please read the instructions carefully. you are … read the instructions carefully. you are...

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Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. Date : 23-01-2011 Duration : 3 Hours Max. Marks : 270 PAPER - 1 CODE 0 PART TEST-6 (PT-6) TARGET : IIT-JEE 2011 INSTRUCTIONS A. General : 1. This Question Paper contains 63 questions. 2. The question paper CODE is printed on the right hand top corner on this sheet of this booklet. 3. No additional sheets will be provided for rough work. 4. Blank paper, clipboard, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets in any form are not allowed. 5. The answer sheet, a machine-gradable Objective Response Sheet (ORS), is provided separately. 6. Do not Tamper / mutilate the ORS or this booklet. 7. Do not break the seals of the question-paper booklet before instructed to do so by the invigilators. 8. Write your Name, Roll No. and Sign in the space provide on the back page of this booklet. B. Filling the bottom-half of the ORS : 9. The ORS has CODE printed on its lower and upper Parts. 10. Make sure the CODE on the ORS is the same as that on this booklet. If the Codes do not match, ask for a change of the Booklet. 11. Write your Roll No., Name and Name of centre and sig with pen in appropriate boxes. Do not write these anywhere else. 12. Darken the appropriate bubbles below your registration number with HB Pencil. 13. Fill the test cities code in ORS Sheet and for details of cities code see last page this test paper booklet. C. Question paper format and Marking scheme : 14. The question paper consists of 3 parts (Chemistry, Mathematics & Physics). Each part consists of Four Sections. 15. For each question in SectionI , you will be awarded 3 marks if you darken the bubble corresponding to the correct answer and zero marks if no bubble is darkened. In case of bubbling of incorrect answer, minus one (1) mark will be awarded. 16. For each question in SectionII , you will be awarded 4 marks if you darken the bubble(s) corresponding to the correct choice(s) for the answer and zero mark if no bubbled is darkened. There is no negative marking for incorrect answer(s) for this this section. 17. For each question in SectionIII, you will be awarded 3 marks for each row in which you have darkened the bubble(s) corresponding to the correct answer. Thus, each question in this section carries a maximum of 12 marks. There is no negative marking for incorrect answer(s) for this this section. 18. For each question in SectionIV, you will be awarded 4 marks if you darken only the bubble corresponding to the correct answer and zero mark if no bubble is darkened. In case of bubbling of incorrect answer, minus one (1) mark will be awarded. DO NOT BREAK THE SEALS WITHOUT BEING INSTRUCTED TO DO SO BY THE INVIGILATOR CLASS-XII/XIII COURSE : ALL INDIA TEST SERIES (VIKALP)

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Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

Date : 23-01-2011 Duration : 3 Hours Max. Marks : 270

PAPER - 1

CODE

0PART TEST-6 (PT-6)TARGET : IIT-JEE 2011

INSTRUCTIONSA. General :

1. This Question Paper contains 63 questions.

2. The question paper CODE is printed on the right hand top corner on this sheet of this booklet.

3. No additional sheets will be provided for rough work.

4. Blank paper, clipboard, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets

in any form are not allowed.

5. The answer sheet, a machine-gradable Objective Response Sheet (ORS), is provided separately.

6. Do not Tamper / mutilate the ORS or this booklet.

7. Do not break the seals of the question-paper booklet before instructed to do so by the invigilators.

8. Write your Name, Roll No. and Sign in the space provide on the back page of this booklet.

B. Filling the bottom-half of the ORS :

9. The ORS has CODE printed on its lower and upper Parts.

10. Make sure the CODE on the ORS is the same as that on this booklet. If the Codes do not match, ask for a

change of the Booklet.

11. Write your Roll No., Name and Name of centre and sig with pen in appropriate boxes. Do not write these

anywhere else.

12. Darken the appropriate bubbles below your registration number with HB Pencil.

13. Fill the test cities code in ORS Sheet and for details of cities code see last page this test paper booklet.

C. Question paper format and Marking scheme :

14. The question paper consists of 3 parts (Chemistry, Mathematics & Physics). Each part consists of Four Sections.

15. For each question in Section�I , you will be awarded 3 marks if you darken the bubble corresponding to the

correct answer and zero marks if no bubble is darkened. In case of bubbling of incorrect answer, minus

one (�1) mark will be awarded.

16. For each question in Section�II , you will be awarded 4 marks if you darken the bubble(s) corresponding

to the correct choice(s) for the answer and zero mark if no bubbled is darkened. There is no negative

marking for incorrect answer(s) for this this section.

17. For each question in Section�III, you will be awarded 3 marks for each row in which you have darkened the

bubble(s) corresponding to the correct answer. Thus, each question in this section carries a maximum of

12 marks. There is no negative marking for incorrect answer(s) for this this section.

18. For each question in Section�IV, you will be awarded 4 marks if you darken only the bubble corresponding

to the correct answer and zero mark if no bubble is darkened. In case of bubbling of incorrect answer,

minus one (�1) mark will be awarded.

DO

NO

T B

RE

AK

TH

E S

EA

LS

WIT

HO

UT

BE

ING

INS

TR

UC

TE

D T

O D

O S

O B

Y T

HE

INV

IGIL

AT

OR

CLASS-XII/XIII COURSE : ALL INDIA TEST SERIES (VIKALP)

RESONANCE

(SPACE FOR ROUGH WORK)

P1R230111C0-1

PART-I

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 - IStraight Objective Type

This section contains 10 multiple choice questions. Each question has choices (A), (B), (C) and (D), out ofwhich ONLY ONE is correct.

1. A solution of 0.2 mole KI (degree of dissociation= 100%) in 1000 g water freezes at T1 0C and boils at T

3°C.

Now to this solution 0.1 mole solid Hg2 is added and the resulting solution freezes at T

2 0C and boils at T

4°C.

Which of the following is correct :

(A) T1 = T

2 , T

3 = T

4(B) T

1 > T

2 , T

3 < T

4(C) T

1 < T

2 , T

3 > T

4(D) None

2. Pb and Sn are extracted from their chief ores by :

(A) Carbon reduction and self reduction (B) Self reduction and carbon reduction(C) Electrolysis and self reduction (D) Self reduction and electrolysis

3. Which of the following statement is incorrect :(A) Enthalpy (numerical value) of physisorption is greater than that of chemisorption(B) Physisorption is not very specific but chomisorption is highly specific in nature(C) Chemisorption takes place at relatively higher temperature(D) In physisorption generally multi�molecular layers are formed on the adsorbent

4. The relationship between osmotic pressure at 273 K when 10 g glucose,10 g urea and 10 g sucrose aredissolved in 250 mL of water to form separate solutions is : [P

1, P

2 and P

3 are osmotic pressure of glucose,

urea and sucrose solution respectively](A) P

1 > P

2 > P

3(B) P

3 > P

1 > P

2(C) P

2 > P

1 > P

3(D) P

2 > P

3 > P

1

RESONANCE

(SPACE FOR ROUGH WORK)

P1R230111C0-2

5.

Which of the following are incorrect on basis of above ellingham diagram for carbon.(A) Upto 710°C, the reaction of formation of CO

2 is energetically more favourable, but above 710°C the

formation of CO is preferred.(B) In principle, carbon can be used to reduce many metal oxide at a sufficiently high temperature.

(C) S (C(s)

+ 21

O2 (g)

CO(g)

) < S (C(s)

+ O2(g)

CO2(g)

)

(D) carbon reduces many oxides at elevated temperature because G° v/s temperature line has a negative slope.

6. Phosphine can be prepared by which one of the following method ?(A) Red phosphorus is treated with I

2 and water.

(B) CaO in water reacts with white phosphours.(C) Phosphonium iodide (PH

4I) is heated with a solution of KOH

(D) (B) and (C) both.

7. For the complete coagulation of 200 mL of As2S

3 solution, 10 mL of 1 M NaCl is required. What is the

coagulating value of NaCl ?(A) 200 (B) 100 (C) 50 (D) 25

RESONANCE

(SPACE FOR ROUGH WORK)

P1R230111C0-3

8. (X) C6H

7N (Aromatic)

(X) cannot be :

(A) Benzoic acid (B) Benzene carbonyl chloride(C) Benzoic anhydride (D) Benzonitrile

9. products ; one of the product is

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

10. (X) solutionNaOH.conc)excess(OCH2

4125 OHC)Y(

OH/H/CrO 23

The compound (X) is :

(A) CH3CH=O (B)

O||

CH�C�CH 33 (C) CH2=O (D) CH

3�CH

2�CH=O

RESONANCE

(SPACE FOR ROUGH WORK)

P1R230111C0-4

SECTION - II

Multiple Correct Answers TypeThis section contains 5 multiple correct answer(s) type questions. Each question has 4 choices (A), (B), (C)

and (D), out of which ONE OR MORE is/are correct.

11. For H3PO

3 and H

3PO

4, the correct choice is:

(A) Number of P�H bond in H3PO

3 is one.

(B) H3PO

3 is dibasic and reducing.

(C) H3PO

4 is tribasic and reducing.

(D) On heating H3PO

3 gets disproportionate into H

3PO

4 and PH

3.

12. Calcium silicate (slag) formed in the slag formation zone in extraction of iron from haematite ore :

(A) does not dissolve in molten iron (B) being lighter floats on the molten iron

(C) is used in cement industry (D) prevents the re-oxidation of molten iron

13. Which of the following is/are correct for an ideal binary solution of two volatile liquids (eg. benzene &

toluene) ?

(A) its vapor is always richer in the more volatile component (compared to the liquid).

(B) the liquid will gradually become richer in the less volatile component if such a mixture is boiled

(distilled).

(C) the pT (ie. the total pressure) above the solution will be the sum of the vapor pressures of the two

pure components.

(D) the boiling point of the solution will be less than the boiling points of the two components.

(SPACE FOR ROUGH WORK)

RESONANCE

(SPACE FOR ROUGH WORK)

P1R230111C0-5

14.)Aromatic(

)X(

The correct statements are :(A) (X) is an aromatic acid.

(B) (Z) can be .

(C) (Y) on heating with Zn forms symmetrical tribromobenzene.(D) (X) can be obtained by fusion of Benzene-1,3-disulphonic acid with NaOH.

15. The correct order(s) is/are :

(A) Ph�CH2�Br > Ph�Cl > Ph�Br .......... (SN reaction with NaOH/ )

(B) > > ..... (Hydrolysis with NaOH)

(C) > CH3�CH

2�COOH > CH

3�COOH ............... (rate of esterification)

(D) HCHO > CH3CHO > PhCHO ............ (Rate of nucleophilic addition reaction)

(SPACE FOR ROUGH WORK)

RESONANCE

(SPACE FOR ROUGH WORK)

P1R230111C0-6

SECTION - IIIMatrix - Match Type

This section contains 2 questions. Each question contains statements given in twocolumns, which have to be matched. The statements in Column-I are labelledA, B, C and D, while the statements in Column-II are labelled p, q, r, s and t. Anygiven statement in Column-I can have correct matching with ONE OR MOREstatement(s) in Column-II. The appropriate bubbles corresponding to the answersto these questions have to be darkened as illustrated in the following example.If the correct matches are A-p, s and t ; B-q and r; C-p and q; and D-s and t; then the correct darkening ofbubbles will look like the following :

16. Column I Column II(Products)

(A) NaNO2 + FeSO4 + H2SO4 (Unbalanced) (p) N2O

(B) HNO3(dil.) + Cu + H2O (Unbalanced) (q) NO2

(C) Pb(NO3)2 (Unbalanced) (r) O2

(D) NH4NO3 (Unbalanced) (s) NO

(t) Atleast one of product is paramagnetic

(SPACE FOR ROUGH WORK)

RESONANCE

(SPACE FOR ROUGH WORK)

P1R230111C0-7

17. Match the compounds of column(I) with the reaction characteristics of column(II)

Column-I Column-II

(A) (p) Reduction with LiAlH4

(B) (q) Nucleophilic addition

(C) (r) Hydrolysis

(D) (s) -halogenation

(t) phenyl-1,2-shift possible by using H+.

(SPACE FOR ROUGH WORK)

RESONANCE

(SPACE FOR ROUGH WORK)

P1R230111C0-8

SECTION - IVInteger Answer Type

This section contains 4 questions. The answer to each of the questions isa single digit integer, ranging from 0 to 9. The appropriate bubble below therespective question number in the ORS have to be darkened.

18. How many oxygen atoms of [SiO4]4� are shared in three dimensional sheet silicate ?

19. How many of the given metals can be obtained by carbon reduction in their extractive metallurgy.

Zn, Pb, Na, Sn, Ag, Au, Mg, Al, Fe

20. Henry�s law constant for CO2 in water is 2.5 × 10 8 Pa at 298K. Calculate mmole of CO

2 dissolved in 162 gm

water at 2.5 atm pressure at 298K.[Take 1 atm = 105N/m2]

21.excess

SOCl)1( 2 excess

NCH 2214

excess

OAg2 /OH2

excess

)CaO(NaOH

Product

How many C14 atoms are present in the product.

(SPACE FOR ROUGH WORK)

(SPACE FOR ROUGH WORK)

RESONANCE P1R230111C0-9

PART- II

SECTION - IStraight Objective Type

This section contains 10 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for itsanswer, out of which ONLY ONE is correct.

22. The greatest integer n such that (42)n divides 2011! is

(A) 330 (B) 331 (C) 332 (D) 333

23. Three identical fair dice are rolled once. The probability that the same number will appear on each of them is

(A) 61

(B) 361

(C) 181

(D) 283

24. If two distinct chords of a parabola y2 = 4ax passing through the point (a, 2a) are bisected by the linex + y = 1, then the length of the latus rectum can be(A) 2 (B) 7 (C) 4 (D) 5

25. The maximum area of the triangle inscribed in the ellipse 2

2

a

x+ 2

2

b

y= 1 is

(A) 433

ab (B) 433

a2 (C) 433

b2 (D) 233

ab

(SPACE FOR ROUGH WORK)

(SPACE FOR ROUGH WORK)

RESONANCE P1R230111C0-10

(SPACE FOR ROUGH WORK)

26. The hyperbola 2

2

a

x� 2

2

b

y= 1 has its conjugate axis 5 and passes through the point (2, �1). The length of a

latus rectum is

(A) 2945

(B) 2985

(C) 29 (D) 429

27. Let f(x) = x + sinx, area bounded by f�1(x), x-axis and x = 0, x = is

(A) 2

2

+ 2 sq.unit (B) 2

2

� 2 sq.unit (C) 2 + 2 sq.unit (D) 2

2� 1 sq.unit

28. If dxdy

= xy + 2x + 3y + 6, then y(�1) � e2y (�3) =

(A) e2 � 1 (B) e2 + 1 (C) 2(e2 � 1) (D) � 2(e2 � 1)

29. If dxdy

+ y = xee , then ey(1) � y(0) =

(A) e � 1 (B) ee + 1 (C) ee � e (D) ee + e

(SPACE FOR ROUGH WORK)

RESONANCE P1R230111C0-11

(SPACE FOR ROUGH WORK)

30. With usual notations. In triangle ABC

222 cba

is always

(A) 36 (B) 34 (C) 33 (D) 38

31. It twice the square of the diameter of a circle is equal to the sum of the squares of the sides of the inscribedtriangle ABC then sin2A + sin2B + sin2C is equal to(A) 2 (B) 3 (C) 4 (D) 1

SECTION - IIMultiple Correct Answer Type

This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for itsanswer, out of which ONE OR MORE is/are correct.

32. If a, b, A be given in a triangle and c1 and c

2 two possible values of third side such that c

12 + c

1c

2 + c

22 = a2,

then A is equal to

(A) 6

(B) 3

(C) 2

(D) 32

33. If sin is the G.M. between sin and cos, then cos2 is equal to

(A) 2sin2

4 (B) 2cos2

4 (C) 2cos2

4 (D) 2sin2

4

(SPACE FOR ROUGH WORK)

RESONANCE P1R230111C0-12

(SPACE FOR ROUGH WORK)

34. If f(x + y) = f(x).f(y) for all x, y and f(1) = 2 and ar = f(r) for r N then the coordinates of a point on the parabola

y2 = 8x whose focal distance is 4 may be(A) (a

1, a

2) (B) (a

1 � a

2) (C) (a

1, a

1) (D) (a

2 , a

1)

35. The locus of extremities of the latus rectum of the family of ellipse b2x2 + y2 = a2b2 is(A) x2 � ay = a2 (B) x2 � ay = b2 (C) x2 + ay = a2 (D) x2 + ay = b2

36. The solution of

2

dxdy

+ 2y cotx

dxdy

= y2 is where c is arbitrary constant.

(A) x = 2sin�1 y2c

(B) x = 2cos�1 y2c

(C) y = xcos�1

c(D) y =

xcos1c

SECTION - III

Matrix - Match TypeThis section contains 2 questions. Each question contains statements given in two

columns, which have to be matched. The statements in Column-I are labelled

A, B, C and D, while the statements in Column-II are labelled p, q, r, s and t. Any

given statement in Column-I can have correct matching with ONE OR MORE

statement(s) in Column-II. The appropriate bubbles corresponding to the answers

to these questions have to be drakened as illustrated in the following example.

If the correct matches are A-p, s and t ; B-q and r; C-p and q; and D-s and t; then the correct darkening of

bubbles will look like the following :

(SPACE FOR ROUGH WORK)

RESONANCE P1R230111C0-13

(SPACE FOR ROUGH WORK)

37. Column-I Column-II

(A) The number of ways, in which 12 red balls, 12 black (p)61

balls and 12 white balls be given to 2 children each 18is

(B) If 6 letter words are formed using the letters of the word (q) 127NUMBER and the words are arranged in dictionaryorder, then the rank of the word NUMBER is

(C) The probability that a divisor of the form 4n + 2, n = 0,1.... (r)52

of the integer 720.

(D) If 3 numbers are selected from the set of the first 10 (s) 469natural numbers the probability the they form an AP is

(t)51

(SPACE FOR ROUGH WORK)

RESONANCE P1R230111C0-14

(SPACE FOR ROUGH WORK)

38. A triangle ABC is inscribed in the parabola y2 = 4x with A at the vertex of the parabola and its orthocentre atthe focus.

Column-I Column-II

(A) The distance of the chord BC from A. (p) 2

(B) The distance of the centriod from A (q) 4

(C) The distance of the circumcentre from A (r)3

10

(D) The inradius of ABC (s)29

(t) 5

(SPACE FOR ROUGH WORK)

RESONANCE P1R230111C0-15

(SPACE FOR ROUGH WORK)

SECTION - IVInteger Answer Type

This section contains 4 questions. The answer to each of the questions isa single digit integer, ranging from 0 to 9. The appropriate bubble below therespective question number in the ORS have to be darkened.

39. Number of polynomials of the form x3 + ax2 + bx + c that are divisible by x2 + 1 where a, b, c {1,2,....9,10}is equal to 2k where k is equal to

40. A point P(x, y) moves in xy plane in such a way that 2 |x + y| + |x � y| 22 . The area of the regionrepresenting all possible positions of the point P is equal to in sq.units.

(SPACE FOR ROUGH WORK)

RESONANCE P1R230111C0-16

(SPACE FOR ROUGH WORK)

41. In the adjacent figure, P is any arbitrary interior point of the triangle ABC. Ha, H

b and H

c are the length of

altitudes drawn from vertices A, B and C respectively. If xa, x

b, x

c represent the distances of P from sides BC,

AC and AB respectively to the opposite sides then a

a

H

x+

b

b

H

x+

c

c

H

x is always equal to

42. There are two teams with n persons in each. The probability of selecting 2 persons from one team and one

person from the other is 76

, then value of n is

(SPACE FOR ROUGH WORK)

RESONANCE P1R230111C0 - 17

PART - III

SECTION - IStraight Objective Type

This section contains 10 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for itsanswer, out of which ONLY ONE is correct.

43. A tank with length 10 m, breadth 8 m and depth 6m is filled with water to the top. If g = 10 m s�2 anddensity of water is 1000 kg m�3, then the thrust on the bottom is(A) 4.8 × 106 N (B) 4.8 × 105 N (C) 1.8 × 106 N (D) 3 × 106 N

44. A metal block is experiencing an atmospheric pressure of 1 × 105 N/m2, when the same block is placed in avacuum chamber, the fractional change in its volume is (the bulk modulus of metal is 1.25 × 1011 N/m2)(A) 4 × 10�7 (B) 2 × 10�7 (C) 8 × 10�7 (D) 1 × 10�7

45. In given figure, let W1 and W

2 be the workdone by the system in process A and B respectively then (initial

and final volumes in both process remains same)

(A) W1 > W

2(B) W

1 = W

2(C) W

1 < W

2

(D) Nothing can be said about the relation between W1 and W

2

46. Water rises in a capillary tube to a height h. it will rise to a height more than h(A) on the surface of sun (B) in a lift moving down with an acceleration(C) at the poles (D) in a lift moving up with an acceleration.

(SPACE FOR ROUGH WORK)

RESONANCE P1R230111C0 - 18

47. 20 gm ice at �10 ºC is mixed with m gm steam at 100 ºC. The minimum value of m so that finally all ice and

steam converts into water is : (Use sice=0.5 cal/gmºC,swater=1 cal/gmºC,L (melting)=80 cal/gm and L

(vaporization)=540 cal/gm)

(A) 3285

gm (B) 1764

gm (C) 1685

gm (D) None of these

48. Heat flows radially outward through a spherical shell of outside radius 3R and inner radius R. Thetemperature of inner surface of shell is

1 and that of outer is

. The radial distance from centre of shell

where the temperature is just half way between 1 and

2 is :

(A) 2R (B) 3R (C) 2R3

(D) 2R5

49. The de Broglie wavelength of an electron moving with a velocity 1.5 × 108 ms�1 is equal to that of a photon.The ratio of the kinetic energy of the electron to that of the energy of photon is :

(A) 2 (B) 4 (C) 2

1(D)

4

1

50. In a uranium reactor whose thermal power is P = 200 MW, if the average number of neutrons liberatedin each nuclear splitting is 2.5. Each splitting is assumed to release an energy E = 100 MeV. The

number of neutrons generated per unit time is -

(A) 4 × 1018 (B) 8 × 1023 (C) 8

25 × 1019 (D)

16125

× 1018

51. If the first minima in a Young�s slit experiment occurs directly infornt of one of the slits. (distance

between slit & screen D = 12 cm and distance between slits d = 5 cm) then the wavelength of theradiation used is :

(A) 2 cm only (B) 4 cm only (C) 2m,32

cm, 52

cm (D) 4cm,34

cm,54

cm

(SPACE FOR ROUGH WORK)

RESONANCE P1R230111C0 - 19

52. Force F is given in terms of time t and distance x byF = A sin C t + B cos D x

Then the dimensions of BA

and DC

are given by

(A) MLT�2, M0L0T�1 (B) MLT�2, M0L�1T0 (C) M0L0T0, M0L1T�1 (D) M0L1T�1, M0L0T0

SECTION - II

Multiple Correct Answer Type

This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its

answer, out of which ONE OR MORE is/are correct.

53. A cyclic process ABCD is shown in the P�V diagram. (BC and DA are isothermal)

Which of the following curves represents the same process?

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

(SPACE FOR ROUGH WORK)

(SPACE FOR ROUGH WORK)

RESONANCE P1R230111C0 - 20

54. In an xray tube the voltage applied is 20KV. The energy required to remove an electron from L shell is 19.9KeV. In the xrays emitted by the tube (hc = 12420 evÅ)

(A) minimum wavelength will be 62.1 pm(B) energy of the characterstic xrays will be equal to or less than 19.9 KeV(C) L

xray may be emitted

(D) L xray may have energy 19.9 KeV

55. The decay constant of a radio active substance is 0.173 (years)-1. Therefore:(A) Nearly 63% of the radioactive substance will decay in (1/0.173) year.(B) half life of the radio active substance is (1/0.173) year.(C) one -forth of the radioactive substance will be left after nearly 8 years.(D) half of the substance will decay in one average life time.

Use approximation n2 = 0.692

56. In an interfrence arrangement similar to Young's double- slit experiment, the slits S1 & S

2 are illuminated

with coherent microwave sources, each of frequency 106 Hz. The sources are synchronized to havezero phase difference. The slits are separated by a distance d = 150.0 m and screen is at very largedistance from slits. The intensity () is measured as a function of , where is defined as shown.Screen is at a large distance. If

0 is the maximum intensity then () for 0 90º is given by:

(A) () = 20 for = 30º (B) () 0 when 90º

(C) () = 0 for = 0º (D) () is constant for all values of

(SPACE FOR ROUGH WORK)

RESONANCE P1R230111C0 - 21

57. A cubical block of wood of edge 10cm and mass 0.92kg floats on a tank of water with oil of rel. density 0.6.Thickness of oil is 4cm above water. When the block attains equilibrium with four of its sides edges vertical:(A) 1 cm of it will be above the free surface of oil(B) 5 cm of it will be under water.(C) 2 cm of it will be above the common surface of oil and water.(D) 8 cm of it will be under water.

SECTION - IIIMatrix - Match Type

This section contains 2 questions. Each question contains statements given in twocolumns, which have to be matched. The statements in Column-I are labelledA, B, C and D, while the statements in Column-II are labelled p, q, r, s and t. Anygiven statement in Column-I can have correct matching with ONE OR MOREstatement(s) in Column-II. The appropriate bubbles corresponding to the answersto these questions have to be drakened as illustrated in the following example.If the correct matches are A-p, s and t ; B-q and r; C-p and q; and D-s and t; then the correct darkening ofbubbles will look like the following :

58. The energy, the magnitude of linear momentum, magnitude of angular momentum and orbital radius of anelectron in a hydrogen atom corresponding to the quantum number n are E,p,L and r respectively.Thenaccording to Bohr's theory of hydrogen atom, match the expressions in column-I with statement in column-II.Column-I Column-II

(A) Epr (p) is independent of n.

(B) Ep

(q) is directly proportional to n

(C) Er (r) is inversely proportional to n.

(D) pr (s) is directly proportional to L.

(t) proportional to nx where x 0, �1,1

(SPACE FOR ROUGH WORK)

RESONANCE P1R230111C0 - 22

59. In a typical Young's double slit experiment, S1 and S

2 are identical slits and equidistant from a point

monochromatic source S of light having wavelength . The distance between slits is represented by d and

that between slits and screen is represented by D. P is a fixed point on the screen at a distance y = o

o

d2

D

from central order bright on the screen: where Do, d

o are initial values of D and d respectively. In each

statement of column-I some changes are made to above mentioned situation. The effect of correspondingchanges is given in column-II. Match the statements in column-I with resulting changes in column-II.

Column-I Column-II(A) The distance d between the slits is doubled (p) fringe width increases .

keeping distance between slits and screen fixed(B) The distance D between slit and screen is doubled (q) Magnitude of optical path difference between

by shifting screen to right interfering waves at P will decrease.(C) The width of slit S

1 is decreased (such that (r) Magnitude of optical path difference

intensity of light due to slit S1 on screen between interfering waves at P

decreases) and the distance D between slit will increase.and screen is doubled by shiftingscreen to right

(D) The whole setup is submerged in water (s) The intensity at P will increase

of refractive index 34

.

(neglecting absorption in medium)(t) The intensity at P will decrease

(SPACE FOR ROUGH WORK)

(SPACE FOR ROUGH WORK)

RESONANCE P1R230111C0 - 23

SECTION - IVInteger Answer Type

This section contains 4 questions. The answer to each of the questions isa single digit integer, ranging from 0 to 9. The appropriate bubble below therespective question number in the ORS have to be darkened.

60. In an experiment on photoelectric effect, light of wavelength 800 nm (less than threshold wavelength) isincident on a cesium plate at the rate of 5.0 W .The potential of the collector plate is made sufficientlypositive with respect to the emitter so that the current reaches its saturation value .Assuming that onthe average one of every 106 photons is able to eject a photoelectron, the photo current in the circuit is

in the form 8x × 10�7 A. Find the x. [h = 3

20× 10�34 J.sec]

61. Consider a point source emitting -particles and receptor of area 1 cm2 placed 1 m away from source.Receptor records any -particle falling on it. If the source contains N

0 =

3.0 × 1016 active nuclei and the

receptor records a rate of A = 50000 counts/second, the decay constant is the form of 21

K 11× 10�7 S�1

Assume that the source emits alpha particles uniformly in all directions and the alpha particles fallnearly normally on the window. Find K.

(SPACE FOR ROUGH WORK)

(SPACE FOR ROUGH WORK)

RESONANCE P1R230111C0 - 24

62. In a YDSE experiment, the distance between the slits & the screen is 100 cm. For a certain distancebetween the slits, an interference pattern is observed on the screen with the fringe width 0.25 mm.When the distance between the slits is increased by d = 1.2 mm, the fringe width decreased to n= 2/3 of the original value. In the final position, a thin glass plate of refractive index 1.5 is kept in frontof one of the slits & the shift of central maximum is observed to be 20 fringe width. The thickness of the

plate in the form of 12x m. Fill 'x' .

63. A spherical tungsten piece of area A = 8.1

1m2 is suspended in an evacuated chamber maintained at 300 K.

The piece is maintained at 1000 K by heating it electrically. The rate at which the electrical energy must besupplied is 1417 x watt. The emissivity of tungsten is 0.30 and the stefan constant is 6.0 × 10�8 W/m2�K4.Find the 'x'.

(SPACE FOR ROUGH WORK)

(Space for rough work)

Name of the Candidate Roll Number

I have read all the instructions andshall abide by them.

-------------------------------- Signature of the Invigilator

I have verified all the informationfilled in by the Candidate.

-------------------------------- Signature of the Candidate

Example for Filling Test Cities Code in ORS :If your Test centre is Bhatinda and test code is 06 then fill in ORS :

(a)

(b)

Test Code Test Centre Test Code Test Centre Test Code Test Centre

01 AHMEDABAD 02 AGRA 03 BENGALURU04 BIKANER 05 BHOPAL 06 BHATINDA07 BHUBNESHWAR 08 BOKARO 09 CHANDIGARH10 DHANBAD 11 DEHRADUN 12 GUWAHATI13 HYEDRABAD 14 INDORE 15 JAIPUR16 KANPUR 17 KOLKATA 18 KOTA19 LUCKNOW 20 MUMBAI- Andheri 21 MUMBAI- Thane22 MUMBAI- Nerul 23 MUMBAI- Dadar 24 MANGLURU25 MUZAFFARPUR 26 NAGPUR 27 NEW DELHI- East28 NEW DELHI- North West 29 NEW DELHI- South 30 PATNA31 RAIPUR 32 RANCHI 33 SRI GANGANAGAR34 SHAKTI NAGAR 35 UDAIPUR 36 UDUPI37 VARANASI 38 BHAGALPUR 39 GWALIOR40 PATHANKOT 41 RAJKOT 42 GORAKHPUR43 BHILAI