PAPER - 2 · PDF file4.Blank paper, clipboard, log tables, ... in any form are not allowed. 5.The answer sheet, ... It does not add with bromine

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

Date : 05-12-2010 Duration : 3 Hours Max. Marks : 252

PAPER - 2

CODE

0

INSTRUCTIONSA. General :

1. This Question Paper contains 72 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 gadgetsin 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 achange of the Booklet.

11. Write your Registration No., Name and Name of centre and sig with pen in appropriate boxes. Do not writethese 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 4 marks if you darken the bubble corresponding to thecorrect answer and zero marks if no bubble is darkened. In case of bubbling of incorrect answer, minusone (�1) mark will be awarded.

16. For each question in Section�II , you will be awarded 4 marks if you darken the bubble(s) correspondingto the correct choice(s) for the answer and zero mark if no bubbled is darkened. Partial marks will beanswered for partially correct answers. No negative marks will be awarded in this Section.MCQ Partial Marking Scheme :(a) If one choice is correct then for correct choice 4 marks, else zero.

(b) If two correct choices are answer then(i) for one correct choice 2 marks. (ii) for two correct choices 4 marks.(iii) If any wrong choice is bubbled then 0 mark.

e.g. : If correct answer is (A, C)(i) If you bubble only (A) then you get 2 marks. (ii) If you bubble only (C) then you get 2 marks(iii) If you bubble (A,C) then you get 4 marks. (iv) If you bubble (A,B) then you get 0 mark.

(c) If three choices are correct(i) for one correct choice 1 mark. (ii) for two correct choices 2 marks.(iii) for three correct choices 4 marks. (iv) If any wrong choice is bubbled then 0 mark.

(d) If four choices are correct(i) for one correct choice 1 mark. (ii) for two correct choices 2 marks.(iii) for three correct choices 3 marks. (iv) for four correct choices 4 marks.(v) If any wrong choice is bubbled then 0 mark.

17. For each question in Section�III, you will be awarded 3 marks if you darken the bubble corresponding tothe correct answer, and zero mark if no bubble is darkened. In case of bubbling of incorrect answer, minusone (�1) mark will be awarded.

18. For each question in Section�IV, you will be awarded 3 marks if you darken the bubble corresponding tothe correct answer, and zero mark if no bubble is darkened. In case of bubbling of incorrect answer, minusone (�1) mark will be awarded.

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PART TEST-4 (PT-4)TARGET : IIT-JEE 2011

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

RESONANCE

(SPACE FOR ROUGH WORK)

P1R141110C0-1

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 8 multiple choice questions. Each question has choices (A), (B), (C) and (D), outof which ONLY ONE is correct.

1. In which of the following solutions, the degree of dissociation of H2O is less than 1.8 10�7 % at 25° C :

(A) 10�6 M HCl (B) 10�5 M NaOH (C) 10�8 M HCl (D) All of these

2. The pKa of acetyl salicyclic acid (aspirin) is 3.5. The pH of gastric juice in the human stomach is about 2�3

and that in the small intestine about 8.0 Aspirin will be.(A) unionized in the small intestine and in the stomach(B) completely ionized in the small intestine and in the stomach(C) ionized in the stomach and almost unionized in the small intestine(D) ionized in the small intestine and almost unionized in the stomach.

3. For O2 gas molecules, the rms speed at T1, average speed at T2 and most probable speed at T3 are all equalto 1.5 × 103 m/sec. Arrange these temperatures in increasing order.(A) T1 = T2 = T3 (B) T3 < T2 < T1 (C) T1 < T2 < T3 (D) T1 < T3 < T2

4. When 0.1 mole HCl gas is added in 1lt of 0.1 M CH3COOH(aq) then which statement is wrong?

(Ka = 2 × 10�5, log 2 = 0.3)

(A) degree of dissociation of CH3COOH decreases sharply.

(B) change in pH would be 1.85(C) conc of [Cl�] = 0.1 M, [CH

3COOH] = 0.1 M, [H+] = 0.2 M in final solution

(D) on addition of HCl, Ka of CH

3COOH does not change.

RESONANCE


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5. The EAN (effective atomic number) of metal atoms in [Fe(CO)2(NO+)2] and Co2(CO)8 respectively are :(A) 34, 35 (B) 34, 36 (C) 36, 36 (D) 36, 35

6. At room temperature, A2 gas (vapour density = 40) at 1 atm pressure and B

2 gas (vapour density = 10) at p

atm pressure are allowed to diffuse through identical pinholes from opposite ends of a glass tube of 1mlength and of uniform cross-section. The two gases first meet at a distance of 60 cm from the A

2 end. The

value of p is :

(A) atm34

(B) atm31

(C) atm43

(D) atm61

7. K

BrHC 52 (A)

Product (A) in above reaction is :

(A) , (inversion) (B) , (retention)

(C) , (racemic) (D) Ph�CH=CH�CH3

8. P, Product P is :

(A) (B) (C) (D) None

RESONANCE


P1R141110C0-3

SECTION - II

Multiple Correct Answers TypeThis 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.

9. The values of Pc and Tc are given below for NO and CCl4 gases

Tc Pc

NO 177 K 6.485 atm

CCl4 550 K 4.56 atm

Select the correct statement (s) :

(A) CCl4 has smaller value of vanderwaal constant 'a'.

(B) NO gas has larger value of vanderwaal constant 'b'.

(C) CCl4 has larger critical volume as compared to NO

(D) NO gas shows less deviation from ideal behaviour than CCl4

10. Which of the following statements are correct about Boyle temperature

(A) Temperature at which 1st virial cofficent becomes Zero

(B) Temperature at which 2nd virial cofficent becomes Zero

(C) According to Vander waal's equation, value of TB = Rba

(D) TB of a gas depends upon nature of gas

11. The pairs of compound which cannot exist together in aqueous solution are :

(A) NaH2 PO4 and Na2HPO4 (B) Na2 CO3 and NaHCO3

(C) NaOH and NaH2 PO4 (D) NaHCO3 and NaOH.

RESONANCE


P1R141110C0-4

12. Which of the following reaction(s) is/are incorrect ?

(A)

(B)

(C)

(D)

SECTION - III

Comprehension TypeThis section contains 2 paragraphs. Based open each paragraph, there are 3 multiple choice questions.

Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

RESONANCE


P1R141110C0-5

Paragraph for Question Nos. 13 to 15Compressibility factor (Z) : Real gas deviate from ideal behaviour due to the following two faulty

assumptions of kinetic theory of gases.

(i) Actual volume occupied by the molecules is negligible as compared to the total volume of gas.

(ii) Forces of attraction and repulsion among the gas molecules are negligible.

To explain the extent of deviation of the real gas from ideal behaviour in terms of compressibility or

compression factor (Z), which is a function of temperature and pressure

Z = nRTPV

for ideal gases Z = 1

for real gases Z > 1 or Z < 1

Graph in between Z and P is shown as t = 0°C

on increasing temp, Z increases and approaches to unity, graph between Z and P at different temperature

for the same gas are as follows.

13. What is the correct increasing order of liquifiability of the gases shown as in above graph ?(A) H2 < N2 < CH4 < CO2 (B) CO2 < CH4 < N2 < H2(C) H2 < CH4 < N2 < CO2 (D) CH4 < H2 < N2 < CO2

14. Which of the following is correct order of temperature shown in the above graph Z Vs P for the samegases.(A) T4 < T3 < T2 < T1 (B) T1 < T2 < T3 < T4 (C) T1 < T2 < T4 < T3 (D) T3 < T4 < T2 < T1

RESONANCE


P1R141110C0-6

15. Which of the following statement is correct for gas A having molar mass 16 g and density 0.75 g/l at 2atm pressure and 27°C temp

(A) Force of attraction are dominating than force of replusion among the gas molecules.(B) Force of repulsion are dominating than force of attraction among the gas molecules.(C) Gas molecules are behaving ideally(D) Gas is more compressible

Paragraph for Question Nos. 16 to 18A compound X containing C, H and O is unreactive towards sodium. It does not add with bromine. It alsodoes not react with Tollens reagent. On reaction with an excess of HI, X yields only one organic product Y, Yon hydrolysis yields a new compound Z which can be converted into Y by reaction with red phosphorus andiodine. The compound Z on oxidation with potassium permanganate gives acetic acid. The equivalent weight

of this acid is 60. (Hint : RCH2�OH 4KMnO

R�COOH )

16. The structure of compounds X is :

(A) (CH3�CH

2�CH

2)2O (B) (C) (CH

3�CH

2)2O (D) (CH

3�O�CH

2CH

3

17. The structure of compounds Y is :

(A) CH3�CH

2�CH

2� (B) CH

3�CH

2� (C) (D) CH

3�CH

2�CH

2�CH

2�

18. Which of the following can give compound Z ?

(A) & CH3� (B) + OH�

(C) + CH3�CH

2�

excess

OH� (D) CH

3�CH

2�CH

2� and OH�

RESONANCE


P1R141110C0-7

SECTION - IV

Integer Answer Type

This section contains 6 questions. The answer to each of the questions is

a single digit integer, ranging from 0 to 9. The appropriate bubble below the

respective question number in the ORS have to be darkened.

19. Compressibility factor (Z) for N2 at � 23ºC and 25 atm pressure is 1.2. Calculate moles of N

2 gas required to

fill a gas cylinder of 7 liter capcacity under the given conditions :

11Kmolatmlt12

1RUse

20. A 1 M weak monoprotic acid (HA) solution is diluted to 100 times. Calculate the change in pH of solution.

(Ka(HA) = 10�4)

21. How many of the following molecules / ions may act as a bidentate ligand ?

(i) NO2� (ii) NH

2 � CH

2 � COO

� (iii) EDTA4�

(iv) C2O

42� (v) NH

2CH

2CH

2NH

2(vi) CH

3COCHCOCH

3�

(vii) CH3C N (viii) SCN� (ix) DMGH�

RESONANCE


P1R141110C0-8

22. A six coordinate complex has the formula CoCl3.5NH

3 .H

2O. Electrical conductance measurements indicate

the presence of three ions in one formula unit. How many moles of AgCl will be percipitated with AgNO3

solution with one mole of complex ?

23. Which of the following compound will yield exclusive (only one) product on dehydrohalogenation by a strong

base. (To report the answer select the code number of correct strucutre)

(1) (2) (3) (4)

24. In the given reaction :

42SOH.conc Alkenes

Total number of alkenes (Including stereo isomers) formed will be.


RESONANCE P2R051210C0-9

PART- II

SECTION - I

Straight Objective Type

This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its

answer, out of which ONLY ONE is correct.

25. If x

and y

be unit vectors and |z|

= 7

2 such that yxzz

and is angle between x

and z

, then the

value of sin is

(A) 21

(B) 23

(C) 1 (D) 0

26. Let c,b,a

be three linearly independent vectors, then ]cba[

]c5ba4cba2cb2a[

=

(A) 0 (B) 1 (C) 2 (D) � 1

27. The value of the nth order determinant

x11

1x1

11x

is given by

(A) (1 � x)n�1 (x + n � 1) (B) (x � 1)n�1 (x + n � 1)

(C) xn � n . xn�2 + n � 1 (D) none of these





28. If A and B are two square matrices such that B = � A�1 BA, then (A + B)2 is equal to(A) 0 (B) A2 + B2 (C) A2 + 2AB + B2 (D) A + B

29. The equation of the plane, passing through the intersection of the planes x + 2y + 3z + 4 = 0 and4x + 3y + 2z + 8 = 0 and whose x-intercept is 4, is(A) x �3y � 7z � 4 = 0 (B) 2x + 3y + 4z = 8 (C) x + y + z � 4 = 0 (D) 6x + 7y + 8z + 16 = 0

30. If a unit vector a� in the plane of b

= j�i�2 and c

= k�j�i� is such that a

^ b

= a

^ d

where

d

= k�2j� , then a� is

(A) 3

k�j�i� (B)

3

k�j�i� (C)

5

j�i�2 (D)

5

j�i�2




31. The function f(x) = (2x � 1)2/5 . (x + 2) has a local maximum at x equal to :

(A) � 67

(B) � 65

(C) � 143

(D) 21

32. The following system of equations : 2x + 6y + 11 = 0, 6x + 20y � 6z + 3 = 0 and 6y � 18z + 1 = 0 are :

(A) consistent with unique solution (B) consistent with infinitely many solution

(C) inconsistent (D) data insufficient to give the answer

SECTION - II

Multiple Correct Answer Type

This section contains 4 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.

33. Tangents are drawn from the origin to the curve y = sin x in such a way that their points of contact lie

on the curve : x2y2 = bx2 + cy2 , then

(A) 2b + c = 1 (B) b + c = 1 (C) c = � 1 (D) b + c = 0




34. If c,b,a

are non coplanar non-zero vectors such that acb

, cba

and bac

, then

(A) |a|

= 1 (B) |b|

= 1 (C) 3|c||b||a|

(D) |a|

= 3

35. The direction ratios of lines intersecting the line 1z

13�y

23�x

at angles 60° are

(A) 1, 1, 2 (B) 1, 2, � 1 (C) 1, � 1, 2 (D) 1, � 2, 1

36. Equation of line of projection of the line 3x � y + 2z � 1 = 0 = x + 2y � z � 2 on the plane 3x + 2y + z = 0 is

(A) 11

1x =

9�1�y

= 15�

1�z(B) 3x � 8y + 7z + 4 = 0 = 3x + 2y + z

(C) 11

12x =

9�8y

= 15

14z (D)

1112x

= 9�8y

= 15�

14z

SECTION - IIIComprehension Type

This section contains 2 paragraphs. Based open each paragraph, there are 3 multiple choice questions.Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.




Paragraph for Question Nos. 37 to 39

k�2j�i�2a

, k�j��i�b

and non zero vector c

are such that c)ba(

= )cb(a

37. Then vector c

may be given as

(A) k�4j�2i�4 (B) k�4j�2�i�4 (C) k�j�i� (D) k�j�4�i�

38. Volume of parallelopiped whose adjacent sides are given by cb,b,a

is

(use c

of previous question)(A) 18 (B) 54 (C) 12 (D) 36

39. A vector along the bisector of angle between the vectors b

and c

(use c

of previous question) is

(A) i�)32( + j�)3�1( + k�)32( (B) i�)32( + j�)3�1( � k�)32(

(C) i�)3�2( + j�)13( + k�)3�2( (D) i�)32( � j�)3�1( + k�)32(





Let L1 and L

2 be the lines whose equation are

13z

18y

33x

and

33x

=

27y

= 4

6z respectively..

A and B are two points on L1 and L

2 respectively such that AB is perpendicular both the lines L

1 and L

2.

Read the above passage and answer the following :

40. Shortest distance between the lines L1 and L

2 is

(A) 30 (B) 2 30 (C) 3 30 (D) none of these

41. Co-ordinates of the point A are(A) (1, 8, 2) (B) (3, 8, 3) (C) (�3, 8, 3) (D) none of these

42. Co-ordinates of the point B are(A) (�3, �7, 6) (B) (2, 7, 6) (C) (1, 6, 3) (D) none of these




SECTION - IVInteger Answer Type

This section contains 6 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.

43. If the tangent at any point P(4a2, 8a3) on the curve x3 � y2 = 0 is also a normal to the same curve, find thevalue of 9a2.

44. A given quantity of metal is to be casted into half cylinder i.e. , with a rectangular base and semicircularends in order that the total surface area is minimum. The ratio of the height of the cylinder to thediameter of the semi-circular ends is : + k ; find k.

45. The function f(x) = x2 e�2x, x > 0. If is maximum value of f(x) then find ][ 1� .

(where [.] represents greater integer function)




46. f(x) = x3 + 4x2 + x + 2 is monotonically decreasing in the largest possible interval

32�

,2� . Then find

greatest value of .

47. Let image of the line 2

4z5

3y3

1x

in the plane 2x � y + z + 3 = 0 be L. A plane

7x + By + Cz + D = 0 is such that it contains the line L and perpendicular to the plane 2x � y + z + 3 = 0,

then find the value of B + 3C + D .

48. If the equation of plane containing lines 1

2z2

3�y3�1x

and 2

7z3�7�y

1x

is

x + By + Cz + D = 0, then find the value of B + C + D.


RESONANCE P2R051210C0 - 17

PART - IIISECTION - I

Straight Objective TypeThis section contains 8 multiple choice questions. Each question has choices (A), (B), (C) and (D), outof which ONLY ONE is correct.

49. Find the current through the 3 resistor shown in figure :

(A) zero (B) 0.5 A

(C) 2A (D) 5 A

50. A galvanometer together with an unknown resistance in series is connected to two identical batterieseach of 1.5 V. When the batteries are connected in series, the galvanometer records a current of 1A,and when the batteries are in parallel the current is 1 A. What is the internal resistance of the battery?

(A) r = 34

(B) r = 1 (C) r = 31

(D) r = 23

51. Shown in the figure below is a meter-bridge set up with null deflection in the galvanometer.

The value of current in the unknown resistor R is(A) 1 A (B) 4 A(C) zero (D) will depend on the resistance of meter bridge wire




52. A spring of force constant has two blocks of mass M and 2M connected toeach end of the spring as shown in figure. Same force f acts at each end thenperiod of vibration is : (Assume friction between the blocks and horizontalsurface is negligible)

(A)

3M2

2 (B)

M

2 (C)

3M2

(D)

3M

2

53. In a torsional pendulum a uniform rod of mass m and length is used. Rod isattached to the torsional wire at its mid�point a shown in diagram. Two equal and

opposite forces F are applied at end of rod to maintain it at angular displacement'

0' in horizontal plane form equilibrium position. Find the period of oscillation :

(A) F3

M2 0

(B) F3

M 0

(C) F3

M2 0

(D) None of these

54. As shown in figure a horizontal platform with a mass m placed on it is executingSHM along x-axis (horizontal plane). If the amplitude of oscillation is 2.5 cm, theminimum period of the motion, for the mass not to slide on the platform. Takeg = 2 m/sec2 and friction coefficient between the block and platform is 0.1 : (A) 1 s (B) 10 s (C) 2 s (D) s

55. Two bars each of mass M and length L is in pure translatory motion with theircentre of mass velocity V as shown in the figure. The bars collides with andsticks to each other. (Assume that it becomes one composite bar of length2L). The angular velocity of the composite bar will be

(A) clockwiseLV

23

(B) clockwiseLV

34

(C) LV

43

counterclockwise (D) LV

23

counterclockwise



56. A uniformly charged thin spherical shell of radius R carries uniform surfacecharge density of per unit area. It is made of two hemispherical shells,held together by pressing them with force F (see figure). F is proportional to F F

(A) 22

0

R1

(B) R

1 2

0

(C) R1 2

0

(D) 2

2

0 R

1

SECTION - IIMultiple Correct Answers 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.

57. For the system shown in the figure initially springs are in natural length (naturallength of both are same). Two blocks 'A' and 'B' of equal mass 'M' are releasedfrom rest simultaneously. The contact between the string and pulley isfrictionlessand pulley is fixed. The masses of string and springs are negligible. (A) Acceleration of both the blocks will be equal at every instant(B) Time period of oscillation of block will be greater than time period ofoscillation for block B.(C) Time period of oscillation of block 'A' and block 'B' will be same(D) Maximum displacement of two blocks 'A' and 'B' will be same indownward direction but the two springs will have different extensionat that instant

58. A uniform thin rod of length is used as a physical pendulum. It is hinged from a point and is displacedslightly from equilibrium position then it will perform angular SHM. Which of the following is/are correctfor the rod :

(A) Minimum time period of oscillation of rod will be 3g

2

(B) Time period of rod can have any value from minimum value of infinite(C) There can exist maximum four points on the rod from which if the rod is suspended then it will havesame time period of oscillation(D) None of these




59. A satellite of mass m is moving in a circular orbit of radius 'r' around the earth.This satellite is shifted in circular orbit of radius 2r. (Mass of the earth is M).

(A) The minimum energy required to shift the satellite in new orbit is r2

GMm

(B) Time period of satellite in new orbit will be double that time period ofprevious orbit

(C) The acceleration of satellite in new orbit becomes 41

of acceleration in previous orbit.

(D) The minimum energy required to shift the satellite in new orbit is r4

GMm

60. A particle is executing SHM between points -Xm and Xm, as shown in figure-I. The velocity V(t) of theparticle is partially graphed and shown in figure-II. Two points A and B corresponding to time t1 and timet2 respectively are marked on the V(t) curve.

-XmO Xm

Figure-I

+x

A

B

V

t

Figure-II

t1

t2

(A) At time t1 , it is going towards Xm.(B) At time t1, its speed is decreasing.(C) At time t2, its position lies in between �Xm and O.(D) The phase difference between points A and B must be expressed as 0° < < 180°.

SECTION - IIIComprehension Type

This section contains 2 paragraphs. Based open each paragraph, there are 3 multiple choice questions.Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.




An uncharged solid conducting sphere of radius �a� is surrounded by a thin concentric conducting shell of

radius 2a. The charge on the conducting shell is q. A point charge q is placed at a distance 4a from commoncentre of conducting sphere and shell. The inner sphere is then grounded.

61. The charge on solid sphere is :

(A) �2q

(B) 4q

(C) �8q

(D) �4q3

62. Net charge on the outer surface of conducting shell will be :

(A) q (B) 4q

(C) 4q3

(D) cannot be calculated due to induction at outer surface because of point charge

63. The potential of outer shell is :

(A) a32q

o(B) a16

q

o(C) a8

q

o(D) a32

q3

o





Three SHMs along x and y axis are given below :x

1 = 3 sint .........()

x2 = 4 cost .........()

y1 = 4 cost .........()

Using these three equations of SHM solve the following questions :

64. Consider the superposition of () and () SHM. Resultant of these two SHMs will represent :(A) SHM along x�axis of amplitude 5 unit (B) circular motion of constant angular velocity(C) SHM of amplitude 7 unit (D) None of these

65. Consider the superposition of () and () SHM. Resultant of these two SHMs is :(A) a circular motion in a circle of radius 5 unit clockwise(B) a circular motion in a circle of radius 5 unit anticlockwise(C) SHM of amplitude 5 unit(D) None of these

66. Consider the superposition of (), () and () SHMs. The resultant of thesethree SHMs will represent motion of a particle along an ellipse as shown in thediagram. The minimum time taken by the particle to travel from A to B will be :

(A) 43

unit (B) 45

unit

(C) 41

unit (D) None of these

SECTION - IVInteger Answer Type

This section contains 6 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.




67. A uniform block of width and height 8

is kept on inclined plane and it

does not slide as shown in figure. Identical blocks are kept on the blockone on the other, each block sticks to the previous block. Find the minimumnumber of blocks for which system will topple.

68. The side of the cube is '' and point charges are kept at each corner as shown indiagram. If interaction electrostatic potential energy of all the charges is represented

by the expression 3

nkq2

. Find the value of n.

69. The charge Q = C is distributed on a thin semicircular ring of radius R = 1m. There is a uniform

electrostatic field |E

| = 2N/C directed horizontally. Initially the ring is in static equilibrium as shown infigure. The semicircular ring can rotate freely about a fixed vertical axis AB. It we want to rotate it aboutthe fixed axis by 90º then minimum work required on the ring is xJ. Find the value of x.



70. In the figure a part of electric circuit is given. The value of each resistance is R and current in some parts isshown in the diagram. If current in AB branch is (25 + x) ampere find the value of x.

71. Two small electric dipoles each of dipole moment p i� are situated at (0, 0, 0) and (r, 0, 0). The electric

potential at a point

0,

2r3

,2r

is 'x' volt then find the value of 'x'.

72. A spherical planet has uniform density 2

× 104 kg/m3. The minimum time period for a satellite in a

circular orbit around it is n × 103 sec. Find the value of n. (Use G = 3

20 × 10�111 2

2

kg

mN ).


(Space for rough work)

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