CAREER POINT RS -11- I - 21A2. The answer sheet, a machine readable Optical Mark Recognition (OMR) is provided separately. 3. Do not break the seal of the question-paper booklet before

CAREER POINT, CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: 0744-3040000 Page # 2

Space for rough work

CAREER POINT

TARGET – IIT JEE

CHEMISTRY, MATHEMATICS & PHYSICS Time : 3 : 00 Hrs. MAX MARKS: 240

Name : _____________________________________ Roll No. : __________________________ Date : _____________

INSTRUCTIONS TO CANDIDATE

A. GENERAL : 1. Please read the instructions given for each question carefully and mark the correct answers against the question

numbers on the answer sheet in the respective subjects. 2. The answer sheet, a machine readable Optical Mark Recognition (OMR) is provided separately. 3. Do not break the seal of the question-paper booklet before being instructed to do so by the invigilators.

B. MARKING SCHEME : Each subject in this paper consists of following types of questions:- Section - I 4. Multiple choice questions with only one correct answer. 3 marks will be awarded for each correct answer and –1 mark for

each wrong answer. 5. Multiple choice questions with multiple correct option. 4 marks will be awarded for each correct answer and –1 mark for

each wrong answer. Section - II

6. Column Matching type questions (4 × 5 type). 8 marks will be awarded for the complete correctly matched answer (i.e. +2 marks for each correctly matched row) and no negative marking for wrong answer.

Section - III

7. Numerical response questions. 4 marks will be awarded for each correct answer and –1 mark for each wrong answer in this section. Answers to this Section are to be given in the form of single digit integer type.

C. FILLING THE OMR :

8. Fill your Name, Roll No., Batch, Course and Centre of Examination in the blocks of OMR sheet and darken circle properly. 9. Use only HB pencil or blue/black pen (avoid gel pen) for darking the bubbles. 10. While filling the bubbles please be careful about SECTIONS [i.e. Section-I (include single correct, reason type, multiple

correct answers), Section –II ( column matching type), Section-III (include integer answer type)]

Section –I Section-II Section-III

For example if only 'A' choice is correct then, the correct method for filling the bubbles is

A B C D E

For example if only 'A & C' choices are correct then, the correct method for filling the bublles is

A B C D E

the wrong method for filling the bubble are

The answer of the questions in wrong or any other manner will be treated as wrong.

For example if Correct match for (A) is P; for (B) is R, S; for (C) is Q; for (D) is P, Q, S then the correct method for filling the bubbles is

P Q R S TA BCD

Ensure that all columns are filled. Answers, having blank column will be treated as incorrect. Insert leading zeros (s)

012

3

4

56

7

8

9

012

3

4

56

7

8

9

012

3

4

56

7

8

9

012

3

4

56

7

8

9

'6' should be filled as 0006

012

3

4

56

7

8

9

0 1 2

3

4

5 6

7

8

9

0 1 2

3

4

5 6

7

8

9

0 1 2

3

4

5 6

7

8

9


0 0 0 00 1 2

3

4

5 6

7

8

9

0 1 2

3

4

5 6

7

8

9

012

3

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012

3

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9


CAREER POINT, CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: 0744-3040000, Fax (0744) 3040050 email : [email protected]; Website : www.careerpointgroup.com

SEA

L

4

RS -11- I - 21A



CHEMISTRY

Section - I Questions 1 to 4 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Mark your response in OMR sheet against the question number of that question. + 3 marks will be given for each correct answer and – 1 mark for each wrong answer.

Q.1 A gaseous alkane was exploded with oxygen. The volume required of O2 for complete combustion relative to formation of CO2 formed was in the ratio 7 : 4. The molecular formula of alkane is :

(A) CH4 (B) C2H6 (C) C3H6 (D) C4H10 Q.2 At low pressure the vander waal's equation is

written as (for 1 mole) :

(A) RTPV =

VRTa–1 (B)

RTPV =

aRTV–1

(C) RTPV =

+

VRTa1 (D) None of these

Q.3 The type of overlap in the bridge bond existing in

Al2(CH3)6 is : (A) sp3 – sp3d – sp3 (B) sp3 – sp2 – sp3 (C) sp3 – s – sp3 (D) sp3 – sp3 – sp3

[k.M - I iz'u 1 ls 4 rd cgqfodYih iz'u gSaA izR;sd iz'u ds pkj

fodYi (A), (B), (C) rFkk (D) gSa, ftuesa ls dsoy ,d fodYi

lgh gSA OMR 'khV esa iz'u dh iz'u la[;k ds lek viuk

mÙkj vafdr dhft;sA izR;sd lgh mÙkj ds fy, + 3 vad fn;s

tk;asxs rFkk izR;sd xyr mÙkj ds fy, 1 vad ?kVk;k tk;sxkA

Q.1 ,d xSlh; ,Ydsu dks vkWDlhtu ds lkFk foLQksfVr fd;k tkrk gSA iw.kZ ngu ds fy, vko';d O2 o CO2 ds vk;ru dk vuqikr 7 : 4 gSA ,Ydsu dk v.kqlw=k gS :

(A) CH4 (B) C2H6 (C) C3H6 (D) C4H10

Q.2 fuEu nkc ij] ok.MjokWy lehdj.k (1 eksy ds fy,)

fdl izdkj fy[kh tk ldrh gS :

(A) RTPV =

VRTa–1 (B)

RTPV =

aRTV–1

(C) RTPV =

+

VRTa1 (D) buesa ls dksbZ ugha

Q.3 Al2(CH3)6 esa mifLFkr lsrq cU/k (bridge bond) esa

vfrO;kiu dk izdkj gS : (A) sp3 – sp3d – sp3 (B) sp3 – sp2 – sp3 (C) sp3 – s – sp3 (D) sp3 – sp3 – sp3



Q.4

O

O O

.)leq(

PhMgBr → .)leq(

MgBrCH3 → .)leq(

OH/H 2 →+

Product is :

(A)

O

OH OH

Me Ph

(B)

O

Me – C – C – Ph

O

(C)

OH

Me – C – COOH

Ph

(D)

O

Ph – C – C – O – Me

O

Questions 5 to 9 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which MULTIPLE (ONE OR MORE) is correct. Mark your response in OMR sheet against the question number of that question. + 4 marks will be given for each correct answer and –1 mark for each wrong answer.

Q.5 Photoelectric effect supports quantum nature of light because :

(A) There is minimum frequency below which no photoelectron are emitted

(B) The maximum K.E. of the photoelectrons depends only on the frequency of light and not on its intensity

(C) Even when the metal surface is faintly illuminated the photoelectrons leave the surface immediately

(D) Electric charge of the photoelectron is quantised

Q.4

O

OO

.)leq(

PhMgBr → .)leq(

MgBrCH3 → .)leq(

OH/H 2 →+

mRikn gS :

(A)

O

OHOH

Me Ph

(B)

O

Me – C – C – Ph

O

(C)

OH

Me – C – COOH

Ph

(D)

O

Ph – C – C – O – Me

O

iz'u 5 ls 9 rd cgqfodYih iz'u gaSA izR;sd iz'u ds pkj fodYi (A), (B), (C) rFkk (D) gSa] ftuesa ls ,d ;k ,d ls vf/kd fodYi lgh gaSA OMR 'khV esa iz'u dh iz'u la[;k ds lek vius mÙkj vafdr dhft,A izR;sd lgh mÙkj ds fy, + 4 vad fn;s tk;saxs rFkk izR;sd xyr mÙkj ds fy, 1 vad ?kVk;k tk;sxkA

Q.5 izdk'k fo|qr izHkko] izdk'k dh Dok.Ve izdfr dk leFkZu djrk gS] D;ksafd :

(A) vkofÙk U;wure gksrh gS ftlds uhps dksbZ izdk'k bysDVªkWu mRlftZr ugha gksrk

(B) izdk'k bysDVªkWu dh vf/kdre xfrt ÅtkZ (K.E.) dsoy izdk'k dh vkofÙk ij fuHkZj djrh gS u fd mldh rhozrk ij

(C) tc /kkrq i"B dh /kqa/kyh ped ds ckn Hkh izdk'k bysDVªkWu rqjUr gh i"B dks NksM+ nsrs gSa

(D) izdk'k bysDVªkWu dk fo|qr vkos'k Dok.Vhdr gksrk gS



Q.6 In the following case (s) hybridisation of underlined atom is affected

(A) PCl5 (solid) dissociates in to PCl4+ and PCl6–

(B) LiH reacts with AlH3 forming LiAlH4 (C) NH3 is protonated (D) H3PO2 is heated forming H3PO3

Q.7 Bauxite is purified by (A) Hall's process (B) Baeyers's process (C) Serpeck's process (D) Bett's process

Q.8 Which of the following reaction (s) follow the same pattern of energy graph for the formation of major product only

P.E.

Reaction progress

(A)

OH

∆→

⊕H (B)

OH

∆→

⊕H

(C)

OH

∆→

⊕H

(D) CH3

∆→

⊕HCH – CH – CH2 – OH CH3

Q.6 fdl fLFkfr esa] js[kkafdr ijek.kq dk ladj.k izHkkfor gksrk gS (A) PCl5 (Bksl) PCl4

+ o PCl6– esa fo?kfVr gks tkrk gS

(B) LiH, AlH3 ls fØ;k djds LiAlH4 cukrk gS (C) NH3 izksVkWuhdr gksrh gS (D) H3PO2 xeZ gksdj H3PO3 cukrk gS

Q.7 ckWDlkbV fdlds kjk ifj'kksf/kr fd;k tkrk gS : (A) gkWy izØe (B) cs;j izØe (C) ljisd izØe (D) csV izØe

Q.8 fuEu esa ls dkSulh vfHkfØ;k] dsoy eq[; mRikn cukus ds fy, ÅtkZ oØ ds leku izØe dk ikyu djrh gS :

P.E.

vfHkfØ;k dh izxfr

(A)

OH

∆→

⊕H (B)

OH

∆→

⊕H

(C)

OH

∆→

⊕H

(D) CH3

∆→

⊕HCH – CH – CH2 – OH CH3



Q.9 Compound which can not be synthesized by Wurtz reaction using one type of halide only :

(A)

(B)

(C)

(D)

Section - II This section contains 2 questions (Questions 1, 2). Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in Column I have to be matched with statements (P, Q, R, S, T) in Column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example. If the correct matches are A-P, A-S, A-T; B-Q, B-R; C-P, C-Q and D-S, D-T then the correctly bubbled 4 × 5 matrix should be as follows :

A B C D

P Q R S T

T S

P

P P Q R

R R

Q Q

S S T

T

P Q R S T

Q.9 dsoy ,d izdkj ds gsykbM dks iz;qä djds] fuEu esa ls dkSulk ;kSfxd oqVZt vfHkfØ;k kjk la'ysf"kr ugha fd;k tk ldrk :

(A)

(B)

(C)

(D)

[k.M - II bl [k.M esa 2 iz'u (iz'u 1, 2) gSaA izR;sd iz'u esa nks LrEHkksa esa dFku fn;s x;s gSa] ftUgsa lqesfyr djuk gSA LrEHk-I (Column I ) esa fn;s x;s dFkuksa (A, B, C, D) dks LrEHk-II (Column II) esa fn;s x;s dFkuksa (P, Q, R, S,T) ls lqesy djuk gSA bu iz'uksa ds mÙkj uhps fn;s x;s mnkgj.k ds vuqlkj mfpr xksyksa dks dkyk djds n'kkZuk gSA ;fn lgh lqesy A-P, A-S, A-T; B-Q, B-R; C-P, C-Q rFkk D-S, D-T gS, rks lgh fof/k ls dkys fd;s x;s xksyksa dk 4 × 5 eSfVªDl uhps n'kkZ;s vuqlkj gksxk :

ABCD

P Q R S T

T S

P

P P Q R

R R

Q Q

S S T

T

P Q R S T



Mark your response in OMR sheet against the question number of that question in section-II. + 8 marks will be given for complete correct answer (i.e. +2 marks for each correct row) and NO NEGATIVE MARKING for wrong answer.

Q.1 Match column I with column II.

Column -I Column-II (A) Ammonium nitrate (P) Fertilizer (B) Sodium thiosulphate (Q) Purgative (C) Mercurous chloride (R) Antichlor (D) Silver bromide (S) Photography

(T) Explosive

Q.2 Match the column:

Column –I Column-II (A) PCl3 (P) At least one of the

hydrolysis product undergoes tautomerism

(B) SO2Cl2 (Q) Products acid/s having basicity of '2' in

hydrolysis. (C) NCl3 (R) Following purely SN1

mechanism for their hydrolysis

(D) H2SO5 (S) Nucleophillic attack takes place at surrounding atoms in their hydrolysis

(T) Nucleophillic attack takes place at central atom in their hydrolysis

vr% OMR 'khV esa iz'u dh iz'u la[;k ds lek viuk mÙkj [k.M-II esa vafdr dhft;sA izR;sd iw.kZ lgh mÙkj ds fy;s +8 vad fn;s tk;saxs ¼vFkkZr~ izR;sd lgh iafDr feyku ds fy, +2 vad fn, tk,saxs½ o xyr mÙkj ds fy, dksbZ _.kkRed vadu ugha gSA

Q.1 LrEHk-I dk LrEHk-II ls feyku dhft, : LrEHk-I LrEHk-II

(A) veksfu;k ukbVªsV (P) mojZd (B) lksfM;e Fkk;kslYQsV (Q) 'kks/kd (C) edZ;qjl DyksjkbM (R) ,f.VDyksj (D) flYoj czksekbM (S) QksVksxzkQh

(T) foLQksVd Q.2 LrEHk lqesfyr dhft,: LrEHk-I LrEHk-II

(A) PCl3 (P) de ls de ,d ty- vi?kfVr mRikn pyko;ork n'kkZrk gS

(B) SO2Cl2 (Q) ty&vi?kVu] mRikn '2' dh kkjh;rk ;qä gksrk gS.

(C) NCl3 (R) buds ty&vi?kVu ds fy, iw.kZ :i ls SN1 fØ;kfof/k dk ikyu djrk gS

(D) H2SO5 (S) buds ty-vi?kVu esa pkjksa vksj ds ijek.kqvksa ij ukfHkd -Lusgh vkØe.k gksrk gSA

(T) buds ty vi?kVu esa dsUnzh; ijek.kq ij ukfHkd -Lusgh vkØe.k gksrk gS



Section - III This section contains 8 questions (Q.1 to 8). +4 marks will be given for each correct answer and –1 mark for each wrong answer. The answer to each of the questions is a SINGLE-DIGIT INTEGER, ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the OMR have to be darkened. For example, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, then the correct darkening of bubbles will look like the following :

0 1 2

3

4

5 6

7

8

9

0 1 2

3

4

5 6

7

8

9

012

3

4

56

7

8

9

0 1 2

3

4

5 6

7

8

9

X Y Z W

Q.1 An inaccurate ammeter and silver coulometer connected in series in a electric circuit through which a constant direct current flows. If ammeter reads 0.6 amperes throughout one hour, the silver deposited on coulometer was found to be 2.16 g. What % error is in the reading of ammeter. Assume 100% current efficiency. [Ag = 108]

[k.M - III

bl [k.M esa 8 (iz-1 ls 8) iz'u gaSA izR;sd lgh mÙkj ds fy;s +4 vad fn;s tk,saxs rFkk izR;sd xyr mÙkj ds fy, 1 vad ?kVk;k tk,sxkAbl [k.M esa izR;sd iz'u dk mÙkj 0 ls 9 rd bdkbZ ds ,d iw.kk±d gSaA OMR esa iz'u la[;k ds laxr uhps fn;s x;s cqYyksa esa ls lgh mÙkj okys cqYyksa dks dkyk fd;k tkuk gSA mnkgj.k ds fy, ;fn iz'u la[;k ¼ekusa½ X, Y, Z rFkk W ds mÙkj 6, 0, 9 rFkk 2 gkas, rks lgh fof/k ls dkys fd;s x;s cqYys ,sls fn[krs gSa tks fuEufyf[kr gSA

012

3

4

56

7

8

9

012

3

4

56

7

8

9

0 1 2

3

4

5 6

7

8

9

0 1 2

3

4

5 6

7

8

9

X Y Z W

Q.1 ,d =kqfV;qä vehVj o flYoj dqykWEc ehVj fo|qr ifjiFk esa Ja[kyk esa tqM+s gq, gSaA ftlesa lh/kh fLFkj /kkjk izokfgr gksrh gSA ;fn vehVj ,d ?k.Vs esa 0.6,Eih;j i<+rk gks] dqykEc ehVj ij laxzfgr flYoj 2.16 g ik;k tkrk gSA ,ehVj ds ikB;kad esa % =kqfV D;k gSA ekuk /kkjk nkrk 100% gksA [Ag = 108]



Q.2 At 20ºC the osmotic pressure of urea solution is

400 mm. The solution is diluted and the

temperature is raised to 35ºC when the osmotic

pressure is found to be 105.3 mm determine

extent of dilution.

Q.3 A certain buffer solution contains equal

concentration of X– and HX. Kb for X– is 10–10

calculate pH of buffer.

Q.4 How many molecule can show tautomerism

OCH3 COCH3 CCl3

O

C– H

O

CH3 – C – C – C– CH3

CH3

CH3 O

CH3

CH3

O

OHOH

Q.2 20ºC ij] ;wfj;k foy;u dk ijklj.k nkc 400 mm

gSA foy;u dks ruq fd;k tkrk gS rFkk rki 35ºC

rd c<+k fn;k tkrk gS tc ijklj.k nkc 105.3mm

ik;k tkrk gSA ruqrk dh ek=kk Kkr dhft,A

Q.3 ,d fuf'pr cQj foy;u esa X– o HX ds lkUnzrk

cjkcj gSA X– ds fy, Kb = 10–10 gSA cQj dh pH

Kkr dhft,A

Q.4 fdrus v.kq pyko;ork n'kkZ ldrs gSa :

OCH3 COCH3 CCl3

O

C– H

O

CH3 – C – C – C– CH3

CH3

CH3 O

CH3

CH3

OOH

OH



Q.5 How many molecule produce CO2 gas on reactionwith NaHCO3

(a)

OH

, (b)

COOH

,

(c)

SO3H

(d)

OH

NO2

NO2NO2

,

(e) RCOOH, (f)

O H

H R ⊕

(g) CH ≡ CH, (h) HCl,

(i) H2SO4

Q.6 Which hydrogen of the given compound is least

acidic

O H

CH3 H

(2)

(3)

(4) H

H H

Q.7 How many racemic mixture can be formed by

monochlorination of isopentane

Q.5 fdrus v.kq] NaHCO3 ds lkFk fØ;k ij CO2 mRikfnr djrs gSa :

(a)

OH

, (b)

COOH

,

(c)

SO3H

(d)

OH

NO2

NO2NO2

,

(e) RCOOH, (f)

O H

H R ⊕

(g) CH ≡ CH, (h) HCl, (i) H2SO4

Q.6 fuEu fn;s x;s ;kSfxd dk dkSulk gkbMªkstu U;wure vEyh; gS :

OH

CH3 H

(2)

(3)

(4) H

HH

Q.7 fdrus jslsfed feJ.k] vkblksis.Vsu ds

eksuksDyksjhuhdj.k kjk cuk;s tk ldrs gSaA



Q.8 How many compounds give ppt on reaction withI2/NaOH

CH3 – C= O

, C – H

O CH3–CH2OH , CH3 – C – CH3

O

, R – C – OHO

Q.8 fuEu esa ls fdrus ;kSfxd I2/NaOH ds lkFk

vfHkfØ;k ij voksi nsrs gSa :

CH3 – C= O

, C – H

O CH3–CH2OH , CH3 – C – CH3

O

, R – C – OHO



MATHEMATICS


Q.1 Consider the graphs of y = Ax2 and y2 +3 = x2 + 4y, where A is a positive constant and x, y ∈ R Number of points in which the two graphs intersects, is -

(A) exactly 4 (B) exactly 2 (C) at least 2 but the number of points varies for

different values of A (D) zero for at least one positive A

Q.2 If f(x) = (2x – 3π)5 + 3x4 + cos x and g is the

inverse function of f, then g′(2π) is equal to -

(A) 37 (B)

73

(C) 3

430 4 +π (D) 430

34 +π






Q.1 oØ y = Ax2 ,oa y2 +3 = x2 + 4y ds ys[kkfp=k dk voyksdu dhft,] tgk¡ A ,d /kukRed vpj gS ,oa x, y ∈ R rks bu nksuksa ys[kkfp=kksa ds izfrPNsnu fcUnqvksa dh la[;k gS -

(A) Bhd 4 (B) Bhd 2 (C) de ls de 2 ijUrq fcUnqvksa dh la[;k A ds

fofHkuu ekuksa ds laxr ifjofrZr gksrh gS (D) de ls de ,d /kukRed A ds fy, 'kwU;

Q.2 ;fn f(x) = (2x – 3π)5 + 3x4 + cos x ,oa g Qyu

f dk izfrykse Qyu gS] rc g′(2π) dk eku gS -

(A) 37 (B)

73

(C) 3

430 4 +π (D) 430

34 +π



Q.3 If α, β are the roots of x2 – 3x + λ = 0 (λ ∈ R) and α < 1 < β, then the true set of values of λ equals -

(A) λ ∈

49,2 (B) λ ∈

∞−

49,

(C) λ ∈ (2, ∞) (D) λ ∈ (–∞, 2)

Q.4 The number of points P(x, y) lying inside or on the circle x2 + y2 = 9 and satisfying the equation tan4x + cot4x +2 = 4 sin2 y, is -

(A) 2 (B) 4 (C) 8 (D) infinite


Q.5 Which of the following statement(s) is/are correct ?

(A) Let f and g be defined on R and c be any real number. If

cxlim

→f(x) = b and g(x) is

continuous at x = b then cx

lim→

g(f(x)) = g(b).

(B) There exist a function f :[0, 1] → R which is discontinuous at every point in [0, 1] and |f(x)| is continuous at every point in [0, 1].

Q.3 ;fn α, β lehdj.k x2 – 3x + λ = 0 (λ ∈ R) ds ewy

gksa ,oa α < 1 < β rc λ ds ekuksa dk lgh leqPp; gS -

(A) λ ∈

49,2 (B) λ ∈

∞−

49,

(C) λ ∈ (2, ∞) (D) λ ∈ (–∞, 2) Q.4 oÙk x2 + y2 = 9 ij fLFkr ;k oÙk ds vUnj fLFkr mu

fcUnqvksa P(x, y) dh la[;k tks lehdj.k tan4x + cot4x +2 = 4 sin2 y dks larq"V djrs gSa] gksxh -

(A) 2 (B) 4 (C) 8 (D) vuUr

iz'u 5 ls 9 rd cgqfodYih iz'u gaSA izR;sd iz'u ds pkj fodYi (A), (B), (C) rFkk (D) gSa] ftuesa ls ,d ;k ,d ls vf/kd fodYi lgh gaSA OMR 'khV esa iz'u dh iz'u la[;k ds lek vius mÙkj vafdr dhft,A izR;sd lgh mÙkj ds fy, + 4 vad fn;s tk;saxs rFkk izR;sd xyr mÙkj ds fy, 1 vad ?kVk;k tk;sxkA Q.5 fuEu esa ls dkSulk dFku lgh gS ?

(A) ekuk fd f o g Qyu R esa ifjHkkf"kr gSa ,oa c dksbZ

okLrfod la[;k gSA ;fn cx

lim→

f(x) = b ,oa g(x);

x = b ij lrr~ Qyu gS] rc cx

lim→

g(f(x)) = g(b)

(B) Qyu f :[0, 1] → R tks fd [0, 1] esa izR;sd fcUnq

ij vlrr gS ,oa [0, 1] esa izR;sd fcUnq ij |f(x)|

lrr~ gS



(C) If f(x) and g(x) are two continuous function defined from R → R such that f(r) = g(r) for all rational number "r" then f(x) = g(x) ∀ x ∈ R

(D) If f(a) and f (b) possesses opposite signs then there must exist atleast one solution of the equation f(x) = 0 in (a, b) provided f is continuous in [a, b].

Q.6 Which of the following hold(s) good for the function f(x) = 2x – 3x2/3 ?

(I) The function has an extremum point at x = 0. (II) The function has a critical number at x = 1. (III) The graph is concave down at every point in

(–∞, ∞). (A) Statement (I) (B) Statement (II) (C) Statement (III) (D) All statement (I), (II) and (III) are true Q.7 Which of the following pairs of function does not

have same graph ?

(A) f(x) =|ecxcos||xsec||ecxcos||xsec| + ; g(x) = |sin x| + |cosx|

(B) f(x) = ∞→n

lim 1x1x

n2

n2

+− ; g(x) = sgn (1 – |x|)

(C) f(x) = sec–1 x ; g(x) = )x(secn 1e

−l

(D) f(x) =xtan1

xsin2+

+xcot1

xcos2+

; g(x) = sin 2x

(C) ;fn f(x) o g(x) nks lrr~ Qyu R → R esa ifjHkkf"kr gksa ,oa f(r) = g(r) lHkh ifjes; la[;k "r" ds fy;s gks] rc f(x) = g(x) ∀ x ∈ R

(D) ;fn f(a) o f (b) ds fpUg foijhr gks] rc lehdj.k

f(x) = 0 esa de ls de ,d gy fo|eku gksxk ;fn

(a, b) lrr~ Qyu [a, b] esa gks

Q.6 fuEu esa ls dkSulk dFku Qyu f(x) = 2x – 3x2/3 ds fy, lgh gS ?

(I) Qyu x = 0 ij pje fcUnq j[krk gS (II) Qyu x = 1 ij Økafrd fcUnq j[krk gS (III) vUrjky (–∞, ∞) esa izR;sd fcUnq ij Qyu dh

xzkQ vory uhps dh rjQ gS (A) dFku (I) (B) dFku (II) (C) dFku (III) (D) lHkh dFku (I), (II) o (III) lgh gSa

Q.7 fuEu esa ls dkSuls Qyuksa ds ;qXe ds xzkQ leku ugha gS ?

(A) f(x) =|ecxcos||xsec||ecxcos||xsec| + ; g(x) = |sin x| + |cosx|

(B) f(x) = ∞→n

lim 1x1x

n2

n2

+− ; g(x) = sgn (1 – |x|)

(C) f(x) = sec–1 x ; g(x) = )x(secn 1e

−l

(D) f(x) =xtan1

xsin2+

+xcot1

xcos2+

; g(x) = sin 2x



Q.8 Which of the following sets can be the subset of the general solution of the equation

1 + cos 3x = 2 cos 2x ?

(A) nπ + 3π (B) nπ +

6π

(C) nπ – 6π (D) 2nπ where n ∈ I

Q.9 If 100C50 can be prime factorised as 2α 3β . 5γ . 7δ …. where α, β, γ, δ, …. are non negative integers, then correct relation is/are -

(A) α < β (B) γ < δ (C) α + δ = β + γ – 1 (D) γ + δ = 0


A B C D

P Q R S T

T S

P

P P Q R

R R

Q Q

S S T

T

P Q R S T

Q.8 lehdj.k 1 + cos 3x = 2 cos 2x ds O;kid gy dk mileqPp; dkSulk gS ?

(A) nπ + 3π (B) nπ +

6π

(C) nπ – 6π (D) 2nπ tgk¡ n ∈ I

Q.9 ;fn 100C50 ds vHkkT; xq.ku[k.M 2α 3β . 5γ . 7δ …. gSa]

tgk¡ α, β, γ, δ, …. v_.kkRed iw.kk±d gS] rks lgh dFku gS -

(A) α < β (B) γ < δ (C) α + δ = β + γ – 1 (D) γ + δ = 0


ABCD

P Q R S T

T S

P

P P Q R

R R

Q Q

S S T

T

P Q R S T



Mark your response in OMR sheet against the question number of that question in section-II. + 8 marks will be given for complete correct answer (i.e. +2 marks for each correct row) and NO NEGATIVE MARKING for wrong answer.

Q.1 Match the column :

Column -I Column-II (A) If the equation x3 + ax2 + bx + 216

= 0 has three real roots in G.P.,

then ab has the value equal to

(P) 2

(B) If x, y ∈ R, satisfying the

equation 4

)4x( 2− + 9y2

= 1

then the difference between the largest and smallest value of

the expression 4

x2 +

9y2

, is

(Q) 4

(C)

+→0xlim

+

+

xx

x1

x11 is equal

to

(R) 6

(D) If y = y(x) and it follows the relation 4xexy = y + 5 sin2x, then y′(0) is equal to

(S) 8 (T) 10


Q.1 LrEHk lqesfyr dhft,: LrEHk-I LrEHk-II

(A) ;fn lehdj.k x3 + ax2 + bx + 216 =

0 ds rhu okLrfod ewy xq-Js- esa gksa]

rc ab dk eku gS

(P) 2

(B) ;fn x, y ∈ R, lehdj.k

4

)4x( 2− +9y2

= 1 dks larq"V djrk gS]

rc O;atd 4

x2 +

9y2

ds egÙke eku

o U;wure eku ds vUrj dk eku gS

(Q) 4

(C)

+→0xlim

+

+

xx

x1

x11 cjkcj gS

(R) 6

(D) ;fn y = y(x) ,oa lcU/k 4xexy = y +

5 sin2x gks] rc y′(0) dk eku gS

(S) 8 (T) 10



Q.2 Let f(α) = sin–1 (cos α) – cos–1 (sin α) + tan–1 (cot α) – cot–1 (tan α) + sec–1 (cosec α) – cosec–1 (sec α)

Column –I Column-II

(A) If α ∈

π−

π−2

, then f(α) = (P) 0

(B) If α ∈

π− 0,

2 then f(α) =

(Q) – π

(C) If α ∈

π

2,0 then f(α) =

(R) 2α

(D) If α ∈

π

π ,2

then f(α) = (S) –2α (T) 2π – 2α

Section - III

This section contains 8 questions (Q.1 to 8). +4 marks will be given for each correct answer and –1 mark for each wrong answer. The answer to each of the questions is a SINGLE-DIGIT INTEGER, ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the OMR have to be darkened. For example, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, then the correct darkening of bubbles will look like the following :

Q.2 ekuk fd f(α) = sin–1 (cos α) – cos–1 (sin α)

+ tan–1 (cot α) – cot–1 (tan α) + sec–1 (cosec α) – cosec–1 (sec α) LrEHk-I LrEHk-II

(A) ;fn α ∈

π−

π−2

, rc f(α) = (P) 0

(B) ;fn α ∈

π− 0,

2 rc f(α) =

(Q) – π

(C) ;fn α ∈

π

2,0 rc f(α) =

(R) 2α

(D) ;fn α ∈

π

π ,2

rc f(α) = (S) –2α (T) 2π – 2α

[k.M - III

bl [k.M esa 8 (iz-1 ls 8) iz'u gaSA izR;sd lgh mÙkj ds fy;s

+4 vad fn;s tk,saxs rFkk izR;sd xyr mÙkj ds fy, 1 vad

?kVk;k tk,sxkAbl [k.M esa izR;sd iz'u dk mÙkj 0 ls 9 rd

bdkbZ ds ,d iw.kk±d gSaA OMR esa iz'u la[;k ds laxr uhps

fn;s x;s cqYyksa esa ls lgh mÙkj okys cqYyksa dks dkyk fd;k

tkuk gSA mnkgj.k ds fy, ;fn iz'u la[;k ¼ekusa½ X, Y, Z

rFkk W ds mÙkj 6, 0, 9 rFkk 2 gkas, rks lgh fof/k ls dkys

fd;s x;s cqYys ,sls fn[krs gSa tks fuEufyf[kr gSA



0 1 2

3

4

5 6

7

8

9

0 1 2

3

4

5 6

7

8

9

012

3

4

56

7

8

9

0 1 2

3

4

5 6

7

8

9

X Y Z W

Q.1 Let the straight line L : tan(cot–1 2) x – y = 4 be rotated through an angle cot–1 3 about the point M (0, –4) in anticlockwise sense. After rotation the line become tangent to the circle which lies in 4th quadrant and also touches coordinate axes. Find the sum of radii of all possible circles..

Q.2 Nine tiles are numbered 1, 2, 3, 4, 5, 6, 7, 8, 9

respectively. Each of the three players A, B and C randomly selects 3 tiles and they sum up those three values as marked on the tiles. The probability that all three players obtain an odd

sum is nm , where m and n are relatively prime

positive integers. Compute the value of 17

)nm( + .

012

3

4

56

7

8

9

012

3

4

56

7

8

9

0 1 2

3

4

5 6

7

8

9

0 1 2

3

4

5 6

7

8

9

X Y Z W

Q.1 ;fn ljy js[kk L : tan(cot–1 2) x – y = 4 dks dks.k cot–1 3 ls fcUnq M (0, –4) ds lkisk okekorZ fn'kk esa ?kqek;k tkrk gSA ?kw.kZu ds i'pkr~ js[kk prqFkZ ikn esa fLFkr ,d oÙk dh Li'kZ js[kk cu tkrh gS ,oa funZs'kh vkksa dks Li'kZ djrh gSA rks lHkh laHkkfor oÙkksa dh f=kT;kvksa dk ;ksx Kkr dhft,A

Q.2 uks VkbYl ij la[;k,sa 1, 2, 3, 4, 5, 6, 7, 8, 9 Øe'k%

vafdr gSA izR;sd rhu f[kykM+h A, B o C ;knPN;k 3VkbYl dk p;u djrs gSa ,oa bu rhuksa la[;kvksa ds ekuksa dk ;ksx djrs gSaA rks lHkh rhuksa f[kykfM+;ksa ds

ekuksa dk ;ksx fo"ke vkus dh izkf;drk nm

gS] tgk¡ m o

n vHkkT; /kukRed iw.kk±d gSA rks 17

)nm( + dk eku

Kkr dhft,A



Q.3 If the coordinates of the point where the linex – 2y + z – 1 = 0 = x + 2y – 2z – 5 intersects theplane x + y – 2z = 7 is (α, β, γ), then find the valueof (|α| + |β| + |γ|).

Q.4 Suppose a parabola y = x2 – ax – 1 intersects the

coordinate axes at three points A, B and Crespectively. The circumcircle of ∆ABC intersectsthe y-axis again at the point D(0, t). Find the valueof t.

Q.5 Let |z| = 2 and ω = 1z1z

−+ where z , ω ∈ C (where

C is the set of complex numbers). If M and mrespectively be the greatest and least modulus of

ω, then find the value of 5

)Mm(3 + .

Q.6 Let S be the set which contains all possible valuesof l, m, n, p, q, r for which

A =

−

−

−

15n0r

q8m0

0p3

2

2

2l

be a non singular

idempotent matrix. If the absolute value of sum ofthe products of elements of the set S taken two at a

time is λ. Find 295λ .

Q.3 ;fn js[kk x – 2y + z – 1 = 0 = x + 2y – 2z – 5

lery x + y – 2z = 7 dks fcUnq (α, β, γ) ij izfrPNsn

djrh gS] rks (|α| + |β| + |γ|) dk eku Kkr dhft,A

Q.4 ekuk fd ijoy; y = x2 – ax – 1 funZs'kh vkksa dks rhu

fcUnqvksa A, B o C ij Øe'k% dkVrk gS ,oa f=kHkqt

∆ABC dk ifjoÙk y-vk ds iqu% fcUnq D(0, t) ij

dkVrk gS] rks t dk eku Kkr dhft,A

Q.5 ekuk fd |z| = 2 ,oa ω = 1z1z

−+ tgk¡ z , ω ∈ C (tgk¡ C

lfEeJ la[;kvksa dk leqPp; gS) ;fn M o m Øe'k% ω ds egÙke ekikad o U;wure ekikad gksa] rks

5

)Mm(3 + dk eku Kkr dhft,A

Q.6 ekuk fd S og leqPp; gS ftlesa l, m, n, p, q, r ds

lHkh laHkkfor eku fufgr gSa ,oa ftuds fy,

A =

−

−

−

15n0r

q8m0

0p3

2

2

2l

O;qRØe.kh; oxZle

eSfVªDl gS] ;fn leqPp; S ds nks&nks vo;oksa dks ysdj

fd;s x;s xq.kuQy dk ;ksx λ gks] rks 295λ dk eku Kkr

dhft,A



Q.7 A curve is define parametrically by the equationsx = t2 and y = t3. A variable pair of perpendicularlines through the origin 'O' meet the curve at P andQ. If the locus of the point of intersection of thetangents at P and Q is ay2 = bx – 1, then find thevalue of (a + b).

Q.8 If ω is the imaginary cube root of unity, then find

the number of pairs of integers (a, b) such that|aω + b| = 1.

Q.7 ,d oØ ds izkpfyd lehdj.k x = t2 o y = t3 gSA ewy

fcUnq 'O' ls gksdj xqtjus okyh nks yEcor~ pj js[kk,sa]

oØ dks P o Q ij feyrh gSaA ;fn P o Q dh Li'kZ

js[kkvksa ds izfrPNsnu fcUnq dk fcUnqiFk ay2 = bx – 1 gks]

rks (a + b) dk eku Kkr dhft,A

Q.8 ;fn ω bdkbZ dk dkYifud ?kuewy gks] rks iw.kk±dksa

ds ;qXeksa (a, b) dh la[;k Kkr dhft,] tcfd

|aω + b| = 1.



PHYSICS


Q.1 A bird is flying towards north with a velocity 40 km/h and a train is moving with a velocity 40 km/h towards east. What is the velocity of the bird noted by a man in the train ?

(A) 40 2 km/h N-E (B) 40 2 km/h S-E

(C) 40 2 km/h N-W (D) 40 2 km/h S-W Q.2 If coefficient of friction between all surfaces is 0.4

then find the minimum force F to have equilibrium of the system -

F 25 kg 15 kg

(A) 62.5 N (B) 150 N (C) 135 N (D) 50 N






Q.1 ,d ikh 40 km/h ds osx ls mÙkj dh vksj mM+ jgk gS rFkk ,d Vªsu 40 km/h ds osx ls iwoZ dh vksj xfreku gSA Vªsu esa cSBs ,d vkneh kjk izsfkr ikh dk osx D;k gS ?

(A) 40 2 km/h N-E (B) 40 2 km/h S-E

(C) 40 2 km/h N-W (D) 40 2 km/h S-W

Q.2 ;fn lHkh lrgksa ds e/; ?k"kZ.k xq.kkad 0.4 gS rks fudk; dks lkE;koLFkk esa j[kus ds fy;s vko';d U;wure cy F Kkr dhft;s -

F 25 kg 15 kg

(A) 62.5 N (B) 150 N (C) 135 N (D) 50 N



Q.3 fp=k esa 2m nzO;eku dh ,d Hkkjh xsan kSfrt lrg ij

fojke esa gS rFkk m nzO;eku dh gYdh xsan dks Å¡pkbZ

h > 2l ls eqDr fd;k tkrk gSA ml k.k ij] tc Mksjh

rU; gks tkrh gS rks Hkkjh xsan dk Å/oZ osx gksxk -

2m

m l

h > 2l

(A) lg32 (B) lg

34

(C) lg31 (D) lg

21

Q.4 iFoh fp=k esa n'kkZ;s vuqlkj lw;Z ds pkjksa vksj

nh?kZoÙkh; dkk esa xfr djrh gSA vuqikr

OA/OB = x gSA B ij iFoh dh pky dk A ij iFoh

dh pky ds lkFk vuqikr yxHkx gS - B

OSun

iFoh A

(A) x (B) x

(C) xx (D) x2

Q.3 In figure a heavy ball of mass 2m rests on the horizontal surface and the lighter ball of mass m is dropped from a height h > 2l. At the instant the string gets taut the upward velocity of the heavy ball will be -

2m

m l

h > 2l

(A) lg32 (B) lg

34

(C) lg31 (D) lg

21

Q.4 The earth moves around the sun in an elliptical orbit as shown in figure. The ratio OA/OB = x. The ratio of the speed of the earth at B to that at A is nearly -

B

O

Sun

EarthA

(A) x (B) x

(C) xx (D) x2



iz'u 5 ls 9 rd cgqfodYih iz'u gaSA izR;sd iz'u ds pkj fodYi (A), (B), (C) rFkk (D) gSa] ftuesa ls ,d ;k ,d ls vf/kd fodYi lgh gaSA OMR 'khV esa iz'u dh iz'u la[;k ds lek vius mÙkj vafdr dhft,A izR;sd lgh mÙkj ds fy, + 4 vad fn;s tk;saxs rFkk izR;sd xyr mÙkj ds fy, 1 vad ?kVk;k tk;sxkA Q.5 r f=kT;k dh pdrh A o B ij fcuk fQlys yq<+dus ds

fy;s ck/; gSA ;fn IysVsa n'kkZ;s vuqlkj osx j[krh gSa rks -

v0

v

ω

3vA

B

(A) pdrh dk dks.kh; osx 2v/r gS (B) pdrh dk js[kh; osx v0 = v gS (C) pdrh dk dks.kh; osx 3v/2r gS (D) buesa ls dksbZ ugha

Q.6 fuEu fLFkfr ds fy;s] mijksDr esa ls dkSulk (;k dkSuls) lgh gSa -

O B+q

d[kks[kyk mnklhu pkyd

R

(A) pkyd dk foHko

)Rd(4q

0 +∈π gS

(B) pkyd dk foHko d4

q0∈π

gS

(C) pkyd dk foHko Kkr ugha fd;k tk ldrk tc rd izsfjr vkos'k forj.k Kkr u gks

(D) pkyd ij izsfjr vkos'kksa ds dkj.k B ij foHko

d)Rd(4qR

0 +∈π− gS


Q.5 The disc of radius r is confined to roll without slipping at A and B. If the plates have velocity as shown then -

v0

v

ω

3vA

B

(A) Angular velocity of disc is 2v/r (B) Linear velocity of disc is v0 = v (C) Angular velocity of disc is 3v/2r (D) None of these

Q.6 For the following situation which of the following is/are correct -

O B +q

d Hollow neutral conductor

R

(A) Potential of conductor is

)Rd(4q

0 +∈π

(B) Potential of conductor is d4

q0∈π

(C) Potential of conductor cannot be determined as distribution of induced charged is not known

(D) Potential at B due to induced charges on

conductor is d)Rd(4

qR0 +∈π−



Q.7 A single battery is connected to three resistance as shown in figure

E

D

6Ω

H G F

B

A

3Ω 12V

C

7Ω

(A) The current through 7Ω resistance is 4A (B) The current through 3Ω resistance is 4A (C) The current through 6Ω resistance is 2A (D) The current through 7Ω resistance is 0

Q.8 A charged particle is fired at an angle θ to a uniform

magnetic field directed along the x-axis. During its

motion along a helical path, the particle will -

(A) never move parallel to the x-axis

(B) move parallel to the x-axis once during every

rotation for all values of θ

(C) move parallel to the x-axis at least once during

every rotation if θ = 45º

(D) never move perpendicular to the x-direction

Q.7 ,d ,dy cSVjh fp=k esa n'kkZ;s vuqlkj rhu izfrjks/kksa

ls la;ksftr gS rks

E

D

6Ω

H G F

B

A

3Ω 12V

C

7Ω

(A) 7Ω izfrjks/k esa /kkjk 4A gS

(B) 3Ω izfrjks/k es /kkjk 4A gS

(C) 6Ω izfrjks/k esa /kkjk 2A gS

(D) 7Ω izfrjks/k esa /kkjk 0 gS

Q.8 ,d vkosf'kr d.k x-vk dh vksj funsZf'kr ,dleku

pqEcdh; ks=k esa θ dks.k ij izksfir fd;k tkrk gSA ,d

gsfydy iFk ds vuqfn'k bldh xfr ds nkSjku] d.k -

(A) dHkh x-vk ds lekUrj xfr ugha djsxk

(B) θ ds lHkh ekuksa ds fy;s izR;sd ?kw.kZu ds nkSjku

,d ckj x-vk ds lekUrj xfr djsxk

(C) izR;sd ?kw.kZu ds nkSjku de ls de ,d ckj x-

vk ds lekUrj xfr djsxk ;fn θ = 45º gS

(D) dHkh x-fn'kk ds yEcor~ xfr ugha djsxk



Q.9 ,d fizTe ds fy;s fopyu dks.k (δ) dks vkiru dks.k (i) ds lkFk vkjsf[kr fd;k x;k gSA lgh dFku pqfu;s -

65º

60ºi1 60º 70º

i

δ

(A) fizTe dks.k 60º gS (B) fizTe dk viorZukad n = 3 gS (C) 65º fopyu ds fy;s] vkiru dks.k i1 = 45º gS (D) 'δ' dk 'i' ds lkFk oØ ijoy; gS


ABCD

P Q R S T

T S

P

P P Q R

R R

Q Q

S S T

T

P Q R S T

Q.9 The angle of deviation (δ) vs angle of incidence (i) plotted for a prism. Pick up the correct statement -

65º

60ºi1 60º 70º

i

δ

(A) The angle of prism is 60º (B) The refractive index of the prism is n = 3 (C) For deviation to be 65º, the angle of incidence

i1 = 45º (D) The curve of 'δ' vs 'i' is parabolic


A B C D

P Q R S T

T S

P

P P Q R

R R

Q Q

S S T

T

P Q R S T




Q.1 ,d vkn'kZ ,dijek.kqd xSl fofHkUu izØeksa ls xqtjrh

gS tks LrEHk-I esa of.kZr gSA LrEHk –II esa lEcfU/kr izHkkoksa

ls feyku dhft;sA vkj vius lkekU; vFkZ j[krs gSA

LrEHk–I LrEHk-II

(A) P = 2V2 (P) ;fn vk;ru c<+rk gS rks rki

Hkh c<+sxk

(B) PV2 = fu;rkad (Q) ;fn vk;ru c<+rk gS rks rki

?kVrk gS

(C) C = Cv + 2R (R) izlkj ds fy;s xSl dks Å"ek

nsuh iM+sxh

(D) C = Cv – 2R (S) ;fn rki c<+rk gS rks xsl kjk

fd;k x;k dk;Z /kukRed gS

(T) dksbZ ugha

Mark your response in OMR sheet against the question number of that question in section-II. + 8 marks will be given for complete correct answer (i.e. +2 marks for each correct row) and NO NEGATIVE MARKING for wrong answer. Q.1 An ideal monoatomic gas undergoes different

types of process which are described in column-I. Match the corresponding effects in column-II. The letters have their usual meanings.

Column –I Column-II

(A) P = 2V2 (P) If volume increases then temperature will also increase

(B) PV2 = constant (Q) If volume increases then

temperature decreases

(C) C = Cv + 2R (R) For expansion heat will have

to be supplied to the gas

(D) C = Cv – 2R (S) If temperature increases then

work done by gas is positive

(T) None



Q.2 ;kaf=kd rjax dh fLFkfr esa ,d d.k dEiu djrk gS rFkk dEiu ds nkSjku bldh xfrt ÅtkZ rFkk fLFkfr ÅtkZ ifjofrZr gksrh gSA

LrEHk-I LrEHk-II

(A) tc izxkeh rjax dk d.k ek/; fLFkfr ls xqtj jgk gS

(P) xfrt ÅtkZ vf/kdre gS

(B) tc izxkeh rjax dk d.k mPpre fLFkfr ij gS

(Q) fLFkfrt ÅtkZ vf/kdre gS

(C) tc vizxkeh rjax esa fuLiUn rFkk izLian ds e/; d.k ek/; fLFkfr ls xqtj jgk gS

(R) xfrt ÅtkZ U;wure gS

(D) tc vizxkeh rjax esa fuLiUn rFkk izLiUn ds e/; d.k mPpre fLFkfr ij gS

(S) fLFkfrt ÅtkZ U;wure gS

(T) dksbZ ugha

Q.2 In case of mechanical wave a particle oscillates and during oscillation its kinetic energy and potential energy changes.

Column -I Column-II

(A) When particle of travelling wave is passing through mean position

(P) Kinetic energy is maximum

(B) When particle of travelling wave is at extreme position

(Q) Potential energy is maximum

(C) When particle between node and antinode in standing wave is passing through mean position

(R) Kinetic energy is minimum

(D) When particle between node and antinode in standing wave is at extreme position

(S) Potential energy is minimum

(T) None



Section - III

This section contains 8 questions (Q.1 to 8).

+4 marks will be given for each correct answer and –

1 mark for each wrong answer. The answer to each of

the questions is a SINGLE-DIGIT INTEGER,

ranging from 0 to 9. The appropriate bubbles below

the respective question numbers in the OMR have to

be darkened. For example, if the correct answers to

question numbers X, Y, Z and W (say) are 6, 0, 9 and

2, respectively, then the correct darkening of bubbles

will look like the following :

0 1 2

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5 6

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8

9

0 1 2

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5 6

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9

012

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0 1 2

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X Y Z W

[k.M - III

bl [k.M esa 8 (iz-1 ls 8) iz'u gaSA izR;sd lgh mÙkj ds fy;s

+4 vad fn;s tk,saxs rFkk izR;sd xyr mÙkj ds fy, 1 vad

?kVk;k tk,sxkAbl [k.M esa izR;sd iz'u dk mÙkj 0 ls 9 rd

bdkbZ ds ,d iw.kk±d gSaA OMR esa iz'u la[;k ds laxr uhps

fn;s x;s cqYyksa esa ls lgh mÙkj okys cqYyksa dks dkyk fd;k

tkuk gSA mnkgj.k ds fy, ;fn iz'u la[;k ¼ekusa½ X, Y, Z

rFkk W ds mÙkj 6, 0, 9 rFkk 2 gkas, rks lgh fof/k ls dkys fd;s

x;s cqYys ,sls fn[krs gSa tks fuEufyf[kr gSA

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X Y Z W



Q.1 In a certain hypothetical radioactive decay process, species A decays into species B and species B decays into species C according to the reactions

A → 2B + particles + energy B → 2C + particles + energy The decay constant for species A is λ1 = 1s–1 and

that for species B is λ2 = 100 s–1. Initially 104 moles of species of A were present while there was none of B and C. It was found that species B reaches its maximum number at a time t0 = 2 ln (10)s. Calculate the value of maximum number of moles of B.

Q.2 Radiation from hydrogen gas excited to first

excited state is used for illuminating certain photoelectric plate. When the radiation from some unknown hydrogen-like gas excited to the same level is used to expose the same plate, it is found that the de-Broglie wavelength of the fastest photoelectron has decreased 2.3 times. It is given that the energy corresponding to the longest wavelength of the Lyman series of the unknown gas is 3 times the ionization energy of the hydrogen gas (13.6 eV). Find the work function of photoelectric plate in eV. [Take (2.3)2 = 5.25]

Q.1 ,d fuf'pr ifjdfYir jsfM;kslfØ; k; izfØ;k esa] izfrn'kZ A izfrn'kZ B esa kf;r gksrk gS rFkk izfrn'kZ B izfrn'kZ C esa fuEu vfHkfØ;k ds vuqlkj kf;r gksrk gSA

A → 2B + d.k + ÅtkZ B → 2C + d.k + ÅtkZ izfrn'kZ A ds fy;s k; fu;rkad λ1 = 1s–1 gS rFkk

izfrn'kZ B ds fy;s λ2 = 100 s–1 gSA izkjEHk esa A ds izfrn'kZ ds 104 eksy mifLFkr Fks tcfd B o C dk dksbZ eksy ugha FkkA ;g ik;k x;k fd izfrn'kZ B ,d le; t0 = 2 ln (10)s ij bldh vf/kdre la[;k ij igq¡p tkrk gSA B ds eksyksa dh vf/kdre la[;k dk eku ifjdfyr dhft;sA

Q.2 gkbMªkstu xSl ds izFke mÙksftr voLFkk esa mÙksftr gksus

ls mRlftZr fofdj.k fuf'pr QksVksxzkfQd IysV dks iznhIr djus ds iz;ksx esa vkrh gSA tc leku Lrj esa mÙksftr gkbMªkstu-ln'k fdlh vKkr xSl ls mRlftZr fofdj.k leku IysV dks izfnIr djus ds dke vkrh gSA ;g ik;k tkrk gS fd rhozre izdk'k bysDVªkWuksa dh Mh-czksXyh rjaxnS/;Z 2.3 xquk de gks xbZ gSaA ;g fn;k x;k gS fd vKkr xSl dh ykbesu Js.kh dh nh?kZre rjaxnS/;Z ls lEcfU/kr ÅtkZ gkbMªkstu xSl dh vk;uu ÅtkZ (13.6 eV) dh 3 xquk gSA izdk'k fo|qr IysV dk dk;ZQyu eV esa Kkr dhft;sA [fyft;s (2.3)2 = 5.25]



Q.3 Determine the de-Broglie wavelength of a proton in 10–14 m, whose kinetic energy is equal to the rest mass energy of an electron. Given that the mass of an electron is 9.1 × 10–31 kg and the mass of a proton is 1837 times as that of the electron.

Q.4 A ray of light strikes a plane mirror at an angle

of incidence 45º as shown in figure. After reflection the ray passes through a prism of refractive index 1.5 whose apex angle is 4º. Through what angle must the mirror be rotated if the total deviation of the ray be 90º ? (Ans. in degrees)

Prism

4º

Q.5 In YDSE find the thickness of a glass slab

in µm (µ = 1.5) which should be placed before the upper slit SI so that the central maximum now lies at a point where 5th bright fringe was lying earliest (before inserting the slab). Wavelength of light used is 5000 Å.

Q.3 ,d izksVkWu dh nh-czksXyh rjaxnS/;Z 10–14 m esa Kkr

dhft;s] ftldh xfrt ÅtkZ bysDVªkWu dh fojke

nzO;eku ÅtkZ ds cjkcj gksrh gSA fn;k x;k gS fd

bysDVªkWu dk nzO;eku 9.1 × 10–31 kg gSa rFkk ,d

izksVkWu dk nzO;eku bysDVªkWu ds nzO;eku dk 1837 xquk gksrk gSA

Q.4 ,d izdk'k fdj.k fp=k esa n'kkZ;s vuqlkj 45º ds

vkiru dks.k ij ,d lery niZ.k ij Vdjkrh gSA

ijkorZu ds i'pkr~ fdj.k viorZukad 1.5 ds ,d

fizTe ls xqtjrh gS ftldk 'kh"kZ dks.k 4º gSA niZ.k dks fdl dks.k ls ?kqek;k tkuk pkfg;s ;fn fdj.k

dk dqy fopyu 90º gks ? (mÙkj fMxzh esa)

fizTe 4º

Q.5 YDSE esa ,d dk¡p dh ifV~Vdk dh eksVkbZ µm esa

(µ = 1.5) Kkr dhft;s tks Åijh fLyV S1 ds lkeus j[kh

tkuh pkfg;s rkfd vc dsUnzh; mfPp"B ml fcUnq ij cus

tgk¡ lcls igys 5oha pedhyh fÝUt cuh Fkh (ifêdk

j[kus ls igys)A iz;qDr izdk'k dh rjxanS/;Z 5000 Å

gSA



Q.6 In figure, ABCEFGA is a square conducting frame of side 2m and resistance 1 Ω/m. A uniform magnetic field B is applied perpendicular to the plane and pointing inwards. It increases with time at a constant rate of 10 T/s. Find the rate (in 102 W) at which heat is produced in the circuit, AB = BC = CD = BH.

H

D E

F B

C

A G Q.7 Find the magnitude of potential difference in

volts between the plates of the capacitor C in the circuit shown in figure. The internal resistance of sources can be neglected.

1V

4V

A B 30Ω

20Ω 10Ω

C

Q.6 fp=k esa ABCEFGA Hkqtk 2m rFkk izfrjks/k 1 Ω/m dk ,d oxkZdkj pkyd Ýse gSA ,d ,dleku pqEcdh; ks=k B ry ds vfHkyEcor~ vkjksfir gS rFkk vUnj dh vksj funsZf'kr gSA ;g 10 T/s dh ,d fu;r nj ij le; ds lkFk c<+rk gSA og nj (102 W esa) Kkr dhft;s ftl ij ifjiFk esa Å"ek mRiUu gksrh gS, AB = BC = CD = BH.

H

D E

F B

C

A G

Q.7 fp=k esa n'kkZ;s x;s ifjiFk esa la/kkfj=k C dh IysVksa ds e/; oksYV esa foHkokUrj dk ifjek.k Kkr dhft;sA L=kksrksa dk vkUrfjd izfrjks/k ux.; ekuk tk ldrk gSA

1V

4V

A B 30Ω

20Ω 10Ω

C



Q.8 A system consists of two identical cubes, each of mass 3 kg, linked together by a compressed weightless spring of force constant 1000 N/m. The cubes are also connected by a thread which is burnt at a certain moment. At what minimum value of initial compression x0 (in cm) of the spring will the lower cube bounce up after the thread is burnt through ?

K = 1000N/m

3 kg

3 kg

Q.8 ,d fudk; nks ,d leku ?kuksa dk cuk gS ftuesa ls izR;sd dk nzO;eku 3 kg gS rFkk os 1000 N/m cy fu;rkad okyh ,d Hkkjghu ladqfpr fLizax kjk ,d-nwljs ls tqM+s gSA ?ku ,d /kkxs kjk Hkh tqM+s gq;s gS tks fdlh ,d fuf'pr k.k ij tyk fn;k tkrk gSA fLizax ds fdl izkjfEHkd ladqpu x0 (cm esa) ds U;wure eku ij fupyk ?ku /kkxs ds ty tkus ds i'pkr Åij dh vksj mNysxk ?

K = 1000N/m

3 kg

3 kg



Time : 3 : 00 Hrs. MAX MARKS: 240

INSTRUCTIONS TO CANDIDATE

A. lkekU; : 1. Ñi;k izR;sd iz'u ds fy, fn, x, funsZ'kksa dks lko/kkuhiwoZd if<+;s rFkk lEcfU/kr fo"k;kas esa mÙkj&iqfLrdk ij iz'u

la[;k ds lek lgh mÙkj fpfUgr dhft,A 2. mRrj ds fy,] OMR vyx ls nh tk jgh gSA 3. ifjohkdksa kjk funsZ'k fn;s tkus ls iwoZ iz'u&i=k iqfLrdk dh lhy dks ugha [kksysaA

B. vadu i)fr: bl iz'ui=k esa izR;sd fo"k; esa fuEu izdkj ds iz'u gSa:- [k.M – I 4. cgqfodYih izdkj ds iz'u ftuesa ls dsoy ,d fodYi lgh gSA izR;sd lgh mÙkj ds fy, 3 vad fn;s tk;saxs o izR;sd xyr mÙkj ds

fy, 1 vad ?kVk;k tk,xkA 5. cgqfodYih izdkj ds iz'u ftuesa ls ,d ;k ,d ls vf/kd fodYi lgh gSaA izR;sd lgh mÙkj ds fy, 4 vad fn, tk;saxs rFkk izR;sd

xyr mÙkj ds fy, 1 vad ?kVk;k tk,xkA [k.M - II 6. LrEHkksa dks lqesfyr djus okys iz'u (4 × 5 izdkj) gSaA iw.kZ :Ik ls lgh lqesfyr mÙkj ds fy, 8 vad fn;s tk;saxs ¼vr% lgh lqesfyr

izR;sd iafDr ds fy, +2 vad fn, tk,saxs½ rFkk xyr mÙkj ds fy, dksbZ _.kkRed vadu ugha gSA [k.M – III

7. x.kukRed izdkj ds iz'u gSaA izR;sd lgh mÙkj ds fy, iz'u 4 vad fn, tk,saxs rFkk bl [k.M esa izR;sd xyr mÙkj ds fy, 1 vad ?kVk;k tk;sxkA bl [k.M esa izR;sd iz'u dk mÙkj bdkbZ ds ,d iw.kk±d esa nhft,A

C. OMR dh iwfrZ :

8. OMR 'khV ds CykWdksa esa viuk uke] vuqØek¡d] cSp] dkslZ rFkk ijhkk dk dsUnz Hkjsa rFkk xksyksa dks mi;qDr :i ls dkyk djsaA 9. xksyks dks dkyk djus ds fy, dsoy HB isfUly ;k uhys/dkys isu (tsy isu iz;ksx u djsa) dk iz;ksx djsaA 10. di;k xksyks dks Hkjrs le; [k.Mks dks lko/kkuh iwoZd ns[k ysa [vFkkZr [k.M I (,dy p;ukRed iz'u] dFku izdkj ds iz'u]

cgqp;ukRed iz'u), [k.M –II (LrEHk lqesyu izdkj ds iz'u), [k.M-III (iw.kkZd mÙkj izdkj ds iz'u½]

Section –I Section-II Section-III

For example if only 'A' choice is correct then, the correct method for filling the bubbles is

A B C D E

For example if only 'A & C' choices are correct then, the correct method for filling the bublles is

A B C D E

the wrong method for filling the bubble are

The answer of the questions in wrong or any other manner will be treated as wrong.

For example if Correct match for (A) is P; for (B) is R, S; for (C) is Q; for (D) is P, Q, S then the correct method for filling the bubbles is

P Q R S TA BCD

Ensure that all columns are filled. Answers, having blank column will be treated as incorrect. Insert leading zeros (s)

012

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Documents

CAREER POINT RS -11- I - 21A2. The answer sheet, a machine readable Optical Mark Recognition (OMR) is provided separately. 3. Do not break the seal of the question-paper booklet before