FIITJEE - s3-us-west-2.amazonaws.com · website: . *4. The densities of two solid spheres A and B of the same radii R vary with radial distance ... have phase angles 0, / 3,

Note: For the benefit of the students, specially the aspiring ones, the question of JEE(advanced), 2015 are also given in this booklet. Keeping the interest of students studying in class XI, the questions based on topics from class XI have been marked with ‘*’, which can be attempted as a test. For this test the time allocated in Physics, Chemistry & Mathematics are 22 minutes, 21 minutes and 25 minutes respectively.

FIITJEE

JEE(ADVANCED) - 2015

CODE

PAPER -2 Time : 3 Hours Maximum Marks : 240

READ THE INSTRUCTIONS CAREFULLY

QUESTION PAPER FORMAT AND MARKING SCHEME :

1. The question paper has three parts: Physics, Chemistry and Mathematics. Each part has three sections.

2. Section 1 contains 8 questions. The answer to each question is a single digit integer ranging from 0 to 9 (both inclusive). Marking Scheme: +4 for correct answer and 0 in all other cases.

3. Section 2 contains 8 multiple choice questions with one or more than one correct option. Marking Scheme: +4 for correct answer, 0 if not attempted and –2 in all other cases.

4. Section 3 contains 2 “paragraph” type questions. Each paragraph describes an experiment, a situation or a problem. Two multiple choice questions will be asked based on this paragraph. One or more than one option can be correct.

Marking Scheme: +4 for correct answer, 0 if not attempted and – 2 in all other cases.

4

JEE(ADVANCED)-2015-Paper-2-PCM-2

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com.

Section 1 (Maximum Marks: 32)

This section contains EIGHT questions.

The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive.

For each question, darken the bubble corresponding to the correct integer in the ORS.

Marking scheme:

+4 If the bubble corresponding to the answer is darkened.

0 In all other cases.

1. An electron in an excited state of 2L i

ion has angular momentum 3h / 2 . The de

Broglie wavelength of the electron in this state is 0

ap π (where 0

a is the Bohr radius).

The value of p is

*2. A large spherical mass M is fixed at one position and two identical point masses m are kept on a line passing through the centre of M (see figure). The point masses are connected by a rigid massless rod of length and this assembly is free to move along the line connecting them. All three masses interact only through their mutual gravitational interaction. When the point mass nearer to M is at a distance r 3 from

M, the tension in the rod is zero for M

m k2 8 8

. The value of k is

3. The energy of a system as a function of time t is given as

2 1

E( t ) A exp t , w he re 0 .2 s

. The measurement of A has an error of 1.25%.

If the error in the measurement of time is 1.50%, the percentage error in the value of E ( t ) at t = 5 s is

PART-I: PHYSICS



*4. The densities of two solid spheres A and B of the same radii R vary with radial distance

r as 5

A B

r r( r ) k a n d (r ) k

R R

, respectively, where k is a constant. The

moments of inertia of the individual spheres about axes passing through their centres

are IA

and IB, respectively. If

I

I

B

A

n

1 0 , the value of n is

*5. Four harmonic waves of equal frequencies and equal intensities I0 have phase angles

0, / 3, 2 / 3 a n d . When they are superposed, the intensity of the resulting wave is

n I0. The value of n is

6. For a radioactive material, its activity A and rate of change of its activity R are defined as d N

A = -d t

and d A

R = - , w h e re N td t

is the number of nuclei at time t. Two radioactive

sources P (mean life ) and Q(mean life 2 ) have the same activity at t = 0. Their rates

of change of activities at QP

t 2 a re R a n d R , respectively. If P

Q

R n

R e , then the value

of n is

7. A monochromatic beam of light is incident at 60° on one face of an equilateral prism of refractive index n and emerges

from the opposite face making an angle n with the normal

(see the figure). For n 3 the value of is 60° and

dm

d n

. The value of m is



8. In the following circuit, the current through the resistor I A m p e re sR 2 is . The value of

I is



Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four

option(s) is(are) correct.

For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS.

Marking scheme:

+4 If only the bubble(s) corresponding to all the correct option(s) is(are) darkened.

0 If none of the bubbles is darkened

2 In all other cases

9. A fission reaction is given by 2 3 6 9 41 4 0

9 2 5 4 3 8U X e S r x y , where x and y are two particles.

Considering 2 3 6

9 2U to be at rest, the kinetic energies of the products are denoted by

X e XS r y

K , K , K 2M e V a n d K 2M e V , respectively. Let the binding energies per nucleon

of 2 3 6 1 4 0 9 4

9 2 5 4 3 8U , X e a n d S r b e 7 .5 M e V , 8 .5 M e V a n d 8 .5 M e V respectively. Considering

different conservation laws, the correct option(s) is(are)

(A) X eS r

x n, y n, K 1 2 9 M e v , K 8 6 M e V

(B)

S r X ex p, y e , K 1 2 9 M e v , K 8 6 M e V

(C) S r X e

x p, y n, K 1 2 9 M e v , K 8 6 M e V

(D) S r X e

x n, y n, K 8 6 M e v , K 1 2 9 M e V



*10. Two spheres P and Q of equal radii have densities 1 2

a n d ,

respectively. The spheres are connected by a massless string and

placed in liquids 21

L a n d L of densities 21

a n d and viscosities

21a n d , respectively. They float in equilibrium with the sphere P

in 1

L and sphere Q in 2

L and the string being taut (see figure). If

sphere P alone in 2

L has terminal velocity P

V and Q alone in 1

L has

terminal velocity Q

V , then

(A) P

Q

1

2

V

V

(B) P

Q

2

1

V

V

(C) QP

V . V 0 (D) QP

V . V 0

11. In terms of potential difference V, electric current I, permittivity 0

, permeability 0

and

speed of light c, the dimensionally correct equation(s) is(are)

(A) 0 0

2 2μ I = ε V (B)

0 0I = V

(C) 0

I = ε cV (D) 0 0

μ c I = ε V

12. Consider a uniform spherical charge distribution of radius 1

R centred at

the origin O. In this distribution, a spherical cavity of radius 2

R , centred

at P with distance 1 2

O P a R R (see figure) is made. If the electric

field inside the cavity at position r is E ( r ) , then the correct

statement(s) is(are)

(A) E is uniform, its magnitude is independent of 2

R but its direction depends on r

(B) E is uniform, its magnitude depends on 2

R and its direction depends on r

(C) E is uniform, its magnitude is independent of a but its direction depends on a

(D) E is uniform and both its magnitude and direction depend on a

*13. In plotting stress versus strain curves for two materials P and Q, a student by mistake puts strain on the y-axis and stress on the x-axis as shown in the figure. Then the correct statement(s) is(are)

(A) P has more tensile strength than Q

(B) P is more ductile than Q

(C) P is more brittle than Q

(D) The Young’s modulus of P is more than that of Q



*14. A spherical body of radius R consists of a fluid of constant density and is in equilibrium under its own gravity. If P(r) is the pressure at r(r < R), then the correct option(s) is(are)

(A) P r 0 0 (B)

P r 3R / 4 6 3

P r 2R / 3 8 0

(C)

P r 3 R / 5 1 6

P r 2R / 5 2 1

(D)

P r R / 2 2 0

P r R / 3 2 7

15. A parallel plate capacitor having plates of area S and plate separation d, has capacitance

1C in air. When two dielectrics of different relative permittivities

1 22 a n d 4 are

introduced between the two plates as shown in the figure, the capacitance becomes 2

C .

The ratio 2

1

C

C is

(A) 6 / 5 (B) 5 / 3

(C) 7 / 5 (D) 7 / 3



*16. An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure). Initially the gas is at

temperature 1

T , pressure 1

P and volume 1

V and the spring is in

its relaxed state. The gas is then heated very slowly to

temperature 2

T , pressure 2

P and volume 2

V . During this

process the piston moves out by a distance x. Ignoring the friction between the piston and the cylinder, the correct statement(s) is(are)

(A) If 2 1 2 1

V 2 V a n d T 3 T , then the energy stored in the spring is 1 1

1P V

4

(B) If 2 1 2 1

V 2 V a n d T 3 T , then the change in internal energy is 1 1

3 P V

(C) If 2 1 2 1

V 3 V a n d T 4 T , then the work done by the gas is 1 1

7P V

3

(D) 2 1 2 1

V 3 V a n d T 4 T , then the heat supplied to the gas is 1 1

1 7P V

6

SECTION 3 (Maximum Marks: 16)

This section contains TWO paragraphs

Based on each paragraph, there will be TWO questions


option(s) is(are) correct

For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS

Marking scheme:

+4 If only the bubble(s) corresponding to all the correct option(s) is(are) darkened


–2 In all other cases



PARAGRAPH 1

Light guidance in an optical fiber can be understood by considering a structure comprising of

thin solid glass cylinder of refractive index 1

n surrounded by a medium of lower refractive index

2n . The light guidance in the structure takes place due to successive total internal reflections at

the interface of the media 1

n and 2

n as shown in the figure. All rays with the angle of

incidence i less than a particular value mi are confined in the medium of refractive index

1n .

The numerical aperture (NA) of the structure is defined as sin mi .

17. For two structures namely 1

S with

1 2 2 1 2

n 4 5 / 4 a n d n 3 / 2 , a n d S w ith n 8 / 5 a n d n 7 / 5 and taking the refractive

index of water to be 4 / 3 and that of air to be 1, the correct option(s) is(are)

(A) 1

N A o f S immersed in water is the same as that of

2S immersed in a liquid of refractive

index 1 6

3 1 5

(B) 1

N A o f S

immersed in liquid of refractive index 6

1 5

is the same as that of 2

S

immersed in water

(C) 1

N A o f S placed in air is the same as that of

2S immersed in liquid of refractive index

4

1 5

.

(D) 1

N A o f S placed in air is the same as that of 2

S placed in water



18. If two structures of same cross-sectional area, but different numerical apertures

1N A a n d

2 2 1N A N A N A are joined longitudinally, the numerical aperture of the

combined structure is

(A) 1 2

1 2

N A N A

N A N A (B)

1 2N A N A

(C) 1

N A (D) 2

N A

PARAGRAPH 2

In a thin rectangular metallic strip a constant current I flows along the positive x-direction, as shown in the figure. The length, width and thickness of the strip are , w

and d , respectively. A uniform magnetic field B is applied on the strip along the positive y-direction. Due to this, the charge carriers experience a net deflection along the z-direction. This results in accumulation of charge carriers on the surface PQRS and appearance of equal and opposite charges on the face opposite to PQRS. A potential difference along the z-direction is thus developed. Charge accumulation continues until the magnetic force is balanced by the electric force. The current is assumed to be uniformly distributed on the cross section of the strip and carried by electrons.

19. Consider two different metallic strips (1 and 2) of the same material. Their lengths are

the same, widths are 21

w a n d w and thicknesses are 21

d a n d d , respectively. Two points

K and M are symmetrically located on the opposite faces parallel to the x-y plane (see

figure). 21

V a n d V are the potential differences between K and M in strips 1 and 2,

respectively. Then, for a given current I flowing through them in a given magnetic field strength B, the correct statement(s) is(are)

(A) 1 2 1 2 2 1

I f w w a n d d 2 d , th e n V 2 V

(B) 1 2 1 2 2 1

I f w w a n d d 2 d , th e n V V

(C) 1 2 1 2 2 1

I f w 2 w a n d d d , th e n V 2 V

(D) 1 2 1 2 2 1

I f w 2 w a n d d d , th e n V V



20. Consider two different metallic strips (1 and 2) of same dimensions (lengths , width w

and thickness d) with carrier densities 1 2

n a n d n , respectively. Strip 1 is placed in

magnetic field 1

B and strip 2 is placed in magnetic field 2

B , both along positive y-

directions. Then 21

V a n d V are the potential differences developed between K and M

in strips 1 and 2, respectively. Assuming that the current I is the same for both the strips, the correct option(s) is(are)

(A) 1 2 1 2 2 1

I f B B a n d n 2n , th e n V 2 V

(B) 1 2 1 2 2 1

I f B B a n d n 2n , th e n V V

(C) 1 2 1 2 2 1

I f B 2B a n d n n , th e n V 0 .5 V

(D) 1 2 1 2 2 1

I f B 2B a n d n n , th e n V V




This section contains EIGHT questions

The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive

For each question, darken the bubble corresponding to the correct integer in the ORS

Marking scheme:

+4 If the bubble corresponding to the answer is darkened


*21. In dilute aqueous 2 4

H S O , the complex diaquodioxalatoferrate(II) is oxidized by 4

M n O .

For this reaction, the ratio of the rate of change of H

to the rate of change of

4M n O

is

*22. The number of hydroxyl group(s) in Q is

23. Among the following, the number of reaction(s) that produce(s) benzaldehyde is

PART – II : CHEMISTRY



24. In the complex acetylbromidodicarbonylbis(triethylphosphine)iron(II), the number of Fe–C bond(s) is

25. Among the complex ions,

+ 3- +

22 2 2 2 2 2 2 4 22 2 4

C o N H - C H - C H - N H C l , C rC l C O , F e H O O H

,

- 2 + 2 +

43 2 2 2 2 3 3 242 2

F e N H C N , C o N H - C H - C H - N H N H C l an d C o N H H O C l

,

the number of complex ion(s) that show(s) cis-trans isomerism is

*26. Three moles of 2 6

B H are completely reacted with methanol. The number of moles of

boron containing product formed is

27. The molar conductivity of a solution of a weak acid H X 0 .0 1 M is 10 times smaller than

the molar conductivity of a solution of a weak acid H Y 0 .1 0 M . If 0 0

X Y

, the

difference in their a

p K values, a a

p K H X p K H Y , is (consider degree of ionization of

both acids to be 1 )

28. A closed vessel with rigid walls contains 1 mol of 2 3 8

9 2U

and 1 mol of air at 298 K .

Considering complete decay of 2 3 8 2 0 6

9 2 8 2U to P b , the ratio of the final pressure to the initial

pressure of the system at 298 K is




This section contains EIGHT questions




Marking scheme:




*29. One mole of a monoatomic real gas satisfies the equation p V b R T where b is a

constant. The relationship of interatomic potential V(r) and interatomic distance r for the gas is given by

(A) (A)

(B)

(C)

(D)



30. In the following reactions, the product S is

(A) (A)

(B)

(C)

(D)

31. The major product U in the following reactions is

(A) (A)

(B)

(C)

(D)



32. In the following reactions, the major product W is

(A) (A)

(B)

(C)

(D)

*33. The correct statement(s) regarding, 2 3 4

i H C lO , ii H C lO , iii H C lO and iv H C lO , is

(are)

(A) The number of C l = O bonds in (ii) and (iii) together is two

(B) The number of lone pairs of electrons on C l in (ii) and (iii) together is three

(C) The hybridization of C l in (iv) is s p3

(D) Amongst (i) to (iv), the strongest acid is (i)

34. The pair(s) of ions where BOTH the ions are precipitated upon passing 2

H S gas in

presence of dilute H C l , is(are)

(A) 2 2

B a , Z n

(B) 3 3

B i , F e

(C) 2 2

C u , P b

(D) 32

H g , B i

*35. Under hydrolytic conditions, the compounds used for preparation of linear polymer and for chain termination, respectively, are

(A) 3 3 3 4

C H S iC l an d S i C H (B) 3 2 3 32

C H S iC l an d C H S iC l

(C) 3 2 32

C H S iC l an d C H S iC l3

(D) 3 3

S iC l an d C H S iC l4



36. When O2 is adsorbed on a metallic surface, electron transfer occurs from the metal to O

2.

The TRUE statement(s) regarding this adsorption is(are)

(A) O2 is physisorbed

(B) heat is released

(C) occupancy of 2 p

of O

2 is increased

(D) bond length of O2is increased


This section contains TWO paragraphs





Marking scheme:


0 In none of the bubbles is darkened


PARAGRAPH 1

When 100 m L of 1 .0 M H C l was mixed with 100 m L of 1 .0 M N aO H in an insulated beaker

at constant pressure, a temperature increase of 5 .7 C was measured for the beaker and its

contents (Expt. 1). Because the enthalpy of neutralization of a strong acid with a strong

base is a constant 1

5 7 .0 k J m o l

, this experiment could be used to measure the

calorimeter constant. In a second experiment (Expt. 2), 100 m L of .0 M2 acetic acid

5

2 .0 1 0

a

K was mixed with 100 m L of 1 .0 M N aO H (under identical conditions to

Expt. 1) where a temperature rise of 5 .6 C was measured.

(Consider heat capacity of all solutions as 1 1

4 .2 J g K

and density of all solutions as -1

1 .0 g m L )

*37. Enthalpy of dissociation (in 1

k J m o l

) of acetic acid obtained from the Expt. 2 is

(A) 1.0 (B) 10.0

(C) 24.5 (D) 51.4



*38. The pH of the solution after Expt. 2 is

(A) 2.8 (B) 4.7

(C) 5.0 (D) 7.0

PARAGRAPH 2

In the following reactions

39. Compound X is

(A) (A)

(B)

(C)

(D)

40. The major compound Y is

(A) (A)

(B)

(C)

(D)





The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive.

For each question, darken the bubble corresponding to the correct integer in the ORS.

Marking scheme:

+4 If the bubble corresponding to the answer is darkened.

0 In all other cases.

41. Suppose that p , q a n d r are three non-coplanar vectors in 3R . Let the components of

a vector s along p , q a n d r be 4, 3 and 5, respectively. If the components of this

vector s along p q r , p q r a n d p q r are x, y and z, respectively,

then the value of 2 x y z is

*42. For any integer k, let k

k kc o s i s in , w h e re i 1

7 7

. The value of the

expression

1 2

k 1

3

k 1

kk 1

4 k 24 k 1

is

*43. Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is 6 : 1 1 and the

seventh term lies in between 130 and 140, then the common difference of this A.P. is

*44. The coefficient of 9x in the expansion of

2 3 1 0 01 x 1 x 1 x ... . . 1 x is

PART – III : MATHEMATICS



*45. Suppose that the foci of the ellipse

2 2

1 2 1 2

x y1 a re f , 0 a n d f , 0 w h e re f 0 a n d f 0

9 5 . Let

1 2P a n d P be two parabolas

with a common vertex at 0, 0 and with foci at 1f , 0 and

22 f , 0 , respectively. Let

1T be

a tangent to 1

P which passes through 2

2 f , 0 and 2

T be a tangent to 2

P which passes

through 1f , 0 . The

1m is the slope of

1 2T a n d m is the slope of

2T , then the value of

2

2 2

1m

m

is

46. Let m and n be two positive integers greater than 1. If

0

c o s

m

n

e e elim

2

then the value of m

n is

47. If 1

1

9 x 3 ta n x

0

2

2

1 2 9 xe d x

1 x

Where 1

ta n x

takes only principal values, then the value of e

3lo g 1

4

is

48. Let f : R R be a continuous odd function, which vanishes exactly at one point and 1

f 12

.

Suppose that

x 1

x x

1 1

F x 1F x f t d t fo r a ll x 1, 2 a n d G x t f f t d t fo r a ll x 1, 2 . If lim

G x 1 4

, then the value of 1

f2

is






option(s) is(are) correct.


Marking scheme:




49. Let

1

1/ 2

3

4

1 9 2 x 1f ' x fo r a ll x R w ith f 0 . If m f x d x M

22 s in x

, then the possible

values of m and M are

(A) m 1 3 , M 2 4 (B) 1 1

m , M4 2

(C) m 1 1, M 0 (D) m 1, M 1 2

*50. Let S be the set of all non-zero real numbers such that the quadratic equation 2

x x 0 has two distinct real roots 1 2

x a n d x satisfying the inequality 1 2

x x 1 .

Which of the following intervals is(are) a subset(s) of S ?

(A) 1 1

,2 5

(B) 1

, 0

5

(C) 1

0 ,

5

(D) 1 1

,25



51. If 1 16 4

3 s in a n d 3 c o s1 1 9

, where the inverse trigonometric functions take only

the principal values, then the correct option(s) is(are)

(A) co s 0 (B) s in 0

(C) c o s 0 (D) co s 0

52. Let 1 2

E a n d E be two ellipses whose centers are at the origin. The major axes of

1 2E a n d E lie along the x-axis and the y-axis, respectively. Let S be the circle

22

x y 1 2 . The straight line x y 3 touches the curves S, 1 2

E a n d E at P, Q and

R, respectively. Suppose that 2 2

P Q P R3

. If 1 2

e a n d e are the eccentricities of

1 2E a n d E , respectively, then the correct expression(s) is(are)

(A) 2 2

1 2

4 3e e

4 0 (B)

1 2

7e e

2 1 0

(C) 2 2

1 2

5e e

8 (D)

1 2

3e e

4

53. Consider the hyperbola 2 2H : x y 1 and a circle S with center 2

N x , 0 . Suppose that

H and S touch each other at a point 1 1 1 1P x , y w ith x 1 a n d y 0 . The common

tangent to H and S at P intersects the x-axis at point M. If l , m is the centroid of the

triangle PM N , then the correct expression(s) is(are)

(A) 2

1

1

1

d 11 fo r x 1

d x 3 x

l

(B) 2

1

1

1

1

xd

fo r x 1d x

3 x 1

m

(C) 2

1

1

1

d 11 fo r x 1

d x 3 x

l

(D) 1

1

d 1fo r y 0

d y 3

m



54. The option(s) with the values of a and L that satisfy the following equation is(are)

4

0

0

t 6 4

t 6 4

d te s in a t c o s a t

L ?

e s in a t c o s a t d t

(A) 4

e 1a 2 , L

e 1

(B) 4

e 1a 2 , L

e 1

(C) 4

e 1a 4 , L

e 1

(D) 4

e 1a 4 , L

e 1

55. Let f , g : 1, 2 R be continuous functions which are twice differentiable on the interval

1, 2 . Let the values of f and g at the points 1, 0 a n d 2 be as given in the following

table:

x 1 x 0 x 2

f x 3 6 0

g x 0 1 1

In each of the intervals 1, 0 a n d 0 , 2 th e fu n c tio n f 3 g " never vanishes. Then the

correct statement(s) is(are)

(A) f ' x 3 g ' x 0 has exactly three solutions in 1, 0 0, 2

(B) f ' x 3 g ' x 0 has exactly one solution in 1, 0

(C) f ' x 3 g ' x 0 has exactly one solution in 0 , 2

(D) f ' x 3 g ' x 0 has exactly two solutions in 1, 0 and exactly two solutions in

0 , 2



56. Let 8 6 4 2

f x 7 ta n x 7 ta n x 3 ta n x 3 ta n x fo r a ll x ,2 2

. Then the correct

expression(s) is(are)

(A)

/ 4

0

1x f x d x

1 2

(B)

/ 4

0

f x d x 0

(C)

/ 4

0

1x f x d x

6

(D)

/ 4

0

f x d x 1


This section contains TWO paragraphs.





Marking scheme:




PARAGRAPH 1

Let F : R R be a thrice differentiable function. Suppose that

F 1 0 , F 3 4 a n d F ' x 0 for all x 1 / 2 , 3 . L e t f x x F x fo r a ll x R .

57. The correct statement(s) is(are)

(A) f ' 1 0 (B) f 2 0

(C) f ' x 0 fo r a n y x 1, 3 (D) f ' x 0 fo r s o m e x 1, 3

58. If

33

11

32a n d x F " x d x 4 0x F ' x d x 1 2 , then the correct expression(s) is(are)

(A) 9 f ' 3 f ' 1 3 2 0 (B)

3

1

f x d x 1 2

(C) 9 f ' 3 f ' 1 3 2 0 (D)

3

1

f x d x 1 2



PARAGRAPH 2

Let 1 2

n a n d n be the number of red and black balls, respectively, in box I. Let 3 4

n a n d n

be the number of red and black balls, respectively, in box II.

59. One of the two boxes, box I and box II, was selected at random and a ball was drawn randomly out of this box. The ball was found to be red. If the probability that this red ball

was drawn from box II is 1

3 , then the correct option(s) with the possible values of

1 2 3 4n , n , n a n d n is(are)

(A) 1 2 3 4

n 3 , n 3 , n 5 , n 1 5 (B) 1 2 3 4

n 3 , n 6 , n 1 0 , n 5 0

(C) 1 2 3 4

n 8 , n 6 , n 5 , n 2 0 (D) 1 2 3 4

n 6 , n 1 2 , n 5 , n 2 0

60. A ball is drawn at random from box I and transferred to box II. If the probability of

drawing a red ball from box I, after this transfer, is 1

3 , then the correct option(s) with the

possible values of 1 2

n a n d n is(are)

(A) 1 2

n 4 , n 6 (B) 1 2

n 2 , n 3

(C) 1 2

n 1 0 , n 2 0 (D) 1 2

n 3 , n 6

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FIITJEE - s3-us-west-2.amazonaws.com · website: . *4. The densities of two solid spheres A and B of the same radii R vary with radial distance ... have phase angles 0, / 3,