ALL PHASE CHEMISTRY, MATHEMATICS, PHYSICS

TARGET COURSE FOR IIT-JEE 2011

ALL PHASE

TEST-2 (TAKE HOME)

PAPER – II

Name : _________________________________________________________ Roll No. : __________________________

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. 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

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56

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9

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'6' should be filled as 0006

012

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0 1 2

3

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5 6

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8

9

0 1 2

3

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5 6

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0 1 2

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0 0 0 00 1 2

3

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012

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SEA

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4

CHEMISTRY, MATHEMATICS, PHYSICS

Date : 6/02/2011Time : 3 : 00 Hrs. MAX MARKS: 240

Corporate Office: CP Tower, Road No.1, IPIA, Kota (Raj Ph: 0744-3040000 (6 lines) || IIT Target || Page # 1

Space for rough work

Important Data (egRoiw.kZ vk¡dM+s)

Atomic Masses: H = 1, C = 12, K = 39, O = 16, Fe= 56, N= 14, I = 127, Ca = 40, Mg = 24, Al = 27, F = 19, Cl = 35.5, S = 32, (ijek.kq nzO;eku) Na = 23 Constants : R = 8.314 Jk–1mol–1, h = 6.63 × 10–34 Js , C = 3 × 108 m/s, e = 1.6 × 10–19 Cb,me = 9.1 × 10–31Kg,

(fu;rkad) : RH = 1.1 × 107 m–1, log 2 = 0.3010, log 3 = 0.4771, log(5.05) = 0.7032; ln2 = 0.693; ln 1.5 = 0.405; ln3 = 1.098

Space for Rough Work (jQ+ dk;Z gsrq LFkku)



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 When copper sulphate solution is electrolysed in a copper voltameter for 30 sec, then m gram of copper was deposited. Time current graph for the electrolysis is

200

100

10 20 30 time (sec)

Cur

rent

(mA)

The electrochemical equivalent of copper from

above plot will be -

(A) Z = m (B) Z = 2m

(C) Z = 5m (D) Z = 2m

[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 le{k 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 tc dkWij lYQsV foy;u dks dkWij okWYVkehVj esa

30 lSd.M ds fo|qr vi?kfVr fd;k tkrk gS rc

dkWij ds m xzke laxzfgr gksrs gSA fo|qr vi?kVu ds

fy, le;-/kkjk oØ fuEu gS

200

100

10 20 30 time (sec)

Cur

rent

(mA)

mijksDRk oØ ls dkWij dk fo|qr jklk;fud rqY;kad gS&

(A) Z = m (B) Z = 2m

(C) Z = 5m (D) Z = 2m



Q.2 PCl5(g) ds fo;kstu ds fy,]

dD

ds lkis{k (1 + α)

ds ifjorZu dks] fdl izdkj n'kkZ;k tkrk gS &

(A)

D/d

(1+x) (B)

D/d

(1+x)

(C)

D/d

(1+x) (D)

D/d

(1+x)

Q.3 fuEu v.kqvksa ds lajpuk esa] π-cU/kksa dh la[;k c<+us dk

lgh Øe gS &

(I) H2S2O6 (II) H2SO3 (III) H2S2O5

(A) I, II, III (B) II, III, I

(C) II, I, III (D) I, III, II

Q.2 For the dissociation of PCl5(g), the variation of (1 +

α) against

dD is represented as -

(A)

D/d

(1+x) (B)

D/d

(1+x)

(C)

D/d

(1+x) (D)

D/d

(1+x)

Q.3 Identify the correct sequence of increasing number

of π-bonds in the structures of the following

molecules -

(I) H2S2O6 (II) H2SO3 (III) H2S2O5

(A) I, II, III (B) II, III, I

(C) II, I, III (D) I, III, II



Q.4 tc NaCl dks AgCl ds larIr foy;u esa /khjs-/khjs feyk;k tkrk gS rc dkSulk oØ lgh gS ?

(A)

Cl–

[Ag+] (B)

Cl–

[Ag+]

(C)

Cl–

[Ag+] (D)

Cl–

[Ag+]

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 le{k 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 ;fn 0.1 M HBr o 0.1M KOH ds leku vk;ruks dks

feyk;k tk;s rks fuEu esa ls dkSuls fodYi] ifjek.kh

foy;u ds lUnHkZ esa lR; gS &

(A) [H3O+] = 1.0 × 10–7 mol L–1 (B) [OH–] = 1.0 × 10–7 mol L–1 (C) [K+] = 0.05 mol L–1 (D) [Br–] = 0.10 mol L–1

Q.4 When NaCl is added gradually to the saturated solution of AgCl then which of the following plot is correct ?

(A)

Cl–

[Ag+] (B)

Cl–

[Ag+]

(C)

Cl–

[Ag+] (D)

Cl–

[Ag+]

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 If equal volumes of 0.1 M HBr and 0.1M KOH are mixed, then which of the following is/are correct about the resulting solution ?

(A) [H3O+] = 1.0 × 10–7 mol L–1 (B) [OH–] = 1.0 × 10–7 mol L–1 (C) [K+] = 0.05 mol L–1 (D) [Br–] = 0.10 mol L–1



Q.6 In which of the following molecules, vacant orbitals take part in hybridization ?

(A) B2H6 (B) Al2Cl6 (C) H3PO3 (D) H3BO3 Q.7 Which of the following is/are correct about the

equilibrium of a reaction ? (A) ∆G = 0 (B) Catalyst does not affect the position of

equilibrium (C) Q = K (D) Equilibrium constant is independent of initial

concentration of reaction

Q.8 The temperature coefficient of cell is PT

E

∂∂ .

Then -

(A) When PT

E

∂∂ = 0, then ∆H = – nFE

(B) When PT

E

∂∂ > 0, then nFE > ∆H and it is

endothermic reaction

(C) When PT

E

∂∂ < 0, then nFE < ∆H and it is


(D) When PT

E

∂∂ = 0, then ∆H > nFE and it is


Q.6 fuEu esa ls fdu v.kqvksa esa] fjDr d{kd ladj.k esa Hkkx ysrs gS ?

(A) B2H6 (B) Al2Cl6 (C) H3PO3 (D) H3BO3 Q.7 fuEu esa ls dkSulk vfHkfØ;k ds lkE; ds fy, lgh gS ?

(A) ∆G = 0

(B) mRiszjd lkE; fLFkfr dks izHkkfor ugh djrk gS

(C) Q = K

(D) lkE; fLFkjkad vfHkfØ;k dh izkjfEHkd lkUnzrk ij

fuHkZj ugh djrk gS

Q.8 lsy dk rki xq.kkad PT

E

∂∂

gks] rks &

(A) tc PT

E

∂∂ = 0, gks rks ∆H = – nFE gksrk gS

(B) tc PT

E

∂∂ > 0, gks rks nFE > ∆H gksrk gS rFkk

vfHkfØ;k Å"ek'kks"kh gS

(C) tc PT

E

∂∂ < 0, gks rks nFE < ∆H gksrk gS rFkk


(D) PT

E

∂∂ = 0, gks rks ∆H > nFE gksrk gS rFkk




Q.9 fuEu esa ls dkSulk lkE; ds lUnHkZ esa lR; gS

(A) lkE; ij ∆G = 0

(B) ;g xfrfd; izdfr dk gS

(C) lkE; ij ∆Gº = –RTlnK

(D) lkE; fdlh Hkh fn'kk esa LFkkfir gks ldrk gS

[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

vr% OMR 'khV esa iz'u dh iz'u la[;k ds le{k 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.9 Which of the following is correct regarding equilibrium

(A) At equilibrium ∆G = 0 (B) It is dynamic in nature (C) At equilibrium ∆Gº = –RTlnK (D) Equilibrium can be attained from either of the

side

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

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 LrEHk lwesfyr dhft, :

LrEHk -I LrEHk -II

(A) pkydrk (P) sm–1

(B) fof'k"V pkydrk (Q) s–1 m

(C) eksyj pkydrk (R) ohm–1 cm2 mol–1

(D) izfrjks/kdrk

(S) s (T) ohm cm

Q.2 LrEHk lwesfyr dhft, :

LrEHk-I LrEHk-II

(A) E° = 0 (P) lsy fujkosf'kr gksrk gS

(B) E = 0 (Q) Q = K

(C) ∆G = 0 (R) 96500 dqyke

(D) 1 QsjkMs (S) 1 eksy bysDVkWu (T) lsy dh lkUnzrk

Q.1 Match the column :

Column -I Column-II

(A) Conductance (P) sm–1

(B) Specific conductance (Q) s–1 m

(C) Molar conductance (R) ohm–1 cm2 mol–1

(D) Resistivity

(S) s (T) ohm cm

Q.2 Match the column:

Column -I Column-II

(A) E° = 0 (P) Cell is discharged

(B) E = 0 (Q) Q = K

(C) ∆G = 0 (R) 96500 coulomb

(D) 1 Faraday (S) 1 mol electrons (T) Concentration cell



Section - III This section contains 8 questions (Q.1 to 8).+4 marks will be given for each correct answer and –1mark for each wrong answer. The answer to each of thequestions is a SINGLE-DIGIT INTEGER, rangingfrom 0 to 9. The appropriate bubbles below therespective question numbers in the OMR have to bedarkened. For example, if the correct answers toquestion numbers X, Y, Z and W (say) are 6, 0, 9 and 2,respectively, then the correct darkening of bubbles willlook 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 If the equilibrium constant of the reaction of weakacid HA with strong base is 109 then pH of 0.1 MNaA is -

Q.2 What is the minimum pH required to prevent theprecipitation of ZnS in a solution i.e., 0.01 M ZnCl2

and saturated with 0.1 M H2S ? Ksp(ZnS) = 10–21,

1aK × 2aK (H2S) = 10–20

[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 ;fn nqcZy vEy HA dh izcy {kkj ds vfHkfØ;k dk lkE;

fLFkjkad 109 gS rks 0.1 M NaA dh pH gSA

Q.2 ,d foy;u esa 0.01 M ZnCl2 rFkk ftls 0.01 M H2S ds lkFk larIr fd;k x;k gS blls izkIr foy;u esa ZnS ds vo{ksi.k dks jksdus ds fy, vko';d U;wure pH D;k gS ?

Ksp(ZnS) = 10–21, 1aK ×

2aK (H2S) = 10–20



Q.3 The Ksp of Mg(OH)2 is 1 × 10–12; 0.01 M MgCl2

will precipitate at limiting pH of ––––– . Q.4 20% of N2O4 molecules are dissociated in a sample

of gas at 27°C and 760 torr. Mixture has the densityat equilibrium equal to -

Q.5 In an experiment, 0.04 F was passed through 400

mL of a 1 M solution of NaCl. What would be the pOH of the solution after the electrolysis ?

Q.6 A current of 2 amp when passed for 5 hour through

a molten salt deposits 22.2 g of metal of atomicmass 177. The oxidation state of the metal in themetal salt is -

Q.7 What weight of solid ammonium carbamate

(NH2COONH4) when vaporized at 200°C will havea volume of 8.96 litre at 1 atm ? Assume that solidcompletely decomposes into CO2 and NH3 at 200°C and 1 atm.

Q.8 Find the pH of 0.5×10–5 H2SO4 solution

Q.3 Mg(OH)2 dk Ksp = 1 × 10–12 gSA 0.01 M MgCl2 fdl lhekUr pH ij vo{ksfir gksxkA

Q.4 20% , N2O4 v.kq] 27°C o 760 VkWj ij xSl ds uewus esa

fo;ksftr gksrs gSA lkE; ij feJ.k dk ?kuRo fdlds cjkcj gSA

Q.5 ,d iz;ksx esa] 0.04 F dks NaCl ds 400 mL foy;u esa

izokfgr fd;k tkrk gS oS|qr vi?kVu ds i'pkr~ foy;u

dh pOH D;k gksxh ?

Q.6 tc 2 ,Eih;j dh /kkjk dks 5 ?k.Vs ds fy,] laxfyr

yo.k ls izokfgr fd;k tkrk gS 177 ijek.kq nzO;eku dh

/kkrq dk 22.2 xzke lapf;r gksrk gSA /kkrq yo.k esa /kkrq

dh vkWDlhdj.k voLFkk gSA

Q.7 Bkslh; veksfu;e dkcsZesV (NH2COONH4) dk Hkkj D;k

gS tc 200°C ij ok"ihdr djus ij 1 atm ij vk;ru

8.96 yhVj gksxk ekuk dh Bksl 200°C o 1 atm ij] iw.kZ

:i CO2 o NH3 eas fo;ksftr gksrk gSA

Q.8 0.5×10–5 H2SO4 foy;u dh pH Kkr dhft,


Corporate Office: CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: 0744-3040000 (6 lines) || IIT Target || Page # 9

MATHEMATICS

Section - I

Questions 1 to 4 are multiple choice questions. Eachquestion has four choices (A), (B), (C) and (D), out ofwhich ONLY ONE is correct. Mark your response inOMR sheet against the question number of thatquestion. + 3 marks will be given for each correct answerand – 1 mark for each wrong answer. Q.1 Range of the function

f(x) = 2347498142

24

24

+−−+−−

xxxxxx is

(A) [1, 3] (B) [2, 3] (C) (2, 3] (D) (1, 2]

Q.2 Number of solutions of the equation [y + [y]] = 2 cosx

is, where y = 31 [sinx + [sinx + [sinx]]] and [.]

denotes the greatest integer function (A) 1 (B) 2 (C) 3 (D) none of these

Q.3 Period of f(x) = xxxx

3coscos3sinsin

++ is

(A) π (B) 2π (C)

4π (D) 2π

[k.M - I iz'u 1 ls 4 rd cgqfodYih iz'u gSaA izR;sd iz'u ds pkjfodYi (A), (B), (C) rFkk (D) gSa, ftuesa ls dsoy ,d fodYi lgh gSA OMR 'khV esa iz'u dh iz'u la[;k ds le{k 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 Qyu f(x) = 2347498142

24

24

+−−+−−

xxxxxx dk ifjlj gksxk

(A) [1, 3] (B) [2, 3] (C) (2, 3] (D) (1, 2]

Q.2 lehdj.k [y + [y]] = 2 cosx tgk¡

y = 31 [sinx + [sinx + [sinx]]] rFkk [.] egÙke iw.kkZad

Qyu dks iznf'kZr djrk gS] ds gyksa dh la[;k gksxh (A) 1 (B) 2

(C) 3 (D) buesa ls dksbZ ugha

Q.3 Qyu f(x) = xxxx

3coscos3sinsin

++ dk vkorZuk¡d gS

(A) π (B) 2π (C)

4π (D) 2π



Q.4 x

xnx

nxxx

x eex

x /1)12(

0

sin)12(lim

−− −

→ + l

l

dk eku gS

(A) e1

ln 2 (B) e

(C) e ln 2 (D) buesa ls dksbZ ugha

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 le{k 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 ;fn f (x) = sin–1x + cos–1x rc 2π cjkcj gS-

(A) f

21– (B) f(k2 – 2k + 3), k ∈ R

(C) f

+ 211k

, k ∈ R (D) f(–2)

Q.6 ;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

lEcU/k gksxk -

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

Q.4 x

xnx

nxxx

x eex

x /1)12(

0

sin)12(lim

−− −

→ + l

l

is equal to

(A) e1

ln 2 (B) e

(C) e ln 2 (D) none of these

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

Q.5 Let f (x) = sin–1x + cos–1x. Then 2π is equal to-

(A) f

21– (B) f(k2 – 2k + 3), k ∈ R

(C) f

+ 211k

, k ∈ R (D) f(–2)

Q.6 If 100C50 can be prime factorised as 2α 3β . 5γ . 7δ ….

where α, β, γ, δ, …. are non negative integers, thencorrect relation is/are -

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



Q.7 fuEu esa ls dkSuls Qyu ;qXe leku xzkQ ugha j[krs gSa?

(A) f(x) =|cos||sec||cos||sec|

ecxxecxx + ; g(x) = |sin x| + |cosx|

(B) f(x) = ∞→n

lim 11

2

2

+−

n

n

xx ; g(x) = sgn (1 – |x|)

(C) f(x) = sec–1 x ; g(x) = )(sec 1 xne−l

(D) f(x) =x

x2tan1

sin

++

x

x2cot1

cos

+; g(x) = sin 2x

Q.8 ;fn 2007Cr ≥ 2007Cr–1 rFkk 2007Cr ≥ 2007Cr+1 gS] rks r

D;k ugha gks ldrk \

(A) 1002 (B) 1003

(C) 1004 (D) 1005

Q.9 mu rjhdksa dh la[;k ftlesa 10 fo|kfFkZ;ksa A1, A2,

……… A10 dks Øe esa bl izdkj j[kk x;k gS fd

A1 lnSo A2 ls Åij jgrk gS] gksxh

(A) 2

!10 (B) 8!10C2

(C) 10P2 (D) 10C2

Q.7 Which of the following pairs of function does not

have same graph ?

(A) f(x) =|cos||sec||cos||sec|

ecxxecxx + ; g(x) = |sin x| + |cosx|

(B) f(x) = ∞→n

lim 11

2

2

+−

n

n

xx ; g(x) = sgn (1 – |x|)

(C) f(x) = sec–1 x ; g(x) = )(sec 1 xne−l

(D) f(x) =x

x2tan1

sin

++

x

x2cot1

cos

+; g(x) = sin 2x

Q.8 If 2007Cr ≥ 2007Cr–1 and 2007Cr ≥ 2007Cr+1 then

r cannot be

(A) 1002 (B) 1003

(C) 1004 (D) 1005

Q.9 The number of ways in which 10 candidates A1, A2,

……… A10 can be ranked, so that A1 is always

above A2, is

(A) 2

!10 (B) 8!10C2

(C) 10P2 (D) 10C2



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

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.

[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

vr% OMR 'khV esa iz'u dh iz'u la[;k ds le{k 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 LrEHk-II (A) ekuk f : R → R; (P) ,dSdh

f(x) = 3 x + tan–1x, }kjk

ifjHkkf"kr gS] rks f(x) gksxk (B) ekuk f :(–∞, ∞) →{–1,0,1}; (Q) vUr%{kZsih f(x) = sin3π (sgn (x2 + 3x + 5)) }kjk ifjHkkf"kr gS] rks f(x) gksxk (tgk¡ sgn(x); x ds flXue Qyu

dks iznf'kZr djrk gS (C) ekuk f : [–2, 2] → (0, e2] ; (R) fo"ke

f(x) = 2xe }kjk ifjHkkf"kr gS]

rks f(x) gksxk (D) ekuk f : (–1, 5) → [0, 3] ; (S) vO;qRØe.kh;

f(x) = 245 xx −+ , }kjk

ifjHkkf"kr gS] rks f(x) gksxk (T) vukorhZ

Q.2 LrEHk-I LrEHk-II

(A) 31

33.)2(3.lim 1 =

−+− +∞→ nnn

n

n nxnn (P) 0

rc x gksxk (;fn n ∈ N)

(B) ;fn2

2

1 ))2((lim

xnbaxx

x −++

→ l fo|eku gS (Q) 1

rks vUrjky (a, b + l) esa iw.kk±d

gksaxs] tgk¡ l lhek dk eku gS

Q.1 Column –I Column –II

(A) Let f : R → R be defined as (P) one-one

f(x) = 3 x + tan–1x, then f(x) is

(B) Let f : (–∞, ∞) → {–1, 0, 1} (Q) into be defined as f(x) = sin3π (sgn (x2 + 3x + 5)) then f(x) is (where sgn x denotes signum function of x) (C) Let f : [–2, 2] → (0, e2] be (R) odd

defined as f(x) = 2xe , then f(x) is (D) Let f : (–1, 5) → [0, 3] be (S) non invertible

defined as f(x) = 245 xx −+ ,

then f(x) is (T) a periodic

Q.2 Column -I Column-II

(A) 31

33.)2(3.lim 1 =

−+− +∞→ nnn

n

n nxnn (P) 0

then x can be (if n ∈ N)

(B) If2

2

1 ))2((lim

xnbaxx

x −++

→ l exists then (Q) 1

integers in interval (a, b+l)

where l is value of limit



(C) l=−

→ xxx

x 20 tan2coscos1lim rks (R) 2

l dk iw.kk±d eku gksxk

(D) x

bae x

x

−→0

lim = 2 rks a, b, a + b (S) 3

gksaxs (T) 4

[k.M - III


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

(C) l=−

→ xxx

x 20 tan2coscos1lim then (R) 2

integral value of l

(D) x

bae x

x

−→0

lim = 2 then a, b, a + b (S) 3

can be (T) 4

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 thequestions is a SINGLE-DIGIT INTEGER, ranging from 0 to 9. The appropriate bubbles below therespective question numbers in the OMR have to bedarkened. For example, if the correct answers toquestion numbers X, Y, Z and W (say) are 6, 0, 9 and 2,respectively, then the correct darkening of bubbles willlook 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 If range of the function f(x) = sin–1 x + 2 tan–1x + x2 + 4x + 1 is [p, q] then

find the value of (p + q)………

Q.2 Let f(x) = π2 (sin–1[x] + tan–1[x] + cot–1 [x]) where

[x] denotes greatest integer less than or equal to x. If A and B denote the domain and range of f(x) respectively, then the number of integers in (A ∪ B) is………

Q.3 Find no. of integral values of a for which

2

2

4348

xxaxax

−+−+ takes all real values for real values of x .

Q.4 Evaluate ∑=∞→ −−

n

rn rrrLt

142 13

4

Q.5 If ±=≠

=otherwise

nxxf

....1,0,πnx2

sin)(

and

==

≠+=

202,0

54

1)(

2

xx

xxxg

then0

lim→x

g[f(x)] is..............

Q.1 ;fn Qyu f(x) = sin–1 x + 2 tan–1x + x2 + 4x + 1dh ijkl [p, q] gks] rks (p + q) dk eku gS………

Q.2 ekukfd f(x) = π2 (sin–1[x] + tan–1[x] + cot–1 [x]) tgk¡

[x] egÙke iw.kk±ad Qyu ≤ x dks n'kkZrk gSA ;fn A oB Øe'k% Qyu f(x) ds izkUr o ifjlj gksa, rks (A ∪ B) ds iw.kk±d ekuksa dh la[;k gS………

Q.3 a ds mu iw.kkZad ekuksa dh la[;k Kkr dhft, ftuds

fy, 2

2

4348

xxaxax

−+−+ ; x ds okLrfod ekuksa ds fy, lHkh

okLrfod eku xzg.k djrh gSA

Q.4 ∑=∞→ −−

n

rn rrrLt

142 13

4 dk eku Kkr djksA

Q.5 ;fn ±=≠

=otherwise

nxxf

....1,0,πnx2

sin)(

,oa

==

≠+=

202,0

54

1)(

2

xx

xxxg

rc0

lim→x

g[f(x)] dk eku gS ..............



Q.6 If

+−++++++++∞→∞→ 2

)1(....4332211limlim

m

mmn nnn nnn nnn nn

nm

= A1 . Then A equals to ...

Q.7 8 Clay targets are arranged as shown. If in x

ways can they be shot (one at a time) if no target can be shot until the target(s) below it have been shot. Find x/70.

Q.8 Number of solutions of the equation

9

792

8101

79

810))(sin(sincos

=

−

−−++=

x

xxxxxdxdxec

will be

Q.6 ;fn

+−++++++++∞→∞→ 2

)1(....4332211limlim

mmmn nnn nnn nnn nn

nm

= A1 rc A dk eku gS

Q.7 8 feV~Vh (clay) ds y{; fuEu izdkj O;ofLFkr gSA ;fn os x izdkj ls Hksns tk ldrs gS (,d le; ,d) ;fn dksbZ Hkh y{; rd ugh Hksnk tk ldrk tc rd fd blds uhps dk y{; Hksn ugh fn;k tk ldrkA rc x/70 dk eku Kkr dhft,A

Q.8 lehdj.k

9

792

8101

79

810))(sin(sincos

=

−

−−++=

x

xxxxxdxdxec

ds gyksa dh la[;k gksxh



PHYSICS

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 hollow vertical cylinder of radius r and height h has a smooth internal surface. A small particle is placed in contact with the inner side of the upper rim, at point A, and given a horizontal speed u, tangential to the rim. It leaves the lower rim at point B, vertically below A. If n is an integer then-

A u

h

r

B

(A) g/h2r2

uπ

= n (B) r2

hπ

= n

(C) h

r2π = n (D) gh2

u = n

[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 le{k 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 r f=kT;k rFkk Å¡pkbZ h okys ,d [kks[kys m/okZ/kj csyu dh vkarfjd lrg fpduh gSA ,d NksVs d.k dks Åijh fje dh vkUrfjd lrg ds lkFk fcUnq A ij lEidZ esa j[kk tkrk gS rFkk bls fje ds Li'kZjs[kh; ,d {kSfrt osx u fn;k tkrk gSA ;g fupys fje dks fcUnq A ds m/okZ/kj uhps fLFkr fcUnq B ij NksM+rk gSA ;fn n iw.kkZd gS rc -

A u

h

r

B

(A) g/h2r2

uπ

= n (B) r2

hπ

= n

(C) h

r2π = n (D) gh2

u = n



Q.2 3r f=kT;k ds fpdus di ij nks leku nzO;eku ds Hkkjh xksys n'kkZ;s vuqlkj j[ks gS tgka r izR;sd xksys dh f=kT;k gS rks di o fdlh Hkh xksys ds e/; izfrfØ;k cy o nks xksyksa ds e/; izfrfØ;k cy dk vuqikr gS–

r r

3r 3r

O

(A) 1 (B) 2 (C) 3 (D) buesa ls dksbZ ugha

Q.3 yEckbZ l < πR/2 dh ,d pSu ,d fpduh lrg ij

j[kh gS ftldk dqN Hkkx {kSfrt rFkk dqN Hkkx

fp=kkuqlkj R f=kT;k ds ,d pkSFkkbZ&oÙk ij gSA izkjEHk

esa pSu dk iwjk Hkkx oÙkh; Hkkx esa jgrk gS ftldk

,d fljk oÙkh; lrg ds 'kh"kZ fcUnq ij gSA ;fn pSu

dk nzO;eku m gS rc iwjh pSu dks {kSfrt Hkkx ij

/khjs&/khjs [khapus esa fd;k x;k vko';d dk;Z gS -

O

R

R

Q.2 Two identical heavy spheres of equal mass are placed on a smooth cup of radius 3r where r is radius of each sphere. Then the ratio of reaction force between cup and any sphere to reaction force between two sphere is –

r r

3r 3r

O

(A) 1 (B) 2 (C) 3 (D) None of these

Q.3 A chain of length l < πR/2 is placed on a smooth surface whose some part is horizontal and some part is quarter circular of radius R as shown. Initially the whole part of chain lies in the circular part with one end at top most point of circular surface. If the mass of chain is m then the work required to pull very slowly the whole chain on horizontal part is -

O

R

R



(A) l

m gR2

Rsin l (B)

l

m gR2

Rcos l

(C) l

m gR2

−

Rsin

Rll

(D) buesa ls dksbZ ugha

Q.4 ,d rSjkd ,d >hy esa 22 m/s fu;r pky ds lkFk mÙkj&iwoZ fn'kk esa rSj jgk gSA og viuk izfrfcEc] iwoZ dh vksj 1 m/s fu;r osx ls xfr djrh ,d cksV esa yxs ,d niZ.k esa ns[krk gSA mlds }kjk ni.kZ esa ns[ks x;s mlds izfrfcEc dk osx gksxk -

(A) 2 m/s (B) 2 2 m/s(C) 52 m/s (D) 3 m/s

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 le{k 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 uhps n'kkZ;k x;k ,d ydM+h CykWd dh xfr dks n'kkZrk gS ftldk nzO;eku 1 kg gS o ftls {kSfrt Vscy ij t = 0 ij ,d izkjfEHkd /kDdk fn;k x;k gS-

4(0, 0)

4

v (m

s–1)

t (s)

(A) l

m gR2

Rsin l (B)

l

m gR2

Rcos l

(C) l

m gR2

−

Rsin

Rll

(D) None of these

Q.4 A swimmer is swimming with constant velocity 22 m/s due North-East in a calm lake. He

observes his image in a mirror fitted at the rear of a boat moving with constant velocity 1 m/s due East. Velocity of his image as observed by him in the mirror will be -

(A) 2 m/s (B) 2 2 m/s(C) 52 m/s (D) 3 m/s

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 The velocity-time graph of the figure shows the motion of a wooden block of mass 1 kg which is given an initial push at t = 0 along a horizontal table-

4(0, 0)

4

v (m

s–1)

t (s)



(A) The coefficient of friction between the block and the table is 0.1

(B) The coefficient of friction between the block and the table is 0.2

(C) If the table was half of its present roughness, the time taken by the block to complete the journey is 4 s

(D) If the table was half of its present roughness, the time taken by the block to complete the journey is 8 s

Q.6 The driver of a car travelling at velocity v suddenly

sees a broad wall in front of him at a distance ‘a’ : (A) If the brakes are applied force required to stop

the car not to be smashed up with wall is

a2mv2

(B) To avoid crashing with wall if the car turns in

circle, then force required is a

mv2

(C) It is better to apply the brakes than to turn the car in circular path to avoid crashing with wall

(D) When car stops then its kinetic energy is expended in work against force of friction

(A) Vscy o CykWd ds e/; ?k"kZ.k xq.kkad 0.1 gS (B) Vscy o CykWd ds e/; ?k"kZ.k xq.kkad 0.2 gS (C) ;fn Vscy vius orZeku [kqjnqjsiu dk vk/kk eku

j[krh gS rks CykWd dks ;k=kk iw.kZ djus esa yxk

le; 4 s gS (D) ;fn Vscy vius orZeku [kqjnqjsiu dk vk/kk eku

j[krh gS rks CykWd dks ;k=kk iw.kZ djus esa yxk

le; 4 s gS Q.6 ,d dkj Mkboj ,d osx v ls ;k=kk dj jgk gS] og

,dk,d vius lkeus ,d ‘a’ nwjh ij pkSMh nhokj ns[krk gS- (A) ;fn cszd yxk;k tkos rks nhokj ls ugha Vdjkus

ds fy, dkj dks jksdus ds fy, vko';d czsd

cy a2

mv2 gS

(B) nhokj ls Vdjkus ls cpk tk ldrk gS ;fn dkj oÙk esa ?kwe tk;s o blds fy, vko';d cy

amv2

gS

(C) nhokj ls Vdjkus ls cpus ds fy, cszd yxkus dh vis{kk dkj dk oÙkh; iFk eas eqM+ tkuk vf/kd vPNk gS

(D) tc dkj jksdh tkrh gS] rc bldh xfrt ÅtkZ] ?k"kZ.k ds fo:) fd;s x;s dk;Z esa O;; gks tkrh gS



Q.7 uhps n'kkbZ fLFkfr esa ,d izdk'k fdj.k {kSfrt :i ls ;k=kk djrh gqbZ ,d lery niZ.k tks m/oZ ls 15º dks.k ij gS ls Vdjkrh gSA AB, l Å¡pkbZ dk ,d O;fDr gSA

A

B

l

Vertical direction

15º

fuEu esa ls lgh dFku pqfu;s - (A) ijkofrZr izdk'k fdj.k {kSfrt ls ,d 30º dks.k

cukrh gS (B) ijkofrZr izdk'k fdj.k niZ.k ls 75º dks.k cukrh gS (C) O;fDr dh Nk;k dh yEckbZ l 3 gS

(D) O;fDr dh Nk;k dh yEckbZ 3l gS

Q.8 ,d leryksÙky ySUl (µ = 1.5) dh Qksdl yEckbZ 20 cm gS bldh lery lrg pk¡nh ysfir fd;k x;k gS - (A) bldh oØ lrg dh oØrk f=kT;k] blh inkFkZ ls

cus mHk;ksÙky ySUl ftldh Qksdl yEckbZ 20 cm gS] dh vk/kh gS

(B) ,d oLrq tks mDr ySUl dh mÙky vksj v{k ij 15 cm nwjh ij fLFkr gS blls 30 cm nwjh ij fLFkr ,d izfrfcEc nsrk gSS

(C) ,d oLrq tks mDr ySUl dh mÙky vksj v{k ij 20 cm nwjh ij fLFkr gS blls 40 cm nwjh ij fLFkr ,d izfrfcEc nsrk gSS

(D) ;g ,d mÙky niZ.k dh rjg O;ogkj djrk gS

Q.7 Horizontally travelling light rays strikes a plane mirror at an angle 15º with vertical. AB is a man of height l. :

A

B

l

Vertical direction

15º

Choose the correct option(s) (A) The reflected light is at an angle 30º with

horizontal. (B) The reflected light is at an angle 75º with mirror. (C) The length of shadow of man is l 3

(D) The length of shadow of man is 3l .

Q.8 A Plano convex lens (µ = 1.5) of focal length 20 cm has its plane side silvered - (A) The radius of curvature of its curved surface is

half that of a surface of equiconvex lens of focal length 20 cm made of same material

(B) An object place at 15 cm on the axis on the convex side gives rise to an image at a distance of 30 cm from it

(C) An object located at a distance of 20 cm on the axis on the convex side gives rise to an image at 40 cm from it

(D) It acts as a convex mirror



Q.9 ,d ekud ;ax f}&fNnz js[kk iz;ksx esa ;fn buesa ls ,d fLyV dks ,d iryh lekUrj dk¡p iVV~hdk ls <d fn;k tk;s rkfd ;g nwljs dh rqyuk esa dsoy vk/kh rhozrk vius esa ls ikjxfer gksus ns-

(A) fÝUt izk:i] <+dh gqbZ fLyV dh vksj foLFkkfir gks tk;sxk

(B) fÝUt izk:i] <+dh gqbZ fLyV ls nwj foLFkkfir gks tk;sxk

(C) pedhyh fÝUt de pedhyh rFkk vnhIr vf/kd pedhyh gks tk;sxh

(D) fÝUt pkSM+kbZ vifjofrZr jgsxh

[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

Q.9 If one of the slits of a standard young‘s double slit experiment is covered by a thin parallel slit glass so that it transmits only one half the light intensity of the other, then:

(A) The fringe pattern will get shifted towards the covered slit

(B) The fringe pattern will get shifted away from the covered slit

(C) The bright fringes will become less bright and the dark ones will become more bright

(D) The fringe width will remain unchanged

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



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 The equation of one dimensional motion of particle is described in column I. At t = 0, particle is at origin and at rest. Match the column I with the statements in column II.

Column -I Column-II

(A) x = (3t2 + 2)m (P) velocity of particle at t = 1 s is 8 m/s

(B) v = 8t m/s (Q) particle moves with uniform acceleration

(C) a = 16 t (R) particle moves with variable acceleration

(D) v = 6t – 3t2 (S) particle will change its direction some time (T) None

Q.2 Refraction of plane surface (FG is parallel to MN)

30°

Aµ1

µ2 C

D

B

F

M N

G

vr% OMR 'khV esa iz'u dh iz'u la[;k ds le{k 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 ,d d.k dh ,dfofe; xfr dh lehdj.k dkWye I esa

nh xbZ gSA t = 0 ij d.k fojke esa gS o ewy fcUnq ij gSA dkWye I ds dFkuksa dk dkWye II ls lgh feyku dhft,

LrEHk -I LrEHk -II

(A) x = (3t2 + 2)m (P) t = 1 s ij d.k dk osx 8 m/s gS

(B) v = 8t m/s (Q) d.k ,dleku Roj.k ds lkFk xfr djrk gS

(C) a = 16 t (R) d.k ifjorhZ Roj.k ds lkFk xfr djrk gS

(D) v = 6t – 3t2 (S) d.k fdlh le; ij viuh fn'kk ifjofrZr djsxk (T) dksbZ ughs

Q.2 ,d lery lrg ls viorZu uhps fp=k esa n'kkZ;k x;k gS (FG, MN ds lekUrj gS)

30°

A µ1

µ2 C

D

B

F

M N

G



Column I Column II (A) Which ray is not possible (P) A

(B) 3

2

2

1 >µµ (Q) B

(C) 12

1 ≤µµ (R) C

(D) 12

1 ≥µµ (S) D

(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 therespective question numbers in the OMR have to bedarkened. For example, if the correct answers toquestion numbers X, Y, Z and W (say) are 6, 0, 9 and 2,respectively, then the correct darkening of bubbles willlook 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

LrEHk I LrEHk II (A) dksulh fdj.k LEHko ugha gS (P) A

(B) 3

2

2

1 >µµ (Q) B

(C) 12

1 ≤µµ (R) C

(D) 12

1 ≥µµ (S) D

(T) dksbZ ugha

[k.M - III


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 An insect moves with a constant velocity v from one corner of a room to other corner which is opposite of the first corner along the largest diagonal of room. If the insect can not fly and dimensions of room is a × a × a, then the minimum time in which the insect can move is a/v times the square root of a number n, then n is equal to ?

Q.2 A track has two inclined surfaces AB and AC each

of length 3 m and angle of inclination of 30º with the horizontal and a central horizontal part of length 4 m as shown in figure. A block of mass 0.2 kg slides from the rest from point A. The inclined surfaces are frictionless. If the coefficient of friction between the block and the horizontal flat surface is 0.2, where will the block finally come to rest from point B? [in 10–1 m]

30ºθ =30º3 m3 m

A D

C B 4 m

Q.3 A block of mass m = 1kg moving on horizontal surface with speed u = 2m/s enters a rough horizontal patch ranging from x = 0.10 m to x = 2.00m. If the retarding force fr on the block in this range is inversely proportional to x over this range i.e.

Q.1 ,d dhMk ,d fu;r osx v ls ,d cM+s dejs ds ,ddksus ls nwljs dksus (tks izFke dksus ds Bhd lkeus gS)rd dejs ds lcls cM+s O;kl ds vuqfn'k xfr djrk gSA;fn dhMk mM+ ugha ldrk rFkk dejs dk vk;ke a × a ×a gS rks og U;wure le; ftlesa dhMk xfr dj ldrkgSA ,d la[;k ds n ds oxZewy dk a/v xquk gS rks n dkeku D;k gS ?

Q.2 ,d Vªsd nks vkur lrg AB o AC j[krk gS] izzR;sd dh

yEckbZ 3m gS o {kSfrt ls vkur dks.k 30º gS o dsUnzh;

{kSfrt Hkkx dh yEckbZ 4 m gS (ns[ksa fp=k)A ,d 0.2 kg

nzO;eku dk ,d CykWd fcUnq A ls fojke ls fQlyuk

'kq: gksrk gSA vkur lrgsa ?k"kZ.kghu gSA ;fn CykWd o

lery lrg ds e/; ?k"kZ.k xq.kkad 0.2 gS] rks fcUnq B ls

fdruh nwjh ij CykWd ifj.kkeh :i ls fojke esa vk

tk;sxk ? [in 10–1 m]

30ºθ =30º3 m3 m

A D

C B 4 m

Q.3 ,d CykWd ftldk nzO;eku m = 1kg ,d {kSfrt lrgij u = 2m/s dh pky ls xfr'khy gSA xfr djrs gq,;g x = 0.10 m ls x = 2.00m ijkl ds [kqjnjs {kSfrtHkkx esa izos'k djrk gSA ;fn ,d vojks/kd cy fr blCykWd ij bl ij nh xbZ ijkl esa CykWd ij dk;Zjr gSAvFkkZr



fr = xk− 0.10 < x < 2.00

= 0 for x < 0.10 and x > 2.00 If k = 0.5 J then the speed of this block as it crosses

the patch is (use ln 20 = 3) in m/s is –

Q.4 A particle of mass 7

10 Kg is moving in the

positive direction of x. Its initial position x = 0 &initial velocity is 1 m/s. The velocity at x = 10 is -

4

x (in m) 10

Power (in watts)

Q.5 Two blocks of mass 2 kg and 4 kg are connected

through a massless inextensible string. Coefficientof friction between 2 kg block and ground is 0.4and between 4 kg block and ground is 0.6. Twoforces F1 = 10 N and F2 = 20 N are applied on theblock as shown in figure. Friction force (in N)acting on 4 kg block minus 10 N is

4 kg 20 N 2 kg 10 N

µ = 0.6 µ = 0.4

fr = xk− 0.10 < x < 2.00

= 0 x < 0.10 o x > 2.00 ds fy, ;fn k = 0.5 J rks bl CykWd dh pky (m/s esa) tc ;g

bl {kSfrt Hkkx dks ikj dj ysrk gS] D;k gksxh (fn;k gSln 20 = 3) in m/s is –

Q.4 ,d d.k ftldk nzO;eku 7

10 Kg gS ,d /kukRed x

fn'kk esa xfr'khy gSA bldh izkjfEHkd fLFkfr x = 0 gS o izkjfEHkd osx 1 m/s gSA x = 10 ij bldk osx D;k gS -

4

x (in m) 10

Power (in watts)

Q.5 nks CykWd ftuds nzO;eku 2 kg o 4 kg gS o ,d

nzO;ekughu vfoLrkj.kh; Mksjh }kjk vkils esa tqMs+ gSA2 kg CykWd o tehu ds e/; ?k"kZ.k xq.kkad 0.4 o 4 kg CykWd o tehu ds e/; ?k"kZ.k xq.kkad 0.6 gSA nks cyF1 = 10 N o F2 = 20 N CykWdks ij n'kkZ, vuqlkj yx jgs gsA 4 kg CykWd ij dk;Zjr ?k"kZ.k cy (N esa) – 10 N dk eku D;k gksxk

4 kg 20 N2 kg10 N

µ = 0.6 µ = 0.4



Q.6 Two rays are incidents on a spherical concavemirror of radius R = 5cm parallel to its optical axisat perpendicular distances 3cm and 4cmrespectively. Determine the value ∆x if distancebetween the points at which these rays intersect theoptical axis after being reflected from the mirror is

∆x × 245 cm.

Q.7 A circular beam of light of diameter d = 2cm falls on a plane surface of glass. The angle of incidenceis 60º and refractive index of glass is

µ =23 . Find the diameter of the refracted beam in

cm. Q.8 In a modified YDSE the region between screen and

slits is immersed in a liquid whose refractive index

varies with time as µl = 25 –

4T until it reaches a

steady state value 45 . A glass plate of thickness 36

µm and refractive index 23 is introduced infront of

one the slits. The speed of the central maximawhen it is at O is …….. × 10–3 m/s

Q.6 nks izdk'k fdj.ksa ,d xksyh; vory niZ.k ftldh oØrk R = 5cm ij bldh izdkf'k; v{k ds lekUrj o yEcor~ nwjh;ksa 3cm o 4cm ij vkifrr gks jgh gSA nwjh ∆x Kkr dhft, ;fn ijkorZu ds i'pkr nksuksa fdj.kksa }kjk izdkf'k; v{k dks dkVus okys fcUnqvksa ds e/; dh

nwjh ∆x × 245 cm gS

Q.7 ,d oÙkh; izdk'k iqat ftldk O;kl d = 2cm gS] ,d

lery dk¡p lrg ij vkifrr gks jgk gSA vkiru dks.k

60º gS o dk¡p dk viorZukad µ =23 gSA rks viofrZr

iqat dk O;kl Kkr dhft,A

Q.8 ,d ifjofrZr YDSE iz;ksx esa LØhu o fLyVkas ds e/;

{ks=k esa ,d nzo Hkjk gS ftldk viorZukad µl = 25 –

4T

ds vuqlkj le; ds lkFk ifjofrZr gksrk gS tc rd

;g fu;r eku 45 rd uk igq¡p tk;sA ,d dk¡p

iV~Vhdk ftldh eksVkbZ 36 µm gS o viorZukad23 gS dks

fLyVksa fd lkeus izosf'kr djk;k x;k gSA dsUnzh; pedhys dh pky tc ;g O ij gS …….. × 10–3 m/s gSA



Space for Rough Work (jQ+ dk;Z gsrq LFkku)



Name : _________________________________________________________ Roll No. : __________________________

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 le{k lgh mÙkj fpfUgr dhft,A 2. mRrj ds fy,] OMR vyx ls nh tk jgh gSA 3. ifjoh{kdksa }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 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 ijh{kk 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

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


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

4

56

7

8

9

012

3

4

56

7

8

9


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