AIATS-5 COVERS 2014 · Test - 5 (Paper-II) All India Aakash Test Series for JEE (Advanced)-2014 1/18 PART - I : PHYSICS SECTION - 1 Only One Option Correct Type This section contains

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

1/18

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 points A and B would be

10 Ω

20 Ω

20 Ω

10 Ω

20 Ω20 Ω

10 Ω

10 Ω

A B

(A) 15 Ω

(B) 12.5 Ω

(C) 13.3 Ω

(D) 20 Ω

2. Consider the arrangement of concentric conducting shells shown in figure. As S is 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


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

2/18

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 2l uniformly charged with linear charge density +λ (C/m) in one half and oppositely in the other.

Find torque of electric field about O.

θO

E

(A) λlE sin θ (B) λl2E sin θ

(C)

2

sin2

lE

λ θ (D) λ l2E

5. Charge on the vertex B is –1 μC. The charge at C so as to attain net force at A along BC would be

+q A

B C

3 m 4 m

(A)27

C64

μ (B)9

C16

μ

(C)64

C27

μ (D)16

C9

μ



3/18

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

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

q

4a

3aa

(A)0

q

πε (B)0

30

q

πε

(C)0

4

q

πε (D)0

9

4

q

πε

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 r1 and outer radius

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

centre inside shell. Choose the correct option/s

(A) Potential at centre is

1 2

1 1 1kq

r r r

⎡ ⎤− −⎢ ⎥

⎣ ⎦

CP = rC

r2

r1

r–q P

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

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

Electric field at A due to charge on inner surface of shell would be 2

kq

b

(C) Electric field at A (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

rπ ε



4/18

8. Potential in space of a field depends upon x, y co-ordinate as V = 2xy.

(A) Electric field at x, y would be ( )ˆ ˆ2 yi xj− +

(B) Electric field at x, y would be ( )ˆ ˆ2 yi xj+

(C) Charge density at x, y would be zero

(D) Energy density at (1, 1, 0) would be 4ε0

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 ρ. A particle of mass having charge –q is suspended

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

(A) Maximum elongation of the spring is

0

2

3

aq

k

ρε (B) Maximum elongation of the spring is

03

aq

k

ρε

(C) Time period of oscillation is 2m

kπ (D) Time period of oscillation is

0

2m

k

ρπε

10. A positive charge q is placed on the y-axis at (0, a, 0). A large conducting plate parallel to x-z plane at y = –d is

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

+qy

P Q Rx

(– , 0, 0)a ( , 0, 0)a

(A) VPQ

> 0 (B) VPQ

< 0

(C) VPR

= 0 (D) VQR

< 0



5/18

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 Ω. Choose the correct statements.

(i) (ii)

Q

12 V

P

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

2 > 6 Ω

(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 E in a dielectric is the superposition of the field E0 of extraneous charge (charges that do not constitute

dielectric molecules) and the field E′ of bound charges (charges appearing as result of polarization of dielectric)

such that we may write E = E0 + E′. However, it is convenient to analyze the dielectric by vector D defined as

0D k E= ε� �

(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

d and

2,

3

d dielectric constants k and 3k and resistivities ρ and 2ρ. A dc voltage V is applied to capacitor. Electric

field is directed from layer 1 and 2.

2ρρk 3k

d/3 2 /3d

V



6/18

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)0kV

d

ε(B)

03 kV

d

ε

(C)0

3

5

kV

d

ε(D) Zero


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

charge density σ is placed on the x-y plane. Gravitational potential energy at centre of disc is taken to be zero.

g

+

++ + +

++

+ +

+

++++

++

++

x

y

zP

S

σ

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



7/18

15. Potential at point S on the y-axis is

(A)0

Rσπε (B)

0

Rσε

(C)0

4

Rσε (D)

2

02

Rσε

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 ONE is correct.

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

consecutive plates is d.A

B

C

D

E

F

G

H

k = 2

V

0Take

AC

d

ε⎛ ⎞=⎜ ⎟⎝ ⎠

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



8/18

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



9/18

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 negative charge of 1mC

3 is moving on the circle about a long charged wire of linear charge density

1C/m

3μ . Find

kinetic energy (in J) of the circulating charge (neglecting other field effect).

19. Three identical parallel plates are placed parallel to each other. A and C are given charges +q and –q. Any capacitance

between two plate formed is C. If

2

40 mJ2

q

C= . Find work done (in J) required to pull out plate B parallel to the

plates.

A B C

F

20. Readings of A1 and A

2 are 20 divisions and 10 divisions respectively in combination (i). In arrangement (ii) reading

are correspondingly changed to 4 division and 2 division. Find value of x, (in Ω) assuming meter are ideal.

A1

A2 ... (i)

A1

A2

x

5 Ω

... (ii)



10/18

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) Al2O

3(D) Fe

2O

3

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

3 is 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



11/18

28. K4[Fe(CN)

6] is used in the identification of

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

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

29. Which ions is/are not paramagnetic?

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

(B) [Ni(CO)4]

(C) [Co(NH3)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



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


On being heated with solid K2Cr

2O

7, concentrated H

2SO

4 and 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

2 and I

2(B) CrO

2Cl

2 only

(C) I2 only (D) CrO

2Br

2

33. The solid X may be

(A) NaBr (B) NaCl

(C) NaI (D) NaF



12/18


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) 1000°C (B) 1500°C

(C) 500°C (D) 1200°C

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

(A) MgO + C ⎯→ Mg + CO (B) ZnO + C ⎯→ Zn + CO

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

SECTION - 4




36. Match the following

Column 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



13/18

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 following

Column 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






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 CoCl3⋅6H

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

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

4 on reaction with following anions

CH3COO–, Cl–, Br–, S–2,

23SO−

, 33BO− ,

2NO− , 2

2 4C O− , I– ?



14/18

PART - III : MATHEMATICS

SECTION - 1



ONE is correct.

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

(A) 1 (B) 2

(C) 3 (D) 4

42. The number of values of x satisfying 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 all x ∈ R. 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 S is defined on the set of real numbers such that S = {(a, b) : a3 + a – ba2 – b ≥ 0} then R is

(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



15/18

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 of x where f(x) = [x] is discontinuous in [2, 6] is 5

(D)20

sin ( [ ])lim 1

[ 2 4]x

x

x x→

π =+ +

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∪ − Δ − ∩ ∩ =

(C) A relation R1 from C to A defined 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}) (tanπ[x]) at x = 0 is equal to 1

(B) If 4 6( ) ( 1) ( 2) ( 3) | |f x k x k x k x= − + − + − is differentiable at x = 0 then number of values of k is one

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

(D) If {sin , Integer( )

, otherwise

x xg x

x

≠= and f(x) = cosx then 0

lim ( ( ))x

f g x→

is equal to 1



16/18

50. If 20

sin3 cos2 ( 1)lim 2

x

x

a x b x c e

x→

+ + − = then

(A)4

3a = − (B) b = 0

(C) c = 4 (D) a = 1

51. Consider that the period of f(x) = cos(cos|cosx|) + cos (cos|sinx|) is T.

(A) If f(x) = [cos2x] + {cos2x} + [sin4x] + {sin4x}, where [ ], { } represent greatest integer function and fractional

function respectively, then period of f(x) is T.

(B) If f(x + 2) + f(x + 4) = 2 then the period of f(x) is 8T

π

(C) If [ ] represents greatest integer function then the period of h(x) = [3x] + [–3x] is 2

3

T

π

(D) If f(x) = f(x + k) then period of f(x) is 2Tk

π

SECTION - 3

Paragraph Type



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


Let

3 – ; 0 1

( ) ; 1 2

3 – ; 2 3

x x

f x x x

x x

< ≤⎧⎪= < <⎨⎪ ≤ <⎩

and h(x) = (fof)(x). Now give the answers of the following questions.

52. The number of points where h(x) is non-differentiable in (0, 3) is

(A) 1 (B) 0

(C) 2 (D) 4

53. If [ ] represents greatest integer function then 0

lim [ ( )]x

h x+→

is

(A) 0 (B) 1

(C) 3 (D) 4



17/18


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 x and

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 a is

(A) 1 (B) 0

(C) 4 (D) log 2

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

(A)1

3(B)

1

4

(C) 1 (D)1

5

SECTION - 4




56. Consider a function f : R → R defined as f(x) = ax3 + bx2 + c sinx + d. In column I conditions on a, b, c and d are

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, b ≠ 0, 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 a ≠ 0, then f(x) is

(R) If (a + b)2 + (c + d)2 = 2ab + 2cd then 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



18/18

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 xf x

x x

+ + +=+

, x > 0, is (2) 3

(R) If logx

2 = a, logxa = b and 2b = a then 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






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 1

2

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 set A has 32 elements. If the total number of relations that are reflexive, is λ10, then λ is ______.

� � �

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

1/10

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

AIATS-5 COVERS 2014 · Test - 5 (Paper-II) All India Aakash Test Series for JEE (Advanced)-2014 1/18 PART - I : PHYSICS SECTION - 1 Only One Option Correct Type This section contains

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