FILE NO. IIT û 213-43 UNIT TEST -7 -PAPER-IQP

FILE NO. IIT – 213/43 (07/11/2008)

CODE GARSHANA

UNIT TEST –07SR IIT SPARK(500X3X2) & SR IIT FTB – I

Test Date: 08 t hNOVEMBER 2008

Time: 3 hours Maximum marks: 246

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

A. General:1. This booklet is your Question Paper containing 69 questions.

The booklet has 20 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 contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which only one is correct.

13. Section II contains 4 multiple correct answer type questions. Each questions has 4 choices (A), (B), (C) and (D), out of which one or more answers are correct.

14. Section III contains 4 Reasoning type questions. Each question contains STATEMENT–1 AND STATEMENT–2.Bubble (A) if both the statements are TRUE and

STATEMENT–2 is the correct explanation of STATEMENT–1.

Bubble (B)if both the statements are TRUE but STATEMENT–2 is NOT the correct explanation of STATEMENT–1.

Bubble (C)if STATEMENT–1 is TRUE and STATEMENT–2 is FALSE.

Bubble (D) if STATEMENT–1 is FALSE and STATEMENT–2 is TRUE.

15. Section IV contains 3 sets of Linked–Comprehension type question. Each set consists of a paragraph followed by 3 questions. Each question has 4 choices (A), (B), (C) and (D), out which only one is correct.

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.

Code: GARSHANA

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

NARAYANA IIT (JEE) ACADEMYNew Nallakunta, – Hyd.

MATHS

PART – ISECTION – 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.1. If and , and , and are the roots of the equations

and respectively where a, b, c are positive real numbers, then a) -1 b) 1 c) 0 d) abc

2. If a, b, c are in geometric progression and the roots of the equations are and and those of are and then a) b) c) d)

3. If and then the values of a and b,

If is HCF of and a) b) c) d)

4. The equation has a) all its solutions real but not all positive b) only two of its solutions realc) two of its solutions positive and two negative d) none of solutions real.

5. Let A be a square Matrix all of whose entries are integers. Then which of the following is True?a) If then exists but all it entries are not necessarily integers.b) If then exists and all it entries are non integers.c) If , then exists ad all its entries are integers.d) If , need not exist.

6. has at least one solution iff

a) b) c) d)

SECTION – II

Multiple Correct Answer Type

NARAYANA IIT (JEE) ACADEMY New Ramalayam Road, New Nallakunta – Hyd. Ph: 23465719

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IIT –NG-ZONE-HYD-ANN-UNIT TEST-7-16-XIIS

Code: GARSHANA 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. If A is a square Matrix such that then

a) b) c) d)

8. If is equal to

a) b) c) d) none

9. If Where a, b are positive integers, then

a) constant term of is 0 b) coefficient of in is 0

c) constant term of is d) constant term in is

10. If where such that

and then

a) b) c) d)

SECTION – III

Reasoning Type

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


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Code: GARSHANA 11. Statement I: Let A be a matrix such that where is a real number then

is Inveritable.Statement I: A square Matrix possess inverse iff it is non-singular.

12. Statement I: Range of is .

Statement II : is an increasing function in its domain.

13. Let where a, b, c are non –zero, unequal real numbers ,

Statement I: divides .

Statement II:

14. Statement I: If then

Statement II: Domain of is and domain of is

SECTION – IV

Linked 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

Consider the equations

15. The complete set of values of a for which the equation (1) holds good is

a) b) c) R d)

16. The set of values of a for which posses solution is

a) b) c) d) R

17. The values of and such that system posses solutions for integral values of ‘a’:

a) b) c) d)


Consider the inequation where ‘a’ is a real parameter. The given inequation has

18. At least one negative solution if


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Code: GARSHANA a) b) c) d)

19. At least one positive solutions if a) b) c) d)

20. At least one solution in if

a) b) c) d)


where a, b, c are constants.

21.

a) b)

c) d)

22. Range of

a) b)

c) d) none

23. __________ When are in AP

a) b) c) d) none


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Code: GARSHANA

PHYSICS

PART – II

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.

24. In the adjoining figure variation of velocity and its co-ordinate with respect the time are given. Curve in parabola. Origin of time coincides in both the graphs

Statement-I Both graphs are showing different motions.Statement-II In both cases particles are coming to rest after 4 second from the start.a) Both statement –I and II are correct.b) Neither I nor II are correct.c) Only I is correct.d) Only II is correct.

25. A water tank of parallelepiped shape is moving on horizontal road with speed increasing from to in t second. If the separation between the longitudinally opposite walls is and lateral ( side) walls are vertical, and tank is completely filled with water and density of water be then the pressure difference between the opposite walls is ( Assume atmospheric pressure P)

a) b) c) d)

26. A rectangular uniform parallelepiped slab is placed on a fixed inclined plane of inclination with the horizontal as shown in the figure. L and R represent the left and right half of the slab. Four observations followed by corresponding conclusions are given below ; Choose the correct one:

a) When the inclined plane is smooth force exerted by inclined plane on right half is greater than that on left half.

b) When inclined plane is sufficient rough to present slipping the force exerted by inclined plane on right half is more than the on left half.


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Code: GARSHANA c) When inclined plan is sufficiently rough to present slipping the force exerted by inclined plane on

right half is less than that’s on the left half.d) When inclined plane is sufficiently rough to present friction the fore exerted by inclined plane is

same on both right and left half.

27. A particle of mass projected at certain angle with the horizontal. Due to air resistance the particle moves in a assymmetric curve. The direction of the acceleration of particle with the direction of velocity, at the highest point of trajectory. Where resistance force is 20N. is ( take g=10 ms-2) ( Assume the resistance force depending on velocity and acting opposite to the velocity )a) b) c) d)

28. In the figure shown a particle of mass m moving with velocity strike a wall ( mass is infinitely large) moving towards the particle with same speed. The work done on the particle during collision is

a)

b) c) d)

29. Two hollow hemispheres of metal are fitted together to form a sphere of radius R. Air from the shall

is pumped out and pressure remained left inside is th the outside atmospheric pressure P0. The

force required to separate the hemisphers is

a) b) c) d)

SECTION – II


This section contains 4 multiple correct answer(s) type questions. Each question has 4 choices (A), (B), (C)


30. Three particles X, Y and Z are placed on straight horizontal line at equal distance from one another. Particle X starts moving vertically up with a constant velocity and particle z vertically down-ward with constant acceleration a without initial velocity. Select the correct option/s from the following about the motion of particle Y so that all the three will be at the same straight line if all begins to move simultaneously

a) Initial velocity upward b) Initial acceleration upward.

c) Initial velocity downward d) Initial acceleration downward.


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Code: GARSHANA

31. In the adjoining figure a bead of mass m is free to slide along the rod of length without friction. Initially the bead is at the middle of the rod and rod is moving horizontally with acceleration ‘a’ which makes an angle with the rod as shown. Choose the in correct option.

a) Acceleration of bead with respect to stationary observer is and directed along the line of action of reaction force.

b) Acceleration of bead with respect to rod is along the rod.c) Both (a) and (b)d) None.

32. A circular ring of radius R and mass 9 m is placed on a perfectly smooth horizontal surface. An ant of mass m starts moving along the ring. Select the correct conclusion/s

a) trajectory of centre of ring is a circle of radius

b) trajectory of ant is also a circle but of radius

c) Ratio of linear speed of centre of ring and that of ant is d) Ratio of angular speeds about a common fixed point is

33. In the figure shown P is the peak of a mountain. From the ground point G; a block of mass m and 2m are lifted slowly to the peak via path I and II respectively. Both paths have same co-efficient of friction. If the work done be respectively Choose the correct option/s a) b) c) loss of energy due to friction is same for both the pathsd) (Where and are workdone per unit mass)


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Code: GARSHANA

SECTION – III

Reasoning Type



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

34. Statement-I: One can’t find exactly and if the time dependence of acceleration is given.

Statement-II: If the time dependence acceleration is given then; for single valued solution for

position vector; boundary condition must be given.

35. Statement-I: Inertial force is caused by the physical interaction of bodies.

Statement-II: Inertial force do not obeys the Newton’s third law of motion.

36. Statement-I: The conservation laws do not depend on the path followed by the particle/body and

nature of forces acting on them.

Statement-II: If external force is non-zero then linear momentum may be conserved in non-inertial

frame of reference.

37. Statement-I: In a closed system total work done by all internal dissipative force is negative in all

frame of reference.

Statement-II: Acceleration of centre of mass is independent of the point of application of force on the

system.


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Code: GARSHANA

SECTION – IV





Passage-I

In the figure shown the velocity of river current grows in proportion to the perpendicular distance from the bank and reaches its maximum

in the middle. A boat is so moving in the river that its velocity relative to the water is constant and perpendicular to the direction ofriver flow. Assume the width of the river is d. and boat starts from point O with reference to the above situation answer the following questions.

38. While going across the river the acceleration of the boat isa) changing its direction but the magnitude remains constant.b) both magnitude and direction remains constant.c) changing its magnitude but direction remain same.d) changing its magnitude as well as its direction.

39. If the boat reached at point P on the other bank of river the ratio of OA and AB is a) b) c) d)

40. With respect to point ‘O’ (origin of co-ordinate system as shown in the figure) location of boat in the river ( in terms of co-ordinate ) when the position vector of boat is making angle with the departing bank of river.a) b) c) d)


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Code: GARSHANA


Passage-II

In the figure there is a trolley moving uniformly on horizontal surface. There is an ideal spring of spring constant K and there is a man in the trolley to perform some experiment with the spring. Trolley is moving with velocity v. Body posture of man while performing experiment is not clearly depicted in the figure. Answer the following questions.

41. In his first experiment man applied force F to stretched the spring and remained standing in the trolley. If the trolley covers an distance L than the work done by man with respect to ground observer and with respect to trolley are respectivelya) b) c) d)

42. Now in his 2nd experiment man stretches the spring through during time t and during the same time trolley covers a distance L. When man stretches the spring man moves opposite to the train. Work performed by man is ground frame is

a) b) c) d)

43. In the 2nd experiment workdone by man to overcome the friction in trolley frame is

a) zero b) c) d)


Passage-III

Two men A and B each of mass m sit in light cages at the ends of a flexible light rope passing over a smooth pulley as shown in the figure. Initially both are at rest. A being higher

than B by h. Suddenly a small ball of mass is handed over to B


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Code: GARSHANA which he instantaneously throws up to A.

44. If the ball takes time t to go from the hand of B to that of A, Then during this internal of time which of the following observation is correct on the basis of known fundamental Principle of Physics.a) motion of A is accelerated and that of B is un accelerated.b) motion of both A and B are accelerated.c) motion of both A and B are un accelerated but that of ball is accelerated. d) motion of all A, B and the ball are accelerated.

45. When A catches the ball, his position is shifted up by . Where is

a) b) c) d)

46. If in the course of motion the maximum height attended by A is

a) b) c) d)


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Code: GARSHANA

CHEMISTRY

PART – III

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.

47. If atoms of radius r form face-centred cubic unit cell of edge length a, the correct relation is:a) b) c) d)

48. For bcc lattice, the edge length of the unit cell is 500 pm. The molar volume of the spheres lattice isa) 72.25 cm3 b) 37.6 cm3 c) 18.8 cm3 d) none of these

49. When NaCl is doped with mole of SrCl2, the number of cation vacancy isa) b) c) d)

50. The non-stoichiometric compound O is formed when of ions are replaced by ions then is a) 6 b) 12 c) 15 d) 18

51. The oxidation of oxalic acid by acidified becomes fast as the reaction progresses due to:

a) Auto catalysis by Mn2+ b) Presence of

c) Presence of d) Presence of

52. On adding few drops of dil. or to freshly precipitated ferric hydroxide, a red coloured colloidal solution is obtained. This phenomenon is known as:a) Peptization b) Dialysis c) protection d) Dissolution

SECTION – II


This section contains 4 multiple correct answer(s) type questions. Each question has 4 choices (A), (B), (C)


53. Which of the following pair of ions have the same scattering power of X-rays?a) b) c) d)

54. Which of the following has antifluorite structurea) CaF2 b) BaF2 c) Li2O d) Na2O

55. In Na2O structure:a) ions constitute ccp and Na+ ions occupy all the octahedral holesb) ions constitute ccp and Na+ ions occupy all the tetrahedral holesc) ions constitute ccp and Na+ ions occupy 50% of tetrahedral holes and 100 % octahedral holes


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Code: GARSHANA d) Na+ ions constitute ccp and ions occupy half of octahedral holes.

56. If the radius of the anion in an ionic solid is 200 pm, what would be the radius of the cation that fits exactly into a cubic hole a) 146.4 pm b) 82.8 pm c) 45 pm d) none of these

SECTION – III

Reasoning Type



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: Frenkel defects are found in silver halides.

Statement I: Frenkel defects are commonly found in ionic solids

58. Statement I: Lead ziroconate is a piezoelectric crystal.

Statement II: Lead ziroconate cryals have no net dipole moment

59. Assertion: The effectiveness of catalyst has found more applications in solid catalyst and gaseous reactant systems.Reason: A large number of industrial preparations are based on this type of reactions.

60. Assertion: Lead tetraethyl acts as inhibitor for combustionReason: It retards the combustion of gasoline.

SECTION – IV





In an ideal crystal there must be regular repeating arrangement of the constituting

particles and its entropy must be zero at absolute zero temperature. However, it is impossible to

obtain an ideal crystal and it suffers from certain defects called imperfections. In pure srystal, these

defects arise either due to disorder or dislocation of the constituting partilcles from their normal

positions or to the movement of the particles even at absolute zero temperature. Such defects

increase with rise in temperature. In addition to this, certain defects arise due to the presence of


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Code: GARSHANA some impurities. Such defects not only modify the existing properties the crystalline solids but also

impart certain new characteristics to them.

61. When LiCl is heated into the vapour of lithium, the crystal acquires pink colour. This is due toa) Schottkty defects b) Frenkel defectcc) Metal excess defect leading to F-centres d) Electronic defect

62. AgCl is crystallized from molten AgCl containing a little CdCl2. The solid AgCl obtained will havea) cataionic vacancies equal to number of Cd2+ ions incorporatedb) cationic vacancies equal to double the number of Cd2+ ionsc) anionic vacanciesd) neither cationic nor anionic vacancies.

63. The second order Bragg’s diffraction of X-rays of wavelength 100 pm from a set of parallel lattice planes in a metal occurs at a grazing angle of 300. The spacing between the successive scattering planes in the crystal isa) 50 pm b) 100 pm c) 150 pm d) 200 pm


Surfactants are the substances which show surface activity. Detergents possess surface activity as well as detergency. Soaps are anionic class of detergent. It is the hydrophilic part of detergent molecule which possesses the tendency to attract water molecules whereas hydrophobic part orients away from water. The hydrophilic-lipopillic balance (HLB) leads to aggregaton of anionic or nonionic or cationic part of detergent to form micelle. Each molecule has the definite concentration at definite temperature at which it starts to aggreagate. It is due to the presence of two moieties in their molecules, surfactants stabilize emulsion ( a water – oil system). Due to larger surface area, the medicines are more effective in emulsion from. Emulsions are w/o or /ow type. A water soluble dye imparts its colour to o/w emulsions.

64. Which is incorrect about soaps:a) Soaps are metal salts of fatty acidsb) Soaps are anionic class of surfactants or detergentsc) Soaps form anionic micelles i.e., carrying –ve charged) neutral molecule of soap act as surfactant.

65. Which of the following forms a cationic micelle:a) Sodium dodecyl sulphate in waterb) Sodium dodecyl benzene sulphonate in waterc) Soldium octanoated) Dodecyl ammonium chloride

66. Which might have lowest value of critical micelle concentration in water:a) Sodium octanoate b) Sodium decanoatec) Sodium hexanoate d) Sodium dodecanoate


Paragraph:

In a closest packed layer of identical spheres, each sphere is intouch with six spheres. A

closed packed three dimensional crystal will be obtained by stacking closed packed layers on top of

one another. For maximum utilization of the space, the spheres of the second layer lie in the

depressions of first layer. The third layer can be added in either of two ways. In one, the spheres are


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Code: GARSHANA placed so that they reproduce first layer, ie., spheres of first and third layers are vertically aligned.

This is known as AB pattern of layers which consists of spheres hexagonally packed (hcp).

67. The vacant space in body centred cubic lattice b.c.c. unit cel is about:a) 32 % b) 10 % c) 23% d) 46 %

68. How many unit cells are present in a cubic shaped ideal crystal of NaCl of mass 1.0 g.a) b) c) d)

69. A substance crystallizes in face centred cubic ( fcc) lattice in which atoms A occupy each corner of the cube and atoms B occupy the centre of each face of the cube. The composition of

is:a) b) c) d) can not be specified

UNIT TEST -7 Dated : 08.11.2008

If you have any genuine question paper problems please contact the following subject concerned persons.

PAPER

SETTERMATHEMATICS PHYSICS CHEMISTRY

HYD-ANNMr. VISWANADHAM

Mobile : 9949320609

Mr. S.K.SINGH

Mobile: 9849911437

Mr. AMARESHWAR

Mobile : 9441552462


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FILE NO. IIT û 213-43 UNIT TEST -7 -PAPER-IQP

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