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CODE # 3 JEE ADVANCED PAPER-II HELD ON SUNDAY 24 MAY, 2015_[Chemistry]

Page # 1

PART II-CHEMISTRY PAPER�IISECTION 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

Q.21electrochemistry + Ionic

The molar conductivity of a solution of a weak acid HX (0.01 M) is 10 times

smaller than the molar conductivity of a solution of a weak acid HY (0.10 M). If 0y

0x , the

difference in their pKa values, pKa(HX) � pKa(HY), is (consider degree of ionisation of both acids tobe << 1)

Ans. 3

Q.22chemical kinetics

A closed vessel with rigid walls contains 1 mol of U23892 and 1 mol of air at

298 K. Considering complete decay of U23892 to Pb206

82 , the ratio of the final pressure to the initial

pressure of the system at 298K isAns. 9Q.23

chemical kineticsIn dilute aqueous H2SO4, the complex diaquodioxalatoferrate(II) is oxidized

by MnO4¯ . For this reaction, the ratio of the rate of change of [H+] to the rate of change of [MnO4¯]

isAns. 8Q.24

Hydrocarbons (11th)The number of hydroxyl group(s) in Q is

H

HOH C3 CH3

H

heat

P 4aqueous dilute KMnO excess

0 C Q

Ans. 4

Q.25Aromatic compounds (12th)

Among the following the number of reaction(s) that produce(s) benzalde-hyde is

(I)3

CO,HCl

Anhydrous AlCl /CuCl

(II)

CHCl2

2H O

100 C



Page # 2

(III)

COCl2

4

H

Pd BaSO

(IV)

CO Me2

2

DIBAL H

Toluene, 78 CH O

Ans. 4

Q.26Coordination compound

In the complex acetybromidodicarbonylbis(triethylphosphine)iron(II), thenumber of Fe�C bond (S) is

Ans. 3

Q.27Coordination compound

Among the complex ions 2 2 2 2 22Co NH CH CH NH Cl

,

3

2 2 4 2CrCl C O

, 2 4 2Fe H O OH

, 3 2 4Fe NH CN

,

2

2 2 2 2 32Co NH CH CH NH NH Cl

and 2

3 24Co NH H O Cl

, the number of com-

plex ion(s) that show(s) cis-trans isomerism isAns. 6

Q.28p-block group-13

Three moles of 2 6B H are completely reacted with methanol. The number of

moles of boron containing product formed isAns. 6

SECTION 2(Maximum Marks : 32)

Q.29Salt analysis

The pairs(s) of ions where BOTH the ions are precipitated upon passing 2H S

gas in presence of dilute HCl, is (are)

(A) 2 2Ba ,Zn (B) 3 3Bi ,Fe (C*) 2 2Cu ,Pb (D*) 2 3Hg ,Bi

Ans. CD


Under hydrolytic conditions, the compounds used for preparation of linearpolymer and for chain termination, respectively, are

(A) 3 3CH SiCl and 3 4Si CH (B*) 3 22

CH SiCl and 3 3CH SiCl

(C) 3 22CH SiCl and 3 3CH SiCl (D) SiCl

4 and 3 3

CH SiCl

Ans. B

Q.31chemical bonding

When 2O is adsorbed on a metallic surface, electron transfer occurs from the

metal to 2O . The TRUE statement(s) regarding the adsorption is(are)

(A) 2O is physisorbed (B*) heat is released

(C*) Occupancy of *2p of 2O is increased (D*) bond length of 2O increased



Page # 3

Ans. BCD

Q.32Gaseous state

One mole of a monoatomic real gas satisfies the equation p V b RT

where b is a constant. The relationship of interatomic potential V(r) and interatomic distance r for thegas is given by

(A)

V(r)0

r (B)

V(r)0

r

(C*)

V(r)0

r (D)

V(r)0

r

Ans. C

Q.33Carbonyl compounds (12th)

In the following reactions, the product S is

H C3 i. O3

ii. Zn, H O2

RNH3 S

(A*)

H C3N

(B)

H C3 N

(C) H C3

N(D)

H C3

N

Ans. A



Page # 4


The major product U in the following reactions is

CH = CH � CH , H2 3

+

high pressure, heat T

radical initiator, O2 U

(A) CH3

OO

H

(B*) O

CH3H3C

OH

(C) CH2

OO

H

(D)

CH2

OO

H

Ans. B


In the following reactions, the major product W is

NH2NaNO , HCl2

0°CV W

OH

, NaOH

(A*) N = N OH (B) N = N

OH

(C) N = N

OH

(D) N = N

HO

Ans. A


The correct statement(s) regarding, (i) HClO, (ii) HClO2, (iii) HClO3 and (iv) HClO4, is(are)(A) The number of Cl = O bonds in (ii) and (iii) togeter is two(B*) The number of lone pairs of electrons on Cl in (ii) and (iii) together is three(C*) The hybridization of Cl in (iv) is sp3

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



Page # 5

Section-3 (Maximum Marks : 16) This section contains TWO paragraphs Based on each pararaph, there will be TWO questions. 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 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.

Paragraph 1In the following reactions

YOHC

SOH,HgSO0H

XHCHC

Heat,H.ii

0H,EtMgBr.i88

424

2

OH,NaOH,OH.ii

HB.i88

H

BaSOPd68

2

222

62

2

4

Q.37Grignard Reagents (XIIth)

Compound X is

(A) CH3

O

(B) CH3

OH

(C*) OH

(D) CHO

Ans. C

Q.38Grignard Reagents (XIIth)

The major compound Y is

(A) CH3 (B) CH3

(C) CH3

CH2

(D*)

CH3

CH3

Ans. D



Page # 6

PARAGRAPH 2

When 100 mL of 1.0 M HCl was mixed with 100 mL of 1.0 M NaOH in an insulated beaker atconstant 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(� 57.0 kJ mol�1), this experiment could be used to measure the calorimeter constant.In a second experiment (Expt. 2), 100 mL of 2.0 M acetic acid (Ka = 2.0 × 10�5) was mixed with 100mL of 1.0 M NaOH (under identical conditions of Expt. 1) where a temperature rise of 5.6°C was

measured.(Consider heat capacity of all solutions as 4.2 J g�1K�1 and density of all solutions as 1.0 g mL�1)

Q.39Thermochemistry

Enthalpy of dissociation (in kJ mol�1) of acetic acid obtained from the Expt. 2 is(A*) 1.0 (B) 10.0 (C) 24.5 (D) 51.4

Ans. A

Q.40Thermochemistry

The pH of the solution after Expt.2 is(A) 2.8 (B*) 4.7 (C) 5.0 (D) 7.0

Ans. B

CODE # 3 JEE ADVANCED PAPER-II HELD ON SUNDAY 24 MAY, 2015_[MATHEMATICS]

BANSAL CLASSES : "POOJA TOWER" 3, GOPAL PURA BY PASS, JAIPUR-302018 (RAJ.) INDIA. TEL. (0141)5118115 - 6, 6511722 Page # 1

PART III - MATHEMATICSSECTION �1 : (MM : 32)

This section contains 8 questions. The answer to each question is a SINGLE DIGIT INTEGERranging fom 0 to 9, both inclusive. [Marking scheme : +4, 0]

Q.41Integration If

= dxx1

x912e

2

21

0

xtan3x9 1

where tan�1 x takes only principal values, then the value of

4

3|1|loge is [Ans: 9]

Q.42Integration Let f : R R be a continuous odd function, which vanishes exactly at one point and f(1) = 2

1.

Suppose that F(x) = dt)t(fx

1

for all x [�1, 2] and G(x) = dt|))t(f(f|tx

1

for all x [�1, 2]. If

14

1

)x(G

)x(Flim

1x

, then the value of f

2

1 is

[Ans: 7]

Q.43Vector Suppose that randq,p

are three non-coplanar vectors in R3. Let the components of a vector

s

along randq,p

be 4, 3 and 5, respectively. If the components of this vector s

along rqp

,

rqp

and rqp

are x, y and z, respectively, then the value of 2x + y + z is

[Ans: 9]

Q.44Complex No. For any integer k, let k = cos

7

k + i sin

7

k, where i = 1 . The value of the expression

12

k 1 kk 1

3

4k 1 4k 2k 1

| |

| |

is [Ans: 4]

Q.45Seq. & ProgSuppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio ofthe sum of the first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh term lies inbetween 130 and 140, then the common difference of this A.P. is [Ans: 9]

Q.46Binomial TheoremThe coefficient of x9 in the expansion of (1 + x) (1 + x2) (1 + x3) ...........(1 + x100) is[Ans: 8]



Q.47Conic Section(ellipse)Suppose that the foci of the ellipse 15

y

9

x 22

are (f1, 0) and (f2, 0) where f1 > 0 and

f2 > 0. Let P1 and P2 be two parabolas with a common vertex at (0, 0) and with foci at (f1, 0) and (2f2,0), respectively. Let T1 be a tangent to P1 which passes through (2f2, 0) and T2 be a tangent to P2 which

passes through (f1, 0). If m1 is the slope of T1 and m2 is the slope of T2, then the value of

2

221

mm

1

is [Ans: 4]

Q.48Limits Let m and n be two positive integers greater than 1. If [Ans: 2]

2

eeelim

m

)cos(

0

n

then the value of n

m is

SECTION �2 : (MM : 32)This section contains 8 questions. Each question has FOUR options (A), (B), (C) and (D). ONE ORMORE THAN ONE of these four option(s) is(are) correct.[Marking scheme : +4, �2]

Q.49IntegrationThe option(s) with the values of a and L that satisfy the following equation is(are)

?L

dtatcosatsine

dtatcosatsine

0

46t

4

0

46t

(A) a = 2, L = 1e

1e4

(B) a = 2, L = 1e

1e4

(C) a = 4, L = 1e

1e4

(D) a = 4, L = 1e

1e4

Ans. A,C

Q.50AOD(monotonocity)Let f, g : [�1, 2] R be continuous function which are twice differentiable on the interval(�1, 2). Let the values of f and g at the points �1, 0 and 2 be as given in the following table:

x = -1 x = 0 x = 2f(x) 3 6 0g(x) 0 1 -1

In each of the intervals (�1, 0) and (0, 2) the function (f � 3g) never vanishes. Then the correct statement(s)is (are)(A) f ' (x) � 3g'(x) = 0 has exactly three solutions in (�1, 0) U (0, 2)(B) f ' (x) � 3g'(x) = 0 has exactly one solution in (�1, 0)(C) f ' (x) � 3g'(x) = 0 has exactly one solution in (0, 2)(D) f ' (x) � 3g'(x) = 0 has exactly two solutions in (�1, 0) and exactly two solutions in (0, 2)

[Ans: BC]



Q.51IntegrationLet f(x) = 7 tan8x + 7 tan6x � 3 tan4x � 3 tan2x for all x

2,

2. Then the correct expression(s)

is(are)

(A) 12

1dx)x(xf

4/

0

(B) 0dx)x(f4/

0

(C) 6

1dx)x(fx

4/

0

(D) 1dx)x(f4/

0

[Ans: AB]

Q.52IntegrationLet f ' (x) = xsin2

x1924

3

for all x R with f

2

1 = 0. If m < Mdx)x(f

1

2/1

, then the possible

values of m and M are

(A) m = 13, M = 24 (B) m = 4

1, M =

2

1

(C) m = �11, M = 0 (D) m = 1, M = 12[Ans: D]

Q.53Quad. Eq.Let S be the set of all non-zero real numbers such that the quadratic equation x2 � x + = 0has two distinct real roots x1 and x2 satisfying the inequality |x1 � x2| < 1. Which of the following intervalsis(are) a subset(s) of S?

(A)

5

1,

2

1(B)

0,

5

1

(C)

5

1,0 (D)

2

1,

5

1

[Ans: AD]

Q.54ITFIf = 3 sin�1

11

6 and = 3 cos�1

9

4, where the inverse trignometric functions take only the

principal values, then the correct option(s) is (are)(A) cos > 0 (B) sin < 0 (C) cos( + ) > 0 (D) cos < 0

[Ans: BCD]

Q.55Conic Section (Ellipse)Let E1 and E2 be two ellipses whose centres are at the origin. The major axes of E1 andE2 lie along the x-axis and y-axis, respectively. Let S be the circle x2 + (y � 1)2 = 2. The straight line x +

y = 3 touches the curves S, E1 and E2 at P, Q and R, respectively. Suppose that PQ = PR = 3

22. If e1

and e2 are the eccentricities of E1 and E2, respectively, then the correct expression(s) is (are)

(A) e12 + e2

2 = 40

43(B) e1e2 =

102

7(C) |e1

2 � e22| =

8

5(D) e1e2 =

4

3

[Ans: AB]



Q.56Conic section (hyperbola)Consider the hyperbola H : x2 � y2 = 1 and a circle S with centre N(x2, 0). Supposethat H and S touch each other at a point P(x1, y1) with x1 > 1 and y1 > 0. The common tangent to H andS at P intersects the x-axis at point M. If (l, m) is the centroid of the triangle PMN, then the correctexpression(s) is (are)

(A) 211 x3

11

dx

d

for x1 > 1 (B)

1x3

x

dx

dm21

1

1 for x1 > 1

(C) 211 x3

11

dx

d

for x1 > 1 (D) 3

1

dx

dm

1

for y1 > 0

[Ans: ABD]

SECTION �3: (MM : 16)This section contains 2 paragraphs. Each paragraph has two questions. Each question has FOURoptions (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is(are) correct.Marking Scheme: [+4, �2]

PARAGRAPH-1Let n1 and n2 be the number of red and black balls, respectively, in box I. Let n3 and n4 be the numberof red and black balls, respectively, in box II.

Q.57ProbabilityOne of the two boxes, box I and box II, was selected at random and a ball was drawn randomlyout of this box. The ball was found to be red. If the probability that this red ball was drawn from box II

is 3

1 , then the correct option(s) with the possible values of n1, n2, n3 and n4 is(are)

(A) n1 = 3, n2 = 3, n3 = 5, n4 = 15 (B) n1 = 3, n2 = 6, n3 = 10, n4 = 50(C) n1 = 8, n2 = 6, n3 = 5, n4 = 20 (D) n1 = 6, n2 = 12, n3 = 5, n4 = 20

[Ans: AB]Q.58ProbabilityA 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 3

1 , then the correct option(s) with the possible values of n1 and n2

is(are)(A) n1 = 4 and n2 = 6 (B) n1 = 2 and n2 = 3(C) n1 = 10 and n2 = 20 (D) n1 = 3 and n2 = 6

[Ans: CD]



PARAGRAPH - 2Let F : R R be a thrice differentiable function. Suppose that F(1) = 0, F(3) = � 4 and F(x) < 0 for all

1x , 3

2

. Let f(x) = x F(x) for all Rx .

Q.59AOD(Monotonocity)The correct statement(s) is(are)(A) f ' (1) < 0 (B) f (2) < 0

(C) f '(x) 0 for any )3,1(x (D) f ' (x) = 0 for some )3,1(x[Ans: ABC]

Q.60AOD(Monotonocity)If 3

1

2 dx)x('Fx = � 12 and

3

1

3 40dx"Fx then the correct expression(s) is(are)

(A) 9f '(3) + f '(1) � 32 = 0 (B)

3

1

12dx)x(f

(C) 9f '(3) � f '(1) + 32 = 0 (D)

3

1

12dx)x(f

[Ans: CD]

CODE # 3 JEE ADVANCED PAPER-II HELD ON SUNDAY 24 MAY, 2015_[PHYSICS]


JEE ADVANCED PAPER�IIPART : I - PHYSICS

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 ORSMarking scheme:

+4 If the bubble corresponding to the answer is darkened0 In all other cases

Q.1Geometrical optics

A monochromatic beam of light is incident at 60° on one face of an equilat-

eral 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 =d

dn

m . The value of m is

60°

Ans: 2


,do.khZ izdk�k dk ,d iqat ,d n viorZukad okys leckgq fizTe ds ,d Qyd ij

60° ds dks.k ij vkifrr gksrk gS rFkk lkeus okys Qyd ls yEc ls (n) dks.k cukrs gq, fudyrk gS ¼fp= nsa[ksa½A

n = 3 ij dk eku 60° gS rFkk =d

dn

m gSA rc m dk eku gS

60°

Ans: 2



Q.2Current electricity

In the following circuit, the current through the resistor R (= 2) is I Amperes. The value of Iisuhps fn;s x;s ifjiFk esa izfrjks/k R (= 2) esa I ,fEi;j /kkjk izokfgr gksrh gSA rc I dk eku gS&

R(=2 ) 1

2

10

8

2

4

6

12

6.5 V

4

Ans: 1Q.3

Modern physicsAn electron in an excited state of Li2+ ion has angular momentum 3h/2. The de Broglie

wavelength of the electron in this state is pa0 (where a

0 is the Bohr radius). The value of p is

Ans: 2Q.3

Modern physicsLi2+ vk;u dh mrsftr voLFkk esa ,d bysDVªkWu dk dks.kh; osx 3h/2 gSA bl voLFkk esa bysDVªkWu dh

Mh&czksXyh rjaxnS/;Z pa0 (tgk¡ a

0 cksj radius gS) gSA p dk eku gSA

Ans: 2Q.4

GravitationA 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 masslessrod of length l and this assembly is free to move along the line connecting them. All three massesinteract only through their mutual gravitational interaction. When the point mass nearer to M is at a

distance r = 3l from M, the tension in the rod is zero for m = k M

288 . The value of k is:

m mM

r l

Ans: 7



Q.4Gravitation

,d cM+k xksykdkj nzO;eku M ,d txg fLFkr gS rFkk nks ,d:i fcUnq nzO;eku m nzO;eku M ds dsUnz ls

gksdj tkus okyh js[kk ij j[ks x;s gSa (fp= ns[ksa) A fcUnq nzO;eku l yEckbZ ds nzO;eku jfgr n`<+ NM+ ls tqM+s gSa

rFkk ;g la;kstu mudks tksM+us okyh js[kk ij xfr dj ldrk gSA lHkh nzO;ekuksa esa dsoy mudk viuk

xq:Rokd"kZ.k gSA tc M ds fudV okyk fcUnq nzO;eku M ls r = 3l dh nwjh ij gS rc m = k M

288 ds fy,

NM+ esa ruko 'kwU; gSA rc k dk eku gS

m mM

r l

Ans: 7Q.5

Error analysisThe energy of a system as a function of time t is given as E(t) = A2exp (�t), where = 0.2 s�1.

The measurement of A has an error of 1.25%. If the error in the measurement of time is 1.50%, thepercentage error in the value of E(t) at t = 5 s is

Ans: 4Q.5

Error analysis,d fudk; dh le; t ij ÅtkZ E(t) = A2exp (�t) Qyu }kjk nh tkrh gS] tgk¡ = 0.2 s�1 gSA A ds ekiu

esa 1.25% dh izfr'kr =qfV gSA ;fn le; ds ekiu esa 1.50% dh =qfV gS rc t = 5 s ij E(t) ds eku esa izfr'kr

=qfV gksxh

Ans: 4Q.6

Rotational dynamicsThe densities of two solid spheres A and B of the same radii R vary with

radial distance r as A

r(r) k

R

and 5

B

r(r) k

R

, respectively, where k is a constant. The

moments of inertia of the individual spheres about axes passing through their centres are IA and I

B,

respectively, If B

A

I n

I 10 , the value of n is

Ans: 6

Q.6Rotational dynamics

R f=T;k ds nks Bksl xksyksa A vkSj B ds ?kuRoksa dk f=T; nwjh r ds lkFk laca/k Øae'k% A

r(r) k

R

rFkk 5

B

r(r) k

R

gSa] tgk¡ k ,d fLFkjkad gSA xksyksa ds vius&vius dsUnz ls gksdj tkus okyh v{kksa ds ifjr%

tM+Rok?kw.kZ Øe'k% IA rFkk I

B gSaA ;fn

B

A

I n

I 10 gS] rc n dk eku gS

Ans: 6



Q.7Mechanical wave

Four harmonic waves of equal frequencies and equal intensities I0 have phase angles 0, /3,

2/3 and . When they are superposed, the intensity of the resulting wave is nI0. The value of n is

Ans: 3

Q.7Mechanical wave

cjkcj vko`fÙk;ksa rFkk rhozrk I0 dh pkj vkorZ rjaxksa dh dyk ds dks.k 0, /3, 2/3 rFkk gSaA rc bu

rjaxksa dks v/;kjksfir lqijiksl (superpose) fd;k tkrk gS rks ifj.kkeh rhozrk nI0 gSA rc n dk eku gS

Ans: 3Q.8

Modern physicsFor a radioactive material, its activity A and rate of change of its activity R are defined as A = �

dN

dt and R = �

dA

dt, where N(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 t = 2 are

RP and R

Q, respectively. If P

Q

R n

R e , then the value of n is

Ans: 2

Q.8Modern physics

,d jsfM;ks/kehZ inkFkZ dh lfØ;rk A ,oa lfØ;rk ifjorZu dh nj R Øe'k% A = �dN

dt rFkk R = �

dA

dtlaca/kksa }kjk ifjHkkf"kr dh tkrh gS] tgk¡ le; t ij ukfHkdksa dh la[;k N(t) gSA nks jsfM;ks/kehZ lzksr P (vkSlr vk;q

) rFkk Q (vkSlr vk;q 2) dh le; t = 0 ij leku lfØ;rk gSA mudh lfØ;rk ifjorZu dh njsa le; t =

2 ij Øe'k% RP rFkk R

Q gSaA ;fn

P

Q

R n

R e , rc n dk eku gS

Ans: 2SECTION 2 (Maximum Marks : 32)

* This section contains EIGHT questions* Each questions 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) darkened0 If none of the bubbles is darkened�2 In all other cases

Q.9Gravitation

A spherical body of radius R consists of a fluid of constant density and is in equilibrium under itsown 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) 63

P(r 2R/ 3) 80

(C) P(r 3R/ 5) 16

P(r 2R/ 5) 21

(D)

P(r R/ 2) 20

P(r R/ 3) 27

Ans: (B,C)



Q.9Gravitation

,d ,dleku ?kuRo ds rjy ds xksykdkj fiaM dh f=T;k R gS rFkk ;g vius Lo;a ds xq:Ro ds izHkko esa

lkE;koLFkk esa gSA ;fn blds dsUnz ls nwjh r(r > R) ij nkc P(r) gS] rc lgh fodYi gS (gSa)

(A) p(r = 0) = 0 (B) P(r 3R/ 4) 63

P(r 2R/ 3) 80

(C) P(r 3R/ 5) 16

P(r 2R/ 5) 21

(D)

P(r R/ 2) 20

P(r R/ 3) 27

Ans: (B,C)Q.10

CapacitanceA parallel plate capacitor having plates of area S and plate separation d, has capacitance C

1 in

air. When two dielectrics of different relative permittivity's (1 = 2 and

2 = 4) are introduced between

the two plates as shown in the figure, the capacitance becomes C2. The ratio

2

1

C

C is

(A) 6/5 (B) 5/3 (C) 7/5 (D) 7/3Ans: (D)Q.10

Capacitance,d lekarj ifV~Vdk la/kkfj= dh ifV~Vdkvksa dk {ks=Qy S rFkk ifV~Vdkvksa ds chp esa nwjh d gSA rFkk bldh

ok;q esa /kkfjrk C1 gSA tc ifV~Vdkvksa ds e/; nks vyx&vyx lkis{k ijkoS|qrkadksa (

1 = 2 rFkk

2 = 4) ds ijkoS|qr

inkFkZ n'kk;Z fp=kuqlkj j[ks tkrs gSa rc bl izdkj cus u;s la/kkfj= dh /kkfjrk C2 gks tkrh gSA rc vuqikr

2

1

C

C

gSA

(A) 6/5 (B) 5/3 (C) 7/5 (D) 7/3



Ans: (D)Q.11

First law of thermodyanmicsAn ideal monatomic gas is confined in a horizontal cylinder by a spring loaded

piston (as shown in the figure). Initially the gas is at temperature T1, pressure P

1 and volume V

1 and

the spring is in its relaxed state. The gas is then heated very slowly to temperature T2, pressure P

2 and

volume V2. 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 V2 = 2V

1 and T

2 = 3T

1, then the energy stored in the spring is

1

4P

1V

1

(B) If V2 = 2V

1 and T

2 = 3T

1, then the change in internal energy is 3P

1V

1

(C) If V2 = 3V

1 and T

2 = 4T

1, then the work done by the gas is

7

3 P

1V

1

(D) If V2 = 3V

1 and T

2 = 4T

1, then the heat supplied to the gas is

17

6 P

1V

1

Ans: (ABC OR B)

Q.11First law of thermodyanmics

,d ,d&ijek.kqd vkn'kZ xSl ,d {kSfrt crZu (horizontal cylinder) esa fLizax&;qDRk fiLVu}kjk cUn gS (n'kkZ;s fp=kuqlkj)A izkjaHk esa xSl dk rkieku T

1, nkc P

1 rFkk vk;ru V

1 gS rFkk fLizax foJkar

voLFkk esa gSa vc xSl dks cgqr /khjs&/khjs rkieku T2 rd xeZ djus nkc P

2 rFkk vk;ru V

2 gks tkrk gSA bl

izfØ;k esa fiLVu x nwjh r; djrk gSA fiLVu ,oa crZu ds e/; ?k"kZ.k dks ux.; ekurs gq,] lgh dFku gS (gSa)

(A) ;fn V2 = 2V

1 rFkk T

2 = 3T

1 gS, rc fLizax esa lafpr ÅtkZ

1

4P

1V

1 gSA

(B) ;fn V2 = 2V

1 rFkk T

2 = 3T

1 gS, rc vkarfjd ÅtkZ esa ifjorZu 3P

1V

1 gSA

(C) ;fn V2 = 3V

1 rFkk T

2 = 4T

1 gS] rc xSl }kjk fd;k x;k dk;Z

7

3 P

1V

1 gSA

(D) ;fn V2 = 3V

1 rFkk T

2 = 4T

1 gS, rc xSl dks nh x;h Å"ek

17

6 P

1V

1 gSA

Ans: (ABC OR B)



Q.12Modern physics

A fission reaction is given by 236 140 9492 54 38U Xe Sr x y, where x and y are two particles.

Considering 23692 U to be at rest, the kinetic energies of the products are denoted by K

Xe, K

Sr, K

x

(2MeV) and Ky (2MeV), respectively. Let the binding energies per nucleon of 236

92 U , 14054 Xe and 94

38Sr

be 7.5 MeV, 8.5 MeV and 8.5 MeV, respectively. Considering different conservation laws, the cor-rect option(s) is (are)(A) x =n, y = n, K

Sr = 129 MeV, K

Xe = 86 MeV

(B) x = p, y = e�, KSr

= 129 MeV, KXe

= 86 MeV(C) x = p, y = n, K

Sr = 129 MeV, K

Xe = 86 MeV

(D) x = n, y = n, KSr

= 86 MeV, KXe

= 129 MeVAns: (AD)

Q.12Modern physics

,d fo[kaMu izfØ;k 236 140 9492 54 38U Xe Sr x y nh x;h gS] tgk¡ x rFkk y nks d.k gSaA

23692 U

fojkekoLFkk esa gS rFkk mRiknksa dh xfrt ÅtkZ,sa Øe'k% KXe

, KSr

, Kx (2MeV) rFkk K

y (2MeV) ls n'kkZ;h x;h

gSA 23692 U , 140

54 Xe rFkk 9438Sr dh izfr U;wfDyvkWu ca/ku ÅtkZvksa dks Øe'k% 7.5 MeV, 8.5 MeV rFkk 8.5 MeV,,

ysaA fofHkUu laj{k.kksa fu;eksa dk /;ku j[krs gq, lgh fodYi gS (gSa)(A) x =n, y = n, K

Sr = 129 MeV, K

Xe = 86 MeV

(B) x = p, y = e�, KSr

= 129 MeV, KXe

= 86 MeV(C) x = p, y = n, K

Sr = 129 MeV, K

Xe = 86 MeV

(D) x = n, y = n, KSr

= 86 MeV, KXe

= 129 MeVAns: (AD)Q.13

Fluid mechanicsTwo spheres P and Q of equal radii have densities

1 and

2, respectively, The spheres are

connected by a massless string and placed in liquids L1 and L

2 of densities

1 and

2 and viscosities

1 and

2, respectively. They float in equilibrium with the sphere P in L

1 and sphere Q in L

2 and the

string being taut (see figure). If sphere P alone in L2 has terminal velocity PV

and Q alone in L1 has

terminal velocity QV

, then

P

Q

L1

L2

(A) P 1

Q 2

| V |

| V |

(B) P 2

Q 1

| V |

| V |

(C) P QV .V 0

(D) P QV .V 0

Ans: (AD)



Q.13Fluid mechanics

cjkcj f=T;k okys nks xksyksa P rFkk Q ?kuRo Øe'k% 1 rFkk

2 gSaA xksyksa dks ,d nzO;eku jfgr Mksjh ls

tksM+dj 1 ,oa

2 ?kuRo okys

1 ,oa

2 ';kurk xq.kkdksa okys nzOkksa L

1 o L

2 of densities

1 and

2 and

viscosities 1 and

2, respectively. They float in equilibrium with the sphere P in L

1 and sphere Q in

L2 and the string being taut (see figure). If sphere P alone in L

2 has terminal velocity PV

and Q alone

in L1 has terminal velocity QV

, then

P

Q

L1

L2

(A) P 1

Q 2

| V |

| V |

(B) P 2

Q 1

| V |

| V |

(C) P QV .V 0

(D) P QV .V 0

Ans: (AD)Q.14

Magnetic effects of currentIn terms of potential difference V, electric current I, permittivity

0, perme-

ability 0 and speed of light c, the dimensionally correct equations is (are)

(A) 0I2 =

0V2 (B)

0I =

0V (C) I =

0cV (D)

0cI =

0V

Ans: (AC)Q.15

ElectrostaticsConsider a uniform spherical charge distribution of radius R

1 centred at the

origin O. In this distribution, a spherical cavity of radius R2, centred at P with distance OP = a = R

1

� R2 (see figure) is made. If the electric field inside the cavity at position r

is E(r)

. then the correct

statements is (are)

(A) E

is uniform, its magnitude is independent of R2 but its direction depends on r

(B) E

is uniform, its magnitude depends on R2 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 the its magnitude and direction depend on a

Ans: (D)



Q.16Elasticity

In plotting stress versus strain curves for two materials P and Q, and student by mistakeputs strain on the y-axis and stress on the x-axis as shown in the figure. Then the correctstatements 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

Ans: (AB)

PARAGRAPH 1In a thin rectangular metallic strip a constant current I flows along the positive x-direction, as shownin the figure. The length, width and thickness of the strip are l, w and d, respectively.

A uniform magnetic field B

is applied on the strip along the positive y-direction. Due to this, thecharge carriers experience a net deflection along the z-direction. This results in accumulation ofcharge carriers on the surface PQRS and appearance of equal and opposite charges on the faceopposite to PQRS. A potential difference along the z-direction is thus developed. Charge accumulationcontinues until the magnetic force is balanced by the electric force. The current is assumed to beuniformly distributed on the cross section of the strip and carried by electrons.

Q.17Magnetic effects of current

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

1 and w

2 and thickness are d

1 and d

2respectively. Two points K and M are

symmetrically located on the oppostite faces parallel to the x-y plane (see figure). V1 and V

2 are the

potential differences between K and M in strips 1 and 2, respectively. Then, for a given current Iflowing through them in a given magnetic field strength B, the correct statement(s) is (are).(A) If w

1 and w

2 and d

1 = 2d

2, then V

2 = 2V

1

(B) If w1 and w

2 and d

1 = 2d

2, then V

2 = V

1

(C) If w1 and 2w

2 and d

1 = d

2, then V

2 = 2V

1

(D) If w1 and 2w

2 and d

1 = d

2, then V

2 = V

1

Ans: (AD)



Q.18Magnetic effects of current

Consider two different metallic strips (1 and 2) of same dimensions (length l,width and thickness d) with carrier densities n

1 and n

2, respectively. Strip 1 is placed in magnetic

field B1 and strip 2 is placed in magnetic field B

2, both along positive y. directions. Then V

1 and V

2

are the potential difference devoloped between K and M is strips 1 and 2, respectively. Assuming thatthe current I is the same for both the strips, the correct options is (are)(A) If B

1 = B

2 and n

1 = 2n

2, then V

2 = 2V

1

(B) If B1 = B

2 and n

1 = 2n

2, then V

2 = V

1

(C) If B1 = 2B

2 and n

1 = n

2, then V

2 = 0.5V

1

(D) If B1 = 2B

2 and n

1 = n

2, then V

2 = V

1

Ans: (AC)

PARAGRAPH-2Light guidance in an optical fiber can be understood by considering a structure comprising of thinsolid glass cylinder of refractive index n1 surrounded by a medium of lower refractive index n2. Thelight guidance in the structure takes place due to successive total internal reflections at the interfaceof the media n1 and n2 as shown in the figure. All rays with the angle of incidence i less than aparticular value im are confined in the medium of refractive index n1. The numerical aperture (NA)of the structure is defined as sin im.


For two structures namely S1 with n1 = 4/45 and n2 = 3/2, and S2 with n1 = 8/5

and n2 = 7/5 and taking the refractive index of water to be 4/3 and that of air to be 1, the correctoption(s) is(are)(A) NA of S1 immersed in water is the same as that of S2 immersed in a liquid of refractive index

153

16

(B) NA of S1 immersed in liquid of refractive index 15

6 is the same as that of S2 immersed in water..

(C) NA of S1 placed in air is the same as that of S2 immersed in liquid of refractive index 15

4.

(D) NA of S1 placed in air is the same as that of S2 placed in water.Ans: (AC)


If two structures of dame cross-sectional area, but different numerical apertures NA1and NA2(NA2 < NA1) are joined longitudinally, the numerical aperture of the combined structure is

(A) 21

21

NANA

NANA

(B) NA1 + NA2 (C) NA1 (D) NA2

Ans: (D)

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