2014 Final Jee Mains 2014 Aceg

8/12/2019 2014 Final Jee Mains 2014 Aceg

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VMC/JEE-2014 1 Final JEE Mains/ACEG

Aggarwal Corporate Heights, 3rd Floor, Plot No. A - 7, Netaji Subhash Place,

Pitampura, Delhi - 110034 Phone: 011-45221191-93

Final JEE Mains/JEE-2014

29/03/2014 M.M. : 360

03:00 PM - 06:00 PMTEST CODE : ACEG

TIME : 3.00 Hrs

Read the following Instructions very carefully before you proceed.

1. The question paper consists of 3 parts (Part I : Chemistry, Part II : Physics, Part III : Mathematics).

Each Part contains 30 Straight Objective Questions.

2. For each question you will be given 4 Marks if you have darkened only the bubble corresponding to the

correct answer. 1 Mark will be deducted for indicating incorrect response for any question.

No deduction from the total score will be made if no response is indicated.

3. There is only One Correct Response for each question. Filling up More than One response in each

question will be treated as Wrong Responseand marks for Wrong response will be deducted.

4. Use Blue/Black Ball Point Pen only for writing particulars/marking responses on the Answer Sheet. Use of

pencil is strictly prohibited. However for rough work, use pencil on question paper itself.

5. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager,

mobile phone, any electronic device, etc., except the Admit Card inside the examination hall/room.

6. Rough work is to be done on the space provided for this purpose in the Test Booklet only.

7. For answering a question, an ANSWER SHEET (OMR SHEET) is provided separately. Please fill your

Test Code, Roll No.and Groupproperly in the space given in the ANSWER SHEET.

8. Do not fold or make any stray marks on the Answer Sheet.

9. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in

the Room/Hall. However, the candidates are allowed to take away this Test Booklet with them.

10. No one will be permitted to leave the test room before the end of the test, i.e. 06.00 PM


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PART - I (CHEMISTRY) 120 MARKS

STRAIGHT OBJECTIVE TYPE

This Part contains 30 Multiple Choice Questions. Each Question has 4 choices A, B, C & D, out of whichOnly One is Correct :

1. One liter of gas A at two atmospheric pressure and two liters of gas B at three atmospheric pressure are

mixed in a four liter flask to form an ideal gas mixture. What will be the final pressure of the gaseous

mixture if the gases initially and finally were at the same temperature?

(A) 1.0 atm (B) 1.5 atm (C) 2.0 atm (D) 2.5 atm

2. 3 mol of a mixture of FeSO4and Fe2(SO4)3 required 100 mL of 2 M KMnO4solution in acidic medium.

Hence, mole fraction of FeSO4in the mixture is:

(A)1

3(B)

2

3(C)

2

5(D)

3

5

3. Which of the following are not correct statements?

I. Carbohydrates are the polyhydroxy alcohols and phenols

II. All amino acids have different isoelectric point

III. Sucrose reduces Tollens reagent

IV. Starch is known as invert sugar also

(A) II only (B) I and III (C) III and IV (D) I, III and IV

SPACE FOR ROUGH WORK


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4. A mixture of nitrogen and hydrogen in the ratio of 1 : 3 reach equilibrium with ammonia when 50% of the

mixture has reacted. If the total pressure is p, the partial pressure of ammonia in the equilibrium mixture

was.

(A)p

2(B)

p

3(C)

p

4(D)

p

6

5. Which of the following compounds reacts most rapidly with the cold AgNO3solution?

(A) CH3CH = CHCl (B) CH3CH2CH2Cl

(C) CH2= CHCH2Cl (D) CH3CH2CH(Cl)2

6. In Cannizzaro reaction given below :

OH2 22PhCHO PhCH OH PhCO

the slowest step is :

(A) The abstraction of proton from the carboxylic group

(B) The deprotonation of PhCH2OH

(C) The attack of OH at the carbonyl group

(D) The transfer of hydride to the carbonyl group

7. Acetone (CH3COCH3) is the major product in:

I.H O3

2 2CH C CH

II.H SO / HgSO / H O2 4 4 2

3CH C CH

III.3BH THF.

3H O /OH2 2

CH C CH

(A) I (B) II (C) III (D) None of these



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8. How much amount of CaCl2(i = 2.47) is dissolved in 2.5L of water so that its osmotic pressure become

0.75 atm at 27 C ?(A) 0.3 mol (B) 0.03 mol (C) 3 mol (D) 0.003 mol

9. The term anomers of glucose refers to :

(A) isomers of glucose that differ in configuration at carbon one (C 1)

(B) isomers of glucose that differ in configuration at carbons one and four (C 1 and C 4)

(C) a mixture of (D)-glucose and (L)-glucose

(D) enantiomers of glucose

10. Which of the following is incorrect statement?

(A) Principal quantum number can not be negative

(B) Azimuthal quantum number can not be negative

(C) Magnetic quantum number can not be negative

(D) Spin quantum number can be negative

11. The product P in the reaction:

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



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12. The transition metals exhibit higher enthalpies of atomization due to :

(A) tendency of exhibiting variable oxidation states

(B) the presence of incompletely filled d-subshell

(C) their atoms existing in the solid state with unpaired electrons

(D) strong interatomic interaction arising because of having large number of impaired electrons in theiratoms

13. Which of the following ionic substances is most effective in coagulating aluminium hydroxide sol?

(A) Soldium chloride (B) Calcium chloride

(C) Ferric sulphate (D) Potassium phosphate

14. The boiling points of F2, Cl2, Br2 and I2 increase as we go down the group. This is best attributed to

difference in :

(A) Covalent bond strengths (B) dipole forces

(C) London dispersion forces (D) colligative forces

15. A gas is heated in such a way so that its pressure and volume both becomes double. Again by lowering

temperature, one fourth of initial number of moles of air has been taken in, to maintain the double volume

and pressure. By what fraction, the temperature must have been raised finally ?

(A)1

5times (B)

4

5times (C)

16

5times (D)

8

5times



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16. In a cube structure of diamond which is made from X and Y, where X atoms are at the corners of the cube

and Y at the face centres of the cube. The molecular formula of the compound is :

(A) X2Y (B) X3Y (C) XY2 (D) XY3

17. The standard oxidation potentials of Zn, Cu, Ag and Ni electrodes are +0.76,0.34, 0.80

and +0.25 V

respectively. Which of the following reactions will provide maximum voltage ?

(A)2

Cu 2Ag (aq) Cu (aq) 2Ag

(B)2

Zn 2Ag (aq) Zn (aq) 2Ag

(C)2 2

Zn Cu (aq) Zn (aq) Cu

(D)2

2Zn 2H (aq) Zn (aq) H

18. Molecules of a gas have Z degree of freedom, where degree of freedom represents the number of

independent methods to express the energy of molecules. Determine the value of .

(A)Z

12

(B)2

1Z

(C)n

21

Z

(D)2

1Z

19. What will be the value of for a0.001 M aq.solution of 3NH ?

Given 5bK 1.6 10 , 1 2 1238ohm cm mol .

(A)1 2 1

31.58 ohm cm mol

(B)1 2 1

42.78 ohm cm mol

(C)1 2 1

29.99 ohm cm mol (D)1 2 1

18.47 ohm cm mol



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20. The isotherm obtained for CO is as follows :

The compressibility factor for the gas at point A will be :

(A)b

1V

(B)b

1V

(C)b

1RT

(D)a

1RTV

21. Ionisation energy of He is 18 119.6 10 J atom . The energy of the stationary state n 1 of 2Li is :

(A)15 1

2.2 10 J atom (B) 17 18.82 10 J atom

(C)16 1

4.41 10 J atom (D) 17 14.41 10 J atom

22. If a reaction is non-spontaneous at its freezing point and becomes feasible at its boiling point, then :(A) H is ve , S is +ve (B) H and S both are +ve(C) H and S both are ve (D) H is +ve, S is ve

23. A substance undergoes first order decomposition. The decomposition follows two parallel first order

reactions as

The percentage distribution of B and C are :

(A) 50% B and 50 % C (B) 76.83% B and 23.17%C(C) 90%B and 10%C (D) 60%B and 40%C



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24. Which of the following statements is/are not correct?

(A) La(OH)3 is less basic than Lu(OH)3

(B) In lanthanide series, ionic radius decrease from La3+

ion

(C) La is actually an element of transition series rather than lanthanides

(D) Atomic radius of Zr and Hf are sane because of lanthanide contraction

25. The ONO angle is maximum in :

(A) 3NO (B) 2NO

(C) 2NO (D) 2NO

26. Name the type of structure of silicate in which one oxygen atom is shared between two 4

4SiO

units.

(A) Linear chain silicate (B) Pyrosilicate

(C) Sheet silicate (D) Three-dimensional

27. Al and Ga have nearly the same covalent radii because of:

(A) Greatest shielding effect of s-electrons of Ga atoms(B) Poor shielding effect of s-electrons of Ga atoms

(C) Poor shielding effect of d-electrons of Ga atoms

(D) Greatest shielding effect of d-electrons of Ga atoms



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28. The IUPAC name of the compound,

2

2

C H C H COOH is :| |OH NH

(A)2-Amino-3-hydroxypropanoic acid

(B)1-Hydroxy-2-aminopropan-3-ioc acid

(C) 1-Amino-2-hydroxypropanoic acid (D) 3-Hydroxy-2-aminopropanoic acid.

29. Aqueous solution of borax acts as a buffer because :

(A) It contains weak acid and its salt, with strong base

(B) It contains tribasic acid and strong base

(C) It contains number of natural water molecules

(D) None of these

30. In which reaction does the oxidation state of the group 14 element change?

(A) 4

4 2Si 4 OH SiO 2H

(B) 4 4 4 62GeCl 2 Et N Cl Et N GeCl

(C) 4 3 2 4SiCl 4NH Si NH 4HCl (D) 4 2 2 2SiH O SiO 2H O



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PART - II (PHYSICS) 120 MARKS



31. In the figure the springsS1S2S3 and have spring constants

K1= 50 N/m, K2= 30 N/m, K3= 30N/m andK4 = 60N/m

respectively. The mass of the block is 10gm.

Find the period of small oscillations of the block.

(A)20

sec

(B)30

sec

(C)40

sec

(D)50

sec

32. For an EM wave traveling along positivex-axis, the electric field vector at a point is 720j . Then magnetic

field vector at the same point is :

(A)6

2 4 10 . k (B) 62 4 10 . k (C) 52 16 10 . k (D) 52 16 10 . k

33. In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to

each other. A charged particle is released from rest in this region. The path of the particle will be :

(A) helix (B) straight line (C) ellipse (D) circle

34. A string is stretched between fixed points separated by 75.0cm. It is observed to have resonant frequencies

of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. Then, the lowest

resonant frequency for this string is :

(A) 105Hz (B) 1.05Hz (C) 1050Hz (D) 10.5Hz


m

S1

S2S3 S4


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35. The circuit has two oppositely connected ideal diodes in

parallel. What is the current flow in the circuit?

(A) 1.71A (B) 2.00A

(C) 2.31A (D) 1.33A

36. If the binding energy per nucleon in7 43 2andLi He nuclei are 5.60MeVand 7.06Mevrespectively, then in

the reaction7 43 22 p Li He energy of proton must be.

(A) 28.24MeV (B) 17.28MeV (C) 1.46MeV (D) 39.2MeV

37. The diagram shows the energy levels for an electron in a certain

atom. Which transition shown represents the emission of a photon

with the most energy?

(A) I (B) II

(C) III (D) IV

38. Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a

planet in circular orbit of radiusRaround the sun will be proportional to :

(A)

1

2

n

R

(B)

1

2

n

R

(C) Rn

(D)

2

2

n

R


12V

4

3 2

D2D1

n = 4

n = 3

n = 2

n= 1I II III IV


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39. A radiation of energyEfalls normally on a perfectly reflecting surface. The momentum transferred to the

surface is :

(A) E/c (B) 2E/c (C) Ec (D) E/c2

40. The total current supplied to the circuit by the battery is :(A) 1A (B) 2A

(C) 4A (D) 6A

41. The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a

vibration magnetometer is 2s. The magnet is cut along its length into three equal parts and three parts are

then placed on each other with their like poles together. The time period of this combination will be :

(A) 2s (B) 2/3s (C) 2 3 s (D) 2 3/ s

42. In anLCRseriesa.c. circuit, the voltage across each of the components, L,CandRis 50V. the voltage

across theLCcombination will be :

(A) 50V (B) 50 2V (C) 100V (D) 0V(zero)

43. A coil having n turns and resistance R is connected with a galvanometer of resistance 4 R .

This combination is moved in time tseconds from a magnetic fluxW1Weber toW2Weber. The induced

current in the circuit is :

(A) 2 1

5

W WRnt

(B) 2 1

5

n W W

Rt(C)

2 1 W W

Rnt(D)

2 1n W W

Rt


26V6

31 5.


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44. A block of mass 15kgis resting on a rough inclined lane as shown in the figure. The minimum horizontal

force F of 50Nis required to prevent down word slipping the coefficient of friction between the surfaces of

contact is.

(A) 1/2

(B) 2/3(C) 3/4

(D) 1/4

45. A particle is projected form the ground with an initial speed of V at an angle with horizontal.

The average velocity of the particle between its point of projection and the highest point of trajectory is:

(A)2

1 22

V

cos (B)2

1 22

V

cos

(C)2

1 32

V

cos (D) vcos

46. The number of images formed by the lens as

shown in the figure is :

(A) 1 (B) 2

(C) 3 (D) 4

47. If the ratio of change in current in emitter and corresponding change in collector current is 1.013, then the

value of is :

(A) 0.987 (B) 75.92 (C) 1.006 (D) 79.68


M

45

F

1 2


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48. The 3 physical quantities are related as3 2

a b

xc

, if the age error ina, b, andcare 2 1 and 4 %, % % ,

respectively, then age error inxis :

(A) 8 % (B) 12 % (C) 14 % (D) 10 %

49. Two identical long, solid cylinders are used to conduct heat from temperature T1 to temperature T2.

Originally the cylinders are connected in series and the rate of heat transfer is H. If the cylinders are

connected in parallel, then the rate of heat transfer would be :

(A) H/4 (B) 2H (C) 4H (D) 8H

50. A disc of massMand radiusRis performing pure rolling motion in the

x-y plane as shown in the figure. The magnitude of angular momentum

of the disc aboutOis :

(A)2

2

MR (B)

2MR

(C)23

2MR (D)

22MR

51. 743 J of heat energy is added to raise the temperature of 5 mol of an ideal gas by 2kat constant pressure.

How much heat energy is required to raise the temperature of the same mass of the gas by 2 Kat constant

volume?

(A) 826J (B) 743J (C) 660 J (D) 620J

52. Three capacitors connected in series have an effective resistance of 2 F . If one of the capacitors is

removed, the equivalent capacitance becomes 3 F . The capacitance of the capacitor that is removed is:

(A) 6 F (B) 1 F (C) 3 2/ F (D) 2 3/ F


O

R R x

y


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53. The angle of declination at any point on the surface of the earth

(A) is equal to 11 5. and same everywhere on the earth

(B) is equal to 8 and same everywhere on the earth(C) has different values at different points on the surface of the earth

(D) is the angle between the axis of the magnetic dipole of the earth and the axis of rotation of theearth

54. A shell at rest at the origin explodes into three fragments of mass 1kg, 2kgandmkilograms. The 1kgand

2kg pieces fly off with speeds of 12 m/salong thex-axis and 8m/s along they-axis, respectively. If the

mkilogram piece files off with a speed of 40m/s, the total mass of the shell would be :

(A) 0.5kg (B) 5kg (C) 3.5kg (D) 4.5kg

55. A point chargeq is placed at the centre of one of the face of cuboid as

shown in figure. Find the electric flux crossing through the upper surface.

(A)06

q

(B)024

q

(C)012

q

(D) Zero

56. If length of a potentiometer wire is 300 cm and in its primary circuit a standard cell of emf 2V and a

rheostat having resistance setting at 4 is connected, the resistance per unit length of potentiometer wire

is 2/ .m If a battery ofemf1Vand internal resistance 0 5. is connected in secondary, then null point will

be obtained at:

(A) 250cm (B) 200cm (C) 150cm (D) 100cm



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57. A block of massm is gently placed over a massive plank moving horizontally over a smooth surface with

velocity 6m/s. The coefficient of friction between the block and plank is 0.2. The distance travelled by the

block till it slides on the plank is (takeg= 10m/s2)

(A) 4m (B) 6m (C) 9m (D) 12m

58. The refractive index of a 60 prism is 7 3/ . The minimum angle of incidence of a ray of light that can

be transmitted through the prism is:

(A) 30 (B) 40 (C) 50 (D) 60

59. A currentIflows through a thin wire shaped as regular polygon ofn sides which can be inscribed in a

circle of radiusR. The magnetic field induction at the centre of polygon due to one side of the polygon is:

(A)0

Itan

R n

(B)

0

4

Itan

R n

(C)

0

2

Itan

R n

(D)

0

2

Icos

R n

60. With reference to the following figure, which of

the following is possible?

(A) A= 0,B= 0,X= 1

(B) A= 0,B= 1,X= 0

(C) A= 1,B= 0,X= 0

(D) A= 1,B= 1,X= 0



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PART - III (MATHEMATICS) 120 MARKS



61. The sum of the series2 3 4 5 6 7

2 1 2 1 2 1 21

3 3 3 3 3 3 3............. upto infinite terms is equal to :

(A)15

8(B)

8

15(C)

27

8(D)

21

8

62. Iffis a positive function such f x T f x where 0T x R then :

2 22 2

4 4n

f x T f x T .............. nf x nTlim n

f x T f x T .......... n f x n T

is :

(A) 2 (B)2

3(C)

3

2(D) None of these

63. The arithmetic mean of a set of observations is X. If each observation is divided by and then is

increased by 10, then the mean of the new series is :

(A) X

(B)

10X

(C)

10X

(D) 10X

64. Letfandgbe twice differentiable function onRand 5 8 5 2f " , g"

then

55 5 5

5 5 5x

f x f x f 'im

g x g x g'

is equal to :

(A) 0 (B) 1 (C) 2 (D) 4



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69. If1

3 3 4

2 3 4 then

0 1 1

A A

is equal to :

(A) A (B) A2

(C) A3

(D) A4

70. If2 1

2

xatan

a

x a

alim

x e

, thenais equal to :

(A) (B) (C)2

(D)

2

71. The roots of the equation2

6 2x x x | | are given by :

(A) 2 2 4 (B) 0, 1, 4 (C) 2 1 4 (D) 0, 2, 4

72. Number of 7 digit telephone numbers that can be created if the first three digits must be 426,427or 428 and

right most digit is divisible by 3, iskthousand thenkis equal to :

(A) 12 (B) 9 (C) 6 (D) 3

73. Let 3 2 4 2 a i j k b i k and 4 2 3c i j k . Sum of distinct values of for which the

equation xa yb zc xi y j zk has non trivial solution is :(A) 1 (B) 4 (C) 7 (D) 8



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74. If the maximum number of distinct elements in a symmetric matrix of ordernis 45, then the value ofnis :

(A) 9 (B) 10 (C) 15 (D) None of these

75. A line passes through origin and is perpendicular to two parallel lines 2 6 0x y and 4 2 9 0x y

then the ratio in which the origin divides this line segment is :

(A) 1 : 2 (B) 1 : 1 (C) 5 : 4 (D) 3 : 4

76. LetRbe the set of real numbers. Consider the following subsets ofR R.

1 and 0 2 is an integerS x y y x x T x y x y .

Which one of the following is true?

(A) NeitherSnorTis an equivalence relation onR

(B) BothSandTare equivalence relations onR

(C) Sis an equivalence relation onRbutTis not

(D) Tis an equivalence relation onRbutSis not

77. Let 1 1

0

1 0

tan xf x x

x

Then which of the following statement isCorrect?

(A) f has a non removable discontinuity of finite type atx= 0

(B) f has a non-removable discontinuity of oscillatory type atx= 0

(C) f has a non-removable discontinuity of infinite type atx= 0

(D) f is continuous on 0 0



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78. If pointAlies on line1 2 3

2 3 4

x y z and pointBlies on line

2 4 6

3 7 6

x y z then AB can

be parallel to :

(A) 2i j k (B) i j k (C) 3i j k (D) 4i j k

79. The range of the function 1 1f x cos x tan x is :

(A)3

4 4

(B)

3

2 2

(C)

5

3 4

(D)

5

4 4

80. The integral

21

ln xdx

ln x is equal to :

(A)

3

1

1c

ln x

(B)

2

1

1c

ln x

(C)

2

1

xc

ln x

(D)

1x

cln x

81. If anda b c are vectors such that andb c are perpendicular, but anda b are not. Let m be a real

number. If x . a m x b c then :

(A)

mb a c

xc . b

(B)

mb a c

xa . b

(C)

mb a . c

xa . b

(D)

mb a c

xa . b



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82. The shelf life, in days for bottles of a certain prescribed medicine is a random variable having the density

function 3

20 0000

100

0 elsewhere

xf x x

, the probability that a bottle of this medicine will have a shelf

life of at least 10 days is :

(A)1

121(B)

21

121(C)

1

11(D)

100

121

83. IfAis a skew-symmetric matrix andnis odd positive integer, thenAnis :

(A) A symmetric matrix (B) A skew-symmetric matrix

(C) A diagonal matrix (D) None of these

84. The smallest natural numbercfor which the equationex=cx2has exactly three distinct solutions, is :

(A) 1 (B) 2 (C) 3 (D) 4

85. The approximate percentage of the interval 5 15 for which the inequality7

44

xx

is satisfied, is :

(A) 55% (B) 65% (C) 60% (D) 45%

86. Ifx1,x2,..,x18are observations such that 18

1

8 9jj

x

and 18

2

1

8 45jj

x

, then the standard

deviation of these observations is :

(A)18

34(B) 5 (C) 5 (D)

3

2



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87. The value of 20

11

x

xx

lim ln t dt x

is equal to :

(A) 0 (B) 1 (C) 1 (D) 2

For Questions 88 - 89

Consider the function 12

2

1

xf x sin x R

x

.

88. Number of points where f x is not differentiable, is :

(A) 0 (B) 1 (C) 2 (D) 3

89. The value of 0f is :

(A) 2 (B) 2 (C) 1 (D) Non existent

90. The integral 1

0

f x dx is equal to :

(A)1

22 2

ln

(B) 22

ln

(C)1

24 2

ln

(D) None of these


s


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2014 Final Jee Mains 2014 Aceg

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