PAPER - 1 - WordPress.com · PAPER - 1 CODE 0 CLASS-XII ALL INDIA OPEN TEST (AIOT) TARGET : IIT-JEE...

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

Date : 30-01-2011 Duration : 3 Hours Max. Marks : 240

PAPER - 1

CODE

0CLASS-XII

ALL INDIA OPEN TEST (AIOT)TARGET : IIT-JEE 2011

INSTRUCTIONSA. General :

1. This Question Paper contains 81 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 city of centre and sign with pen in appropriate boxes. Do not write

these anywhere else.

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

C. Question paper format and Marking scheme :

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

Sections.

14. 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.

15. 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 partial

marking and no negative marking for incorrect answer(s) for this section.

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

the correct answer and zero marks if no bubble is darkened.. There is no partial marking and no negative

marking for incorrect answer(s) for this section.

17. For each question in Section�IV, you will be awarded 2 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

RESONANCE P1AIOTXII300111C0 - 1

(SPACE FOR ROUGH WORK)

PART-IAtomic 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 4 choices (A), (B), (C) and (D) for itsanswer, out of which ONLY ONE is correct.

1._ If we consider no mixing of �2s� and �2p� orbitals, then the bond order and magnetic nature of the diatomic

molecule C2 is :(A) 3 and diamagnetic (B) 2.5 and diamagnetic(C) 2 and diamagnetic (D) 2 and paramagnetic

2._ HCOOH (g) CO2 (g) + H

2 (g) decomposition reaction has rate constant 2.31 × 10�1 min�1 at 30ºC.

Calculate ratio of initial rate of diffusion of HCOOH to the rate of diffusion of mixture at 3 minute. Initialpressure of HCOOH is 2 atm in closed container at 30ºC.

(A) 92

(B) 32

(C) 94

(D) 278

3._ NH4HS (s) NH

3 (g) + H

2S (g) K

p = 2.25 atm2

Initially 2 moles of only NH4HS(s) is present in 2 L container, enclosed with piston at 300 K. If system is

expanded by reversible isothermal process then at what volume of container, pressure of container starts todecrease continuously ?(A) 2 lit (B) 4.8 lit (C) 32.8 lit (D) 63.6 lit



4. Equilibrium constant (KC) for the given reaction A(s) + 2B (aq.) 2C (s) + D (aq.) is 1020 at 300 K.

Starting with mixture of 1 mole of A and 31

mole/litre of B in 2 L container at 300 K, the equilibrium concentration

of B is :(A) ~ 4 × 10� 11 M (B) ~ 2 × 10� 10 M (C) ~ 2 × 10� 11 M (D) ~ 10� 10 M

5. A metal nitrate (X) gives a white precipitate with ammonia solution but the precipitate get dissolve on addingammonium salt. Lead dioxide and concentrated nitric acid on boiling with a dilute solution of metal nitrate (X)produces a violet-red (or purple) colour solution. Small amount of metal nitrate (X) gives an amethyst-redbead with borax in oxidising flame when cold. The cation of metal nitrate is :(A) Bi3+ (B) Mg2+ (C) Zn2+ (D) Mn2+

6. Hydrolysis of XeF4 with excess water gives :

(A) XeOF4

(B) XeO2F

2(C) Xe (D) XeO

4

7. Which of the following is not correctly matched with respect to the processes involved in the extractivemetallurgy of the respective metal ?

(A) Al2O3.2H2O Al : Leaching, precipitation, calcination and electrolytic reduction (molten state).

(B) Ag2S Ag : Leaching and displacement method.

(C) PbS Pb : Froth flotation process, roasting and self reduction.

(D) KCl.MgCl2.6H2O Mg : Dehydration by simple heating and electrolytic reduction (molten state).




8. )solventAprotic(

NaOH)1( 3PBr)2(

DMSO

KOH)3( 2SOCl)4(

(II) Product

In this reaction I and II are :

(A) Enantiomers (B) Structure isomers(C) Geometrical isomers (D) Identical compounds

9. )excess(NaNH2 (y')

X�R 3O

CH3�CH

2�COOH

What is true about (x, y) and R�X respectively (y' is a salt of y, which is an isomer of x).

(A) Functional isomers, Ethyl halide. (B) Positional isomers, Methyl halide.

(C) Geometrical isomers, Propyl halide. (D) Positional isomers, Ethyl halide.

10. The mononitration mainly occurs in ring .................

CH2 NO2

srqp

ionMononitrat

(A) p (B) q (C) r (D) s




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.

11._ Select the correct statement(s) from the following :(A) In mono-molecular layer adsorption, rate of adsorption first increases then decreases with increase in temperature.(B) Lyophobic colloidal particles do not settle down under the force of gravity even on ultra centrifugation.(C) Standard enthalpy of dissociation of H

2O() into its aqueous ions at 298 K is nearly 57.1 kJ/mole.

(D) Molar entropies of monoclinic sulphur and rhombic sulphur become same at absolute zero temperature.

12._ Select incorrect statement(s) :(A) Higher the value of K

H (Henry�s law constant) at given pressure the lower is the solubility of the gas in the liquid.

(B) Under same conditions, NH3 has lower solubility than that of CO

2 in water.

(C) Svap

of solution containing non volatile and non dissociable electrolyte is lower than Svap.

of solution ofnon volatile and 100% ionisable electrolyte at same conditions.

(D) For alcohol-water solution observed vapour pressure is less than the calculated (theoretical) vapour pressure.

13. Select the correct statement(s).(A) Passage of sulphur dioxide or of hydrogen sulphide (not in excess) in to a solution of an iodate acidified

with dilute hydrochloric acid, liberates iodine.(B) Phosphate rock, Ca

3(PO

4)

2 on heating with sand and coke in electric furnace at 1400-1500ºC yields

dimeric phosphorus pentaoxide.(C) Reaction of H

2S on aqueous solution of sodium sulphite yields sodium thiosulphate.

(D) Sodium hypophosphite on warming with copper sulphate solution gives red precipitate of copper(I) hydride.



14.

H)ii(

,NaOHCHCl)i( 3 (P > Q) % yield

Select the correct options :(A) Boiling point , (P > Q) (B) Melting point , (Q > P)(C) Water solubility , (P < Q) (D) Acid Strength , (Q < P)

15. Select the correct options, which indicate correct reactions.

(A) (X) nationMonochlori

Single product , (X = )

(B) (R) H

+ ; (R = )

(C) NaOH

(D) CH3MgBr (excess) + COCl

2

OH)ii(

ether)i(

2

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 ONE OR MORE THAN ONE is/are correct.




Paragraph for Question Nos. 16 to 18The process of using an electric current to bring about chemical change is called electrolysis.Electrolysis is a process of oxidation and reduction at the respective electrodes due to external currentpassed in the electrolyte.

The product obtained during electrolysis depends on following factors.

The nature of the electrolyte The concentration of electrolyte The nature of the electrode.

Anode (+)

key

Cathode (�)

Ag rod Pt coated electrode

2 L solution

1M Cu (aq), 1M SO2+ 2�4 (aq)

1M Zn (aq), 2M Cl2+ �(aq)1M M (aq), 2M Br2+ �(aq)

Consider the electrolysis of following cellcontaining aq. solution of CuSO4, ZnCl2 andMBr2 by using pure silver rod as a cathode andPt electrode as anode. Assume that M2+ doesnot further oxidise and can not form complexwith NH3. Assume no hydrolysis of any ion.

34.0E0Cu/Cu2

V; 10.0�E0M/M2

V; ; 76.0�E0Zn/Zn2

V; 828.0�E0H/OH 22

V; ; 80.0E0Ag/Ag

V,

FRT303.2

= 0.06

16._ After passing 20 amp current from battery for 28950 sec. the remaining conc. of ions in solution given inpassage would be : (Assume current efficiency to be 100%).(A) [Cu2+] = 0.5M, [M2+] = 0.5M, [Zn2+] = 0.1M (B) [Cu2+] 0 M, [M2+] = 0.5M, [Zn2+] = 0.5M(C) [Cu2+] = 0.5M, [M2+] = 0.5M, [Zn2+] = 0.5M (D) [Cu2+] 0 M, [M2+] = 0.5M, [Zn2+] = 1M

17._ What will be the volume of gases formed at anode at STP by electrolysis of above solution after passing20 amp current for 28950 sec. (Assume current efficiency to be 100% and one mole of gas occupies 22.4 Lvolume at STP).(A) 44.8 L Br

2(B) 22.4 L Br

2(C) 22.4 L Cl

2(D) 44.8 L Cl

2

18._ If 36 mol of NH3(g) is passed in electrolytic solution given in comprehension (assume no volume change by

addition of NH3), then what would be decreasing order of reduction potential of following :

{ Kf [Cu(NH

3)

4]2+ = 1 × 1012 and K

f [Zn (NH

3)

4]2+ = 1 × 109 }

(A) M2+ > Cu2+ > Zn2+ (B) Cu2+ > M2+ > Zn2+ (C) M2+ > Zn2+ > Cu2+ (D) Cu2+ > M2+ > Zn2+




Paragraph for Question Nos. 19 to 21

[C H ]16

(x)16 4KMnO.Dil

[C H ]18

(y)16 2O

[] = 0, Achiral

[y]

[r]

[s]

Conc. H SO2 4

H O 4

[x] OH/Zn)ii(

O)i(

2

3

H)ii(

NaOH/)i( 2 yellow ppt. + Benzene carboxylic acid.

19. The compound [s] is :

(A) Ph�C

O

�Ph (B) Ph�C

O

�Me (C) Ph�C

O

�C

O

�Ph (D) CH3

COOH

20. The compound [r] is :

(A) CH �C3 �C�Ph

O CH3

Ph

(B) Ph�C�C�CH3

O CH3

Ph

(C) Ph�C�C�CH3

CH2

CH2

(D) Ph�C=CH�CH3

Ph

21. The compound [y] is :

(A)

Ph

Ph

CH3

HO CH3

OH (B)

Ph

OH

CH3

CH3Ph

OH (C)

OH

Ph

Ph

CH3 OH

CH3

(D) Ph�C

O

�C

O

�Ph



SECTION - IVTrue & False Type

This Section Contains 6 questions. Each statement is either true (T) or false (F).

22._ The number of ions as next nearest neighbour of Cs+ in cesium chloride structure are six.

23._ By addition of catalyst Gibbs energy change would be more negative and rate of reaction become muchfaster.

24. The octahedral species, [NiF6]2� and [Ni(H

2O)

6]2+ are high-spin paramagnetic complexes.

25. In single chain silicates the repeating unit is Si2O

52�.

26. > ..... (Ka order)

27. > H2 C H2N� �N

NH

..... (Kb order)



RESONANCE P1AIOTXII/XIII300111C0-9

PART- II



28. If x, y R, satisfy the equation 4

)4�x( 2

+ 9y2

= 1, then difference between largest and smallest value of the

expression 4x2

+ 9y2

, is

(A) 6 (B) 2 (C) 9 (D) 8

29. The total number of integers between 1 and 3600 (both excluded), that are relatively prime to 3600, is (m, nare relatively prime if LCM of m and n is mn)(A) 959 (B) 1200 (C) 1199 (D) 2640

30. If f(x) is a non constant thrice differentiable function defined on R such that f(x) = f(6 � x) and

f(0) = 0 = f(2) = f(5), then minimum number of zeroes of g(x) = (f(x))2 + f(x) f(x) in the interval [0, 6] is equalto

(A) 13 (B) 12 (C) 10 (D) 11

31. If (k) = dxkkxx

nx

022

(k > 0) and k(k) � (1) = 3

, then value of k is

(A) 3

1(B) 3 (C) 3e (D) e3/2





32. Let curves y = Pi(x) = a

ix2 + b

ix + c

i , i = 1, 2,3,...., n on xy plane intersect the line

r = 2

j�i� + )k�j�i�( , R. If a

i, b

i, c

i I, a

i < a

i+1 and |P

i(x)| 9, then

n

1i

1

1�

ii )x(P)1(� dx is equal to

(A) 1 (B) 0 (C) �1 (D) 2

33. If three 1 × 1 squares are selected at random from a 8 × 8 chessboard, then the probability that they form the

letter �L� is

(A) 3

64 C

196(B)

364 C

49(C)

364 C

36(D)

364 C

93

34. Let f : R [�1, 1] and g : R B, where R be the set of all real numbers and

g(x) = sin�1

)x(f�4

2

)x(f 2+

3

. If y = f(x) and y = g(x) are both surjective, then set B is given by

(A)

3,

3� (B)

3

2,0 (C)

3,0 (D) [0, ]

35. Given 2006 vectors on a plane. Sum of every 2005 vectors is a scalar multiple of the other vector. Not allvectors are scalar multiple of each other. The sum of all these vectors is of magnitude(A) 0 (B) 2005 (C) 2006 (D) 20052




36. Let y = y(t) be a solution to the differential equation y + 2t y = t2, then ty

Limt

is

(A) zero (B) 21

(C) 1 (D) Does not exist

37. In a tennis match, being played by two equally strong players A and B, the probability of the server winning

on his service game is 32

and the probability of his losing on his service game is 31

. As per the rules of lawn

tennis a player winning six games is winner of match. They serve alternately for each game. A has won thetoss and has elected to serve. The probability of A winning the match at score 6 � 1 is

(A) 73

40(B)

63

40(C) 73

8(D) 73

32

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.




38. Let function f(x) be thrice differentiable and satisfies f )x(f = 1 � x for all x [0, 1].

If J = 1

0

)x(f dx and f

5

4= 0, then which of the following are TRUE?

(A)

32

f31

f = 1. (B) The value of J equal to 21

.

(C) f (x) = 0 has atleast one root in x

43

,41

. (D) f (x) = 0 has atleast one root in x

54

,21

39. Let an =

n

n1

1

, n N. Which of these are TRUE?

(A) an 2 (B) a

n < 3 (C) a

n < 4 (D) a

n < 2

40. Let ABC be a triangle with AA1, BB1, CC1 as medians and G as centroid. If the points A, C1, G, B1 areconcyclic then which of the following relations are FALSE? (where a = BC, b = CA and c = AB)(A) 2a2 = b2 + c2 (B) 3b2 = c2 + a2 (C) 4c2 = a2 + b2 (D) 3a2 = b2 + c2

41. If the line 3z

2y

1x

intersects line 32x + 3(1 � 2)y + z = 3 = � 21

(62x + 3(1 � 2) y + 2z) then point

(, , 1) lies on plane

(A) 2x � y + z = 4 (B) x + y � z = 2 (C) x � 2y = 0 (D) 2x � y = 0




42. For the function f(x) =

2 2x

0

4t

dt)t4(e

(A) a local maximum occurs at x = 2 (B) a local maximum occurs at x = � 2

(C) a local maximum occurs at x = 0 (D) a local minimum occurs at x = 0


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 ONE OR MORE THAN ONE is/are correct.


Let p, q, r be positive real numbers, not all equal. Consider equationspx2 + 2qx + r = 0 ,qx2 + 2rx + p = 0 ,rx2 + 2px + q = 0.

43. If any two of these equations have a common root , then(A) is positive (B) is negative (C) is imaginary (D) none of these

44. Which of the following statements is/are TRUE ?(A) Atleast one of these equations have real roots.(B) All equations have imaginary roots.(C) Atleast two of these equations have real roots.(D) If two of these equations have a common root then other equation has imaginary roots.




45. If p,q,r are permutation on set {1, 2, 3} and are distinct then(A) exactly two of these equations have real and distinct roots.(B) exactly one of these equations have real and distinct roots.(C) exactly one of these equations have imaginary roots.(D) all equations have real roots.


Let A be the set of all 3×3 symmetric matrices whose entries are 1,1,1,0,0,0,�1, �1, �1. B is one of the

matrix in set A and

X =

z

y

x

U =

0

0

0

V =

0

0

1

.

46. Number of such matrices B in set A is , then lies in the interval(A) (30, 40) (B) (38, 40) (C) (34, 38) (D) (25, 35)

47. Number of matrices B such that equation BX = U has infinite solutions(A) is at least 6 (B) is not more than 10 (C) lie between 8 to 16 (D) is zero.

48. The equation BX = V(A) is inconsistent for atleast 3 matrices B.(B) is inconsistent for all matrices B.(C) is inconsistent for at most 12 matrices B.(D) has infinite number of solutions for at least 3 matrices B.





This Section Contains 6 questions. Each statement is either true (T) or false (F).

49. If g is the inverse of function f and f (x) = 2x1

1

, then g (x) = 1 + g3(x).

50. If , , and be the eccentric angles of the four points of intersection of ellipse and any circle, then + + + = n, n

51. f(x) =

Qx;6x

Qx;x2

is continuous at only 2 points.




52. Let f : R R and g : R R be two one-one and onto functions such that they are mirror image of each otherin line y = a. If h : R R is a function such that h(x) = f(x) + g(x) then h(x) is many-one into.

53. If function f(x) is discontinuous at a point x = a then x = a is not necessarily a point of extrema.

54. A, B, C are three non-collinear points whose position vectors are c,b,a

respectively then c,b,a

are

always non-coplanar.



PART- III



55. In the circuit shown initial current is zero. Potential difference across 'C' is V and '2C' is uncharged initially.There is no resistance in the circuit. The maximum current in the circuit is :

(A) LC

V (B) L3C2

V (C) L2C3

V (D)L2

C

56. A fixed container is filled with a liquid of density up to a height 4m. A horizontal slit of small width but ofarea = 0.5 m2 is made at a height of 2m form bottom. The speed of top surface of the water level is (area oftop surface of container is 4 m2 and g = 10 m/s2) :

(A) 6320

m/sec (B)

6340 m/sec (C)

6380 m/sec (D) None of these



57. In the circuit shown steady state is already reached. Now the inductance issuddenly doubled. The potential difference across 'R' just after this is :

(A) 0 (B) v

(C) 2v (D) v/2

58. A small bob of mass �m� is suspended by a massless string from a

cart of the same mass �m� as shown in the figure.The friction between

the cart and horizontal ground is negligible. The bob is given a velocityV0 in horizontal direction as shown. The maximum height attained bythe bob is, (initially whole system (bob + string + cart) was at rest).

(A) g

V2 20

(B) g

V 20

(C) g4

V 20

(D) g2

V 20

59. Consider the rays shown in the diagram as paraxial. 'F' isfirst focus of lens. The image of the virtual point object O isformed by thin spherical lens LL' is (Given PO' > PF) : (A) Virtual,Located below the principal axis and Located to the left of the lens(B) Real,Located below the principal axis and Located to the left of the lens(C) Real,Located above the principal axis and Located to the left of the lens(D) Real,Located below the principal axis and Located to the right of the lens

60. A bead is connected at one end of an inextensible massless string whoseother end is fixed to a fixed cylinder. Cylinder does not rotate. The bead canmove on a horizontal smooth surface. The bead is given a velocity v0perpendicular to the string. The bead moves on a curve and consequentlycollides on the cylinder after sometime. Then, before it collides :(A) Work done by string on the bead is positive(B) The average speed of the bead is v0.(C) The tension in the string remains constant.(D) Kinetic energy of bead increases gradually.



61. The uniform spool shown in the figure is placed on a rough horizontal surface andhas inner radius r and outer radius R. A string is wound on the inner radius of spool.The angle between the applied force and horizontal can be varied. The angle () forwhich the spool does not roll and does not slide is given by :

(A) = cos�1

Rr

(B) = cos�1

Rr2

(C) = cos�1 Rr

(D) = sin�1

Rr

.

62. When a monochromatic light falls on a metallic surface of work function 5.3 eV, electrons are ejected.An ejected electron of maximum kinetic energy collides inelastically with a hydrogen atom which is atrest in ground state and free to move. Select the highest wavelength of light so that hydrogen atom getexcited (hc = 12400 eVÅ):

(A) 750 Å (B) 850 Å (C) 600 Å (D) 500 Å

63. A heavy nucleus x(A = 180) breaks into two nuclie y (A = 140) andz(A = 40). Energy released during fission reaction is :

(A) 110 MeV

(B) 220 MeV

(C) 200 MeV

(D) Energy is not released

64. Light of intensity is incident on a fixed plane surface at an angle 30º with the surface. If 50% light is reflected

and remaining light is absorbed then radiation pressure on the plate is (speed of light is c):

(A) c2

(B) c8

3(C)

c89

(D) c4




SECTION - II

Multiple Correct Answer TypeThis 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.

65. A particle is subjected to two simple harmonic motions along x and y axis according to, x = 3 sin 100 t,y = 4 sin 100 t.(A) The path of the particle will be ellipse and it is moving in clockwise direction.(B) Motion of particle will be on a straight line.(C) Motion will be a simple harmonic motion with amplitude 5.

(D) Phase difference between two motions is 2

.

66. A rod of length 0.3 m having variable linear mass density from A to B as =

0x(x is distance from A in meter), where

0 = 100 kg/m2 is suspended

by two light wires of same length. Ratio of their linear mass density is2 : 9. Then which of the following is/are correct : (A) Ratio of wave speed in wire�1 to wire�2 is 3 : 2

(B) Ratio of wave speed in wire�1 to wire�2 is 3 : 1

(C) Second harmonic in wire�1 has same frequency as third harmonic in wire�2

(D) Third overtone in wire�1 has same frequency as fifth overtone in wire�2

67. A charged particle moves with a constant velocity ( j�i� )m/s in a magnetic field )k�3i�2(B

T and uniform

electric field )k�cj�bi�a(E

N/C, then (assuming all quantities in S.I. unit) :

(A) a = �3 (B) b = 3 (C) c = �2 (D) a2 + b2 + c2 = 22




68. Switch S1 is closed for a long time while S

2 remains open. Now at t = 0 S

2

is closed while S1 is opened. All the batteries are ideal and connecting

wires are resistanceless.The capacitor 'C' is initially uncharged.

(A) At time t = 0, reading of ammeter is R5

.

(B) At time t = 0, reading of ammeter is zero

(C) Heat developed till time t = 5RC n2 in resistance 3R is 2C

409

(D) After time t > 0 charge on the capacitor follows the equation RC5t

eC

69. A monoatomic ideal gas undergoes a cyclic process ABCDEA as shown in the P-V diagram. (BC isisothermal and P

3V

1 < P

1V

3). Then which of the following curve(s) is/are correctly converted :

(A) (B)

(C) (D)




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 ONE OR MORE THAN ONE is correct.


In the figure shown the loop placed in the plane of the paper has radius 'R', self inductance 'L' and zeroresistance. A uniform magnetic field B = B

0sint is applied (B

0 and are positive constants) normal to the

plane of the paper. Initially the loop has zero current :

70. Direction of current in the loop at t =

3 :

(A) clockwise (B) anticlockwise(C) no current will flow at that time (D) cannot be determined

71. The current in the loop at time t =

65

is :

(A) L2

RB 20 clockwise (B)

L2

RB 20 anticlockwise

(C) L2

RB 3 20 clockwise (D)

L2

RB 3 20 anticlockwise

72. The magnitude of self induced emf in the loop will :(A) depend on value of L (B) not depend on value of R(C) not depend on B

0(D) depend on B

0




A uniform disc of mass 'm' and radius 'R' is free to rotate in horizontal plane about a vertical smooth fixed axispassing through its centre. There is a smooth groove of small width along the radius of the disc and one small

ball of same mass is attached to a spring as shown in figure. Initially spring is in its natural length of 2R

. The

disc is given initial angular velocity 0 and released (spring constant k =

2

m 20 )

73. Angular velocity of disc when elongation in spring becomes 2R

will be :

(A) 20 (B)

0(C)

40 (D)

4

3 0

74. Radial velocity of ball when elongation in spring becomes 2R

will be :

(A) 0R (B)

2

R0 (C) 4

R0 (D) 4

R3 0

75. Rate of change of energy of spring with respect to time when elongation in spring becomes 2R

will be:

(A) 4

Rm 230 (B)

2

Rm 230 (C) m

03R2 (D)

8

Rm 230




This Section Contains 6 questions. Each question is either true (T) or false (F).

76. A non�conducting charged particle is placed on the surface of a charged conductor. the electric force on

charged particle due to conductor must be zero.

77. Resultant magnetic force on a closed current carrying loop in a magnetic field must be zero.

78. An RLC series circuit is in resonance with an ideal AC voltage source. Now L and C can be changedsimultaneously to keep the circuit in resonance with the same source.

79. In a hot wire instrument (AC voltmeter or AC ammeter), readings are non�uniformly marked. Reading are

crowded on higher side of values.

80. The intensity of light at perpendicular separation from the axis of a long line source of light is inverselyproportional to distance from source.

81. A thin spherical converging lens of focal length 1 m and diverging lens of focal length 0.25 m are kept 0.75meter apart co-axially. A parallel paraxial beam of light first passes through the converging lens then throughthe diverging lens and finally focused at 0.5 m away from diverging lens.


(Space for rough work)

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