JEE Advanced-2014_Test-5 (Paper-II) - Code-B.pdf

8/10/2019 JEE Advanced-2014_Test-5 (Paper-II) - Code-B.pdf

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Space for Rough Work

Test - 5 (Paper-II) All India Aakash Test Series for JEE (Advanced)-2014

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PART - I : PHYSICS

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.

1. The equivalent resistance between pointsAand Bwould be

10

20

20

10

20 20

10

10

A B

(A) 15

(B) 12.5

(C) 13.3

(D) 20

2. Consider the arrangement of concentric conducting shells shown in figure. As Sis closed, how much charge will

be grounded ?

2q

2R

qq

3R

R

O

S

(A) q (B) +q

(C)4

3

q(D)

6

q

TEST - 5 (Paper - II)Time : 3 Hrs. MM : 186


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All India Aakash Test Series for JEE (Advanced)-2014 Test - 5 (Paper-II)

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3. Choose FALSE statement.

(A) Alloys of metals usually have greater resistivity than that of their constituent metals

(B) Attraction between two charge bodies always reveals that bodies have opposite charges

(C) It is possible to have a point where electric field and potential both would be zero

(D) If net electric flux through a closed surface is zero, then electric field on surface may be zero, may not be.

4. A rod of length 2luniformly charged with linear charge density + (C/m) in one half and oppositely in the other.Find torque of electric field about O.

O

E

(A) lEsin (B) l2

Esin

(C)2

sin2

lE

(D) l2E

5. Charge on the vertex Bis 1 C. The charge at Cso as to attain net force atAalong BCwould be

+q A

B C

3 m 4 m

(A)27

C64

(B)9

C16

(C)64

C27

(D)16

C9


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6. A fly, symmetrical sector of arc length aand radius 3a, mounted on the vertical axis. A charge qis placed at height

4afrom the centre along its axis. The flux that passes through fly would be

q

4a

3a a

(A)0

q

(B)0

30

q

(C)0

4

q

(D)0

9

4

q

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. Figure shows a conducting shell having inner radius r1and outer radius

r2. Conducting shell is neutral. A point charge qis placed at other than

centre inside shell. Choose the correct option/s

(A) Potential at centre is1 2

1 1 1kq

r r r

CP = rC

r2

r1

rq P

(B) Consider a pointA whose distance from centre is a(r1< a< r

2). b is to be its distance from charge (q).

Electric field atAdue to charge on inner surface of shell would be 2kq

b

(C) Electric field atA(described in options B) due to inner shell would be zero

(D) Electrostatic pressure at outer surface of shell would be

2

2 2

0 232

q

r


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8. Potential in space of a field depends uponx, yco-ordinate as V= 2xy.

(A) Electric field atx, ywould be ( ) 2 yi xj +

(B) Electric field atx, ywould be ( ) 2 yi xj +

(C) Charge density atx, ywould be zero

(D) Energy density at (1, 1, 0) would be 40

9. A non-conducting sphere having a spherical cavity centred at distance a from centre of sphere. Charge on the

sphere is distributed uniformly with volume charge density . A particle of mass having charge qis suspended

vertically from light non-conducting spring of force constant k. Evaluate the correct statements.

(A) Maximum elongation of the spring is0

2

3

aq

k

(B) Maximum elongation of the spring is

03

aq

k

(C) Time period of oscillation is 2 m

k (D) Time period of oscillation is

0

2 m

k

10. A positive charge qis placed on the y-axis at (0, a, 0). A large conducting plate parallel to x-zplane at y= dis

lying. Choose the correct statement/s about the potential difference between the given points

+q y

P Q Rx

( , 0, 0)a ( , 0, 0)a

(A)VPQ

> 0 (B) VPQ

< 0

(C) VPR

= 0 (D) VQR

< 0


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11. A conical shaped wire of uniform resistivity and ratio of radii of end cross-section is 1 : 2. Resistance of the wire

is 12. Choose the correct statements.

(i) (ii)

Q

12 V

P

(A) Resistance of first half is R1> 6 (B) Resistance of second half is R

2> 6

(C) Potential at PQ, V< 6 V (D) Potential at PQ, V> 6 V

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

The field Ein a dielectric is the superposition of the field E0of extraneous charge (charges that do not constitute

dielectric molecules) and the field Eof bound charges (charges appearing as result of polarization of dielectric)such that we may write E= E

0+ E. However, it is convenient to analyze the dielectric by vector Ddefined as

0D k E=

(for linear isotropic dielectric) where E is field in dielectric. Gauss theorem for D

is given as

ExtraneousDds q=

.

The gap between the plates of a parallel plate capacitor is filled up with two dielectric layers 1 and 2 with thicknesses

3

dand

2,

3

ddielectric constants kand 3kand resistivities and 2. A dc voltage Vis applied to capacitor. Electric

field is directed from layer 1 and 2.

2

k 3k

d/3 2 /3d

V


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12. Value of electric field in layer 1 would be

(A)3V

d(B)

3

5

V

d

(C)6

5

V

d(D)

V

d

13. Surface charge density of extraneous at boundary between the dielectric layers.

(A) 0

kV

d

(B)

03 kV

d

(C) 03

5

kV

d

(D) Zero


A particle charge +q, is released from P(0, 0, z) along the vertical z-axis. Charge sheet of radius Rand surface

charge density is placed on thex-yplane. Gravitational potential energy at centre of disc is taken to be zero.

g

+

+ + +

+

++ + +

+

+++

+

++++

x

y

zP

S

14. The variation of potential energy U(electric potential energy + gravitational potential energy) with z-axis is best

plotted as

(A)

U

z

(B)

U

z

(C)

U

z

(D)

U

z


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15. Potential at point Son the y-axis is

(A)0

R

(B)0

R

(C)0

4

R

(D)

2

02

R

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. Four large and parallel conducting plates are placed as shown in figure. Each surface area isAand distance between

consecutive plates is d.A

B

C

D

E

F

G

H

k= 2

V

0Take

AC

d

=

Column I Column II

(P) qC

(1) Zero

(Q)qD

(2)3

4

CV

(R) qG

(3)4

CV

(S) qA

+ qH

(4)2

CV

Codes :

P Q R S

(A) 4 3 2 1

(B) 4 2 3 1

(C) 3 4 2 1

(D) 3 2 4 1


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17. Time constants of the given circuits in column I are in column II. Match the respective values.

Column I Column II

(P) R

R

C(1) RC

(Q) R

R C

R (2) 2RC

(R) R

C

R (3)2

RC

(S)

RC

RR (4)

3

2RC

Codes :

P Q R S

(A) 2 3 4 1

(B) 3 4 1 2

(C) 1 2 4 3

(D) 4 2 1 3


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PART - II : CHEMISTRY

SECTION - 1



ONE is correct.

21. The matte is impure substance obtained during extraction of

(A) Cu (B) Fe

(C) Pb (D) Al

22. CO on passing over heated nickel gives

(A) NiCO3

(B) Ni(CO)4

(C) CO2+ H

2(D) CO + H

2

23. Which is acidic flux?

(A) CaO (B) SiO2

(C) Al2O3

(D) Fe2O3

24. Which element has highest melting point?

(A) Mn (B) Cr

(C) Mo (D) Cu

25. In III group analysis of basic radicals if NH4NO

3is added instead of NH

4Cl then which ion of the next group can be

precipitated in this group?

(A) Ba2+ (B) Zn2+

(C) Mn2+ (D) Co2+

26. The geometry of [Ag(NH3)2]+and [Cu(NH

3)4]2+are respectively

(A) Tetrahedral and octahedral (B) Tetrahedral and square planar

(C) Linear and square planar (D) Square planar and linear

SECTION - 2




27. Which of the following options are correct about [Mn(CN)6]4?

(A) Its hybridisation d2sp3 (B) It is octahedral

(C) The number of unpaired electron is 1 (D) The number of unpaired electron is 5


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28. K4[Fe(CN)

6] is used in the identification of

(A) Ca2+ions (B) Fe+3ions

(C) Cu+2ions (D) Cd+2ions

29. Which ions is/are not paramagnetic?

(A) [Ni(NH3)4]2+

(B) [Ni(CO)4](C) [Co(NH

3)6]3+

(D) [Ni(CN)4]2

30. Which is/are the ores of copper?

(A) Chalcopyrite (B) Gibsite

(C) Azurite (D) Siderite

31. On treatment with H2S gas, the solution of two salts in dil. HCl produce a black precipitate. The salt may be

(A) A copper salt (B) A lead salt

(C) An iron salt (D) A nickel salt

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).


On being heated with solid K2Cr

2O7, concentrated H

2SO

4and the solid X mixture gives vapour of a dark red colour

which form a yellow solution with aqueous NaOH. On acidification with acetic acid followed by treatment with lead

acetate, the yellow solution gives a yellow precipitate.

32. The vapour of dark red colour contains

(A) CrO2Cl

2and I

2(B) CrO

2Cl

2only

(C) I2only (D) CrO

2Br

2

33. The solid X may be

(A) NaBr (B) NaCl

(C) NaI (D) NaF


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The Ellingham diagram

500 1000 1500 2000

1000

800

600

400

2002C + O 2CO

2

2Zn + O 2ZnO2

Temperature (C)

2Mg+O

2MgO2

34. At what temperature zinc and carbon have equal affinity for oxygen?

(A) 1000C (B) 1500C

(C) 500C (D) 1200C

35. At 1100C, which reaction is spontaneous to a maximum extent?

(A) MgO + C Mg + CO (B) ZnO + CZn + CO

(C) MgO + Zn Mg + ZnO (D) ZnO + Mg MgO + Zn

SECTION - 4


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.

36. Match the followingColumn I Column II

Alloys Constituents

(P) Gun metal (1) Lead + Tin

(Q) German silver (2) Copper + Tin + Zinc

(R) Brass (3) Copper + Zinc

(S) Solder (4) Copper + Zinc + Nickel


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Codes :

P Q R S

(A) 2 4 3 1

(B) 4 2 3 1

(C) 2 4 1 3

(D) 2 3 4 1

37. Match the followingColumn I Column II

(Complex) (Spin only value in BM)

(P) K3[MnF

6] (1) 1.7

(Q) K3[VF

6] (2) 2.8

(R) K3[Mn(CN)

6] (3) 3.8

(S) K3[TiF

6] (4) 4.9

Codes :

P Q R S

(A) 4 2 1 3

(B) 4 2 2 1(C) 2 4 3 1

(D) 2 3 4 1

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

38. Oxidation state of Fe in Mohr's salt is +x. The value of x is _______.

39. How many hydrate isomers are possible for CoCl36H

2O? Assume that the co-ordination number of Co is six.

40. How many anions will give colourless acid vapour/gas with concentrated H2SO

4on reaction with following anions

CH3COO, Cl, Br, S2, 2

3SO , 3

3BO ,

2NO , 2

2 4C O , I ?


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PART - III : MATHEMATICS

SECTION - 1



ONE is correct.

41. If2 2( ) ( 4 4) 6f x x x x = + + is minimum then the number of values ofxis

(A) 1 (B) 2

(C) 3 (D) 4

42. The number of values ofxsatisfying the equation ( ) ( )2 3 2

log (log (log )) 8 8x x x + is

(A) 0 (B) 1

(C) 3 (D) 4

43. Let f(x) be a differentiable function for allxR. The derivative of f(x) is an even function. If the period of f(2x) is 1

then the value of f(2) + f(4) f(6) f(8) is/can

(A) 1 (B) 2

(C) 0 (D) Not be determined

44. A relation Sis defined on the set of real numbers such that S= {(a, b) : a3+ a ba2 b0} then Ris

(A) Equivalence (B) Symmetric

(C) Not transitive (D) Reflexive

45. Consider that n(S) represents the number of elements in set S. If ( ) 40n A B C = , ( ' ') 5n A B C = ,

( ' ') 10n B A C = , ( ' ') 6n C B A = then number of elements belongs to at least two of the sets is

(A) Less than 19 (B) More than 19

(C) 19 (D) 20

46. Let [ ] represents the greatest integer function and [x3+x2+ 1 +x] = [x3+x2+ 1] +x. The number of solution(s)

of the equation log|[x]| = 2 |[x]| is

(A) 1 (B) 0

(C) 3 (D) 2


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SECTION - 2




47. If [ ], { } represent the greatest integer function and fractional function respectively then which of the following

is/are not true?

(A)

0

sin[sin ]lim 1

[sin ]x

x

x=

(B)

0

sin {sin }lim 1

[ ]x

x x

x

=

(C) The number of values ofxwhere f(x) = [x] is discontinuous in [2, 6] is 5

(D)2

0

sin ( [ ])lim 1

[ 2 4]x

x

x x

=

+ +

48. Consider that n(S) represents the number of elements in set S. If ( ) 10n A B = and ( ') 5n A B C = then

(A) ( )(( ) ( )) (( ) ( )) (( ) ( )) ( ) 5n A B B A A C C A B C C B n A B C =

(B) ( )( )( ) ( ) ) 5n A B A B A B C =

(C) A relation R1from CtoAdefined as R

1= {(1, 2), (2, 3), (3, 4), (4, 5)} cannot be a function

(D) The minimum number of elements in ( ) 15n A B C =

49. [ ], { } represent greatest integer function and fractional function respectively then

(A) The left hand derivative of f(x) = (x{x}) (tan[x]) atx= 0 is equal to 1

(B) If4 6( ) ( 1) ( 2) ( 3) | |f x k x k x k x = + + is differentiable atx= 0 then number of values of kis one

(C) Right hand derivative of f(x) = ([x] {x}) atx= 1 is equal to 2

(D) If {sin , Integer ( ) , otherwisex x

g xx

= and f(x) = cosxthen

0

lim ( ( ))x

f g x

is equal to 1


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Consider f(x) is a real valued function such that f(x+ y) = f(x) + f(y) + 2xy. If f(x) is differentiable for all xand

f (0) = 0 then give the answers of the following questions.

54. If ( ) (sin )0 0

(sin )lim 1 (sin ) lim

(tan )

a

f x

x x

f xf x

f x + = , then the value of ais

(A) 1 (B) 0

(C) 4 (D) log 2

55. If g :ABdefined by g(x) = f(x2) + f(x) + 1 is onto then the least value of element in set Bis

(A)1

3(B)

1

4

(C) 1 (D)1

5

SECTION - 4


This section contains 2 multiple choice questions. Each question has matching Columns. The codes for the Columnshave choices (A), (B), (C) and (D) out of which ONLY ONEis correct.

56. Consider a function f : RRdefined as f(x) = ax3+ bx2+ c sinx+ d. In column I conditions on a, b, cand dare

given and in column II the name of f(x) is given. Now match column I to column II.

Column I Column II

(P) If a4+ a2c2+ a2+ c2= 0, b0, then f(x) is (1) Even function only

(Q) If the equation bx2+ cx+ d = 0, has (2) Odd function only

more than two roots and a0, then f(x) is

(R) If (a+b)2+ (c + d)2= 2ab+ 2cdthen f(x) is (3) Even and odd both

(S) If a2+ b2+ c2+ d2+ 4 = 2(a+ b+ c+ d) (4) Neither even nor odd

then f(x) is

Codes :

P Q R S

(A) 4 3 2 1

(B) 2 1 3 4

(C) 2 1 4 3

(D) 1 2 3 4


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57. Match column-I with column-II and select the correct answer using the code given below

Column I Column II

(P) If f(x) is differentiable function and (f(x))3 3f(x) +x= 0, where (1) 0

f(x) 1, then the value of ( )9 2f is

(Q) The minimum value of

22 2

2

2 2( )

x x x x x f x

x x

+ + +=

+

,x> 0, is (2) 3

(R) If logx

2 = a, logxa= band 2b= athen the value of x is (3) 2

(S) If [ ], { } represent greatest integer function and fractional function (4) 1

respectively, then the value of ( ) ( ) { }[ ]f x x x x = + is

Codes :

P Q R S

(A) 4 2 3 1

(B) 1 2 3 4

(C) 4 2 1 3

(D) 3 2 1 4

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

58. The number of integers in the domain of ( ) ( )( )2 3 12

log log logf x x =

is _________.

59. The number of points of non-differentiability of f(x) = ||x|2 4|x| + 3| in [4, 4] is ________.

60. The power set of setAhas 32 elements. If the total number of relations that are reflexive, is 10, then is ______.


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Test - 4 (Paper - II) (Answers & Hints) All India Aakash Test Series for JEE (Advanced)-2014

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TEST - 4 (Paper - II)

PHYSICS

1. (A)

2. (B)

3. (B)

4. (C)

5. (B)

6. (A)

7. (A, C)

8. (A, B, D)

9. (A, B)

10. (B, C)

11. (A)

12. (D)

13. (A)

14. (A)

15. (A)

16. (C)

17. (B)

18. (2)

19. (8)

20. (1)

CHEMISTRY

21. (C)

22. (B)

23. (A)

24. (D)

25. (B)

26. (A)

27. (A, B, C, D)

28. (A, B)

29. (A, B, C, D)

30. (A, B, C)

31. (A, B)

32. (A)

33. (A)

34. (D)

35. (A)

36. (C)

37. (B)

38. (1)

39. (2)

40. (4)

MATHEMATICS

41. (B)

42. (A)

43. (C)

44. (C)

45. (C)

46. (D)

47. (A, D)

48. (A, B)

49. (B, C, D)

50. (A, B, C)

51. (B, D)

52. (D)

53. (C)

54. (Deleted)

55. (Deleted)

56. (C)

57. (D)

58. (7)

59. (5)

60. (1)

ANSWERS


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JEE Advanced-2014_Test-5 (Paper-II) - Code-B.pdf

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