AIATS-6 COVERS 2014 - WordPress.com · Test - 6 (Paper-II) All India Aakash Test Series for JEE (Advanced)-2014 3/20 SECTION - 2 One or More Options Correct Type This section contains

Space for Rough Work

Test - 6 (Paper-II) All India Aakash Test Series for JEE (Advanced)-2014

1/20

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. Figure shows a long conducting cylinder with inner radius a and outer radius b.

The cylinder carries a current into the page with current density J = αr2. The

magnetic field at a point a < r < b from the axis is

(A) ( )4 40

2r a

r

μ α− (B) ( )4 40

4

μ α−r a

r

a+

b

(C) ( )3 30

2

μ α−r a

r

(D) ( )3 30

4

μ α−r a

r

2. A long solid conducting cylinder of radius R carries a current i. The energy stored by the cylinder in the form of

magnetic field by 1 m length of the cylinder in the region 0 ≤ r ≤ R is

(A)20

4

μπi (B)

20

8

μπi

(C)20

12

μπi (D)

20

16

μπi

3. Two current carrying circular loops are placed closely as shown in figure. The integral Bdr∫ along axis of the loops

within range –∞ to ∞ would be

axis

I 3 I

(A) μ0I (B) 2 μ

0I

(C) 4 μ0I (D) Zero

TEST - 6 (Paper - II)Time : 3 Hrs. MM : 186


All India Aakash Test Series for JEE (Advanced)-2014 Test - 6 (Paper-II)

2/20

4. A conducting loop moves with constant velocity 2 m/s in

nonuniform and variable magnetic field B = t2x2 T (where x is in

meter and t is in second) as shown in figure. The magnitude of

emf induced at t = 1 s is

(A) 2 volt (B)20

3 volt

b = 1m

y

x

B ⊗t = 0

a=1m

V = 2 m/s

(0,0)

(C)14

3 volt (D)

68

3 volt

5. A metallic rod of length L is rotated in a horizontal plane with an angular velocity ω where no magnetic field exists.

The emf induced in the rod, if the charge and mass of electron is e and m respectively, is

O

ω L

A

(A)

2ω�m

e

(B)

2

2

ω�m

e

(C)

2 2ω �m

e

(D)

2 2

2

ω �m

e

6. The arrangement shows two long metallic rails connected to resistance R forming an inclined plane. Magnetic field

is vertical in the region. A slider of mass m and length � will move with the terminal velocity (incline is smooth)

θ

B

R

�

m

θ

(A) 2 2 2

cos

sin

θθ�

mgR

B(B) 2 2 2

sin

cos

θθ�

mgR

B

(C)2 2

tan θ�

mgR

B(D) 2 2

tanθ�

mgR

B



3/20

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. Two parallel long resistanceless rails are joined at ends by a resistance R. A slider of mass m, length �, has been

imparted a velocity V0. System is kept in horizontal plane submerged in a uniform magnetic field B.

Q

P

�

m

V0

⊗B

R

(A) The distance travelled by slider before it stops is 0

2 2�

mV R

B

(B) The direction of current in slider is from P to Q

(C) The velocity of slider at time 0

2 2isVmR

teB

=�

(D) The velocity of slider at time 0

2 2is

2

VmRt

B=

�

8. A direct current I flows along lengthy straight wire from the point O, the current spreads radially all over an infinite

conducting plane perpendicular to wire. X and Y are two points at r distance from wire just above and just below

conducting plane respectively as shown in figure. Choose the correct option(s)

X

Y

r

rO(A) Net magnetic field at 0

4

iX

r

μ=

π

(B) Magnetic field at X due to conducting plane will be 0

4

i

r

μπ directed outward

(C) Net magnetic field at Y would be zero

(D) Magnetic field at Y due to conducting plane would be 0

4

i

r

μπ directed inward



4/20

9. Figure shows an ac circuit. The rms voltage of the source is e0. The rms current through the source when

R C

C R

~

L

(A) The frequency of ac generator is very low (near zero) is 2

rmsV

R

(B) The frequency of ac generator is very low (near zero) is 2

rmsV

R

(C) The frequency of the source is very high (much higher than resonant frequency) is2

rmsV

R

(D) The frequency of the source is very high (much higher than resonant frequency) is2

rmsV

R

10. A current I flows in a long straight wire with cross-section having the form of a thin half-pipe of radius R. An equal

and opposite current flows in a long wire placed along the axis of the pipe. Choose the correct options.

R

(A) Magnetic field at a point on the axis of the pipe is 0

22

μπI

R

(B) Magnetic field at a point on the axis of the pipe is 0

2

μπ

I

R

(C) The force per unit length of the central wire is

2

0

2

μπI

R

(D) The force per unit length of the central wire is

2

0

22

μπI

R



5/20

11. A charged particle having charge q and mass m moves with velocity 0ˆ at 0=v i t at origin.

q m, V0

X

Y

E0

B0

(A) The Y-coordinate of the particle when it cuts the Y axis for the nth time is

2 2

0

2

0

2 E mn

qB

π

(B) The Y-coordinate of the particle when it cuts the Y axis for the nth time is

2 2

0

2

0

4 E mn

qB

π

(C) The angle made by the velocity vector with Y axis when it cuts the Y axis for nth time is 1 0

0

tan2

− ⎛ ⎞⎜ ⎟π⎝ ⎠

BV

nE

(D) The angle made by the velocity vector with Y axis when it cuts the Y axis for nth time is 1 0

0

tan4

− ⎛ ⎞⎜ ⎟π⎝ ⎠

BV

nE

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

Let S to be a static frame of reference in which electric field E

��

and magnetic field B

��

are equal to zero and 0

ˆB k

respectively. And a charge q and mass m moves with velocity ˆ

v vi=�

.

12. The value of electric field in frame S' moving with ,̂vi would be

(A) Zero (B) ˆBvj−

(C) ˆBvj (D) ˆBvk



6/20

13. Let E' and B' are electric field and magnetic field in frame S' moving with respect to S at velocity v

�

. Which of

following equation is/are wrong?

(A)2

'z

y y

vEB B

c= + (B)

2

'z

y y

vBE E

c= −

(C) '

y y zB B vE= + (D) Both equations given in option (B) & (C)


Figure shows a cylindrical region of radius R, having a uniform magnetic field B0. Outside this region, there is a

ring of mass m, radius 2R and having linear charge density λ. Ring is kept on a rough horizontal surface having

coefficient of friction μ.

2RR

B0

m, λ

14. If the magnetic field is switched off all of a sudden, then angular velocity acquired by the ring is

(A)0

4

πλRBm

(B)0

2

λπ B R

m

(C)0

4

λπR B

m(D)

0

2

λπR B

m

15. The number of revolutions made by the ring before it stops is

(A)

2 2 2

0

28

λμR B

g m(B)

2 3 2

0

28

R B

g m

π λμ

(C)

2 2

0

28

λμR B

g m(D)

2 2

0

28

πλμR B

g m



7/20

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. Match the circuits with their respective time constants in the codes given below the columns.

Column I (Circuit) Column II (Time Constant)

(P) 2Ω3H

6H

2ΩV (1) 2 s

(Q)

2Ω 8H

6Ω3Ω

V

(2)1s

2

(R)1Ω

V

3Ω

6H

3H

(3) 1 s

(S)

V6H

2Ω 6Ω

4Ω3Ω

(4) 3 s

Codes :

P Q R S

(A) 1 2 4 3

(B) 1 2 3 4

(C) 3 1 2 4

(D) 3 2 1 4



8/20

17. Match the dimensional formulae with corresponding units in the codes given below the columns.

Column I (Dimensional formula) Column II (Unit)

(P) ML2 T–2 A–1 (1) farad

(Q) M–1 L–2 T4 A2 (2) weber

(R) ML2 T–2 A–2 (3) ohm

(S) ML2 T–3 A–2 (4) henry

Codes :

P Q R S

(A) 2 1 3 4

(B) 2 1 4 3

(C) 3 4 1 2

(D) 3 4 2 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

18. A charge q, having mass m enters a circular region of radius R, having magnetic field B. If the velocity of the particle

is ( )

,n RqB

m

then it passes through the centre of the circular region O. Find n

30°v0

RO

B



9/20

19. Three charges are located on the vertices of an equilateral triangle of side a. System is rotated with an angular

velocity ω about an axis perpendicular to the plane of triangle and passing through centroid. Magnetic dipole moment

of this system is

2

. Find .

q an

n

ω

q, m

G ω

a

q, m q, m

20. After a long time switch is swapped from 1 to 2 at t = 0. The time when energy on capacitor and inductor will be

same for the first time is .

πLC

n Find n.

1 2

CLV

PART - II : CHEMISTRY

SECTION - 1



ONE is correct.

21. Of the given compounds which will be more reactive towards SN2 reaction?

H

CH3

Br

H

CH3

H

(I) (II)

CH3

HBr

H

H

CH3

(A) (II) is more reactive than (I) (B) (I) is more reactive than (II)

(C) Both (I) and (II) are equally reactive (D) Both (I) and (II) do not undergo SN2 reaction



10/20

22. Which one of the following compounds is the most acidic?

(A)

+

NH3

(B)

NH3

OH

+

(C)

NH3

CH3

+

(D)

NH3

NO2

+

23. Phenoxide ion is more stable than phenol due to better resonance stabilisation of phenoxide ion. Which one of the

following resonating structures of phenoxide ion is most stable?

(A)

O–

(B)

O

–

(C)

O

–

(D)

O

–

24. Identify the product (P) in the following reaction

OH

H+

(P)

(A)

OH

(B)

O CH3

(C)

OH

CH3

(D)

OH

25. Hydroboration followed by oxidation of 1-methylcyclohexene gives

(A) 1-Methylcyclohexanol (B) Trans-2-Methylcyclohexanol

(C) Cis-2-Methylcyclohexanol (D) Both (B) & (C)



11/20

26. Predict the product formed when Br2 reacts 1-methylcyclopentene

(A)Br H

Me Br

(B)MeBr

Br H

(C) Me H

Br Br

(D) Both (A) & (B)

SECTION - 2




27. Identify the products (A) and (B) formed in the following reaction

(B)C H ONa

2 5

+C H OH2 5

CH3 CH CH

2

conc.H SO2 4

+C H OH2 5

(A)

O

(A) A: CH3

CH CH2

OH

OC H2 5

(B) B: CH3

CH CH2

OH

OC H2 5

(C) A: CH3

CH CH2

OH

OC H2 5

(D) B: CH3

CH CH2

OH

OC H2 5

28.

OHHO

(A)NaBH

4 (B)H /

+ Δ(C)H

+

Which of the following is correct about the products (A) and (C)?

(A)

O

A: (B)

O

A:

(C) C: (D) C:



12/20

29. When p-cresol is treated with CHCl3 and NaOH followed by acidification, 2-hydroxy-5-methylbenzaldehyde is obtained.

Which of the following species are involved in the above reaction as intermediates?

(A)

O

H–

CCl2

CH3

(B)

O–

CHCl2

CH3

(C)OH

CH3

O–

CH Cl

(D)

OH

CCl2

–

30. Identify the reagent (X) used in the following reaction

CH OH2

(X)CH Cl

2

(A) Conc. HCl/Anh.ZnCl2

(B) PCl5

(C) PCl3

(D) SOCl2

31. Identify the product(s) formed in the following reaction

CH3

CH3

(1) O3

(2) Zn/H O2Product(s)

(A)

CHO

CHO

(B) CH3

C CHO

O

(C) CH2

CHO

CH3

(D) CH3 C

O

C CH3

O



13/20

SECTION - 3

Paragraph Type



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


Nucleophilicity is the reactivity of a nucleophile. Generally a negatively charged species and a neutral molecule

with at least one atom with a lone pair of electrons acts as a nucleophile. The same species can act as a base by

abstracting proton from another species. The basic strength of a given species is directly related to charge density.

Higher the charge density higher will be the basic strength. Whereas the nucleophilicity of a given species depends

on the polarisability and size of the species.

32. The correct basicity order is

(A) HO– > C2H

5O– > H

2N– > Cl– > CH

3COO– (B) Cl– > H

2N– > CH

3COO– > HO– > C

2H

5O–

(C) C2H

5O– > HO– > H

2N– > CH

3COO– > Cl– (D) H

2N– > C

2H

5O– > HO– > CH

3COO– > Cl–

33. Nucleophilicity order in a polar aprotic (DMSO) solvent is

(A) HO– > CH3O– > (CH

3)2CHO– > (CH

3)3CO– (B) CH

3O– > (CH

3)2CHO– > HO– > (CH

3)3CO–

(C) (CH3)3CO– > (CH

3)2CHO– > CH

3O– > HO– (D) HO– > (CH

3)3CO– > (CH

3)2CHO– > CH

3O–


Organic compounds having phenolic –OH, –COOH, and –SO3H groups show acidic character. The strength of acid

is dependent on inductive effect and resonance. The acidic strength of ortho substituted benzoic acids are explained

by ortho effect.

34. The correct order of acidic strength is

(A)

OH OH OH

NO2

>

NO2

>

OH

NO2

> (B)

OH OH OH

NO2

>

NO2

>

OH

>

NO2

(C)

OH OH OH

NO2

>

NO2

>

OH

>

NO2

(D)

OH OH OH

> >

OH

>

NO2

NO2

NO2



14/20

35. Consider the following ortho substituted benzoic acids and choose the strongest acid

(A)

COOH

CH3

(B)

COOH

Cl

(C)

COOH

OH

(D)

COOH

NO2

SECTION - 4




36. Match the column

Column I Column II

(P) HC ≡≡ CH + Cu2Cl

2/NH

4OH (1) Electrophilic addition

(Q) HC ≡≡ CH + Cu2Cl

2/NH

4Cl (2) Acid-base reaction

(R) HC ≡≡ CH + HCl (3) Polymerisation

(S) HC ≡≡ CH + HCN/Ba(CN)2

(4) Nucleophilic addition

Codes :

P Q R S

(A) 2 3 1 4

(B) 3 2 1 4

(C) 2 3 4 1

(D) 4 1 3 2



15/20

37. Match the column

Column I Column II

(P) OH

CH3

Lucas

Reagent(1) Green colour

(Q) OHVictor

Meyer test (2) Violet colour

(R) CH OH2

K Cr O /H2 2 7

+

(3) White turbidity

(S) OHNeutral FeCl Sol.3

(4) Blue colour

Codes:

P Q R S

(A) 3 1 4 2

(B) 1 3 2 4

(C) 3 4 1 2

(D) 2 4 1 3

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. Number of isomers (including stereomers) obtained on dichlorination of cyclopentane is ______.

39. Number of hyperconjugation structures of propene is _______.

40. How many optically active isomers are obtained on monochlorination of isopentane?



16/20

PART - III : MATHEMATICS

SECTION - 1



ONE is correct.

41. The function f(x) = |αx – β| + γ. |x| ∀ x∈(–∞, ∞), where α > 0, β > 0, γ > 0, assumes its minimum value only at a

point if

(A) α ≠ β (B) α ≠ γ

(C) β ≠ γ (D) α = β = γ

42. The equation 8x3 – ax

2 + bx – 1 = 0 has three real roots in G.P. If λ1 ≤ a ≤ λ

2, then ordered pair (λ

1, λ

2) can be

(A) (–2, 2) (B) (24, 29)

(C) (–10, –3) (D) (–∞, ∞)

43. The value of

2

2013

cosec 2013

cos

xdx

x

−∫ is equal to

(A) 2013

cot

(cos )

xc

x

− + (B) 2013

tan

(cos )

xc

x

+

(C) 2013

(tan )

(cos )

xc

x

− + (D) Not integrable

44. The value of 6 2

sin2 2tan

(cos 6cos 4)

x x

x x

++ +∫ dx is equal to

(A)

2

7

1 cos2

cos

xc

x

+ + (B)

2

1

7

1 1 costan

cos2

xc

x

− ⎡ ⎤+ +⎢ ⎥⎢ ⎥⎣ ⎦

(C)

2

7

1 1 coslog

12 cos

xc

x

⎛ ⎞+ +⎜ ⎟⎜ ⎟⎝ ⎠

(D)

6 2

6

1 cos 6cos 4ln

12 cos

x xc

x

+ + +

45. If

1

01

te

k dtt

=+∫ , then

1

0

log (1 )t

e t dt+∫ is equal to

(A) k (B) 2k

(C) e log2 – k (D) e log2 + k



17/20

46. If k∈N and Ik =

2

2

| sin | [sin ]

k

k

x x dx

π

− π∫ , (where [.] denotes greatest integer function), then the value of

50

1

k

k

I

=∑ equals to

(A) –10200 (B) –5100

(C) –2550 (D) –20400

SECTION - 2




47. If the equation x5 – 10a3x

2 + b4x + c5 =0 has three equal roots, then

(A) 2b2 – 10a

3b

2 + c5 = 0 (B) 6a5 +c

5 = 0

(C) 2c5 – 10 a3

b2 + b4

c5 = 0 (D) b

4 = 15a4

48. The values of parameter 'α' for which the point of local minima of the function f(x) = 1 + α2x – x3 satisfies the

inequality

2

2

20

5 6

x x

x x

+ + <+ +

are

(A) ( )2 3, 3 3 (B) ( )3 3, 2 3− −

(C) ( )2 3, 3 3− (D) ( )3 2, 2 3−

49. Let { }2 2 4 2

0

( ) ( 1)( 1) ( 1) ( 1) .

x

f x a t t a t t dt= − + + − + + +∫ Then the value of 'a' for which f'(x) = 0 has two distinct real

roots are

(A) (–∞, –2) (B) (2, ∞)

(C) (–2, 2) (D) (–∞, ∞)

50. The values of parameter 'a' so that the line (3 – a)x + ay + (a2 – 1) = 0 is a normal to the curve x3y = 1, is/are

(A) (3, ∞) (B) (–∞, 0)

(C) (0, 3) (D) (–∞, ∞)

51. If 1 1

sin ( ).sin ( ) ,1 1

x xdx f x g x c

x x

− −= − ++ +∫ then which of the following(s) is/are correct?

(A) f(x) = x + 1 (B) f(x) = x

(C) g(x) = x (D) g(x) = x



18/20

SECTION - 3

Paragraph Type



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


We consider two curves y = f1(x) and y = f

2(x) where f

1(x) ≥ f

2(x) in the interval [a, b] where x = a and

x = b are the points of intersection of these two curves shown by the graph, then the area bounded by these two

curves is given by ( )1 2( ) ( )

b

a

f x f x dx−∫ , on the basis of above information, answer the following questions:

y

x0

y = ( )f x2

y = ( )f x1

x b = x a =

52. If f(x) = a + bx + cx2, c > 0, b2 – 4ac < 0, then area enclosed by the co-ordinate axes, the line x = 2 and the curve

y = f(x) is given by { }1(0) (1) (2)

3f f f+ λ + square units, then λ equals

(A) 2 (B) 4

(C) 6 (D) 8

53. The area bounded by the parabola y2 = 4ax and the line y = ax is 1

3 square unit, then the area enclosed by the

curve y = 4x with the parabola y2 = 4ax is given by

(A)2

3 sq. unit (B)

5

3 sq. unit

(C)4

3 sq. unit (D)

8

3 sq. unit



19/20


Let α + β = 1, α2 + β2 = 1

2 and f(x) be a continuous function such that f(x) + f(x + 2) = 2 ∀ x∈ [0, 2] and

4

0

( ) 4,p f x dx qα= − =β∫ . On the basis of above information, answer the following questions

54. The value of p is

(A) 0 (B) 1

(C) 2 (D) 3

55. The value of q is

(A) 0 (B) 1

(C) 2 (D) 3

SECTION - 4




56. Match the items of column I with those of column II

Column I Column II

(P) If the curves xy = a(a > 0) and y2 = 4x cut orthogonally, (1) 6

then the value of 2 2

a

is

(Q) Tangent at (a, b) to the curve x3 + y3 = c3 meets the curve (2) 2

again in (a1, b

1). Then

1 1a b

a b

+ =

(R) Value of c in LMVT for 2( ) 4f x x= − on the interval [2, 4] is (3) 1

(S) If c is a value in Rolle's theorem for f(x) = e–x sin x on the (4) –1

interval [0, π], then tan c is equal to

Codes :

P Q R S

(A) 3 2 1 4

(B) 2 4 1 3

(C) 4 3 2 1

(D) 1 2 3 4



20/20

57. Match the items of Column I with those of Column II

Column I Column II

(P)

/2

01 sin

dx

x

π

=+∫ (1)

1

2−

(Q)2 2 2

1 2lim ...

1 1 1→∞

⎛ ⎞+ +⎜ ⎟⎜ ⎟− − −⎝ ⎠n

n

n n n

(2) 1

(R)

/2

0

( )

( )2

f xdx

kf x f x

π π=π⎛ ⎞+ −⎜ ⎟

⎝ ⎠

∫ where k is (3) 4

(S) The area common to the curves y2 = x and x2 = y is (4)1

3

Codes :

P Q R S

(A) 2 1 3 4

(B) 4 2 1 3

(C) 3 4 1 2

(D) 1 2 3 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. If θ is an angle of intersection of the curves y = 3x–1. logex and y = xx – 1, then the value of 2cosθ is equal to _____.

59. If [t] denotes the integral part of t, then the value of

1

1

0

sin x dx−⎡ ⎤

⎢ ⎥⎢ ⎥⎣ ⎦∫ is equal to ________.

60. Let 2( ) min { 1, 1} for 0 2.f x x x x= + + ≤ ≤ If A is the area bounded by f(x), the x-axis in the interval [0, 2], then the

integral part of A is ________.

� � �

TEST - 5 (Paper - II)

PHYSICS

1. (C)

2. (C)

3. (B)

4. (B)

5. (C)

6. (B)

7. (A, B, D)

8. (A, C, D)

9. (A, C)

10. (A, C, D)

11. (A, C)

12. (B)

13. (B)

14. (A)

15. (A)

16. (A)

17. (B)

18. (1)

19. (0)

20. (5)

CHEMISTRY

21. (A)

22. (B)

23. (B)

24. (C)

25. (C)

26. (C)

27. (A, B, C)

28. (B, C)

29. (B, C, D)

30. (A, C)

31. (A, B)

32. (B)

33. (B)

34. (A)

35. (D)

36. (A)

37. (B)

38. (2)

39. (3)

40. (6)

MATHEMATICS

41. (A)

42. (B)

43. (C)

44. (D)

45. (C)

46. (B)

47. (A, C, D)

48. (A, B, C)

49. (B, D)

50. (A, B, C)

51. (A, B, C)

52. (B)

53. (A)

54. (B)

55. (C)

56. (D)

57. (A)

58. (0)

59. (5)

60. (4)

ANSWERS

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

1/8

Documents

AIATS-6 COVERS 2014 - WordPress.com · Test - 6 (Paper-II) All India Aakash Test Series for JEE (Advanced)-2014 3/20 SECTION - 2 One or More Options Correct Type This section contains