file no. iit – 248-24 jr iit spark ex dt 15-11-08

FILE NO. IIT – 248/24(14-11-2008) CODE SURYA

JR IIT SPARK (500×3×2) TWO YEAR CLASS ROOM PROGRAM [69-Bits model test]

EX.DT: 15-11-2008

Time: 3 hours Maximum marks: 246

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

INSTRUCTIONSA. General:

1. This booklet is your Question Paper containing 69 questions. The booklet has 16 pages.

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

3. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers, and electronic gadgets in any form are not allowed to be carried inside the examination hall.

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

5. DO NOT TAMPER WITH / MUTILATE THE ORS OR THE BOOKLET.

B. Filling the ORS6. On the lower part of the ORS, write in ink, your name in box L1, your

Registration No. in box L2 and Name of the Centre in box L3. Do not write these anywhere else.

7. Write your Registration No. in ink, in the box L4 provided in the lower part of the ORS and darken the appropriate bubble UNDER each digit of your Registration No. with a good quality HB pencil.

8. The ORS has a CODE printed on its lower and upper parts.9. Make sure the CODE on the ORS is the same as that on this booklet

and put your signature in ink in box L5 on the ORS affirming that you have verified this.

10. IF THE CODES DO NOT MATCH, ASK FOR A CHANGE OF THE BOOKLET.

C. Question paper format:11. The question paper consists of 3 parts (Part I: Mathematics, Part II:

Physics, Part III: Chemistry). Each part has 4 sections.12. Section I consists of Questions 1 to 9.These are single correct answer

type. For each correct answer 3 marks will be awarded and each incorrect choice 1 mark will be deducted

13. Section II contains 4 questions numbered 10 to 13. Each question contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason). Each question has 4 choices (a), (b), (c), and (d) , out of which ONLY ONE is correct. For each correct answer 3 marks will be awarded and each incorrect choice 1 mark will be deducted. 14.

14. Section III contains 2 paragraphs. P14-16

and P17-19

. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (a), (b), (c), and (d) , out of which ONLY ONE is correct. For each correct answer 4 marks will be awarded and each incorrect choice 1 mark will be deducted.

15. Section IV contains 3 questions. 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) 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, B-q, B-r, C-p, C-q and D-s, then the correctly bubbled matrix should be as follows: For each correct answer 6 marks will be awarded. There is no negative marking for these questions. There could be a single answer or multiple answer.

D. Marking Scheme:16. For each questions in Section I, you will be awarded 3 marks if you

have darkened only the bubble corresponding to the correct answer and zero mark if no bubble is darkened. In all other cases, minus one (–1) mark will be awarded.

17. For each question in Section II, you will be awarded 4 marks if you have darkened all the bubble(s) corresponding to the correct answer and zero mark for all other cases. If may be noted that there is no negative marking for wrong answer.

18. For each question in Section III, you will be awarded 3 marks if you darken only the bubble corresponding to the correct answer and zero mark if no bubble is darkened. In all other cases, minus one (–1) mark will be awarded.

19. 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 all other cases, minus one (–1) mark will be awarded.

Name of the Student Roll Number

I have read all the instructions and shall abide by them

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

I have verified all the information filled in by the Candidate

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

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VSP – RB(AC CAMPUS) /JR IIT SPARK /CPT-10 – IIT (69BITS) MODEL/15-11-2008

MATHEMATICSPART – I

SECTION – IStraight Objective Type

This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.1. The centre of the ellipse is :

(a) (-2,-1) (b) (-2, 1) (c) (2, -1) (d) (2, 1)2. If C is the centre of the ellipse 9x2+16y2=144 and S is one focus, then the ratio of CSto the semi

major axis is : (a) (b) (c) (d)

3. The equation of the ellipse with major axis along x-axis and minor axis along y-axis and passing through the points (4,3) and (6,2) is :

(a) (b) (c) (d)

4. If the segment joining the foci of an ellipse subtends angle of 900 at an extremity of the minor axis, then the eccentricity is :

(a) (b) (c) (d)

5. are vertices of an ellipse with foci . Then the length of the latus rectum is:

(a) (b) (c) (d)

6. The equation represents standard ellipse then :

(a) (b) (c) (d) r = 6

SECTION – IIMultiple Correct Answer Type

This section contains 4 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.

7. An ellipse has foci and passes through the point (4,1). Then

(a) Equations of the ellipse is (b) equation of the ellipse

(c) eccentricity of the ellipse is (d) eccentricity of the ellipse is

NARAYANA IIT ACADEMY

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8. For the ellipse which one of the following are correct?

(a) eccentricity is (b) eccentricity is

(c) latusrectum is (d) latusrectum is

9. For the ellipse which of the following are correct?

(a) The point of intersection of tangents drawn at the points

(b) The foot of the perpendicular drawn from focus onto a tangent lies on

(c) equation of the directrix corresponds to the focus (ae,0) is

(d) If are the two foci and B is one end of the minor axis such that is equilateral then the

eccentricity of the ellipse is

10. For the ellipse (a > b), the length of the latus rectum is 10 and the distance between the

foci is equal to the length of the minor axis. Then

(a) eccentricity is (b) semi major axis is 10

(c) foci are (d) vertices are SECTION – III

Reasoning TypeThis section contains 4 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

CODE(A) STATEMENT–1 is True, STATEMENT–2 is True; STATEMENT–2 is a correct explanation for STATEMENT–1(B) STATEMENT–1 is True, STATEMENT–2 is True; STATEMENT–2 is NOT a correct explanation for STATEMENT–1(C) STATEMENT–1 is True, STATEMENT–2 is False(D) STATEMENT–1 is False, STATEMENT–2 is True 11. Statement - I : The angle between the tangents drawn from the point (2,3) to the ellipse

is 900


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Statement - II : Locus of the point of intersection of perpendicular tangents to the ellipse is

the circle

12. Statement - I :P is a point on the ellipse whose eccentricity is e and foci . If The

angle then

Statement - II : In where s is the semiperimeter of

13. Statement - I : The eccentricity of the ellipse is

Statement - II : The eccentricity e of the ellipse (a>b) is given by 14. Statement - I :If P(x,y) is a point on the ellipse and Then

Statement - II : In an ellipse, the sum of the distances of a point on the ellipise from the foci is always constant

SECTION – IVLinked Comprehension Type

This section contains 3 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Paragraph for Questions Nos. 15 to 17

PASSAGE –IParagraph for Question Nos.15 to 17

F is one of the foci of the ellipse with ‘O’ as centre. and are major and minor axes

respectively. If OF = 6 and the diameter of the incircle of is 2, Then answer the questions 15, 16, 17)

15. (a) (b) (c) (d)

16. eccentricity of the ellipse is :

(a) (b) (c) (d)

17. ( AB) (CD) is equal to :(a) 45 (b) 55 (c) 65 (d) 75

PASSAGE –II


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Paragraph for Question Nos.18 to 20A rod AB of 20 units length with its ends ‘A’ on x-axis and B on the y-axis is sliding between the

axes. P is a marked point on AB such that AP = 8 Answer the questions 18, 19, 2018. The locus of P is :

(a) (b) (c) (d)

19. The eccentricity of the conic is :

(a) (b) (c) (d)

20. The locus of the point of inter section of perpendicular tangents is : (a) (b) (c) (d)

PASSAGE –III

Paragraph for Question Nos.21 to 23

is the standard ellipse ( ie a > b). Answer the Questions

21. If the tangent at P meets the direction in Q and S is (a e, 0), then Angle PSQ is :

(a) (b) (c) (d) 22. If PQ is a focal chord, and are their eccentric angles, Then

(a) (b)

(c) (d)

23. If P and Q are ends of a focal chord with eccentric angles respectively, then

(a) (b)

(c) (d)

PHYSICS


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PART – IISECTION – I

Straight Objective TypeThis section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

24. Which of the following statements is correct for thermometer.(a) Co-efficient of cubical expansion of liquid must be greater than that of bulb material (b) Bulb of the thermometer is made of a poorly conducting material (c) Sole purpose of making walls of the bulb thin is to provide maximum possible space for liquid.(d) None of these.

25. A metal ball immersed in alcohol weighs at 00 C and at 500C. The coefficient of cubical expansion of the metal is less than that of alcohol. If the density of the metal is large compared to that of alcohol, then

(a) w1 > w2 (b) w1 = w2 (c) w1 < w2 (d) can not be determined26. Two rods one of aluminum and the other made of steel, having initial lengths l1 and l2 are

connected together to form a single rod of length l1 + l2. If the length of each rod increases by

the same amounts on increasing the temperature by l0 C, the ratio in terms of

coefficients of linear expansions is given by.

(a) (b) (c) (d)

27. Two metal wires each of length l and having the same area of cross sections are joined end to end and fixed between two rigid supports. The distance through which the joint would move if the system is cooled by temp ‘t’ (The two metals have coefficients of linear expansions , and young modules y1 , y2)

(a) (b)

(c) (d)

28. Two bodies of different materials but of equal mass are heated at uniform rate under identical conditions from . One body melts at after heating for 2 minutes while the other melts at


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after heating for 4 minutes. The ratio of their specific heats is : (a) 1 : 5 (b) 1 : 3 (c) 1 : 4 (d) 1 : 2

29. Steam at is passed into 1.1kg of water contained in a calorimeter of water equivalent 0.02kg at till the temperature of the calorimeter and its contents rises to . The mass of the steam

condensed in kg is ( latent heat of vaporization of water – 540 cal / g , specific heat of water 1 cal/g)(a) 0.13 (b) 0.065 (c) 0.26 (d) 0.135



30. A metal rod is shaped into a ring with a small gap. If this is heated.(a) The length of the rod will increase(b) The gap will decrease(c) The gap will increase(d) The diameter of the ring will increase in the same ratio as the length of the rod

31. Which of the following statements are not true (a) Heat is a macroscopic quantity (b) Heat is intrinsic property of body (c) Heat is stored in a body as internal energy (d) Heat is path independent

32. A vessel is partly filled with a liquid. Coefficient of cubical expansion of material of the vessel and liquid are respectively. If the system is heated then volume unoccupied by the liquid will necessarily (a) increase if (b) decrease if (c) remains un changed if (d) Increase if

33. Some water at 00 C placed in a large insulated enclosure. The water vapour formed is pumped out continuously. If the latent heat of vapourisation is seven times the latent heat of fusion

(a) of initial mass of water freezes

(b) If 10kg of water is placed in the enclosure, mass of vapor formed is 1.25kg.(c) mass of vapor formed is independent of latent heat.(d) Data is insufficient to arrive at conclusion

SECTION – IIIReasoning Type


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This section contains 4 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

CODE(A) STATEMENT–1 is True, STATEMENT–2 is True; STATEMENT–2 is a correct explanation for STATEMENT–1(B) STATEMENT–1 is True, STATEMENT–2 is True; STATEMENT–2 is NOT a correct explanation for STATEMENT–1(C) STATEMENT–1 is True, STATEMENT–2 is False(D) STATEMENT–1 is False, STATEMENT–2 is True34. Assertion (A ):-Two identical rectangular strips, one of copper and the other of steel are riveted

together to form a bimetallic strip. the strip bends with steel on convex side upon cooling. Reason(R):- Change in length of copper is greater with change in temperature

35. Assertion (A) : Food gets cooked faster in a pressure cooker Reason (R) : Water boils at a temperature higher than at higher pressure .

36. Assertion (A) : A body (of coefficient of cubical expansion ) floating an a fluid of cubical

expansion coefficient would sink in the fluid at some higher temperature ‘t’ if Reason (R) : Buoyant force decreases with increase in temperature if

37. Assertion (A) :Calorie is defined as the amount of Heat required to raise temperature of 1g of water by at all temperatures

Reason (R) : Heat required to raise temperature of 1g of water by depends on the temperature of water.




Four rods A, B, C, D of the same length and material but of different radii and 2r respectively are held in parallel between two rigid walls. The temperature of all rods is increased through the same range. If the rods do not bend, then answer the following questions. 38. The stresses in the rods A, B, C and D are in the ratio :

(a) 1 : 1 : 1 : 1 (b) 1 : 2 : 3 : 4 (c) 4 : 3 : 2 : 1 (d) 4 : 3 : 2 : 139. The force on the rods exerted by the wall are in the ratio :

(a) 1 : 1 : 1 : 1 (b) 1 : 2 : 3 : 4 (c) 4 : 3 : 2 : 1 (d) 4 : 3 : 2 : 1

40. The energy stored in the rods due to elasticity are in the ratio :


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(a) 1 : 1 : 1 : 1 (b) 1 : 2 : 3 : 4 (c) 4 : 3 : 2 : 1 (d) 4 : 3 : 2 : 1

PASSAGE –IIParagraph for Question Nos.41 to 43

A substance is in the solid form at . The amount of heat added to this substance and its temperature is plotted in the following graph.

If the relative specific heat capacity of the solid substance is 0.541. What is the mass of the substance ?

(a) 0.01kg (b) 0.02kg (c) 0.03kg (d) 0.04kg42. The specific latent heat of the melting process is :

(a) 10000cal/kg (b) 20000cal/kg (c) 30000 cal/kg (d) 40000 cal/kg43. The specific heat of the substance in the liquid State is

(a) (b) (c) (d)

PASSAGE –IIIParagraph for Question Nos.44 to 46

An iron rod of length 1m is measured using a meter scale made up of copper at . The coefficient of linear expansion for iron and copper is : 44. The length of the iron rod measured by copper scale at is

(a) 0.99985 m (b) 1.00015m (c) 0.9985m (d) None of these45. Actual increase in length of rod at is

(a) 0.36mm (b) (c) (d) None 46. % error in the measurement of the length of the rod: at

(a) 0.15% (b) 0.1% (c) 0.5% (d) None

CHEMISTRY


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PART – IIISECTION – I

Straight Objective TypeThis section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

47. Arrange the following molecules in the increasing order of acidic nature.

1) 2) 3)

a) b) c) d)

48. Which of the following is a weak acid?

a) b)

c) d)

49. Decreasing order of basicity for the following

a) b) c) d)

a) b) c) d)

50. Increasing order of stability in the following resonance structures

a) b) c)

a) b) c) d)

51. Which is more basic in the following?

a) b)

a) b) c) d) Cannot be predicted.

52. Which of the following statement is/are correct?


NO2

OHCCl3

OHCl

OH

NN

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a) Ka order = I > III > II

I II III

b) Acidic nature I > II > III

I II III

c) > basic nature d) Basic nature



53. Which one of the following statement is/are correct?

a) According to Hyper conjugation bond length

b) +I inductive effect of

c) Kb order: I > II > III d) basicity order = y > x >z

54. Which is the following statement is/are correct according to stability


ONOH OH

NO2

NO2

O2NNO2

OH

NO2NO2

NO2

NO2

NH2

N

(y)

N

H

(Z)

NH2 (X)

N

(I) HN

N(II)

NH2 (III)

(II)

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a)

b) >

c) >

d)

55.

I II III IV

Which is/are correct statements

a) I is more basic than II b) All are aromatic bases

c) II is more basic than I, III & IV d) In IV hydrogen’s are acidic at “a”, basic at “b”

56. Which is/are less acidic than Benzoic acid?

a) b) c) d)

SECTION – IIIReasoning Type


COOH

3CH

COOH

2NO

Cl Cl+

+

O

3 2 3 2CH C CH CH C CH O

NH

NH2

N

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This section contains 4 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Code(A) STATEMENT–1 is True, STATEMENT–2 is True; STATEMENT–2 is a correct explanation for STATEMENT–1

(B) STATEMENT–1 is True, STATEMENT–2 is True; STATEMENT–2 is NOT a correct explanation for STATEMENT–1

(C) STATEMENT–1 is True, STATEMENT–2 is False.

(D) STATEMENT–1 is False, STATEMENT–2 is True.

57. Statement – I: Allyl radical does not contain one carbon – carbon single bond and one carbon –

carbon double bond.

Statement – II: Because of Resonance, it contains two identical bonds.

58. Statement – I: more stable than

Statement – II: In methyl benzene hyper conjugation cannot take place.

59. Statement – I: Dipole moment & are not equal to zero

Statement – II: Substituents in both have non-linear moments.

60. Statement – I: Squaric acid is a strong acid.

Statement – II : delocalisation is greater in the system hence it can donate OH- group faster.



CH3

OH

OH

COO Et

COO Et

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Basic nature of N-compounds depend upon

a) Resonance effects b) Hybridisation

c) Steric effects d) Solvent effects

61. Which of the following will have high ?

a) b)

c) d)

62. Which of the following will have high ?

.

a) b) c) d)

63. Which of the following will have high basic nature?


llO

NH

llO

llO

NH

NH2

CH3

NH2

CH3

NH2

CH3

NH2

NH

ll0

NH0

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a) b) c) d)

PASSAGE –IIParagraph for Question Nos.64 to 66

Electronic effects are most important. In order to explain stability, Reactivity, Bond length, dipole

moment etc., Based upon the effects explain the following:

64. In which of the following resonance, inductive and hyper conjugative effects can take place

a) b) c) d)

65. Which of the following set had same conjugated base

a) b) Pyridine & pyrrol

c) d) &

66. The fraction of the charge that exist in ortho-nitro phenol,is 0.25 & bond length in 2A0

Calculate the dipole moment offered by NO2 group. If dipole moment of OH

group is 1D (Assume presence of intra H-bond angle decreased to 560 .

a) 1.5D b) 2.4D c) 3D d) 3.5D

PASSAGE –IIIParagraph for Question Nos.67 to 69


OH

NO2

cx3

NO2

OH

NO2

NO2

NR2

OHCH3

CF3

NH2

R CNH2

NH2

R CNH

NH2

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The effect of the solvent on acidity solvation of any species decreases the entropy of the solvent

because the solvent molecules become much more ordered as they surround molecules of the

solute.

Ex: Solvation of is stronger the solvent, the solvent molecules become more orderly

around it. for the ionization of ,therefore, is negative. This means that the

term in makes an acid-weakening positive contribution to , In fact the

term contributes more to than . Hence depending upon above facts for

ionization of is positive.

67. Which of the following statement is / are in polar protic solvent

a) The charge transfer by anion towards solvent is basicity

b) The charge that remain’s after solvation is called nucleophilicity

c) Basicity is kinetic property

d) Nucleophilicity is kinetic property

68. X (organic carbocation )+

For which of the reaction is more negative with respect to product.

a) b)

c) d)

69. Consider the reaction


3 3 2CH C O H H O H O H H C C O H H O

CH3

CH3

CH3

CH3H

H

A B

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What is the composition of the equilibrium mixture at .

a) b) c) d)

PAPER SETTER : VSP-RB (AC CAMPUS)

Mr. G.S.N. Murthy MATHS 9849127144

Mr. Manoj Kumar PHYSICS 9491569945

Mr. Krishna Kishore CHEMISTRY 9912343666


file no. iit – 248-24 jr iit spark ex dt 15-11-08

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