C. on a horizontal smooth table. The particle is projected with initial velocity v. The velocity of particle when the string becomes taut is

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

4v

10 Two thin rods: each of mass m and length l 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 end and perpendicular to both the end is

A) 22

7ml B)

2

6ml C) 25

3ml D) 2ml



Section-2 (One or More options Correct Type)

This section contains 5 multiple choice questions. Each question has four choices (A) (B)(C) and (D) out of which ONE or MORE are correct. . 11. Which of the following graphs cannot represent one dimensional motion a particle ?

A) B)

C) D)

12 Two bodies are moving with constant speed v clockwise and are initially diagonally

opposite . The particle B now achieves a tangential acceleration of 2/a m s . Then :

A)they collide after time Ra

B) they collide after time 2 Ra

C) relative velocity just before collision is aR

D) relative velocity just before collision is 2 aR



13 A disc is given an initial angular velocity 0 and placed on rough horizontal surface as shown. The quantities which will not depend on the coefficient of friction is/are

A)The time until rolling begins B)The displacement of the disc until rolling begins C) The velocity when rolling begins D) The work done by the force of friction 14 The angular acceleration of the toppling pole shown in figure is given by

sin ,k where is the angle between the axis of the pole and the vertical , and k is a constant. The pole starts from rest at 0 . Choose the correct options

A) The tangential acceleration of the upper end of the pole is sinlk B)The centripetal acceleration of the upper end of the pole is 2 1 coskl C)The tangential acceleration of the upper end of the pole is 2 1 coskl D)The centripetal acceleration of the upper end of the pole is sinlk



15 In the figure shown, the plank is being pulled to the right with a constant velocity v. If the cylinder does not slip, then

A)the speed of the centre of mass of the cylinder is 2v B)the speed of the centre of mass of the cylinder is zero C)the angular velocity of the cylinder is v/R D)The angular velocity of the cylinder is zero

Section-3

(Integer Value Correct Type) This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive). 16. A block of mass 2kg starts from rest with spring unstretched on a rough inclined plane.

Force constant of spring is 8K N/m, coefficient of kinetic friction 1 .8k What is the

speed of the block (in m/s) when it slides a distance 0.5x m down the incline plane ?

17 A small ball is projected from point p on floor towards a wall as shown in fig. It hits the

wall when its velocity is horizontal. Ball reaches point p after one bounce on the floor. If the coefficient of restitution is the same for the two collisions, and its value is 1/x, then the value of x is



18 A thin uniform rod AB of mass m=1.0kg moves translationally with acceleration 22.0 /a m s due to two antiparallel forces 1 2F and F as shown in figure. The distance

between the points at which these forces are applied is equal to y=20cm. Besides, it is known that 2 5.0F N . Find the length of the rod (in m)

19 A uniform rod of mass m=5.0 kg length L=90cm rests on a smooth horizontal surface.

One of the ends of the rod is struck with the impulse J=3.0N.s in a horizontal direction perpendicular to the rod. Find the force (in Newton) with which one half of the rod will act on the other half during the process of motion

20 A roller of diameter 6cm rides between two horizontal bars moving in opposite direction

as shown in figure. Find the distance y (in cm) of the instantaneous centre of rotation of the roller (Assuming,there is no slipping at any contact )



CHEMISTRY 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 21. The major product formed in the following reaction is

dil.NaOH3 2 3

CH CO CH CHO Major product

(A) CHO

O

(B) CHO

(C)

CHO

(D)

O

22. OH

CH2

H

X ; X is

(A)

(B)

(C)

(D)

23.

Which of the following is correct comparison of rate of haloform reaction with various

halogens?

(A) 2 2 2Cl Br Ir r r (B)

2 2 2I Br Clr r r (C) 2 2 2Br Cl Ir r r (D)

2 2 2Cl Br Ir r r



24. Which of the following compound(s) can undergo predominantly Cannizaro reaction?

I. II. III. IV.O CHO

CH3 CH C

CH3

H

O

N

CHO

H3C CH3

H3C C

CH3

CH3

C

O

H

A) only I, IV B) only I, II, IV C) I, II, III and IV D) only I, III, IV 25. The amines shown are isomers. Choose the one with the lowest boiling point

A)

B)

C)

D)

26. Which of the following Carboxylic acid donot undergo decarboxylation on heating?

A)

O

COOH

COOH

B) COOHO

C)

OHOOC

D) CH2-COOH

27. Which one of the following compounds is less acidic than benzoic acid?

A) O

O

O

OH OH

B)

OO

OH OH

C)

COOH

NO2

D)

COOH

OMe

28. Which is correct about the three C-N bond lengths marked as ‘a’, ‘b’ and ‘c’ in the following molecules.

H3C

NH2

CH3

CH3

NO2

NH2

NO2

NO2

NO2

C

NO2

NO2

Na b

c

A) a = b > c B) a > b > c C) b > a > c D) a = b = c



29. Increasing order of the reactivity of the following compounds towards the nitration will be

(I) (II) (III) (IV)O

O

O

O

O

O

O O

A) I > IV > III > II B) IV > I > III > II C) III > IV > I > II D) IV > I > II > III 30. Reason for retention of configuration in the following reaction is

N-K

+

O

O

+NH

O

OTs

Ph

O

NHO

Ph

O

N OO

(A) OTs is an excellent leaving group. (B) Neighboring group participation by NH group. (C) Neighboring group participation by Ph group. (D) The reaction involves SNi mechanism.




This section contains 5 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 statement is correct regarding above reaction

A)The reaction mechanism involves initial formation of alkyl chlorosulfite

B) 6 5from C H N HCl

can bring SNi displacement of very good leaving group 2ClSO

C) overall 100% retention takes place during the reaction D) overall 50% retention and 50% Inversion takes place during the reaction.

32. Which among the following compounds is/are not formed as the main product in the

given reaction?

H+

A)

B)

Ph

C) Ph

D)

33. Which of the following will produce aromatic compound as product?

(A) Re d hot Fe tube3CH C CH

(B) Al O2 3

6 14 oCr O /600 C2 3nC H ...

(C) N

H

+ tBuO3CHCl ...

(D)

NH2

NH2

+

CHO

CHO

......



34.

CH3

CH3

KMnO4

A

Phenol

H+B (Product)

Which of the following is correct regarding product ‘B’

A) ‘B’ is colourless in acidic medium

B) ‘B’ is pink colour in basic medium

C) ‘B’ has Benzenoid form in Basic medium

D) ‘B’ exists in Ionic form in Basic medium 35 .

H3CO NO2CH2 O CH2

One mole of HI

Product Products are A)

CH2IH3CO

B) CH2IO2N

C)

CH2OHH3CO

D) CH2OHO2N



Section-3

(Integer Value Correct Type) This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive). 36. An alkyne gives ethanoic acid as the only product on ozonolysis. The total number of

cyclic isomers of that alkyne is 37. The number of esters formed in the following reaction is

OH

O

+ CH3

H

DOH Con.H2SO4

38. The number of compounds which give white precipitate of AgCl with aqueous AgNO3 is

ClCl

Cl

Cl

Cl

CH3Cl

ClCH3

Cl

39. 3 2 3 dil acidCH CH CH O CH CH X Y (positive haloform test) The number of possible isomers for X excluding stereo isomers and including X.

40. During the conversion of Glycerol into Allyliodide number of moles of HI molecules

consumed is.



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. Consider the point A(0,1) and B(2,0) and P be a point on the line 4 3 9 0.x y

Coordinates of P such that PA PB is maximum, are

A) 12 17,5 5

B) 84 13,5 5

C) 6 17,5 5

D)(0,-3)

42 Let 0ax by c be a variable straight line, where ,a b and c are 1st, 3rd and 7th terms of an

increasing A.P. Then the variable straight line always passes through a fixed point which lies on_______([ ] and { } are step and fractional functions respectively)

A) | | | | 5x y B)[x]+[y]=1 C){x}+{y}=1 D) | | 5xy 43 If (sin ,cos ), 0, 2 and (1,4) lie on the same side or on the line 3 1 0,x y then the

maximum value of sin will be

A)1 B)0 C) 12

D) 312

44 The value of for which the points , 2 is an interior point of the smaller segment of

the circle 2 2 4 0x y made by the chord whose equation is 3 4 8 0x y is

A) 20,7

B) 2,0 C) 20, 2,0

7

D) No value of

45 Let P be any moving points on the circle 2 2 2 1x y x . AB be the chord of contact of this point with respect to the circle 2 2 2 0x y x . The locus of the circumcentre of the triangle CAB,(C centre of the circles ) is

A) 2 22 2 4 1 0x y x B) 2 2 4 1 0x y x C) 2 2 4 2 0x y x D) 2 22 2 4 3 0x y x



46 Let , 0f x y be the equation of a circle. If 0, 0f y has equal roots y 3,3 and f(x,0)

has roots 11,2

x

, then centre of the circle is:

A) 3 , 34

B) 3 , 32

C) 3 ,34

D)Circle is not possible

inconsistent

47 If positive number 1 1 1, ,a b c are in A.P., then product of roots of equation

2 101 101 1012 0x kx b a c k R

A) has +ve sign B)has –ve sign C)equal to zero D)no definite sign

48 If 2 3 2 3 2 31 2 3 4

1 4 1 4 1 4

3 , , ,a a a a a a then a a a aa a a a a a

are in

A) A.P B) G.P C)H.P D) A.G.P` 49 Locus of points in the argand plane, which have constant real part is of the form ( and

are real numbers) 0 ) A) ( ) 0z z i B) ( ) 0z z C) ( ) 0z z i D) ( ) 0z z

50 The point of intersection of the curves sin sin cos2 10 10xy and y

, where [.] denotes

the greatest integer function, is given by n I A) (4 1,1)n B) (4 1, 1)n C) (4 1,1)n D) (2 ,0)n




This section contains 5 multiple choice questions. Each question has four choices (A) (B)(C) and (D) out of which ONE or MORE are correct.

51. If 1 1 21 2 3

1 1 2

2 cos sin , ,2 cos sin

iz z z i and z z ziz z z i

are non zero complex numbers, then

A) 1 2

1

z zz is purely real B) 1

2

zz

is purely real C) 1 2

1 2

z zz z

is purely real D) none of these

52 The points , 2 2 1,2 4 ,6 2k k k k and k k are collinear for A) All values of k B) k=-1 C)k=1/2 D) no value of k 53 If the lines 2 , 1 2x a m y and y mx are concurrent, then the value of a can lie any

where interval A) 1a B) 1a C) 1 1a D) 0a 54 The equation of straight line(s) passing through ordered pairs ( , )a b satisfying equation 2 2sec ( 2) 1 0,a b a b

And having slope 12

is

A) 2 0x y B) 2 1x y C) 2x y D) 2 0x y

55 The value of in [0, 2 ] so that 2 2 2 sin (cos 1) 0x y x having intercept on x-

axis always greater than 2 is/are

A) ,4 2

B) ,4

C) 5,4 4

D) 0,



Section-3 (Integer Value Correct Type)

This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive). 56. If the circle passing through the distinct points (1,t),(t,1) and (t,t) for all values of t R also

passes through fixed point ( , )a b then 2 2a b is equal to 57 If the ratio of the area of equilateral triangles made of the common chord of the circle

2 2 4x y and 2 2 8 4 0x y x and their respective pairs of tangents drawn from points on the positive x-axis is57 24 3 : k then k is________

58 The number of integral value of a for which the point ( 1, 1)a a lies in the larger

segment of the circle 2 2 6 0x y x y cut by the chord whose equation is 2 0x y is equal to

59 If ,n N the 30

( 3) ( 1)nn

r rr

r r

cnc

is equal to

60 The number of pairs ( , )x y satisfying the equation sin sin sin( )x y x y and 1x y is

equal to

P1-QP

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