2015_05_18_17_49_33

Academic Session: 2014-15

JJEEEE PPRREEPPAARRAATTOORRYY TTEESSTT--22 ((JJPPTT--22))((JJEEEE AADDVVAANNCCEEDD PPAATTTTEERRNN))

TTaarrggeett :: JJEEEE ((MMaaiinn++AAddvvaanncceedd)) 22001155

Please read the next page & last page of this booklet for the instructions.(Ñi;k funsZ'kksa ds fy;s bl iqfLrdk ds vxys ,oa vfUre i`"B dks i<+sA)

RReessoonnaannccee EEdduuvveennttuurreess PPvvtt.. LLttdd..CCOORRPPOORRAATTEE OOFFFFIICCEE :: CCGG TToowweerr,, AA--4466 && 5522,, IIPPIIAA,, NNeeaarr CCiittyy MMaallll,, JJhhaallaawwaarr RRooaadd,, KKoottaa ((RRaajj..)) -- 332244000055PPhh..NNoo.. :: ++9911--774444--33001122222222,, 66663355555555 || TToollll FFrreeee :: 11880000 220000 22224444 || 11880000 110022 66226622 || 11880000 225588 55555555

RReegg.. OOffffiiccee :: JJ--22,, JJaawwaahhaarr NNaaggaarr,, MMaaiinn RRooaadd,, KKoottaa ((RRaajj..))--332244000055 || PPhh.. NNoo..:: ++9911--774444--33119922222222 || FFAAXX NNoo.. :: ++9911--002222--3399116677222222WWeebbssiittee ::wwwwww..rreessoonnaannccee..aacc..iinn || EE--mmaaiill :: ccoonnttaacctt@@rreessoonnaannccee..aacc..iinn || CCIINN:: UU8800330022RRJJ22000077PPTTCC002244002299

DDaattee:: 1177 MMaayy,, 22001155 || DDuurraattiioonn :: 33 HHoouurrss || MMaaxx.. MMaarrkkss:: 118800

CCOODDEE -- 0PPAAPPEERR--11

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CCOOUURRSSEE :: VVIIJJEETTAA ((JJPP)),, VVIISSHHWWAAAASS ((JJFF)),, VVIIJJAAYY ((JJRR)) && VVIIVVEEKK ((JJCCCC))

IIMMPPOORRTTAANNTT IINNSSTTRRUUCCTTIIOONNSS // eeggÙÙooiiww..kk ZZ ffuunnss ZZ''kkA. lkekU; % A. General :

1. This booklet is your Question Paper. Do not break the

seals of this booklet before being instructed to do so

by the invigilators.

1. ;g iqfLrdk vkidk iz'ui=k gSA bldh eqgjsa rc rd u rksMsatc rd fujh{kdksa ds }kjk bldk funsZ'k u fn;k tk;sA

2. Blank spaces and blank pages are provided in the

question paper for your rough work. No additional

sheets will be provided for rough work.

2. dPps dke ds fy;s [kkyh i"B vkSj [kkyh txg bl iqfLrdk esa gh gSAdPps dke ds fy, dksbZ vfrfjDr dkxt ugha fn;k tk;sxkA

3. Blank papers, clipboards, log tables, slide rules,

calculators, cameras, cellular phones, pagers and

electronic gadgets are NOT allowed inside the

examination hall.

3. dksjs dkxt] fDyi cksMZ (CLIP BOARD)] ykWx rkfydk]LykbM:y] dSYdqysVj] dSejk] lsyQksu] istj vkSj fdlh izdkjds bysDVªkfud midj.k ijh{kk de esa vuqefr ugha gSA

4. Write you name and roll number in the space provided

on the back cover of this booklet.

4. bl iqfLrdk ds fiNys i`"B ij fn, x, LFkku esa viuk ukevkSj jksy uEcj fyf[k,A

5. Using a black ball point pen, darken the bubbles

on the upper original sheet.5. Åijh ewy i`"B ds cqycqyksa (BUBBLES) dks dkys ckWy IokbaV

dye ls dkyk djsaA

6. DO NOT TAMPER WITH/MUTILATE THE ORS OR

THE BOOKLET.

6. vks-vkj-,l- (ORS) ;k bl iqfLrdk esa gsj&Qsj@foÑfr u djsaA

7. On breaking the seals of the booklet check that it

contains all the 60 questions and corresponding

answer choices are legible. Read carefully the

Instructions printed at the beginning of each section.

7. bl iqfLrdk dh eqgjsa rksM+us ds i'pkr~ Ñi;k tk¡p ysa fd blesalHkh 60 iz'u vkSj muds mÙkj fodYi Bhd ls i<+s tk ldrs gSaAlHkh [kaMksa ds izkjaHk esa fn;s gq, funsZ'kksa dks /;ku ls i<+saA

B. Filling the ORS

Use only Black ball point pen only for filling the ORS.

8. Write your Roll no. in the boxes given at the top left

corner of your ORS with black ball point pen. Also,

darken the corresponding bubbles with Black ball point

pen only. Also fill your roll no on the back side of your ORS

in the space provided (if the ORS is both side printed).

B. vks-vkj-,l (ORS) HkjukORS dks Hkjus ds fy, dsoy dkys ck¡y iSu dk mi;ksx dhft,A

8. ORS ds lcls Åij cka;s dksus esa fn, x, ck¡Dl esa viuk jksy uEcjdkys ck¡y ikbUV ls fyf[k, rFkk laxr xksys Hkh dsoy dkys isu lsHkfj;sA ORS ds ihNs dh rjQ Hkh viuk jksy uEcj fyf[k, (;fnORS nksuksa rjQ Nih gqbZ gSA)

9. Fill your Paper Code as mentioned on the Test Paper

and darken the corresponding bubble with Black ball

point pen.

9. ORS ij viuk isij dksM fyf[k, rFkk laxr xksyksa dks dkysck¡y isu ls dkys dhft,A

10. If student does not fill his/her roll no. and paper code

correctly and properly, then his/her marks will not be

displayed and 5 marks will be deducted (paper wise)

from the total.

10. ;fn fo|kFkhZ viuk jksy uEcj rFkk isij dksM lgh vkSj mfprrjhds ugha Hkjrk gS rc mldk ifj.kke jksd fy;k tkosxk rFkkiz'u&i=k esa izkIrkad ls 5 vad dkV fy, tkosaxsaA

11. Since it is not possible to erase and correct pen filled

bubble, you are advised to be extremely careful while

darken the bubble corresponding to your answer.

11. pawfd isu ls Hkjs x, xksys feVkuk vkSj lq/kkjuk laHko ugha gSblfy, vki lko/kkuh iwoZd vius mÙkj ds xksyksa dks HkjsaA

12. Neither try to erase / rub / scratch the option nor make the

Cross (X) mark on the option once filled. Do not scribble,

smudge, cut, tear, or wrinkle the ORS. Do not put any

stray marks or whitener anywhere on the ORS.

12. fodYi dks u feVk,a@u Ldzsp djsa vkSj u gh xyr (X) fpUg dksHkjsaA ORS dks dkVs u gh QkMs u gh xUnk ugha djsa rFkk dksbZHkh fu'kku ;k lQsnh ORS ij ugha yxk;sA

13. If there is any discrepancy between the written data

and the bubbled data in your ORS, the bubbled data

will be taken as final.

13. ;fn ORS esa fdlh izdkj dh fy[ks x, vkadMksa rFkk xksys fd,vkadMksa esa fojks/kkHkkl gS] rks xksys fd, vkadMksa dks gh lgh ekuktkosxkA

JJEEEE PPRREEPPAARRAATTOORRYY TTEESSTT--22 ((JJPPTT--22)) ((JJEEEE AADDVVAANNCCEEDD PPAATTTTEERRNN))CCOOUURRSSEE :: VVIIJJEETTAA ((JJPP)),, VVIISSHHWWAAAASS ((JJFF)),, VVIIJJAAYY ((JJRR)) && VVIIVVEEKK ((JJCCCC)) CCOODDEE -- 0PPAAPPEERR--11

DDAATTEE :: 1177--0055--22001155

Space for Rough Work / (dPps dk;Z ds fy, LFkku )

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PART – I : MATHEMATICS

SECTION – 1 : (Only One option correct Type)[k.M – 1 : (dsoy ,d lgh fodYi çdkj)

This section contains 17 multiple choice questions. Each question has four choices (A), (B), (C)and (D) out of which ONLY ONE is correct.bl [k.M esa 17 cgqfodYi ç'u gSaA çR;sd ç'u esa pkj fodYi (A), (B), (C) vkSj (D) gSa] ftuesa ls dsoy ,d lgh gSA

1. The tangent and normal to the parabola y2 = 8x drawn at (2,4) intersect the line x + y = 3 at thepoints A and B respectively. If AB subtends a right angle at the vertex of the parabola then sum ofall possible values of isijoy; y2 = 8x ds fcUnq (2,4) ij Li'kZ js[kk rFkk vfHkyEc] ljy js[kk x + y = 3 dks Øe'k% A rFkk B ijdkVrs gSaA ;fn AB ijoy; ds 'kh"kZ ij ledks.k vUrfjr djrk gS] rks ds lHkh laHko ekuksa dk ;ksx gS&(A) 2 (B) 1 (C) 0 (D) –1

2. Number of integral values of x such that the inequality 10

2x 2007log 0

x 1

satisfied, is

vlfedk 10

2x 2007log 0

x 1

ds lR; gksus ds fy, x ds iw.kk±d ekuksa dh la[;k gS &

(A) 1004 (B) 1005 (C) 2007 (D) 2008

3. The sum of all integral values of a for which one root of equation (a – 5) x2 – 2ax + a – 4 = 0 issmaller than 1 and the other root is greater than 2, must be equal toa ds mu iw.kk±d ekuksa dk ;ksxQy ftlds fy, lehdj.k (a – 5) x2 – 2ax + a – 4 = 0 dk ,d ewy 1 ls derFkk nwljk ewy 2 ls cMk gS] cjkcj gS&(A) 18 (B) 259 (C) 262 (D) 261


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4. Area of triangle formed by common tangents to the circle x2 + y2 – 6x = 0 and x2 + y2 + 2x = 0 iso`Ùkksa x2 + y2 – 6x = 0 vkSj x2 + y2 + 2x = 0 dh mHk;fu"B Li'kZ js[kkvksa ls cus f=kHkqt dk {ks=kQy gS&(A) 3 3 (B) 2 3 (C) 9 3 (D) 6 3

5. The ratio of the greatest value of 2 – cosx + sin2x to its least value is

2 – cosx + sin2x ds vf/kdre eku o U;wure eku dk vuqikr gS&

(A)7

4(B)

9

4(C)

13

4(D)

5

4

6. A variable chord of the hyperbola2

2

x

a–

2

2

y

b = 1 is a tangent to the circle x2 + y2 = c2. The locus of

middle point of the chord is

vfrijoy;2

2

x

a–

2

2

y

b = 1 dh ,d pj thok o`Ùk x2 + y2 = c2 dh ,d Li'kZ js[kk gS] rks thok ds e/; fcUnq dk

fcUnqiFk gS &

(A)

22 2

2 2

x y–

a b

= c22 2

4 4

x y

a b

(B)

2 2

2 2

x y

a b

= c2

2 2

4 4

x y–

a b

(C)

22 2

4 4

x y–

a b

= c22 2

2 2

x y

a b

(D)

22 2

2 2

x y

a b

= c2

2 2

4 4

x y

a b

7. If (1 + x2)5 (1 + x)4 = a0 + a1x + a2x2 + a3x

3 +..........,then value of a5 is

(A) 30 (B) 40 (C) 60 (D) None of these

;fn (1 + x2)5 (1 + x)4 = a0 + a1x + a2x2 + a3x

3 +..........,gks] rks a5 dk eku gS&(A) 30 (B) 40 (C) 60 (D) buesa ls dksbZ ugha


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8. If x =a

b – c, y =

b

c – aand z =

c

a – b where a b c then

;fn x =a

b – c, y =

b

c – avkSj z =

c

a – btgk¡ a b c gS] rks

(A) 1 + x + y + z = 0 (B) 1 + xyz = 0(C) 1 + xy + yz + zx = 0 (D) xy + yz + zx = xyz

9. Tangent is drawn to the ellipse x2 + 2y2 = 6 at point (2, 1). If A and B are the feet of perpendicularsfrom the two focii on the tangent, then length AB is equal tonh?kZo`Ùk x2 + 2y2 = 6 ds fcUnq (2, 1) ij Li'kZ js[kk [khaph tkrh gS ;fn A rFkk B Li'kZ js[kk ij ukfHk;ksa dsyEcikn gS rc AB dh yEckbZ gS(A) 3 (B) 2 (C) 6 (D) 12

10. The length of latus rectum of the parabola whose parametric equations are x = t2 + t + 1, y = t2 – t + 1,

where t R, is equal to

ijoy; ftlds izkpfyd lehdj.k x = t2 + t + 1, y = t2 – t + 1, tgk¡ t R, ds ukfHkyEc dh yEckbZ cjkcj gS&(A) 2 (B) 4 (C) 8 (D) 6

11. If A, B and C are three events such that P(B) =3

4, P(A B C) =

1

3 and P(A B C) =

1

3 then

P(B C) =

;fn A, B ,oa C rhu ?kVuk,¡ bl izdkj gS fd P(B) =3

4, P(A B C) =

1

3,oa P(A B C) =

1

3rc

P(B C) =

(A)1

12(B)

5

12(C)

3

4(D)

1

3


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12. A line passes through a point A with position vector ˆ ˆ ˆ3 i j k and is parallel to the vector

ˆ ˆ ˆ2 i j 2k . If P is a point on this line such that AP = 15 units, then the position vector of the point

P is/are

,d js[kk fcUnq A ls xqtjrh gS ftldk fLFkfr lfn'k ˆ ˆ ˆ3 i j k gS vkSj lfn'k ˆ ˆ ˆ2 i j 2k ds lekUrj gSA

;fn bl js[kk ij ,d fcUnq P bl izdkj gS fd AP = 15 bdkbZ] rks fcUnq P dk fLFkfr lfn'k gS@gSa&

(A) ˆ ˆ ˆ13 i 4 j 9k (B) ˆ ˆ ˆ13 i 4 j 9k (C) ˆ ˆ ˆ7 i 6 j 11k (D) ˆ ˆ ˆ7 i 6 j 11k

13. Rolle's Theorem holds for the function f(x) = x3 + bx2 + cx, 1 x 2 at x =4

3 , then the value of b + c is

Qyu f(x) = x3 + bx2 + cx, 1 x 2 ds fy, x =4

3ij jksy izes; lR;kfir gksrh gS rks b + c dk eku gS&

(A) 2 (B) 3 (C) 4 (D) 5

14. Let f(x) be a polynomial in x. Then the second derivative of f(e x) w.r.t. x is

;fn f(x), x esa ,d cgqin gS rc f(ex) dk x ds lkis{k f}rh; vodyt gS &

(A) f (ex). e x + f (ex) (B) f (ex). e2 x + f (ex). e2 x

(C) f (ex) e2 x (D) f (ex). e2 x + f (ex). ex


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15. If c is an arbitrary constant then a solution of the differential equationdx

x+

dy

y = 0, is

;fn c LoSPN vpj gS rc vody lehdj.k dx

x+

dy

y = 0 dk gy gS&

(A) xy = c (B) x + y = c (C) log x log y = c (D) x2 + y2 = c

16. The area bounded by parabola y2 = x, straight line y = 4 and y-axis is -

ijoy; y2 = x, ljy js[kk y = 4 vkSj y-v{k ls ifjc) {ks=kQy gS&

(A)16

3(B)

64

3(C) 7 2 (D)

32

3

17. Let ˆ ˆ â i j k

, ˆ ˆ ˆb i – j 2k

and ˆ ˆ ˆc xi (x – 2) j – k

. If the vector c

lies in the plane of a

and

b

, then x is equal to

ekuk ˆ ˆ â i j k

, ˆ ˆ ˆb i – j 2k

vkSj ˆ ˆ ˆc xi (x – 2) j – k

. ;fn lfn'k c

, a rFkk b

ds lery esa fLFkr

gS] rks x cjkcj gS&(A) 0 (B) 1 (C) – 4 (D) – 2


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SECTION – 2 : (Matching list Type)[k.M – 2 : (lqesyu lwph izdkj)

This section contains 3 multiple choice questions. Each question has matching lists. The codes forthe lists have choice (A), (B), (C) and (D) out of which ONLY ONE is correct.bl [k.M esa 3 cgqfodYi iz'u gSA izR;sd iz'u esa lqesyu lwph gSA lwfp;ksa ds fy, dksM ds fodYi (A), (B), (C)

rFkk (D) gS , ftuesa ls flQZ ,d lgh gSA

18. Match List I with List II and select the correct answer using the code given below the lists :lwph I dks lwph II ls lqesfyr dhft, rFkk lwfp;ksa ds uhps fn, x, dksM dk ç;ksx djds lgh mÙkj pqfu;s %List - I /lwph - I List - II/ lwph- II

P. The maximum number of point of 1. 128intersection of 6 straight lines and 4 circles is6 ljy js[kkvksa ,oa 4 o`Ùkksa ds izfrPNsn fcUnqvksa dh vf/kdre la[;k gS&

Q. The number of even factors of 38808 is 2. 7538808 ds le xq.ku[k.Mksa dh la[;k gS&

R. Number of ways of distributing 7 different books to 2 children is 3. 547 fofHkUu iqLrdksa dks 2 cPpksa esa ckaVus djus ds rjhdksa dh la[;k gS&

S. 3 fair dice are thrown. The probability that the sum of the 4. 108numbers appearing is 15 is equal to 5/p, then p =rhu fu"i{kikrh ikls QSads tkrs gSA mu ij vkus okys vadksa dk ;ksxQy15 vkus dh izkf;drk 5/p gks] rks p =

Codes :P Q R S

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


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19. Match List I with List II and select the correct answer using the code given below the lists :lwph I dks lwph II ls lqesfyr dhft, rFkk lwfp;ksa ds uhps fn, x, dksM dk ç;ksx djds lgh mÙkj pqfu;s %List - I /lwph - I List - II/ lwph- II

P. The greatest distance between x2 + y2 – 2x – 2y + 1 = 0, 1. 3x2 + y2 – 10x + 4y + 20 = 0 is 3, then is equal too`Ùkksa x2 + y2 – 2x – 2y + 1 = 0 rFkk x2 + y2 – 10x + 4y + 20 = 0

ds e/; vf/kdre nwjh 3gS] rks =Q. Numerical value of radius of the circle circumscribed about 2. 7

a square of area 200 sq. units is200 oxZ bdkbZ {ks=kQy ds ,d oxZ ds ifjo`Ùk dh f=kT;k dk la[;kRed eku gSa&

R. x2 + y2 + 2xy + 2x + 2y + = 0 does not represent a pair of real 3. 0straight line if is equal tox2 + y2 + 2xy + 2x + 2y + = 0 ,d okLrfod ljy js[kk ;qXe dks iznf'kZrugha djrk gS] ;fn =

S. If a chord of the circle x2 + y2 – 4x – 2y + k = 0 4. 10

is trisected at the points1 1

,3 3

and8 8

,3 3

and

is the length of the chord then2

is equal to

;fn o`Ùk x2 + y2 – 4x – 2y + k = 0 dh thok fcUnqvksa 1 1,

3 3

rFkk 8 8,

3 3

ij lef=kHkkftr gksrh gS rFkk thok dh yEckbZ gS] rks2

cjkcj gS &Codes :

P Q R S(A) 1 4 3 4(B) 2 4 2 1(C) 1 4 1,2,4 2(D) 2 1 1,2,3,4 2


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20. Match List I with List II and select the correct answer using the code given below the lists :

lwph I dks lwph II ls lqesfyr dhft, rFkk lwfp;ksa ds uhps fn, x, dksM dk ç;ksx djds lgh mÙkj pqfu;s %

List - I /lwph - I List - II/ lwph- II

P. If Argz

=2

and Arg(z) =

6

then Arg(z) is 1.

2

3

;fn Argz

=2

vkSj Arg(z) =6

rc Arg(z) gS&

Q. If z z 0 , then Arg(z) – Arg() is 2.12

;fn z z 0 , rc Arg(z) – Arg() gS&

R. If z = 1 + i and Arg() =3

then Arg( z ) is 3.

3

;fn z = 1 + i vkSj Arg() =3

rc Arg( z ) gS&

S. If Arg(–z) =3

and Arg() =

3

then Arg(z100) is 4.

2

;fn Arg(–z) =3

vkSj Arg() =3

rc Arg(z100) gS&

Codes :P Q R S

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

Space for Rough Work / (dPps dk;Z ds fy, LFkku)

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PART - II : PHYSICS

SECTION-1 : (Only One option correct type)

[k.M–1 : (dsoy ,d lgh fodYi çdkj)This section contains 17 multiple choice questions. Each question has four choices (A), (B), (C)

and (D) out of which ONLY ONE is correct.

bl [k.M esa 17 cgqfodYi ç'u gSA çR;sd ç'u esa pkj fodYi (A), (B), (C) vkSj (D) gS] ftuesa ls dsoy ,dlgh gSA

21. Two particles are projected from a point at the same instant with velocities whose horizontal

components and vertical components are (u1, v1) and (u2, v2) respectively such that there is

another common point (other than origin) on their trajectories. The time interval between their

passing through the other common point of their path (other than origin) is :

nks d.k ,d gh fcUnq ls ,d gh le; ij dqN osxksa ls iz{kSfir fd;s tkrs gS] muds {kSfrt rFkk Å/okZ/kj ?kVdØe'k% (u1, v1) rFkk (u2, v2) bl izdkj gS fd muds iFk ij ewy fCkUnq ds vfrfjDr vU; dksbZ mHk;fu"B fcUnq HkhgSA muds iFk ds vU; mHk;fu"B fcUnq (ewy fcUnq ds vfrfjDr) ls muds xqtjus ds e/; le; vUrjky gksxkA

(A) 1 1 2 2

1 2

v u v u2

g u u

(B) 1 2

2 2

1 2

v v2

g u u

(C) 1 2

2 2

1 2

u u2

g v v

(D) 1 2 2 1

1 2

v u v u2

g u u

22. Which of the following dimensional formula is incorrect.

(A) [permittivity of the free space × electric field] = [Mº L–2 T1 A1 ]

(B) [electrical conductivity] = [M–1 L–3 T3 A1]

(C) [viscous force] = [M1 L1 T–2]

(D)Electric field

Magnetic field

= [Mº L1 T–1 ]

fuEu esa ls dkSulk foeh; lw=k xyr gS &(A) [eqDr {ks=k dh oS|qr'khyrk × oS|qr {ks=k] = [Mº L–2 T1 A1 ]

(B) [oS|qr pkydrk] = [M–1 L–3 T3 A1]

(C) [';ku cy] = [M1 L1 T–2]

(D)oS|qr {ks=k

pqEcdh; {ks=k = [Mº L1 T–1 ]


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23. In the diagram shown, a conducting rod is being translated on two perpendicular rails with a

constant velocity V1 i + V2 j . If a uniform magnetic field B is directed perpendicular into the plane

of the paper then find out the motional emf induced in the triangular loop at the instant shown.

iznf'kZr fp=k esa ,d pkyd NM+ nks yEcor~ iVfj;ksa ij fu;r osx V1 i + V2 j ls LFkkukUrfjr xfr djrh gSA;fn ,d leku pqEcdh; {kS=k B dkxt ds ry ds yEcor~ vUnj dh vksj gSA rc f=kHkqtkdkj ywi esa fn[kk;s x;s{k.k ij izsfjr xfrd fo|qr okgd cy Kkr djksA

X X X X X X X X X X X X X X XX X X X X X X X X X X X X X XX X X X X X X X X X X X X X XX X X X X X X X X X X X X X XX X X X X X X X X X X X X X XX X X X X X X X X X X X X X XX X X X X X X X X X X X X X XX X X X X X X X X X X X X X XX X X X X X X X X X X XX X X X X X X X X X X X X X XX X X X X X X X X X X X X X XX X X X X X X X X X X X X X X

(L1,0)

(0,L2)

(A) 1 1 2 2BL V BL V (B) 1 2 2 1BL V BL V (C) 1 2 2 1BL V BL V (D) 1 1 2 2BL V BL V

24. Starting from t = 0, activity of a radioactive sample is A1 at time t1 and A2 at time t2. If is average

life of sample then the number of nuclei decayed in time (t2 – t1) is

t = 0 ls izkjEHk djrs gq,, ,d jsfM;ks/kehZ izfrn'kZ dh lfØ;rk t1 le; ij A1 rFkk t2 le; ij A2 gSA ;fn blizfrn'kZ dh vkSlr vk;q gks rks (t2 – t1) le; esa fo?kfVr gksus okys ukfHkdksa ds la[;k gksxh &

(A) A1 t1 – A2 t2 (B) 1 2(A A )

2

(C) (A1 – A2) (t2 – t1) (D) (A1 – A2) .


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25. A is uniform solid cylinder, B is uniform thin hollow cylinder. Both have same mass and same

radius. C is a uniform plank. A, B and C each have same mass equal to m. Friction is sufficient so

that there is no slipping anywhere. Find the time period of small oscillations of the above system

when the plank is disturbed slightly.

A ,d ,dleku Bksl csyu gS] rFkk B ,d ,dleku iryk [kks[kyk csyu gS] nksuksa dk nzO;eku rFkk f=kT;kleku gSA C ,d ,dleku Iykad gSA A, B rFkk C izR;sd dk nzO;eku leku gS] rFkk m ds cjkcj gSA ?k"kZ.kbruk i;kZIr gS] fd fdlh Hkh txg dksbZ fQlyu ugha gksrh gSA tc r[rs dks FkksM+k lk foLFkkfir fd;k tkrkgSA rc mijksDr fudk; ds vYi nkSyu dk vkorZdky Kkr dhft,A

K

C

A B

(A)8m

215K

(B)15m

28K

(C)4m

27K

(D)7m

4K

26. Two identical uniform large rings each of mass M are connected through a bead of mass m which

can move freely. When bead is released it starts sliding down. The large rings move apart over a

sufficient rough horizontal surface. Whole system is released from rest as shown in figure,

acceleration of the bead at the initial moment is : (Neglect friction between bead and large rings)

(use M = 2m)

M nzO;eku dh nks ,d ,dleku le:i cMh oy; m nzO;eku ds euds ls tqM+h gqbZ gS] tks Lora=krkiwoZd xfrdj ldrs gSA tc eudk NksM+k tkrk gS] rc ;g uhps dh vksj fQlyrk gSA cM+h oy;s i;kZIr [kqjnjh {kSfrtlrg ij ,d nwljs ls nwj xfr dj ldrh gSA vc fudk; dks fojke voLFkk ls fp=k esa fn[kk;s vuqlkj NksM+ktkrk gSA rc izkjfEHkd {k.k ij euds dk Roj.k gksxkA (euds rFkk cM+h oy;ksa ds e/; ?k"kZ.k ux.; gSA)

(M = 2m dk mi;ksx djsaA)

45°

(A)2g

3(B)

g

9(C)

g

4 (D)

g

6


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27. A ray of light traveling along the positive z–axis is reflected twice by plane mirrors :

(i) for the first time, by a mirror whose normal is along – ˆ ˆ( i + k)

(ii) for the second time, by a mirror whose normal is along ˆ ˆ ˆ( i j k) ,

where the symbols have their usual meanings. The final ray is along/kukRed z–v{k ds vuqfn'k lapfjr ,d izdk'k dh fdj.k lery niZ.k }kjk nks ckj ijkofrZr djrh gSA(i) izFke ckj ml niZ.k }kjk ftldk vfHkyEc – ˆ ˆ( i + k) ds vuqfn'k gSA(ii) f}rh; ckj ml niZ.k }kjk ftldk vfHkyEc ˆ ˆ ˆ( i j k) ds vuqfn'k gSAtgk¡ ldsarksa ds vius lkekU; vFkZ gS] vfUre fdj.k fdlds vuqfn'k gksxhA(A) ˆ ˆj k (B) ˆ ˆk + i (C) ˆ ˆ ˆ2j + 2k - i (D) ˆ ˆ ˆ(j + k - 2i)

28. An infinitely long, straight wire carrying current I1 passes through the center of a circular loop ofwire carrying current I2 as shown in figure.The infinite wire is perpendicular to the plane of the loop. Which of the following describes themagnetic force on the loop due to the infinite wire.(A) Force on the loop due to infinite wire is upward, along the axis of the loop.(B) Force on the loop due to infinite wire is downward, along the axis of the loop.(C) Although net force on the loop due to infinite wire is zero, but due to magnetic interaction

between infinite wire and loop, a tensile stress is developed in the loop.(D) There is no magnetic force on the loop due to infinite wire.

x

I1

I2

vuUr yEckbZ ds lh/ks rkj esa I1 /kkjk izokfgr gS ;g rkj I2 /kkjk izokfgr o`Ùkkdj ywi ds dsUnz ls xqtjrk gS tSlkfd fp=k esa iznf'kZr gSAvuUr yEckbZ dk rkj ywi ds ry ds yEcor~ gSA ywi ij lh/ks rkj ds dkj.k vkjksfir pqEcdh; cy ds fy,fuEu esa ls dkSulk fodYi lgh gSA(A) vuUr yEckbZ ds rkj ds dkj.k ywi ij vkjksfir cy] ywi dh v{k ds vuqfn'k Åij dh vksj gSA(B) vuUr yEckbZ ds rkj ds dkj.k ywi ij vkjksfir cy] ywi dh v{k ds vuqfn'k uhps dh vksj gSA(C) vuUr yEckbZ ds rkj ds dkj.k ywi ij vkjksfir cy ;|fi 'kwU; gksxk ijUrq rkj rFkk ywi ds e/; pqEcdh;

vU;ksU; fØ;k ds dkj.k ywi esa ,d ruu izfrcy mRiUu gks tkrk gSA(D) vuUr yEckbZ ds rkj ds dkj.k ywi ij dksbZ pqEcdh; cy vkjksfir ugha gksxk


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29. A string fixed at both the ends of length 2 m, vibrating in its 7th overtone. Equation of the standing

wave is given by y = A sin kx cos (t + /3), All the symbols have their usual meaning. Mass per unit

length of the string is 0.5 gm/cm. Given that A = 1 cm and = 100 rad/sec. After what time starting

from t = 0 sec, energy of vibration is completely potential for the second time. (Use 2 = 10)

2 m yEckbZ dh jLlh nksuksa fljksa ij tM+or~ cU/kh gqbZ gS, ;g 7 osa vf/kLojd esa dEiUu dj jgh gSA blesamRiUu vizxkeh rjax dh lehdj.k y = A sin kx cos (t + /3) }kjk nh tkrh gSA ;gk¡ lHkh izrhdksa ds lkekU;vFkZ gSA jLlh dh bdkbZ yEckbZ dk nzO;eku 0.5 gm/cm gSA fn;k gS A = 1 cm rFkk = 100 rad/secAizkjfEHkd le; t = 0 sec lsd.M+ ds i'pkr~ og le; D;k gksxk tc bldh nkSyu ÅtkZ nwljh ckj lEiw.kZLFkfrt ÅtkZ ds :i esa izkIr gksxh (2 = 10)

(A)1

sec150

(B)1

sec60

(C)9

sec500

(D)7

sec600

30. 32 resistors are connected in a circuit as shown in the figure. The resistance of each resistor are

same and have magnitude of 8 . Find equivalent resistance across AB.

32 izfrjks/k ifjiFk esa fp=kkuqlkj tqM+s gq, gSA izR;sd izfrjks/kd dk izfrjks/k leku gS] rFkk 8 ifjek.k dk gSAAB ds fljksa ij rqY; izfrjks/k Kkr djksA

(A) 3 (B) 4 (C) 8 (D) 12


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31. The density of a solid at normal pressure is . When the solid is subjected to an excess pressure

p, the density changes to ' if the bulk modulus of the solid is K then the ratio '/ is :

lkekU; nkc ij Bksl dk ?kuRo gSA tc Bksl ij p nkc vkf/kD; vkjksfir fd;k tkrk gS rks bldk ?kuRoifjofrZr gksdj ' gks tkrk gSA ;fn Bksl dk vk;ru izR;kLFkrk xq.kkad K gks rks vuqikr'/ gksxk :

(A) 1 +p

K(B) 1 –

p

K(C)

p2

K (D)

p2

K

32. An immersion heater of constant power takes time t1 to raise the temperature of a mass M of a

liquid from a temperature T1 to its normal boiling point T2 . In a further time t2 , a mass m of the

liquid is vaporized. If the specific heat capacity of the liquid is c and heat losses to the atmosphere

and to the containing vessel are ignored, the latent heat of vaporisation is :

,d fu;r 'kfDr dk ghVj M nzO;eku ds nzo dk rki T1 ls blds lkekU; DoFkukad fcUnq T2 rd c<+kus esa t1

le; ysrk gSA t2 le; esa nzo dk m nzO;eku okf"ir gks tkrk gSA ;fn nzo dh fof'k"B Å"ek /kkfjrk c gS] rFkkok;qe.My o ik=k dks Å"ek gkfu ux.; gSA rc ok"iu dh xqIr Å"ek gksxhA

(A) 2 1 2

1

Mc(T T )t

mt

(B) 2 1 2

1

mc(T T )t

MT

(C) 1 2

1

McT T

mt(D) 1

2 1 2

mt

Mc(T T )t

33. Three protons and a positron are held stationary by the means of external forces of proper

magnitude and direction, such that a proton is at each vertex of an equilateral triangle of side a

and positron is lying on the axis of the equilateral triangle, separation between positron and

centroid of equilateral triangle is2

a3

. Mass of positron is negligible in comparison to mass of

proton. Now binding forces are sudden removed, kinetic energy of positron after sufficiently long

time will be :

(A)2

0

e

A (B)

2

0

e

4 a (C)

2

0

3e

4 a (D) Data insufficient

rhu izksVkWu rFkk ,d iksftVªkWu mi;qDr ifjek.k rFkk fn'kk ds ckg~;k cyksa ds }kjk fLFkj voLFkk esa fLFkr gSAizksVkWu a Hkqtk ds leckgq f=kHkqt ds izR;sd 'kh"kZ ij fLFkr gS] rFkk iksftVªkWu leckgq f=kHkqt dh v{k ij fLFkr gSA

iksftVªkWu rFkk leckgq f=kHkqt ds dsUnzd ds e/; nwjh 2a

3 gSA iksftVªkWu dk nzO;eku izksVkWu ds nzO;eku dh

rqyuk esa ux.; gSA vc cU/ku cyksa dks vpkud gVk fn;k tkrk gSA i;kZIr yEcs le; ds ckn iksftVªkWu dhxfrt ÅtkZ gksxhA

(A)2

0

e

A (B)

2

0

e

4 a (C)

2

0

3e

4 a (D) vkdM+s vi;kZIr gSA


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34. A sound source moving with speed 50 m/s along x–axis and observer at rest on y–axis. If the

frequency observed by observer when source crosses the origin is 96 Hz, then the original

frequency of source is N × 10 Hz. Find N : (speed of sound in given medium is 200 m/s)

,d /ofu L=kksr 50 m/s dh pky ls x– v{k ds vuqfn'k xfr'khy gS rFkk izs{kd y–v{k ij fojke voLFkk esa gSA;fn izs{kd }kjk izsf{kr vkofÙk 96 Hz gS, tc L=kksr ewy fcUnq dks ikj djrk gSA rc L=kksr dh ewy vko`fÙkN × 10 Hz gS rks N Kkr djksA (fn;s x;s ek/;e esa /ofu dh pky 200 m/s gSA)

(A) 9 (B) 8 (C) 7 (D) 6

35. Assume all surfaces to be frictionless. The blocks A and B slide on the incline plane as shown

without breaking sliding contact with it. The acceleration of A and B are 5m/s2 and 4m/s2

respectively, find acceleration of block C.

ekfu;sa fd lHkh lrg ?k"kZ.kghu gSA CykWd A rFkk B urry ij] blls lEidZ VwVs fcuk fp=kkuqlkj fQlyrs gSA A

o B ds Roj.k Øe'k% 5m/s2 rFkk 4m/s2 gS] CykWd C dk Roj.k Kkr dhft,A

(A) 3.5 m/s2 (B) 4.5 m/s2 (C) 9m/s2 (D) 1m/s2


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36. Three gases A, B and C are mixed at NTP such that ratio of their volumes is 1 : 2 : 3. A is ideal

linear triatomic gas, B is ideal diatomic gas and C is ideal monatomic gass. Ratio of specific heat

at constant volume to specific heat at constant pressure for a sample of this mixture at NTP is :

rhu xSls A, B rFkk C, NTP ij bl izdkj feyk;h tkrh gS] fd muds vk;ruksa dk vuqikr 1 : 2 : 3 gSA A ,dvkn'kZ jsf[k; f=kijekf.od xSl gS] B vkn'kZ f}ijekf.od rFkk C ,d vkn'kZ ,dijekf.od xSl gSA NTP ij blfeJ.k ds uequs ds fy, fu;r vk;ru ij fof'k"V Å"ek rFkk fu;r nkc ij fof'k"V Å"ek dk vuqikr gksxkA

(A)2

3(B)

5

6(C)

4

5(D)

3

4

37. A uniform heavy plank of length L is resting on two rods of identical length and area of cross

section, made up of different materials. It is observed that to keep the planks horizontal, one rod is

to be at the end of the plank (say rod A) and another rod is to be at separationL

4 from centre of

plank as shown in figure. Now the rods are kept between two rigid walls such that separation

between the walls is equal to the natural length of the rod. Now temperature of both the rods is

gradually increased in same manner, it is observed that thermal stress developed in rod A is

always thrice the thermal stress developed in another rod. Ratio of coefficient of linear expansion

of rod A to coefficient of linear expansion of another rod will be :

L yEckbZ dk ,d ,dleku r[rk fHkUu&fHkUu inkFkksZ ls cuh gqbZ ,dleku yEckbZ rFkk ,d leku vuqizLFk dkVdh nks NM+ks ij fojkekoLFkk ij gSA ;g izSf{kr gksrk gS] fd r[rsa dks {kSfrt j[kus ds fy, ,d NM+ (NM+ A)

r[rs ds ,d fljs ij rFkk vU; NM+ r[rs ds dsUnz esa L

4nwjh ij j[kh gqbZ gSA vc NM+s nks Å/okZ/kj n`<+ nhokjksa

ds e/; bl izdkj j[kh gS] fd nhokjksa ds e/; nwjh NM+ dh ewy yEckbZ ds cjkcj gSA vc nksuksa NM+ks dk rkileku rjhds ls /khjs&/khjs c<+k;k tkrk gSA ;g izSf{kr gksrk gS] fd NM+ A esa mRiUu rkih; izfrcy vU; NM+ esamRiUu rkih; izfrcy dk lnsao rhu xquk gksrk gSA NM+ A ds jsf[k; izlkj xq.kkad dk vU; NM+ ds jsf[k; izlkjxq.kkad ds lkFk vuqikr gksxkA

/2 /4

Rod-A

Rod-A•

(A) 6 (B)2

3(C) 2 (D) 4


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SECTION – 2 : (Matching List Type)[k.M – 2 : (lqesyu lwph çdkj)

This section contains 3 multiple choice questions. Each questions has matching lists. Thecodes for the lists have choices (A), (B), (C) and (D) out of which ONLY ONE is correct.bl [k.M esa 3 cgqfodYi ç'u gSaA çR;sd ç'u esa lqesyu lwph gSA lwfp;ksa ds fy, dksM ds fodYi (A), (B), (C)

vkSj (D) gSa] ftuesa ls dsoy ,d lgh gSA38. In List- an optical system is shown. List- tells about optical events. Match the proper entries from

List- to List- and select the correct answer using the code given below.

List- List-(P) (1) Parallel beam of light which incidents from

medium M-1 emerges out as converging in

medium M-2

(Q) (2) Parallel beam of light which incidents from

medium M-1 at angle i 0 emerges out as

parallel beam in medium M-2, will have lesser

diameter than the diameter of incident beam.

(Assume No TIR)

(R) (3) Parallel beam of light which incidents frommedium M-1 emerges out as diverging inmedium M-2.

(S) (4) Parallel beam of light which incidents frommedium M-1 at angle i 0 emerges out asparallel beam in medium M-2 will have largerdiameter than the diameter of incident beam.(Assume No TIR)

Codes :

P Q R S

(A) 3 4 2 1

(B) 3 2 4 1

(C) 2 4 1 3

(D) 4 3 1 2


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lwph–I esa izdkf'kd fudk; n'kkZ;k x;k gSA lwph-II izdkf'kd ?kVukvksa ds ckjs esa crykrh gSA lwph-II esa nh xbZizosf'k;ksa dks lwph-I esa fn;s x;s dFkuksa ls lqesfyr dhft,] rFkk uhps fn;s x;s dksMks dh lgk;rk ls lgh fodYidk p;u dhft,A

lwph-I lwph-II(P) (1) ek/;e M-1 ls vkifrr izdk'k dk lekUrj iaqt

ek/;e M-2 esa vfHklkfjr iqat ds :i esa ckgjfudyrk gSA

(Q) (2) ek/;e M-1 ls i 0 dks.k ij vkifrr izdk'k dklekUrj iaqt ek/;e M-2 esa lekUrj iqat ds :iesa fuxZr gksrk gS] ftldk O;kl vkifrr iaqt dsO;kl dh rqyuk esa de gksrk gSA (;g ekfu;s fdiw.kZvkUrfjd ijkorZu ugha gksrk gSA)

(R) (3) ek/;e M-1 ls vkifrr izdk'k dk lekUrj iaqtek/;e M-2 esa vilkfjr iqat ds :i esa ckgjfudyrk gSA

(S) (4) ek/;e M-1 ls i 0 dks.k ij vkifrr izdk'k dklekUrj iaqt ek/;e M-2 esa lekUrj iqat ds :iesa fuxZr gksrk gS] ftldk O;kl vkifrr iaqt dsO;kl dh rqyuk esa vf/kd gksrk gSA (;g ekfu;s fdiw.kZvkUrfjd ijkorZu ugha gksrk gSA)

Codes :

P Q R S

(A) 3 4 2 1

(B) 3 2 4 1

(C) 2 4 1 3

(D) 4 3 1 2


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39. In list- a system is shown, 2 numbers x and y are defined for each system. Value of either x or y isgiven in list-. Choose the proper value of either x or y from list- to list- and choose the correctanswer from the code given below :

List- List-(P)

4R

4

R

3R1

A solid sphere of radius R is made up by freezing two liquids one of density3 and another density , core of sphere of radius R1 is made up by liquid ofdensity 3 and rest by another liquid. Sphere is floating in a cylindricalcontainer having liquid of density 4, radius 4R and sufficient height. It is half

submerged. A ratio x is defined as : x =3

31

R

R

Now temperature is raised, neglect expansion due to increase intemperature everywhere, when whole liquid is melt its found that height of

liquid column in container raises by h. A ratio y is defined as : y =R

h

(1) 2

(Q)

2

3

2

h1

h0

h2

A uniform solid cylinder of density 2height h is floating inside 3-liquids asshown. All the three liquids are perfectly immiscible. There are movableseparators between each interface and so they stay at their place. Theseseparators doesn't apply any tangential force on cylinder, pressure variation

doesn't change due to separator. A quantity X is defined as : x = 2

1

2h

h

Now we define a number , such that if we displace the cylinder slightlydown wards and then it further goes down own its own value of is 1, if itscomes back then value of is 2. Similarly we define another number , suchthat if we displace the cylinder slightly upward and then if it further goesupward own its own value of is 3, if its comes back then value of is 4.Another number y is defined as : y =

(2) 5


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(R)

+q

+q

+q

+qR

Four identical charges are fixed on the periphery of a non conducting ring ofradius R as shown. Ring is rotated with constant angular velocity w.r.t. anaxis perpendicular to plane of the ring and passing through the centre of thering. Force acting on any of the charge particle only due to the magnetic

interaction between the charges is F =2 2

0q 1

Here & are pure number. x is defined as x =3

8

y is defined as y =

5

2

(3) 6

(S)

S

A B

C D

37°

53°

We have a spherical bubble of radius R, made up by liquid having surfacetension S. AB and CD are two parallel planes as shown in figure. Net force

of surface tension on part ABCD due to rest of the part isRS

. There is

no common factor in and . x is defined as x =3

14

y is defined as y =

5

(4) 3

Codes :P Q R S

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


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lwph–I esa ,d fudk; n'kkZ;k x;k gSA nks la[;k x rFkk y izR;sd fudk; ds fy, ifjHkkf"kr gSA x ;k y dk ekulwph-II esa fn;k x;k gSA lwph-II esa fn;s x;s x ;k y ds eku dks lwph-I esa nh xbZ la[;k ls lqesfyr dhft,A uhpsfn;s x;s dksMks dh lgk;rk ls lgh fodYi dk p;u dhft,A

lwph- lwph-(P)

4R

4

R

3R1

R f=kT;k dk ,d Bksl xksyk 3 ?kuRo rFkk ?kuRo ds nks nzo dks tekdj cuk;k x;kgSA R1 f=kT;k ds xksys dk ,d [kksy 3 ?kuRo ds nzo }kjk cuk;k x;k gS] rFkk vU;[kksy ?kuRo ds nzo ds }kjk cuk;k x;k gSA xksyk 4R f=kT;k rFkk i;kZIr Å¡pkbZ ds,d csyukdkj ik=k ftlesa 4 ?kuRo dk nzo gS] esa rSj jgk gSA ;g vk/kk Mqck gqvk gSA

vuqikr x fuEu izdkj ifjHkkf"kr gSA x =3

31

R

Rvc rki c<+k;k tkrk gSA rki esa o`f) ds

dkj.k izR;sd txg gksus okys izlkj dks ux.; ekusa tc lEiw.kZ nzo fi?ky tkrk gSA rc;g izkIr gksrk gS] fd ik=k esa nzo LrEHk dh Å¡pkbZ h ls c<+ tkrh gSA vuqikr y fuEUkizdkj ifjHkkf"kr gSA y =

R

h

(1) 2

(Q)

2

3

2

h1

h0

h2

h Å¡pkbZ ,oa 2 ,d leku ?kuROk dk ,d csyu 3-nzoksa esa fp=kkuqlkj rSj jgk gSA lHkh3-nzo iw.kZ :i ls vfeJ.kh; gSA izR;sd nzo xfr dj ldus okys foHkktd }kjkfoHkkftr gS] ftlds dkj.k izR;sd nzo vius LFkku ij fLFkr gSA ;s foHkktd csyu ijvU; dksbZ Li'kZ jsf[k; cy vkjksfir ugha djrk gSA foHkktd ds dkj.k nkc esa dksbZifjorZu ugha gksrk gSA jkf'k X fuEu izdkj ifjHkkf"kr gSA x = 2

1

2h

hvc ge la[;k

dks blizdkj ifjHkkf"kr djrs gS] fd ;fn ge csyu dks uhps dh vksj FkksM+k lk foLFkkfirdjs rFkk fQj ;g Loa; gh vksj uhps dh vksj vk tkrk gSA rc dk eku 1 gSA ;fn;g okil vkrk gSA rc dk eku 2 gSA blh izdkj ge vU; la[;k dks bl izdkjifjHkkf"kr djrs gSA fd ;fn ge csyu dks FkksM+k lk Åij dh vksj foLFkkfir djs] rFkkfQj ;g Loa; gh vksj Åij dh vksj pyk tkrk gSA rc dk eku 3 gSA ;fn ;gokil vkrk gSA rc dk eku 4 gSA vU; la[;k y fuEu izdkj ifjHkkf"kr gSA y =

(2) 5


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(R)

+q

+q

+q

+qR

pkj ,d leku vkos'k R f=kT;k dh vpkyd oy; dh ifjf/k ij fp=kkuqlkj fLFkj gSAoy; blds ry ds yEcor~ rFkk blds dsUnz ls xqtjus okyh v{k ds lkis{k fu;rdks.kh; osx ls ?kw.kZu djrh gSA vkos'kksa ds e/; pqEcdh; vU;ksU; fØ;k ds dkj.k

fdlh Hkh vkosf'kr d.k ij dk;Zjr cy F =2 2

0q 1

gSA

;g¡k rFkk 'kq) la[;k gSA

x dks x =3

8

ds :i esa ifjHkkf"kr djrs gSA

y dks y =5

2

ds :i esa ifjHkkf"kr djrs gSA

(3) 6

(S)

S

A B

C D

37°

53°

R f=kT;k ds xksyh; cqycqys dks S i`"B ruko ds nzo }kjk cuk;k tkrk gSA AB rFkkCD fp=kkuqlkj nks lekUrj ry gSA ABCD Hkkx ij 'ks"k Hkkx ds dkj.k i`"B ruko dk

dqy cy RS

gSA rFkk esa dksbZ leku xq.kkad ugha gSA

x dks x =3

14

ds :i esa ifjHkkf"kr djrs gSaA

y dks y =5

ds :i esa ifjHkkf"kr djrs gSaA

(4) 3

Codes :P Q R S

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


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40. Consider a given series LCR circuit as shown in figure. There are 10 switches. In list- switcheswhich are closed, is given and corresponding value is asked. In list- these values are given.Choose the proper value from list- to list- using the codes given below:

S1 S2 S3 S4

RXL = R XC

S5 S6 S7

S8 S9 S10

E2E1

E1 = E0 sint E2 = E0 sin(t + )List- List-

(P) It is observed that effective current in (1)2

5

the circuit in case if either S8, S6 and S7

or if S5 S6 S9 S10 or if S8, S9 and S10 are closed(Rest open) remains same. Value of is :

(Q) Switch S8, S9 & S10 are closed. Now its (2)2

observed if rest switches are opened orswitches S3, S4 are closed (remaining opened)effective value of current in the circuit is same

value of C4 X

5R

(R) Switch S8, S6, S7 are closed. Now effective (3)2

3

current if S1, S2 closed (Rest opened) is I1 and

if S3S4 closed (Rest Opened) is I2 value of

2

1

2

is

(S) Switch S5, S6, S9 and S10 are closed. Peak (4)8

5

value current if rest are opened is I3 and if

S2, S3 closed (Rest opened) is I4. Value of

2

3

4

is

Consider a given series LCR circuit as shown in figure. There are 10 switches. In list-I switcheswhich are closed, is given and corresponding value is asked. In list-II these values are given.Choose the proper value from list-II to list-I using the codes given below:Codes :

P Q R S(A) 2 4 1 3(B) 2 3 1 4(C) 3 1 2 4(D) 3 4 1 2


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fp=k esa iznf'kZr LCR Js.kh ifjiFk ij fopkj djrs gSA ;gk¡ 10 fLop gS] lwph- esa fn;s x;s fLop cUn gS] rFkkmuds laxr eku iwNs x;s gSA lwph- esa muds eku fn;s x;s gS] lwph- esa fn;s x;s dFkuksa dks dksMksa dh lgk;rkls lwph- esa fn;s x;s muds laxr ekuksa ls lqesfyr dhft,A

S1 S2 S3 S4

RXL = R XC

S5 S6 S7

S8 S9 S10

E2E1

E1 = E0 sint E2 = E0 sin(t + )lwph- lwph-

(P) ;s izSf{kr gksrk gS] fd ;fn fLop (1)2

5

S8, S6 rFkk S7 ;k ;fn S5 S6 S9 S10 ;k S8, S9 rFkk S10 cUn gSA('ks"k fLop [kqys gq, gSA) rc ifjiFk esa izHkkoh /kkjk leku gSA dk eku gksxkA

(Q) fLop S8, S9 rFkk S10 cUn gSA vc ;s izSf{kr gksrk gSA (2)2

fd ;fn 'ks"k fLop [kqys gq, gS] ;k fLop S3, S4 cUn gSA('ks"k [kqys gq, gSA) rc ifjiFk esa /kkjk dk izHkkoh eku leku gSA

C4 X

5R

dk eku gksxkA

(R) fLop S8, S6, S7 cUn gSA vc ;fn fLop (3)2

3

S1, S2 cUn gSA ('ks"k [kqys gq, gSA) rc ifjiFk esa izHkkoh /kkjk I1 rFkk;fn S3, S4 cUn ('ks"k [kqys gq, gSA) gSA rc ifjiFk esa

izHkkoh /kkjk I2 gSA2

1

2

dk eku gksxkA

(S) ;fn fLop S5, S6, S9 rFkk S10 cUn gS] rFkk 'ks"k [kqys gq, gSA (4)8

5

rc ifjiFk esa izHkkoh /kkjk I3 gS] rFkk ;fn S2, S3 cUn gSA

('ks"k [kqys gq, gSA) rc izHkkoh /kkjk I4 gSA2

3

4

dk eku gksxkA

Codes :P Q R S

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

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Space for Rough Work ¼dPps dk;Z ds fy, LFkku½



Toll Free : 1800 200 2244 | 1800 258 5555| CIN: U80302RJ2007PTC024029P1JPT2170515C0-25

PART III : CHEMISTRY

Atomic masses : [H = 1, D = 2, Li = 7, C = 12, N = 14, O = 16, F = 19, Na = 23, Mg = 24, Al = 27, Si = 28,

P = 31, S = 32, Cl = 35.5, K = 39, Ca = 40, Cr = 52, Mn = 55, Fe = 56, Cu = 63.5, Zn = 65, As = 75,

Br = 80, Ag = 108, I = 127, Ba = 137, Hg = 200, Pb = 207]

SECTION – 1 : (Only One option correct Type)[k.M – 1 : (dsoy ,d lgh fodYi çdkj)

This section contains 17 multiple choice questions. Each question has four choices (A), (B), (C)and (D) out of which ONLY ONE is correct.bl [k.M esa 17 cgqfodYi ç'u gSaA çR;sd ç'u esa pkj fodYi (A), (B), (C) vkSj (D) gSa] ftuesa ls dsoy ,d lgh gSA

41. A hydrogen gas electrode is made by dipping platinum wire in a solution of HCl of pH = 10 and by

passing hydrogen gas around the platinum wire at one atm pressure. The oxidation potential of

electrode would be:

,d gkbMªkstu xSl bySDVªksM IySfVue rkj dks gkbMªksDyksfjd vEy ds pH = 10 foy;u esa Mqcksdj o blds pkjksarjQ 1 atm nkc ij gkbMªkstu xSl izokfgr djds cuk;k x;kA bysDVªkWM dk vkWDlhdj.k foHko fuEu esa ls D;kgksxk %(A) 0.59 V (B) 0.118 V (C) 1.18 V (D) 0.059 V

42. Dry air is first passed through a 0.1M KCl in water & then through 6M KCl solution. Which of the

following statements is not true ?

(A) dilute solution will show loss in weight

(B) dilute solution will show gain in weight

(C) change in weight of dilute solution is proportional to its vapour pressure.

(D) concentrated solution will show gain in weight.

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'kq"d ok;q dks igys ty esa 0.1M KCl foy;u ls rFkk fQj 6M KCl foy;u esa izokfgr fd;k x;kA fuEu esa ls

dkSulk dFku lR; ugha gS \

(A) ruq foy;u] Hkkj esa deh n'kkZ;sxkA

(B) ruq foy;u] Hkkj esa o`f) n'kkZ;sxkA

(C) ruq foy;u ds Hkkj esa ifjorZu] blds ok"i nkc ds lekuqikrh gSA

(D) lkUnz foy;u] Hkkj esa o`f) n'kkZ;sxkA

43. Which of the following orders is correct for the size ?

vkdkj ds lanHkZ esa fuEu esa ls dkSuls Øe lgh gSa \

(1) Mg2+ < Na+ < F– < Al

(2) Te2– > I– > Cs+ > Ba2+

(3) Fe3+ < Fe2+ < Fe4+

(4) Mg > Al > Si > P

(A) (1), (2) & (4) (B) (2), (3) & (4) (C) (1), (3) & (5) (D) (1), (2), (3) & (4)

44. In which of following vacant orbital take part in hybridisation?

fuEu esa ls fdlesa fjDr d{kd ladj.k esa Hkkx ysrk gS\

(A) BF3 (B) CH4 (C) B2H6 (D) 3NH

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45. For the following equilibrium reaction

N2O4(g) 2NO2(g)

NO2 is 50% of the total volume at a given temperature. Hence vapour density of the equilibrium

mixture is :

fuEufyf[kr lkE;koLFkk vfHkfØ;k N2O4(g) 2NO2(g) ds fy;s]

fdlh fn, x, rki ij NO2 dk vk;ru] dqy vk;ru dk 50% gSA blizdkj lkE; feJ.k dk ok"i ?kuRo gS&

(A) 34.5 (B) 25 (C) 23 (D) 20

46. A cylindrical container with a movable piston initially holds 1.5 mol of gas at a pressure of 4.0 atm

and a volume of 2.5 L. If the piston is moved at constant temperature to create a volume of 5.0 L,

while simultaneously withdrawing 0.75 moles of gas, what is the final pressure ?

,d xfr'khy fiLVu ;qDr ,d csyukdkj ik=k esa izkjEHk esa] 4.0atm ds nkc rFkk 2.5L vk;ru ij] ,d xSl ds

1.5 eksy mifLFkr gSaA ;fn fiLVu ds pyus ds dkj.k] fu;r rki ij vk;ru 5.0 L gks tkrk gS rFkk lkFk gh

xSl ds 0.75 eksy ckgj fudkys tkrs gSa rc vfUre nkc D;k gksxk ?

(A) 0.50 atm (B) 1.0 atm (C) 2.0 atm (D) 4.0 atm

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47. Consider the following complex : [Cr(NH3)4(NO2)2]

The oxidation number, number of d-electrons of metal ion, number of unpaired d-electrons on the

metal ion and number of isomers are respectively :

fuEu ladqy ij fopkj dhft, : [Cr(NH3)4(NO2)2]

blesa /kkrq vk;u ij vkWDlhdj.k vad] /kkrq vk;u ds d-bysDVªkWuksa dh la[;k] v;qfXer d-bysDVªkWuksa dh la[;krFkk leko;oh;ksa dh la[;k Øe'k% gS &(A) 3, 3, 3, 2 (B) 2, 4, 0, 6 (C) 2, 4, 2, 6 (D) 2, 4, 4, 4

48. Identify the INCORRECT statement

(A) Orbitals of a subshell have same value of ( n + ) but the orbitals having same (n + ) value

may not belong to same subshell.

(B) The orbital having value of = 2 will have 2 orientations in space.

(C) 3p and 3d orbitals have directional character.

(D) Orbits in Bohr’s model are two dimensional in nature.

xyr dFku dks igpkfu;sA

(A) fdlh midks'k esa mifLFkr d{kdksa ds fy,] ( n + ) ds eku leku gksrs gSa] ijUrq d{kd ftlds fy, ( n + )

ds eku leku gS] os leku midks'k ls lEcfU/kr gksa] ;g vko';d ugha gSA

(B) og d{kd ftlds fy;s dk eku 2 gS] ds fy, f=kfoe (space) esa nks izdkj ds vfHkfoU;kl (orientations)

gksxsaA(C) 3p ,oa 3d d{kd fn'kkRed izd`fr (directional character) ds gksrs gSaA(D) cksgj ds ijek.kq izfr:i esa d{kkvksa (Orbits) dh izdfr f}fofe; (two dimensional) gksrh gSA

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49. The following flow diagram represents the manufacturing of sodium carbonate ?

2 NH3 + H2O + CO2 (NH4)2CO3(a)NH4HCO3

(b)

Which of the following option describes the underlined reagents, products and reaction conditions?

Option (a) (b) (.c) (d)

(A) Carbon dioxide NaCl NaHCO3 Heat

(B) Carbon dioxide NaOH (NH4)2CO3 catalyst

(C) Higher tempt. NaOH NaHCO3 Heat

(D) Higher pressure NaCl (NH4)2CO3 Catalyst

fuEu js[kh; vkjs[k] lksfM;e dkcksZusV ds fuekZ.k dks iznf'kZr djrk gS2 NH3 + H2O + CO2 (NH4)2CO3

(a)NH4HCO3(b)

fuEu esa ls dkSulk fodYi] v|ksjs[kkafadr vfHkdeZdksa] mRiknksa rFkk vfHkfØ;k ifjfLFkfr;ksa dk o.kZu djrk gS ?

fodYi (a) (b) (.c) (d)

(A) dkcZuMkbZvkWDlkbM NaCl NaHCO3 Å"ek(B) dkcZuMkbZvkWDlkbM NaOH (NH4)2CO3 mRizsjd(C) mPp rki NaOH NaHCO3 Å"ek(D) mPp nkc NaCl (NH4)2CO3 mRizsjd

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50. One mole of a substance is cooled at the rate of 0.4 kJ/min as shown in the graph at constantpressure.

AB represent cooling of liquid, BC represent conversion of liquid to solid, CD represent cooling ofsolid. The molar entropy of fusion is :fu;r nkc ij] ,d inkFkZ ds ,d eksy dks fuEu n'kkZ;s x;s vkjs[k ds vuqlkj 0.4 kJ/min dh nj ls B.Mk fd;ktkrk gSA

AB, nzo ds B.Ms gksus dks n'kkZrk gSA BC nzo ls Bksl ds ifjorZu dks n'kkZrk gSA CD Bksl ds B.Ms gksus dksn'kkZrk gS] rc xyu (fusion) dh eksyj ,UVªkWih gS&(A) 10 J mole–1 K–1 (B) 20 J mole–1 K–1 (C) 30 J mole–1 K–1 (D) 40 J mole–1 K–1

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51. The correct IUPAC name of following compound is :

fn;s x;s ;kSfxd dk lgh IUPAC uke gS–

(A) 1,3-Dihydroxypropane-1,3-diol (B) 2-formyl-3-Hydroxypropanoic acid

(C) 3-Hydroxy-2-oxopropanoic acid (D) 2,3-Dioxopropane-1,3-diol

(A) 1,3-MkbgkbMªkWDlhizksisu-1,3-MkbvkWy (B) 2-QkWfeZy-3-gkbMªkWDlhizksisukWbd vEy(C) 3-gkbMªkWDlh-2-vkWDlksizksisuksbd vEy (D) 2,3-MkbvkWDlksizksisu-1,3-MkbvkWy

52. Which is correctly matched ?

(A) and are enantiomers.

(B) and are positional isomers.

(C) and are functional isomers.

(D) and are enantiomers.

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fuEu esa dkSulk lgh lqesfyr gS \

(A) rFkk izfrfcEc:ih leko;oh gSaA

(B) rFkk fLFkfr leko;oh gSaA

(C) rFkk fØ;kRed leko;oh gSaA

(D) rFkk izfrfcEc:ih leko;oh gSaA

53. In the direct nitration of aniline by using HNO3/H2SO4 at 288 K, a mixture of products if formed in

which –

(A) p-nitroaniline and o-nitroaniline are major products and m-nitroaniline is not formed

(B) p-nitroanline and m-nitroaniline are major products and o-nitroaniline is minor product

(C) p-nitroaniline and o-nitroaniline are major products and m-nitroaniline is minor product

(D) o-nitroaniline and m-nitroaniline are major products and p-nitroaniline is minor product

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288 K rki ij HNO3/H2SO4 ds mi;ksx ls ,fufyu ds lh/ks ukbVªhdj.k esa ;fn mRiknksa dk feJ.k curk gS rks

bl feJ.k esa gksrs gS&

(A) p-ukbVªks,fufyu o o-ukbVªks,fufyu eq[; mRikn curk gS o m-ukbVªks,fufyu ugha curk gSA

(B) p-ukbVªks,fufyu o m-ukbVªks,fufyu eq[; mRikn curk gS o o-ukbVªks,fufyu U;wu mRikn curk gSA

(C) p-ukbVªks,fufyu o o-ukbVªks,fufyu eq[; mRikn curk gS o m-ukbVªks,fufyu U;wu mRikn curk gSA

(D) o-ukbVªks,fufyu o m-ukbVªks,fufyu eq[; mRikn curk gS o p-ukbVªks,fufyu U;wu mRikn curk gSA

54. 4SO2H.dilP 4SO2H.conc

Q ; Identify Q.

42SOHruqP 42SOHlkUnz

Q ; Q dks igpkfu;sA

(A) (B) (C) (D)

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55. Which of the following polymer is biodegradable?fuEu esa ls dkSulk cgqyd tSovi?kVuh; gS \

(A) ( CH2–C=CH–CH2 )n

Cl

(B) ( CH2–CH=CH–CH2–CH2–CH )n

CN

(C) ( O–CH–CH2–C–O–CH–CH2–C )n

CH3 CH2CH3O O

(D) ( N–(CH2)6–N–C–(CH2)4–C )n

H O OH

56. Observe the following reactions & identify reactions that correctly match with their productsfuEu vfHkfØ;k dk voyksdu dfj;s o lgh mRikn ;qDr vfHkfØ;k dh igpku dhft,A

(P)

HO

2SOCl

Cl

(Q)

F

Alcoholic KOH

KOH

,YdksgkWfyd

(R)

Br

Alcoholic KOH

KOH

,YdksgkWfyd

(A) P,Q (B) Q, R (C) P,R (D) P,Q,R

57. The compound X (C7H9N) reacts with benzensulfonyl chloride to give Y (C13H13NO2S) which is

insoluble in alkali. The compound X is :;kSfxd X (C7H9N) csUthulYQksfuy DyksjkbM ds lkFk vfHkfØ;k djds ;kSfxd Y (C13H13NO2S) nsrk gS tks{kkj esa v?kqyu'khy gSA vr% ;kSfxd X gS&

(A)

NH 3CH

(B)

NH2

CH3

(C)CH3

NH2

(D)H C3

NH2

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SECTION – 2 : (Matching list Type)[k.M – 2 : (lqesyu lwph izdkj)

This section contains 3 multiple choice questions. Each question has matching lists. The codes forthe lists have choice (A), (B), (C) and (D) out of which ONLY ONE is correct.bl [k.M esa 3 cgqfodYi iz'u gSA izR;sd iz'u esa lqesyu lwph gSA lwfp;ksa ds fy, dksM ds fodYi (A), (B), (C)

rFkk (D) gS , ftuesa ls flQZ ,d lgh gSA

58. List-I List-II

(P) Solution obtained by mixing (1) Anionic hydrolysis

1 mole CH3COONa & 0.5 mole HCl

(Q) Solution obtained by mixing (2) Buffer solution

1 mole HCOOK & 1 mole HNO3

(R) Solution obtained by mixing (3) Amphiprotic species

1 mole Na2CO3 & 1 mole HCl

(S) Solution obtained by mixing (4) Solution of weak acid

1 mole H2C2O4 & 2 mole of KOH

Code :

(P) (Q) (R) (S)

(A) 1 2 3 4

(B) 2 4 3 1

(C) 3 1 2 4

(D) 4 3 1 2

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lwph–I lwph –II

(P) 1 eksy CH3COONa rFkk 0.5 eksy HCl (1) _.kk;fud tyvi?kVu

dks fefJr djus ls izkIr foy;u

(Q) 1 eksy HCOOK rFkk 1 eksy HNO3 (2) cQj foy;u


(R) 1 eksy Na2CO3 rFkk 1 eksy HCl (3) mHk;izksfVd Lih'kht


(S) 1 eksy H2C2O4 rFkk 2 eksy KOH (4) nqcZy vEy dk foy;u


dksM :

(P) (Q) (R) (S)

(A) 1 2 3 4

(B) 2 4 3 1

(C) 3 1 2 4

(D) 4 3 1 2

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59. List-I List-II

graphs are given for non Area under the curve will

reacting ideal gas. give magnitude of :

lwph–I lwph –II

vfØ;'khy vkn'kZ xSl ds fy, oØ ds vUrxZr {ks=kQy dk ifjek.kvkjs[k fn;s x;s gSaA n'kkZrk gS %

(P)

T

S

(1) qrev

(Q)

S

T

(2) (G)p

(R)

P

V

(3) (G)T

(S)

V

P

(4) Wrev

Code dksM:(P) (Q) (R) (S)

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

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60. Choose the correct option

lgh fodYi dk p;u dhft,A

List-I List-II

lwph-I lwph-II

(P) CH2=CH–CH=O 4NaBH (1) Acetal (,lhVsy)

(Q) C6H5CHO + Ph–NH2H (2) Schiff's base (f'kQZ {kkj)

(R) C6H5COCH3 + (CH3)2NH H (3) Unsaturated alcohol (vlarÌr ,YdksgkWy)

(S) R–CH=O + 2RCH2OH H (4) Enamine (,ukfeu)

Code (dksM+) :

(P) (Q) (R) (S)

(A) 2 4 1 3

(B) 2 3 4 1

(C) 4 2 3 1

(D) 3 2 4 1

IIMMPPOORRTTAANNTT IINNSSTTRRUUCCTTIIOONNSS // eeggÙÙooiiww..kk ZZ ffuunnss ZZ''kkC. Question Paper Format

The question paper consists of three parts

(Mathematics, Physics and Chemistry). Each part

consists of two sections.

14. Section 1 contains 17 multiple choice questions.

Each question has Four choices (A), (B), (C) and (D)

out of which only ONE is correct.

C. iz'u&i=k dk izk:i

bl iz'u&i=k rhu Hkkx ¼xf.kr] HkkSfrd foKku vkSj jlk;u

foKku½ gSA gj Hkkx ds nks [k.M gSaA

14. [kaM 1 esa 17 cgqfodYi iz'u gSaA gj iz'u esa pkj fodYi (A),

(B), (C) vkSj (D) gSa ftuesa ls dsoy ,d lgh gSA

15. Section 2 contains 4 multiple choice questions.

Each questions has matching lists. The codes for the

lists have choices (A), (B), (C) and (D) out of which

ONLY ONE is correct.

15. [kaM 2 esa 4 cgqfodYi iz'u gSaA gj iz'u esa lqesyu lwph gSA

lwfp;ksa ds fy, dksM ds fodYi (A), (B), (C) vkSj (D) gSa ftuesa

ls dsoy ,d lgh gSaA

D. Marking Scheme

16. For each question in Section 1, you will be awarded

3 marks if you darken all the bubble(s) corresponding

to only the correct answer and zero mark if no

bubbles are darkened. In all other cases, minus one

(–1) mark will be awarded.

D. vadu ;kstuk16. [kaM 1 esa gj iz'u esa dsoy lgh mÙkj okys cqycqys (BUBBLES)

dkyk djus ij 3 vad vkSj dksbZ Hkh cqycwyk dkyk ugha djus ij

(0) vad iznku fd, tk;saxsA vU; lHkh fLFkfr;ksa esa _.kkRed ,d

(–1) vad iznku fd;k tk;sxkA

17. For each question in Section 2, you will be awarded

3 marks if you darken the bubble corresponding to

only the correct answer and zero mark if no bubbles

are darkened. No negative marks will be awarded for

incorrect answers in this section.

17. [kaM 2 esa gj iz'u esa dsoy lgh mÙkj okys cqycqys

(BUBBLES) dks dkyk djus ij 3 vad vkSj dksbZ Hkh cqycwyk

dkyk ugha djus ij (0) vad iznku fd, tk;saxsA bl [kaM ds

iz'uksa esa xyr mÙkj nsus ij dksbZ _.kkRed vad ugha fn;s tk;saxsA

PPAAPPEERR--11DDAATTEE :: 1177--0055--22001155 CCOODDEE -- 0

DDAATTEE

Name of the Candidate (ijh{kkFkhZ dk uke) :

I have read all the instructions and shallabide by themeSaus lHkh funsZ'kksa dk i<+ fy;k gS vkSj eSa mudkvo'; ikyu d:¡xk@d:¡xhA

......................................Signature of the Candidate

ijh{kkFkhZ ds gLrk{kj

Roll Number (jksy uEcj) :

I have verified all the information filled bythe candidate.ijh{kkFkhZ }kjk Hkjh xbZ lkjh tkudkjh dks eSusatk¡p fy;k gSA

......................................Signature of the Invigilator

ijh{kd ds gLrk{kj

JJEEEE PPRREEPPAARRAATTOORRYY TTEESSTT--22 ((JJPPTT--22)) ((JJEEEE AADDVVAANNCCEEDD PPAATTTTEERRNN))CCOOUURRSSEE :: VVIIJJEETTAA ((JJPP)),, VVIISSHHWWAAAASS ((JJFF)),, VVIIJJAAYY ((JJRR)) && VVIIVVEEKK ((JJCCCC))

2015_05_18_17_49_33

Documents

ds ipkr

kdksa ds

ds fcunq

ds lr gksus ds

bl iqflrdk ds finys

b ij fn

line x y

rough work dpps dkz