JEE Main 2015

1. As an electron makes a transition from an excited stateto the ground state of a hydrgone-like atom/ion:(1) kinetic energy, potential energy and total energy

decrease(2) kinetic energy decreases, potential energy in-

creases but total energy remains same(3) kinetic energy and total energy decrease but po-

tential energy increases(4) its kinetc energy increases but potential energy

and total energy decreaseSol. [4]2. The period of oscillation of a simple pendulum is

T Lg 2 . Measured value of L is 20.0 cm known to1 mm accuracy and time for 100 oscillations of the pen-dulum is found to be 90 s using a wrist watch of 1 sresolution. the accuracy in the determination of gi s(1) 3% (2) 1%(3) 5% (4) 2%

Sol. [1]3. A long cylindrical shell carries positive surface charge

in the upper half and negative surface charge int he lower half. The electric field lines around thecylinder will look like figure tgiven in:(figure are schematic and not drawn to scale)

(1) (2)

(3) (4)

Sol. [4]4. A signal of 5 kHz freq2uency is amplitude modulated

on a carrier wave of frequency 2 MHz. The frequenciesof the resultant signal is/are:(1) 2005 kHz, and 1995 kHz(2) 2005 kHz, 200 kHz and 1995 kHz(3) 2000 kHz and 1995 kHz(4) 2 MHz only

Sol. [2]

5. Consider a spherical shell of radius R at temperature T.The black body radiation inside it can be considered asan ideal gas of photons with internal energy per unit

volume u UV T 4 and pressure p UV

FHG IKJ132 . If theshell now undergoes an adiabatic expasnion the rela-tion between T and R is(1) T e R 3 (2) T R

1

(3) T R13 (4) T e R

Sol.

6. An inductor L H 003.b g and a resistor R k 015. b gare connected in series to a bettery of 15 V EMF in acircuit shown below.The key K1 has been kept closedfor a long time.then at t K 0 1, is opened and key K2is closed simultaneously. At t 1ms , the current inthe circuit will be : e5 150e j

(1) 67 mA (2) 6.7 mA(3) 0.67 mA (4) 100 mA

Sol. [3]7. A pendulum made of a uniform wire of cross sectional

area A has time period T. When an additional mass Mis added to its bob, the time period changes to TM . Ifthe Young's modulus of the material of the wire is Ythen 1Y is equal to(g = gravitational acceleration)

(1) TTMgA

MFHG IKJ LNMMOQPP

21 (2) 1

2 FHG IKJLNMM

OQPP

TT

AMg

M

(3) 12

FHG IKJLNMM

OQPP

TT

AMgM (4)

TT

AMgM

FHG IKJ LNMM

OQPP

21

Sol. [4]

Physics

JEE Main 20158. A red LED emits light at 0.1 watt uniformly around it.

The amplitude of the electric field of the light at a dis-tance of 1 m from the diode is(1) 2.45 V / m (2) 5.48 V / m(3) 7.75 V / m (4) 1.73 V / m

Sol. [1]9. Two coaxial solenoids of different radii carry current I

in the same direction. Let F1 be the magnetic force onthe inner solenoid due to the outer one and F2 be themagnetic force ont he outer solenoid due to the innerone. Then:(1) F1 is radially inwards and

F2 is radially outwards(2) F1 is radially inwards and

F2 0(3) F1 is radially outwards and

F2 0(4) F F1 2 0

Sol. [3]10. Consider an ideal gas confined in an isolated closed

chamber. As the gas undergoes an adiabatic. As thegas undergoes an adiabatic expansion, the average timeof collison between molecules increases as V q , where

V is the volume of the gas. The value ofq is : FHG IKJCCpv(1) 3 56

(2) 12(3) 12 (4)

3 56

Sol. [2]11. An LCR circuit is equivalent to a damped pendulum. In

an LCR circuit the capacitor is charged to Q0 and thenconnected to the L and R as shwon below:

If a student plots graphs of the square of maximumcharge QMax2e j on the capacitor with time (t) for twodifferent values L1 and L L L2 1 2b g of L then whichof the following represents this graph correctly? (plotsare schematic and not drawn to scale)

(1)

(2)

(3)

(4)

Sol. [4]12. From a solid sphere of mass M and radius R, a spheri-

cal porition of radius R / 2 is removed, as shown in thefigure. Taking gravitational potential V = 0 at r ,the potential at the centre of the cavity thus formed is:(G = gravitational constant)

(1) GMR (2)23GMR

(3) 2GMR (4)GM

R2Sol. [3]13. A train is moving on a straight track with speed 20 ms

1. It is blowing its whistle at the frequency of 1000 hz.The percentage change in the frequency heard by asperson standing near the track as the train passes himis (speed of sound = 320 ms1) close to:(1) 12% (2) 18%(3) 24% (4) 6%

Sol. [2]

JEE Main 201514. Given in the figure are two blocks A and B of weight 20

N and 100 N, respectively. These are being pressedagainst a wall by a force F as shwon. If the coefficientof friction between teh blocks is 0.1 and between blockB and the wall is 0.15, the frictional force applied by thewall on block B is

(1) 80 N (2)120 N(3) 150 N (4) 100 N

Sol. [2]15. Distance of the centre of mass of a solid uniform cone

from its vertex is z0 . If the radius of tis base is R and itsheight is h then z0 is equal to

(1) 34h (2) 58

h

(3) 382hR (4)

hR2

4Sol. [1]16. A rectangular loop of sides 10 cm and 5 cm carrying a

current I of 12 A is placed in different orieintations asshown in the figures below:

(a)

(b)

(c)

(d)

If there is a uniform magnetic field of 0.3 T in the posi-tive z-direction, in which orientations the loop wouldbe in (i) stable equilibrium and (ii) unstable equilib-rium?(1) (a) and (c), respectively(2) (b) and (c), respectively(3) (b) and (d), respectively(4) (a) and (b), respectively

Sol. [3]

17. In the circuit shown, the current in the 1 resistro is

(1) 0 A (2) 0.13 A, from Q to P(3) 0.13 A, from P to Q (4) 1.3 A, from P to Q

Sol. [2]18. A uniformly charged solid sphere of radius R has po-

tential V0 (measured with respect to ) on its sur-face. For this sphere the equipotential surfaces withpotentials 32

54

34

0 0 0V V V, , and V04 have radius R1 ,R2 , R3 and R4 respectively. Then(1) R1 0 and R R R R2 1 4 3 b g b g(2) R1 0 and R R R2 4 3 b g(3) 2 4R R(4) R1 0 and R R R2 4 3 b g

Sol. [2]

JEE Main 201519. In the given circuit, charge Q2 on the 2 F capacitor

changes as C is varied from 1 F to 3 F. Q2 as afunction of 'C' is given properly by : (figure are drawnschematically and are not to scale)

(1)

(2)

(3)

(4)

Sol. [2]20. A particle of mass m movign in the x direction with

speed 2v is hit by another particle of mass 2m movingin the y direction with speed v. If the collision is per-fectly inelastic, the percentage loss in the energy dur-ing the collision is close to(1) 50% (2) 56%(3) 62 % (4) 44%

Sol. [2]

21. Monochromatic light is incident on a glass prism ofangle A. If the refractive index of the material of theprims is , a ray, incident at an angle , on the face ABwould get transmitted through the face AC of the prismprovided:

(1) FHG IKJFHG

IKJ

LNMM

OQPP sin sin sin1 1

1A

(2) FHG IKJFHG

IKJ

LNMM

OQPP cos sin sin1 1

1A

(3) FHG IKJFHG

IKJ

LNMM

OQPP cos sin sin1 1

1A

(4) FHG IKJFHG

IKJ

LNMM

OQPP sin sin sin1 1

1A

Sol. [4]22. From a solid sphere of mass M and radius R a cube of

maximum possible volume is cut. Moment of inertia ofcube about an axis passing through its center and per-pendicular to one of its faces is

(1) MR2

16 2 (2)49 3

2MR

(3) 43 32MR (4)

MR232 2

Sol. [2]

JEE Main 201523. MatchList-I (Fundamental Experiment) withList-II (its

conclusion) and select the correct option from thechoices given below the list:

List-I List-II(A) Franck-Hertz (i) Particle nature of

Experiment. light(B) Photo-electric (ii) Discrete energy

experiment levels of atom(C) Davison - Germer (iii) Wave nature of

electron(iv) Structure of atom

(1) (A) (ii) (B) (iv) (C) (iii)(2) (A) (ii) (B) (i) (C) (iii)(3) (A) (iv) (B) (iii) (C) (ii)(4) (A) (i) (B) (iv) (C) (iii)

Sol. [2]24. When 5V potential difference is applied across a wire

of length 0.1 m, the drift speed of electrons is25 10 4 1. ms . If the electron density in the wire is8 1028 3 m , the resistivity of the material is close to(1) 16 10 7. m (2) 16 10 6. m(3) 16 10 5. m (4) 16 10 8. m

Sol. [3]25. For a simple pendulum, a graph is plotted between its

kinetic energy (KE) and potential energy (PE) againstits displacement d. Which one of the following d.Which one of the following represents these correctly?(graphs are schematic and not drawn to scale)

(1)

(2)

(3)

(4)

Sol. [1]26. Two stones are thrown up simultaneosuly fromt he

edge fo a cliff 240 m high with initial speed of 10 m, / sand 40 m / s respectively. Which of the following graphbest represents the time variation of relative positionof second stone with respect to the first?(Assume stones do nto rebound after hitting theground and neglect awir resistance, take g 10 2m/ s )(The figures are schematic and not drawn to scale)

(1)

(2)

(3)

(4)

Sol. [2]

JEE Main 201527. A solid body of constant heat capacity 1 J / oC is being

heated by keeping it in contact with reservoirs in twoways"(i) Sequentially keeping in contact with 2 reservoirs

such that each reservoir supplies same amount ofheat.

(ii) Sequentially keeping in contact with 8 reservoirssuch that each reservoir supplies same amount ofheat.

In both the cases body is brough from initialtemperatgure 100 oC to final temperature 200 oC.entropy change of the body in the two cases re-spectively is

(1) ln2, ln2 (2) ln2, 2ln2(3) 2ln2, 8ln2 (4) ln2, 4ln2

Sol. [1]28. Assuming human pupil to have a radius of 0.25 cm and

a comfortable viewing distance of 25 cm, the minimumseparation between two objects that human eye canresolve at 500 nm wavelength is(1) 30 m (2)100 m(3) 300 m (4) 1 m

Sol.29. Two long current carrying thin wires, both with current

I, are held by insulating threasds of length L and are inequilibrium as shown in the figure, with threads mak-ing and angle with the vertical. if wires have mass per unit length then the vlaue of 1 is(g = gravitational acceleration)

(1) 20

sin cos

g L (2) 20

g L tan

(3) g L0

tan (4) sin cos

g L0

Sol. [1]30. On a hot summer night, the refractive index of air is

amllest near the ground and increases with height fromthe ground. When a light beam is directed horizontally,the Huygen's principle leads us to conclude that as ittravels, the light beam:(1) goes horizontally without any deflection(2) bends downwards(3) bends upwards(4) becomes narrower

Sol. [3]

JEE Main 2015

31. The molecular formula of a commercial resin used forexchanging ions in water softening is C H SO Na8 7 3(Mol. wt 206). Ca2 ions by the resin when expressedin mole per gram resin?

(1) 1103 (2)1206

(3) 2306 (4)1412

Sol. [4] 2 mol of water softner require one mole of Ca2

32. Sodium metal crystallizes in a body centered cubic lat-tice with a unit cell edge of 4 29. . The radius of so-dium atom is approximately.(1) 186. (2) 3 22. (3) 5 72. (4) 0 93.

Sol. [1] r a BC C. . . . . . 34173 4 29

4 186

33. Which of the following is the energy of a possibleexcited state of a possible excited state of hydrogen?(1) 136. eV (2) 68. eV(3) 34. eV (4) 68. eV

Sol. [3] E zn eV 13622.

n 2 (First Excited state) E eV 34.

34. The intermolecular interaction that is dependent on theinverse cube of distance between the molecules is:(1) ion-ion interaction (2) ion-dipole interaction(3) London fforce (4) hydrogen bond

Sol. [4] Hydrogen bond is the type of dipole-dipole interac-tion.

Chemistry35. The following reaction is performed at 298 K.

2 2NO g O g( ) ( ) 2NO (g)The standard free energy of formation of NO(g) is 86.6kJ/mol at 298 K. What is the standard free energy offormation of NO g2 ( ) at 298 K ? Kp 16 1012.e j(1) R( ) ln .298 16 10 8660012 e j(2) 86600 298 16 10 12 R( ) ln .e j(3) 86600 16 10298

12

ln .( )

e jR

(4) 05 2 86 600 298 16 10 12. , ( ) ln . R e jSol. [4] 2 22 2NO O NO

G RT Kp lnG RT ln .16 1012 G G GNO NO 2 22G RNO2 05 2 86 600 298 16 1012 . , ln .b g e j

36. The vapour pressure of acetone at 20 is 185 torr. When1.2 g of a non-volatile substance was dissolved in100 g of acetone at 20 C, its vaopour pressure was183 torr. The molar mass (g mol1) of the substance is(1) 32 (2)64(3) 128 (4) 488

Sol. [2] O p ppw MM w

o ss

solute solventsolute solvent

2

w g molsolute 64 1

JEE Main 201537. The standard gibbs energy change at 300 K for the

reaction 2A B + C is 2494.2 J. At a given time,the composition of the reaction mixture isA B 12 2, and C

12 . The reaction proceeds

in the : [R = 8.314 J/K/mol, e = 2.718](1) forward direction because Q KC(2) reverse direction because Q KC(3) forward direction because Q KC(4) reverse direction because Q KC

Sol. [2] G RT Kp ln

Kp e eG RT /.

.2494 2

8 314 300

Kp e e 1 1 1

2 718 036. .

QP

FHG IKJ

2 1212

42

Q Kp p backward

38. Two Faraday of electricity is passed through a solu-tion of CuSO4 . The mass of copper deposited at thecathode is: (at. mass of Cu = 63.5 amu)(1) 0 g (2) 63.5 g(3) 2 g (4) 127 g

Sol. [2] Cu aq e Cu s 2 2( ) ( )2F 1 mol Cu = 63.5 g Cu

39. Higher order (>3) reactions are rare due to :(1) low probability of simultaneous collision of all thereacting species(2) increase in entropy and activation energy as moremolecules are involved(3) shifting of equilibrium towards reactants due to elas-tic collisions(4) loss of active species on collision

Sol. [1] According to collision theory

40. 3 g of activated charcoal was added to 50 mL of aceticacid solution (0.06N) in a flask. After qan hour it wasfilered and the strenght of tyhe filtrate was found to be0.042 N. The amount of acetic acid adsorbed (per gramof charcoal) is:(1) 18 mg (2) 36 mg(3) 42 gm (4) 54 mg

Sol. [1] Initial moles of CH COOH3 006 501000 3 103.

Finial moles of CH COOH3 0 042 501000 21 103. .

CH COOH3 adsorbed 30 10 21 103 3. . 09 10 3.

Mass 09 60 10

3 183. Mg

Adsorb per gram of charcoal

41. The ionic radii (in ) of N O3 2 , and F arerespectively:(1) 1.36, 1.40 and 1.71 (2) 1.36, 1.71 and 1.40(3) 1.71, 1.40 and 1.36 (4) 1.71, and 1.36 and 1.40

Sol. [3] N O F 3 2

In isoelectronic series size decreases as ze increases .

42. In the context of the Hall - Heroult process for the ex-traction of Al, which of the following statements isfalse?(1) CO and CO2 are produced in this process(2) Al O2 3 is mixed with CaF2 which lowers the melt-ing point of the mixture and brings conductivity(3) Al3 is reduced at the cathode to form Al(4) N a A lF3 6 serves as the electrolyte

Sol. [4] Refer to NCERT

JEE Main 201543. Form the following statements regarding H O2 2 ,

choose the incorrect statement:(1) It can act only as an oxidizing agent(2) It decompose on exposure to light(3) It has to be stored in plastic or was lined glassbottles in dark(4) It has to be kept away form dust

Sol. [1] It is disproportionating agent.44. Which one of the following alkaline earth metal

sulphates has its hydration enthalpy greater than itslattice enthalpy ?(1) CaSO4 (2) BeSO4(3) BaSO4 (4) SrSO4

Sol. [2] Among alkaline earth metal sulphates BeSO4 andMgSO4 are water soluble due to high hydrationenthalpy of Be2 and Mg2 .

45. Which among the following is the most reactive ?(1) Cl2 (2) Br2(3) I2 (4) ICI

Sol. [4] Interhalogen compounds are more reactive.46. Match the catalysts to the correct processes:

Catalyst Process(A) TiCl3 (i) Wacker process(B) PdCl2 (ii) Ziegler - Natta polymeron(C) CuCl2 (iii) Contact process(D) V O2 5 (iv) Deacon's process(1) A iii B ii C iv D i ( ), ( ), ( ), ( )(2) A ii B i C iv D iii ( ), ( ), ( ), ( )(3) A ii B iii C iv D i ( ), ( ), ( ), ( )(4) A iii B i C ii D iv ( ), ( ), ( ), ( )

Sol. [2]TiCl3 - Ziegler - Natta polymeronPdCl2 - Wacker processCuCl2 - Deacon's processV O2 5 - Contact process

47. Which one has the highest boiling point ?(1) He (2)Ne(3) Kr (4) Xe

Sol. [4] Boiling point Molecular mass48. The number of geometric isomers that can exist for

square planar Pt Cl py NH NH OH( ) ( ) 3 2b gb g is (py =pyridine):(1) 2 (2) 3(3) 4 (4) 6

Sol. [2]

49. The color of KMnO4 is due to :(1) M L charge transfer transition(2) d d transition(3) L M charge transfer transtion(4) * transition

Sol. [3]50. Assertion: Nitrogen and Oxygen are the main compo-

nents in the atmosphere but these do not react to formoxides of nitrogen.Reason: The reaction between nitrogen and oxygenrequires high temperature.(1) Both assertion and reason are correct, and the rea-son is the correct explanation for the assertion(2) Both assertion and reason are correct, but the rea-son is the not correct explanation for the assertion(3) The asswertion is incorrect, but the reason is cor-rect(4) Both the assertion and reason are incorrect

Sol. [1]51. In carius method of estimation of halogens, 250 mg of

an organic compound gave 141 mg of AgBr. The per-centage of bromine in the comkpound is (at mass Ag =108, Br = 80)(1) 24 (2)36(3) 48 (4) 60

Sol. [1] % of Br Atomic mass of Br Mass of AgBr

Molecular mass of AgBr Mass of Compound

JEE Main 201552. Which of the following compounds will exhibit geo-

metrical isomerism?(1) 1-Phenyl - 2 butene(2) 3-Phenyl-1-butene(3) 2-Phenyl-1-butene(4) 1,1-Diphenyl-1-propane

Sol. [1] H C CH CH CH Ph3 2 53. Which compound would give 5-keto-2-methyl hexanal

upon ozonlysis?

(1) (2)

(3) (4)

Sol. [2]CH3

CH3o o

54. The synthesis of alkyl fluorides is best accomplishedby:(1) Free radical fluorination(2) Sandmeyer's reaction(3) Finkelstein reaction(4) Swarts reaction

Sol. [4] R X AgF R F AgX

55. In the following sequence of reactions:Toluene KMnO SOCl H PdBaSOA B C4 2 2 4

/ ,the product C is:(1) C H COOH6 5 (2) C H CH6 5 3(3) C H CH OH6 5 2 (4) C H CHO6 5

Sol. [4] A = C H COOH6 5 , B = CH COCl5 C = C H CHO6 5

56. In the reaction

the product E is

(1)

(2)

(3) (4)

Sol. [3] Sand mayer reaction57. Which polymer is used in the manufacture of paints

and lacquers ?(1) Bakelite (2)Glyptal(3) Polypropene (4) Poly vinyl chloride

Sol. [2]58. Which of the vitamins given below is water soluble?

(1) VitaminC (2)Vitamin D(3) VitaminE (4) Vitamin K

Sol. [1] Vitamin B and C are water soluble.59. Which of the following compounds is not an antacid ?

(1) Aluminium hydroxide(2)Cimetidine(3) Phenelzine (4) Ranitidine

Sol. [3]60. Which of the following compounds is not colored yel-

low ?(1) Zn Fe CN2 6b g (2) K CO NO3 2 6b g(3) NH As Mo O4 3 3 10 4b g b g(4) BaCrO4

Sol. [1]

JEE Main 2015

61. Let A and B be two sets containing four and two ele-ments respectively. Then the number of subsets of theset A B, each having at least hree elemnts is:(1) 219 (2)256(3) 275 (4) 510

Sol. [1]

62. A complex number z is said to be unimodular if z 1 .Suppose z1 and z2 are complex numbers such thatz z

z z1 2

1 22

2 is unimodular and z2 is not unimodular. Then

the point z1 lies on a:(1) straight line parallel to x-axis.(2) straight line parallel to y-axis.(3) circle of radius 2.(4) circle of radius 2

Sol. [3]

63. Let and be the roots of equation x x2 6 2 0 If an n n , for n 1, then the value ofa a

a10 8

92

2 is equal tyo

(1) 6 (2) 6(3) 3 (4) 3

Sol. [3]

64. If Aa b

LNMMM

OQPPP

1 2 22 1 2

2is a matrix satsfying the equation

AA IT 9 , where I is 3 3 identity matrix, then theordered pair (a, b) is equal to :(1) (2, 1) (2) (2, 1)(3) 2 1,b g (4) 2 1,b g

Sol. [4]

65. The sets of all values of for which the system oflinear equations:2 21 2 3 1x x x x 2 3 21 2 3 2x x x x x x x1 2 32 has a non-trivial solution,(1) is an empty set(2) is a singleton.(3) contains two elements(4) contains more than two elements

Sol. [2]

66. The number of integers greater than 6,00 than can beformed, using the digits 3, 5, 6, 7 and 8, without repeti-tion, is(1) 216 (2)192(3) 120 (4) 72

Sol. [2]67. The sum of coefficients of integral powers of x in the

binomial expansion of 1 2 50 xe j is(1) 12 3 1

50 e j (2) 12 350e j(3) 12 3 1

50 e j (4) 12 2 150 e jSol. [1]68. If m is the A.M. of two distinct real numbers l and n

l n, 1b g and G G1 2, and G3 are three geometricmeans between l and n, then G G G14 24 342 equals.(1) 4 2l mn (2) 4 2lm n(3) 4 2lmn (4) 4 2 2 2l m n

Sol. [2]69. The sum of first 9 terms of the series

11

1 2 31 3 5

3 3 3 3 .... is

(1) 71 (2)96(3) 142 (4) 192

Sol. [2]

70. lim cos costanxx x

x x

01 2 3

4b gb g is equal to :

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

Sol. [3]71. If the function.

g x k x xmx x( ),,

RS|T|1 0 32 3

is differentiable, then the value of k m is

(1) 2 (2) 165

(3) 133 (4) 4Sol. [1]

Mathematics

JEE Main 2015

72. The normal to the curve, x xy y2 22 3 0 at 1 1,b g(1) does not meet the curve again.(2) meets the curve again in the second quadrant(3) meets the curve again in the third quadrant(4) meets the curve again in the fourth quadrant

Sol. [4]

73. Let f x( ) be a polynomial of degree four having ex-

treme values at x 1 and x 2 . If lim ( )xf xx

LNM OQP 0 21 3then f ( )2 is equal to :(1) 8 (2) 4(3) 0 (4) 4

Sol. [2]

74. The integral dxx x2 4 3 21z e j / equals:

(1) x x c44

1 41FHGIKJ

/(2) x c4 1 41 e j /

(3) x c4 1 41e j / (4) FHGIKJ x x c

44

1 41 /

Sol. [4]75. The integral

loglog log

xx x x dx

22 2

2

4

36 12 z e j(1) 2 (2) 4(3) 1 (4) 6

Sol. [3]76. The area (in sq. units) of the region described by

( , ) :x y y x y x2 2 4 1 ando t is(1) 732 (2)

564

(3) 1564 (4)932

Sol. [4]

77. Let y x( ) be the solution of the differential equation

x x dydx x xlog log ,b g 2 x 1b gThey y(e) is equal to :(1) e (2) 0(3) 2 (4) 2e

Sol. [2]

78. The number of points, having both co-ordinates asintegers, that lie in the interior of the triangle withvertices 0 0 0 41, ,b gb g and 41 0,b g is :(1) 901 (2)861(3) 820 (4) 780

Sol. [3]79. Locus of the image of the point (2, 3) in the line

2 3 4 2 3 0x y k x y b g b g , k R , is a :(1) straight line parallel to x-axis.(2) straight line parallel to y-axis.(3) circle of raidus 2.(4) circle of radius 3.

Sol. [3]80. The number of common tangents to the circles

x y x y2 2 4 6 12 0 andx y x y2 2 6 18 26 0 , is(1) 1 (2) 2(3) 3 (4) 4

Sol. [3]81. The area (in sq. units) of the quadrilateral formed by

the tangents at the end points of the latera recta to the

ellipse x y2 2

9 5 1 , is

(1) 274 (2) 18

(3) 272 (4) 27Sol. [4]82. Let O be the vertex and Q be any point on the parabola,

x y2 8 . If the point P divides the line segment OQinternally in the ratio 1 : 3, then the locus of P is(1) x y2 (2) y x2 (3) y x2 2 (4) x y2 2

Sol. [4]83. The distance of the point (1, 0, 2) from the point of

intersection of the line x y z 231

42

12 and theplane x y z 16, is(1) 2 14 (2) 8(3) 3 21 (4) 13

Sol. [4]

JEE Main 201584. The equation of the plane containing the line

2 5 3x y z ; x y z 4 5 , and parallel to theplane, x y z 3 6 1, is(1) 2 6 12 13x y z (2) x y z 3 6 7(3) x y z 3 6 7(4) 2 6 12 13x y z

Sol. [3]

85. Let a b, and c be three non-zero vectors such that no

two of them are collinear and a b c b c a e j 13 .

If is the angle between vectors b and c, then avalue of sin is

(1) 2 23 (2) 23

(3) 23 (4)2 33

Sol. [1]86. If 12 identical balls are to be placed in 3 identical boxes,

then the probability that one of the boxes containsexcatly 3 balls is

(1) 55323

11FHG IKJ (2) 55 2310FHG IKJ

(3) 220 1312FHG IKJ (4) 22 13

11FHG IKJSol. [1]87. The mean of the data set comprising of 16 observa-

tions is 16. If one of the observation valued 16 is de-leted and three new observations valued 3, 4 and 5 areadded to the data, then the mean of the resultant data,is(1) 16.8 (2) 16.0(3) 15.8 (4) 14.0

Sol. [4]

88. If the angles of elevation of the top of a tower fromthree collinear points A, B and C, on a line leading tothe foot of the tower, are 30o, 45o and 60o respectively,then the ratio, AB : BC, is(1) 3 1: (2) 3 2:(3) 1 3: (4) 2 : 3

Sol. [1]

89. Let tan tan tan FHG IKJ1 1 1 221y x xx ,

where x 13 . Then a value of y is

(1) 31 332

x xx

(2)

31 3

32

x xx

(3) 31 332

x xx

(4)

31 3

32

x xx

So l. [1]

90. The negation of ~ s r s b g is equivalent to(1) s r ~ (2) s r s ~b g(3) s r s ~b g (4) s r

So l. [3]

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