jee advanced 2014_test 2 (paper ii) code b

8/10/2019 JEE Advanced 2014_Test 2 (Paper II) Code B

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Space for Rough Work

Test - 2 (Paper-II) All India Aakash Test Series for JEE (Advanced)-2014

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PART - I : PHYSICS

SECTION - 1

Only One Option Correct TypeThis section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY

ONE is correct.

1. A spring of spring constant kconnected to a block of mass m is placed on a rough horizontal surface having

coefficient of friction . The spring is given initial elongation3mg

kand the block is released from rest. For the

subsequent motion, the maximum speed of the block is

(A) m

gk

(B) 2 m

gk

m

3 mg

k

(C) 2 mgk

(D)2

mgk

2. As shown in figure mass of the block resting on the floor is 3 m while that of hanging block is m. The floor is

frictionless and horizontal and all pulleys ideal. The system is initially held stationary with the inclined thread making

an angle = 30 with the horizontal. The blocks are now released from rest and allowed to move. The hangingblock falls through a height hbefore hitting the floor and at this time the value of becomes 60. The speed withwhich the hanging block hits the floor is

3m

m

(A) 2

4

gh(B)

3

4

gh

(C) 2gh (D) 2

7

gh

TEST - 2 (Paper - II)Time : 3 Hrs. MM : 186


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All India Aakash Test Series for JEE (Advanced)-2014 Test - 2 (Paper-II)

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3. Two steel spheres, having radii aand 2aare released from a height has shown in

figure. Assume that during motion the centres of the spheres lies on a vertical line.

Large sphere collides with the ground and recoils and collides with the small sphere.

Collisions are perfectly elastic. Velocity of small sphere just after its collision is

(A)9

2 ( 2 )5

g h a (B)9

2 ( 2 )23

g h a

a

h

2a

(C)5

2 ( 2 )9

g h a (D)23

2 ( 2 )9

g h a

4. As shown in figure a solid sphere is rolling without slipping on rough ground. It collides with an identical sphere at

rest elastically. Radius and mass of each sphere is Rand m. There is no friction between the two spheres. The

net angular impulse about its centre, imparted to second sphere after impact is

v

at rest

(A)5

7mRv (B)

3

7mRv

(C)2

7mRv (D)

4

7mRv

5. A uniform disc of radiusRlies in x-yplane with its centre at origin. Its moment of inertia about the axis17

2=y R

and z= 0 is equal to moment of inertia about the axis x= dand y= 0. The value of dis

R

(0 0)

y=172 R

d

x

y

(A) 3R (B) 4R

(C) R (D) 2R


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6. As shown in figure an object comprises of a uniform chordABand a ring of radius R(not necessarily both made

of the same material). Which of the following cannot be the centre of mass of object?

y

x

B

A(0, 0)

(A) ,4 4

R R

(B) ,3 3

R R

(C) ,3 3

R R

(D)2 2

,5 5

R R

SECTION - 2

One or More Options Correct Type

This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONE

OR MORE are correct.

7. A plank of length Land mass Mis placed at rest on a smooth horizontal surface. As shown in figure a small block

of mass mis projected with a velocity v0. The coefficient of friction between the block and the plank is , plank is

very long so that block eventually comes to rest on it.

m

M

v0

Smooth

(A) The final common velocity is 0mv

vM m

=

+

(B) The work done by friction on the plank is =

2

2

02

1

2( )+

m Mv

m M

(C) The work done by friction on the block is2

02

1 ( 2 )

2 ( )

+=

+

mM M mv

M m

(D) The net work done by friction is2

0

1

2=

+

mMv

M m


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8. A ball of mass mmoving at a speed vmakes a head on collision with an identical ball at rest. The kinetic energy

of the balls after the collision is3

4th of original. Choose the correct statements

m

v

m

v2

m

v1

(A) 1 1is2

ev v+

(B)2

1is2

ev v

(C) Coefficient of restitution is1

2(D) Coefficient of restitution is

1

2

9. A uniform slender rod of length Land mass Mis pivoted at one end. It is held horizontal and released. Given that

the pivot is frictionless, select the correct alternative(s).

L

M

(A) The angular acceleration of the stick immediately after it is released is

3

2

g

L

(B) The angular acceleration of the stick immediately after it is released is2

3

g

L

(C) The force F0exerted on the stick by the pivot immediately after release is

4

Mg

(D) The force F0exerted on the stick by the pivot immediately after release is

2

Mg

10. The net force (F) acting on a particle depends on its position (x) as shown in figure. Choose the correct statement.

F

A

B

C x

(A)Ais the point of stable equilibrium (B) Cis the point of unstable equilibrium

(C) Bis the point of neutral equilibrium (D) Bis the point of stable equilibrium


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11. A particle of mass mis suspended from a string of length Rand at the bottom it

is given velocity 3=u gR . Choose the correct velocity and tension for different

points given in the figure.

(A) Velocity at point B is 7gR (B) Tension at point B is 7mg

D B

C

u

R

(C) Velocity at point C is 5gR (D) Tension at point Cis 4mg

SECTION - 3

Paragraph Type

This section contains 2 paragraphs. Each describing theory, experiment, data etc. Four questions relate to two 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).

Paragraph for Question Nos. 12 to 13

A constant horizontal force F= mgstarts acting on a suspended pendulum bob of mass m, initially at rest.

m F

12. The maximum angular deflection of the string

(A)3

(B)

6

(C)2

(D)

4

13. Tension is maximum at angular deflection of the string

(A)3

(B)

6

(C)2

(D)

4


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Two smooth balls Aand B, each of mass mand radius Rhave their centres at (0, 0, R) and at (5R, R, R)

respectively, in a coordinate system as shown. Before collision, ballAis moving along positivex-axis with speed

of 4 m/s and ball Bis stationary. The collision between the balls is elastic.

x(m)

y

A

B

14. Velocity of the ballAjust after collision is

(A) 3i j (B) 3+i j

(C) 3 +i j (D) 3 i j

15. Impulse of the force exerted byAon Bduring collision is equal to

(A) 3 3mi mj (B) 3 3+mi mj

(C) 3 3+mi mj (D) 3 3mi mj

SECTION - 4

Matching Column Type

This section contains 2 multiple choice questions. Each question has matching Columns. The codes for the Columns

have choices (A), (B), (C) and (D) out of which ONLY ONEis correct.

16. The figure shows a fixed hemisphere of radius R. A small ball of mass mis projected horizontally along the tangent

with a speed vfrom a point C. The centre O, lowest pointAand point Clie in same vertical plane.

Column I Column II

(P) Angular momentum about O (1) mvR

(Q) Angular momentum about C (2) 2mvRcos2

A

O

C

(R) Angular momentum aboutA (3) mvRsin

(S) Angular momentum about OA (4) Zero


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Codes :

P Q R S

(A) 1 3 4 2

(B) 3 2 1 4

(C) 1 4 2 3

(D) 4 2 1 3

17. When a wheel rolls without slipping on a horizontal surface, any point (B) on its circumference moves along a

curved path called cycloid. Consider a point Bon the circumference, initially in contact with the surface, consider

that point as origin. Match column I having coordinate of point Band velocity of point Bafter the time interval twith

the column II.

v

B

c

Column I Column II

(P) x-coordinate of point B (1) cos cv t

r rr

(Q)y-coordinate of point B (2) cos c

c c

v tv v

r

(R) Horizontal component of velocity of point B (3) sin

c

c

v tv t r

r

(S) Vertical component of velocity of point B (4) sin c

c

v tv

r

Codes :

P Q R S

(A) 1 3 2 4

(B) 3 1 2 4

(C) 3 2 1 4

(D) 4 2 3 1


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SECTION - 5

Integer Value Correct Type

This section contains 3 questions. The answer to each of the question is a single digit integer, ranging from 0 to 9. The

appropriate bubbles corresponding to the respective question numbers in the ORS have to be darkened. For example,

if the correct answers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of

bubbles will look like the following :

0

X

Y

Z 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

18. A uniform rod of mass mand length Iis free to rotate about hinge O. A slight disturbance causes the rod to rotate

freely about O. Horizontal force applied on rod by hinge just before the rod hits the surface is .xmg

yFind the value

ofx+ y.

O

l

19. The system of blocks must be released from >nmg

hk

with the spring unstretched so that after perfectly inelastic

collision (e= 0) with ground, Bmay be lifted off the ground. Find the least possible value of n. (kis spring constant).

m

2m

A

B

h


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25. The solubility of Ag2CO

3in presence of Na

2CO

3is expressed by

(A)sp

23

2K

CO (B)

sp

23

K1

2 [CO ]

(C)sp

1[Na ]

2K

+ (D) 2Ksp

[CO32]

26. The entropy change when 1 mole of ideal gas expands reversibly from an initial volume of 2 litres to final volume of

20 litres at 25C is

(A) 19.15 JK1mol1 (B) 4.6 JK1mol1

(C) 0.1914 JK1mol1 (D) 46.06 JK1mol1

SECTION - 2




27. Cp

Cv= R. This R is not equal to

(A) Change in KE

(B) Change in rotational energy

(C) Work done which system can do on expanding the gas per mol per degree increase in temperature

(D) Change in PE

28. Chemical equilibrium for a reversible change means for

(A) The forward reaction proceeds as fast as the backward reaction i.e. velocity of opposing reaction is equal

(B) No change in concentration of reaction species with time

(C) Dynamic equilibrium

(D) The concentration of reactant molecules must be equal to the concentration of product molecules

29. Which of the relationships is/are correct?

(A) av8RT

CM

=

(B) rms3RT

CM

=

(C) PM = dRT (D) Cav

= 0.816 Crms


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30. For which reactions given fact(s) is /are correct?

(A)2 2 3

H S H O H O HS+ + + : Kcis ionisation constant for acid

(B)2 2 3

H O H O H O OH+ + + : Kcis ionic product of water

(C)3 2 2 3 3

CH NH H O CH NH OH

++ + : Kcis ionisation constant of base

(D) 2 23 3 4

Cu 4NH [Cu(NH ) ]+ ++ : Kcis stability constant of complex

31. In the reaction2 4 2

Cl OH Cl ClO H O + + + ; Chlorine (Cl2) is

(A) Oxidised

(B) Reduced

(C) Disproportionated

(D) Neither oxidised nor reduced

SECTION - 3

Paragraph Type

This section contains 2 paragraphs. Each describing theory, experiment, data etc. Four questions relate to two paragraphs


(A), (B), (C) and (D).


The methods employed for the determination of equilibrium constant are different for different equilibria depending

on the nature of the system and the types of reaction. In simple gaseous dissociation such as

2 4 2N O (g) 2NO (g) ; 1 mole of N2O4(g) is decomposed under atmospheric condition at 25C.

32. Value of KPincreased by when degree of dissociation becomes equal to 50% at constant temperature

(A) 1.5 times (B) Remains constant

(C) 2 times (D) Decreases

33. If the degree of dissociation of the above equilibrium is 50%, then observed vapour density is

(A) 30.6 (B) 54.22

(C) 90.23 (D) 25.46


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Iron metal is produced commercially by reducing iron (III) oxide into iron ore with carbon monoxide as follows

2 3 2Fe O (s) 3CO(g) 2Fe(s) 3CO (g)+ +

Fe O2 3

CO (g) Fe (s) CO (g)2

H (kJ/mol)f

S (J/mol K)824.0 110.5 0 393.587.5 197.5 27.0 213.5

34. The standard free energy change for the reaction at 25C is

(A) + 15.0 kJ (B) 29.3 kJ

(C) 15.0 kJ (D) 20 kJ

35. Choose the correct statement

(A) The reverse reaction becomes spontaneous at a lower temperature

(B) The reverse reaction becomes spontaneous at a higher temperature

(C) The reverse reaction is not spontaneous at any temperature

(D) The forward reaction is not spontaneous at any temperature

SECTION - 4




36. Match the following

Column I Column II

(Mixture) (pH values)(P) 0.1 M CH

3COOH + 0.1 M (1) 7.4

CH3COONa (pK

aof CH

3COOH = 4.74)

(Q) 100 ml of 0.1 M HCl + 100 ml of 0.1 M NaOH (2) 9.26

(R) 100 ml of 0.1 M NH4OH (3) 7.0

(pKb

= 4.74) + 50 ml of 0.1 M HCl

(S) Blood buffer (4) 4.74


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Codes :

P Q R S

(A) 1 2 3 4

(B) 2 3 4 1

(C) 4 3 2 1

(D) 4 2 3 1


Column I Column II

(P) 2

Cu Cu Cu+ + + (1) Oxidation

(Q)3

ClO Cl (2) Reduction

(R) 24 4

MnO MnO (3) Disproportionation

(S) 2 22 7 4

Cr O CrO (4) Neither oxidation nor reduction

Codes :

P Q R S

(A) 3 2 1 4

(B) 2 3 1 4

(C) 3 2 4 1

(D) 3 1 2 4

SECTION - 5



appropriate bubbles corresponding to the respective question numbers in the ORS have to be darkened. For example,if the correct answers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of


0

X

Y

Z 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9


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38. The n-factor of the underline compound is

4 3 2 2NH NO N O 3H O +

39. 100 ml of 0.75 N NH4OH is mixed with 100 ml of 0.50 N HCl. The K

bof NH

4OH is 2 105.Hence pOH of the

solution is _________.

40. The ratio of excluded volume and actual molecular volume of real gas is _________.

PART - III : MATHEMATICS

SECTION - 1

Only One Option Correct Type

This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY

ONE is correct.

41. Number of positive integers n2014 such that '6' is a factor of n2+ 3n+ 2 is

(A) 2014 (B) 1342

(C) 1343 (D) 1341

42. Sides of a triangle are distinct positive integers in an arithmetic progression. If the smallest side is 20 cm, then the

number of such triangles is

(A) 20 (B) 30

(C) 21 (D) 19

43. Let A= {1, 2, 3,.........., 12}, B= {101, 102,..........., 106}, number of functions defined from A to B such that

f(1) + f(2) +........ + f(12) is even is

(A) 612 (B) 3. 611

(C) 611 (D) 312 1

44. LetAdenote the matrix0

0

i

i

, i2= 1 and let Idenote the identity matrix1 0

0 1

, thenA+ A2+ ..... +A2020is

equal to

(A)0 0

0 0

(B)1

1

i

i

(C)0

0

i

i

(D)1 0

0 1


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45. A= {x1,x

2,x

3,.........., x

2n},x

iI, i= 1, 2, .............., 2n. Elements ofAare arranged along a circle in that order.

If each number is equal to average of its two adjacent numbers. If 21

n

m

m

x k

=

= , then sum of all numbers is

(A) 0 (B)2

2

k k+

(C) 2k (D) 4k

46. LetAbe n nmatrix such that it is idempotent matrix. The value of (I+ A)2nis equal to (where Iis the identity

matrix of order n)

(A) I+ A (B) I+ 2nA

(C) I+ 22nA (D) I+ (22n 1)A

SECTION - 2




47. 1 2 3 42 6 10 14

1 ....up to3 3 3 3

S = + + + + +

84 2 3

2 3 . 3 . 3 ....up toS = then

(A)S1> S

2(B)S

1< S

2

(C) Number of positive divisors of S1+ S

2is 6 (D) S

1= 2S

2

48. Letx1,x

2,x

3,......x

50be fifty nonzero numbers such thatx

i+ x

i+1= kfor all 1 i 49. Ifx

14= a,x

27= b, then

(A) x20

+ x37

= 3a+ 2b (B)x20

+x37

= 2k (a+ b)

(C) x20

+x37

= a+ b (D) x20

+x37

= 2k

49. Letx1 andx2be the roots of the equationx2 3x+ a= 0,x3 andx4 be roots of the equationx2 12x+ b= 0,x4,x

5be roots of equation ofx2+ cx+ d= 0, ifx

1< x

2< x

3< x

4< x

5< x

6are in G.P., then

(A)ab= 64 (B) c+ d= 564

(C) c +d = 560 (D) |c d| = 464

50. Let S3n

= 1 22+ 33+ 4 52+ 63+ .... up to 3n terms then

(A)S3n

is always divisible by 3 (B) S3n

is always divisible by 6

(C) S30

is divisible by 10 (D) S30

is not divisible by 10


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51. IfAis a square matrix of order 3 such that A3= Iand (A+ I)3+ (A I)3 6A= B,where Iis the identify matrix

of order 3, then

(A)B= 2I (B)B= 3I

(C) |B|= 2 (D) |B|= 8

SECTION - 3

Paragraph TypeThis section contains 2 paragraphs. Each describing theory, experiment, data etc. Four questions relate to two paragraphs


(A), (B), (C) and (D).


Let a1, a

2, a

3,......, a

nbe npositive real numbers then

1/1 2

1 2 3

...( . . ... ) nn

n

a a aa a a a

n

+ + + equality holds when

a1= a

2= .... = a

n.

52. For x > 3the minimum value of

22 12 26

( ) 3

x xf x

x

+ +

= + is

(A) 8 (B) 4

(C) 6 (D) 12

53. Ifx+ y+ z= 55,x, y, z> 0 thenx2y4z5will be maximum whenxis equal to

(A)55

3(B) 5

(C) 22 (D) 10


Suppose that each term in the sequence x1,x

2,x

3,......x

n(nis even) is either 1 or 1 or 0. Let Srepresent sum

of product of terms taken two at a time i.e. all xix

j(0


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55. Maximum value of Sis

(A)2

1

2

n n +

(B)2

2

n

(C)2

2

n n+

(D)2

2

n n

SECTION - 4




56. LetA= {1, 3, 5}. A number is selected from set Awith replacement and this process is done 920 times for each

i= 1, 3, 5. Let f(i) represents the number of times the number ( i) is selected i.e. f(1) + f(3) + f(5) = 920, Let S

be sum of all 920 numbers selected. If S3= 405 f(1). f(3). f(5) then match the statement in column I with statement

in column II and select appropriate code.

Column I Column II

(P) f(1) (1) 120

(Q) f(3) (2) 200

(R) f(5) (3) 600

(S) Harmonic mean of f(1), f(3), f(5) is (4) 100Codes :

P Q R S

(A) 2 3 2 1

(B) 3 2 1 4

(C) 3 2 1 2

(D) 1 2 3 4


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Column I Column II

(P) Letx 2y= 1,x y+ az= 2, ay+ 9z= b. (1) 6

Number of values ofafor which given system

of equations does not possess unique solution is

(Q) For above given equation(s) in part (P) number of (2) 2

ordered pair (a, b) for which given system of

equations have infinite solution is

(R) If5 2

2 1A

=

andA1= A+ Ithen is equal to (3) 12

(S) Let N= 253253, number of divisors of Nwhich are (4) 11

of the form 8+ 4, Nis

Codes :

P Q R S

(A) 2 2 1 4

(B) 2 2 1 3

(C) 1 1 2 3

(D) 2 1 3 4

SECTION - 5



appropriate bubbles corresponding to the respective question numbers in the ORS have to be darkened. For example,if the correct answers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of


0

X

Y

Z 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9


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58. a, b, c, dbe positive real numbers such that a+ b+ c+ d= 12 and abcd= 27 + ab+ ac+ ad+ bc+ bd+ cd

then value of2( )

3

a d b c + + +is __________

59. If

4 4 4

24 4 4 1 2 3

1 1 11 3 .... (2 1)

14 4 4

1 1 1

2 4 .... (2 )4 4 4

n

k n k n k

n

+ + +

= + +

+ + +

then k1 k

2+ k

3 is equal to

60. Let

4 1 6

6 4 9

5 0 5

A

=

. If |adj adjA| = 5k, then kis equal to


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Test - 1 (Paper - II) (Answers & Hints) All India Aakash Test Series for JEE (Advanced)-2014

TEST - 1 (Paper - II)

PHYSICS

1. (B)

2. (C)

3. (A)

4. (D)

5. (B)

6. (C)

7. (B, C)

8. (A, B)

9. (A, C)

10. (A, C, D)

11. (A, B, C, D)

12. (B)

13. (C)

14. (D)

15. (D)

16. (B)

17. (C)

18. (9)

19. (3)

20. (2)

CHEMISTRY

21. (C)

22. (D)

23. (B)

24. (D)

25. (B)

26. (A)

27. (A, B, D)

28. (A, C)

29. (A, D)

30. (A, C, D)

31. (C)

32. (A)

33. (B)

34. (D)

35. (D)

36. (B)

37. (A)

38. (5)

39. (9)

40. (4)

MATHEMATICS

41. (B)

42. (C)

43. (A)

44. (D)

45. (D)

46. (B)

47. (A, B)

48. (A, C)

49. (A, B)

50. (A, B)

51. (A, B, D)

52. (A)

53. (B)

54. (C)

55. (A)

56. (C)

57. (D)

58. (4)

59. (2)

60. (4)

ANSWERS

jee advanced 2014_test 2 (paper ii) code b

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