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3. The test is of 3 hours duration.

4. The Test Booklet consists of 90 questions. The maximum marks are 360.

5. There are three parts in the question paper A,B,C consisting of Physics, Chemistry andMathematics having 30 questions in each part of equal weightage. Each question is allotted4 (four) marks for correct response.

6. One Fourth mark will be deducted for indicated incorrect response of each question.No deduction from the total score will be made if no response is indicated for an item in theAnswer Sheet.

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Form Number : )0000CJA103118009)Paper Code

(0000CJA103118009)

EN

GLI

SH

CLASSROOM CONTACT PROGRAMME(Academic Session : 2018 - 2019)

Test Type : ALL INDIA OPEN TEST Test Pattern : JEE-Main

TEST DATE : 23 - 12 - 2018

TARGET : JEE (MAIN) 2019LEADER & ENTHUSIAST COURSE

All India Open Test/Leader & Enthusiast Course/JEE(Main)/23-12-2018

E-1/160000CJA103118009

SPACE FOR ROUGH WORK

PART A - PHYSICSBEWARE OF NEGATIVE MARKING

HAVE CONTROL ¾® HAVE PATIENCE ¾® HAVE CONFIDENCE Þ 100% SUCCESS

1. The self energy of a conducting shell ofradius R & charge Q is :-

(1) 2kQ

R (2) 2kQ

2R (3) 22kQ

R (4) 23kQ

5R

2. A small ball connected to a thread issubmerged in a liquid and made to oscillatelike a simple pendulum. The time periodis T1 if we consider buoyant force as wellas viscous force . If there is no viscous forcebut there is a buoyant force, the time periodis T2 :-

(1) T1 can be equal to T2

(2) T1 is always equal to T2

(3) T1 > T2

(4) T1 < T2

3. An electric iron rated at 120 V has apower of 400 W. When it is switched on,the voltage across the socket drops from124 V to 120 V. What is the resistance ofconnecting wire :-(1) 3.6 W (2) 1.2 W(3) 2.4 W (4) 4.8 W

4. What is the moment of inertia of a uniformrigid rectangular wire frame about itsdiagonal? (mass of frame = m)

(1) 2m

6l

(2) 24 m15

l

2l

l l

2l(3)

22m9l

(4) None of these5. Two polarizers are placed parallel to each

other in the path of a beam of unpolarizedlight of intensity I0. The intensity of

emergent beam is 0I2 . If the first polarizer

is rotated about the line shown :-I0

I /20

(1) Intensity of emergent beam remainsconstant.

(2) Intensity of emergent beam decreases

to zero and then increases to 0I2

again(3) The intensity of emergent beam

increases and then decreases.(4) The intensity of emergent beam

decreases (but not to zero) and then

increases again to 0I2

0000CJA103118009E-2/16



6. A series LR circuit is connected to an ACsource and ideal AC ammeter reads 1A. Ifthe inductive reactance is 30 W andresistance is 40W, what is the powerconsumed by the circuit?

A

V

~(1) 50 W (2) 100 W(3) 80 W (4) 40 W

7. What is the approximate wavelength of 1st

line of paschen series of hydrogen atom ?(1) 1870 nm(2) 2460 nm(3) 656 nm(4) 122 nm

8. If the sides of a rectangle are 45.1 cm and2.32 cm, what is the perimeter correct tosignificant digits ?(1) 94.84 cm(2) 94.8 cm(3) 95 cm(4) 94.862 cm

9. A road is banked at an angle of 37°. If a carmoving at 54 km/hr does not experience anyfriction force while negotiating the curve,the radius of curve is :-

(1) 67.5 m

4 (2) 45 m

(3) 54 m (4) 30 m10. A simple pendulum has a string of length

1m. If the angular amplitude is 1°, whichof the following can represent its angulardisplacement from mean position as afunction of time :-

(1) 12 sec t

q 1°

(2) 2sec t

q

1°

4sec

(3) 2sec

t

q

1°

(4) 2sec t

q

1°


E-3/160000CJA103118009


11. Infinite line charge of charge/length 5nC/mlies along line x = y in the xy plane. Findthe electric field at (0, 0, 4)m :-

(1) Vˆ22.5km (2) ( )22.5 Vˆ ˆi j

m2+ -

(3) Vˆ22.5km

- (4) ( )22.5 Vˆ ˆi jm2

- +

12. The efficiency of a carnot cycle on amonoatomic gas is 50%. The lowesttemperature during the cycle is 27°C. Ifthere are 3 mole of gas, what is the changein its internal energy during adiabaticexpansion during the cycle ?(1) –11.25 kJ (2) 11.25 kJ(3) 101.25 J (4) –101.25 J

13. A rod of length l, coefficient of thermalexpansion a is heated by a temperaturedifference DT. It was constrained betweentwo walls at a distance l. As a result, itbends to form a circular arc. The radius ofarc is :-

(1) 2 TaDl

(2) 6 TaDl

R R

l

(3) 2 6 TaDl

(4) 3 3 TaDl

14. The depletion region of a p–N junctiondiode contains immobile ions. Which of thefollowing figures correctly show the signof those ions :-

(1)

+ ++ ++ ++ ++ +

p n

(2)

– –

p n– –– –– –– –– –– –– –

(3)

+ –

p n–––––––

++++++

+++++++

––––––––

(4) p n

+++++++

+++++++

––––––––

––––––––

0000CJA103118009E-4/16



15. For an npn transistor Rout = 1.2 × 105 W,Rin = 6000 W, b = 50. It is connected toamplify an input signal in active mode incommon emitter configuration. The inputsignal is :

t

1mV

–1mV

The output signal looks like.

(1) t–0.5V

0.5V

(2) t

–1V

1V

(3) t–0.5V

0.5V

(4) t

–1V

1V

16. Light emitted from a star (assumed to be ablack body) has a maximum intensity atwavelength l. If a helium gas sample hassame temperature as that of the star,de-broglie wavelength of its atoms movingat vrms would be proportional to :-

(1) l (2) 1l

(3) l2 (4) 21l

17. A uniform magnetic field B = kt is passingperpendicular to plane of a ring ofresistance R. k is a constant and t is time.If resistance of the ring is constant, thecurrent flowing through the ring is :-

× × × ×××× ××

×× ×

×

××××× ××

××

××

× ××

× ×

(1) Clockwise and constant(2) Anticlockwise and constant(3) Zero(4) Anticlockwise and increasing with time


E-5/160000CJA103118009


18. A wheel of radius R is rolling inside a fixedcircular cylinder of radius 2R as shown.What is the trajectory followed by a pointon the rim of the wheel :-

R

2R

(1) Circle (2) Cycloid(3) Straight line (4) None of these

19. A string fixed at both the ends is oscillatingin its 3rd overtone. If the tension in thestring is 10N, its mass is 1gm and length is4m, what is its frequency ?(1) 75 Hz (2) 100 Hz (3) 125 Hz (4) 10 Hz

20. The correct order of most probablespeed (vmp), root mean square speed (vrms),and average speed (vav) of molecule in anideal gas is :-(1) vav > vmp > vrms (2) vrms > vmp > vav

(3) vmp > vrms > vav (4) vrms > vav > vmp

21. A balloon of volume 20 m3 is filled withhelium. It rises to a height of 180 m in 30secstarting from rest. The mass of balloon andequipment (excluding payload and helium)is 12 kg. If density of air is 1.29 kg/m3 anddensity of helium is 0.18 kg/m3 and areconstant, find the mass of payload liftedby the balloon :-(1) 7.5 kg (2) 8 kg (3) 8.8 kg (4) 9.2 kg

22. A lead bullet flying with a velocity of100 m/s pierces a fixed board after whichits velocity becomes 60 m/s. If 40% of energylost increases the temperature of bullet,find change in its temperature. Specificheat capacity of lead = 125 J/kg K :-(1) 10.2 °C (2) 6.3 °C (3) 12.1 °C (4) 0.2 °C

23. A projectile is to be projected on a levelground. Its speed of projection remainsfixed at u, but the angle of projection q withhorizontal can change from 0° to 90°. Plotrange on the level ground against q :-

(1)

R

90° q

(2)

R

90° q

(3)

R

90° q

(4)

R

90° q

24. Two parallel long wires of length 100 meach are separated by a distance of 40 cmfrom each other. The current in each ofthem is 200 A. The current flows in thesame direction. The force acting betweenthe two wires is :-(1) 2N repulsive (2) 2N attractive(3) 0.02 N repulsive (4) 0.02 N attractive

0000CJA103118009E-6/16



25. A U tube filled with a liquid is acceleratinghorizontally with an acceleration a. Theacceleration of the tube is :-

10 cm

15 cm20 cm

10 cm

(1) 5 m/s2 (2) 10 m/s2

(3) 15 m/s2 (4) 20 m/s2

26. A real object is at a distance of 1m from itsvirtual image formed by a diverging lens.Determine the focal length of the lens ifmagnification is 0.6 :-(1) – 3.25 m (2) – 2.5 m(3) – 3.75 m (4) – 1.25 m

27. An electron flying in vacuum into a uniformmagnetic field of B = 128p × 10–4 T at a rightangle to the magnetic field moves in a circleof radius R = 2 cm. The potential differencewhich accelerated the electron before itenters the magnetic field is V. Find V. Takeme = 9.1 × 10–31 kg & e = 1.6 × 10–19C:-(1) 14 kV (2) 25 kV(3) 78 kV (4) 57.6 kV

28. The resistance of a galvanometer isnormally measured using :(1) Post office box(2) Potentiometer(3) Half deflection method(4) Meter bridge

29. Find the steady state charge on thecapacitor :-

r 2r

Cr

4r 3r

0.4re

(1) 0.2 Ce (2) 0.4 Ce(3) 0.1 Ce (4) 0.45 Ce

30. A ground receiver station receives signalat 80 MHz, transmitted from a groundtransmitter at a height of 300 m located ata distance of 100 km from it. This signalcould have come via :-(1) ground wave propagation.(2) sky wave propagation.(3) space wave propagation using satellite.(4) space wave propagation using LOS

communication.


E-7/160000CJA103118009


31. 2 mole of an ideal gas at 27ºC expandsisothermally and reversibly from a volumeof 4 litre to 40 litre. The work done (in kJ)by the gas is (R = 8 J/mol K ; ln10 = 2.3)(1) 28.72 kJ (2) 11.04 kJ(3) 5.73 kJ (4) 4.988 kJ

32. An amount of 5 mol H2O(l) at 100ºC and1 atm is converted into H2O(g) at 100ºC and5 atm. DG for the process is -(1) zero (2) 1865 × (ln 5) cal(3) 3730 × (ln 5) cal (4) –3730 × (ln 5) cal

33. Choose the CORRECT option for thefollowing statements.(i) Spring reaction is used for the

preparation of sodium thiosulphite.

(ii) SO2 + C D¾¾® A + B, where SO2 actsas reducing agent.

(iii) H2SO4 is better dehydrating agent than P2O5.

(iv) SO2(g) + 12 O2(g) ¾® SO3(g)

DH = (+)ve(1) TTFT (2) TFFT(3) FFFF (4) TFFF

PART B - CHEMISTRY

34. D+ ¾¾® ¾¾¾® + +2H O

elemental solidhavingatomicity 12

Mg Black ' X' ' Y ' ........ .......

'Y' + CO ¾® 'Z'

which of the following statement isCORRECT?

(1) Maximum number of atoms are lying inone plane is 4 for 'Z'.

(2) Y has no electron deficiency.(3) 'X' is a covalent compound.(4) Y has eight 2c-2e bond.

35. What is the CORRECT order of reactivityof the following compounds in aromaticnucleophilic substitution reactions whentreated with aq. NaOH?

(I)

F

NO2

(II)

Cl

NO2

(III)

Br

NO2

(IV)

I

NO2

(1) I > II > III > IV

(2) IV > III > II > I

(3) II > III > I > IV

(4) IV > II > I > III

0000CJA103118009E-8/16



36. Which of the following will give differentosazone than the other three ?

(1) H OH

HOHH

HOHOH

CHO

CH – OH2

D-glucose

(2) H OH

HOHO

H

HHOH

CHO

CH – OH2

D-galactose

(3) HOHO

HH

HH

OH

CHO

CH – OH2

D-mannose

OH

(4) HO

HH

H

OH

CHO

CH – OH2

D-fructose

OH

C = O

37. When ( NH2CH2COOH.HCl) is treatedwith NaOH , pH at first half equivalencepoint is 2.4 and the pH at second halfequivalence point is 9.6. The pH at firstequivalence point is -(1) 2.4 (2) 9.6(3) 6 (4) 7.2

38. Lyophobic colloids are -(1) Reversible (2) irreversible(3) water loving (4) solvent loving

39. Which of the following Ellingham diagramensures that at temperature T3, A canreduce CO, B can reduce AO, and B canreduce CO but 'A' cannot reduce BO (whereA, B and C are three unknown element).(1) C

CO®

B®BO

A®AODG°

T1 T2 T3T

(2) C CO®

B®BO

A®AO

DG°

T2 T1 T3T

(3) C CO®

A®AODG°

T1 T3 T2T

B O®B

(4) C CO®

A®AO

DG°

T1 T2 T3T

B O®B


E-9/160000CJA103118009


40. a/ b3 3 2 4Ma b Ma b- +¾¾¾®

which of the isomer of reactant compoundwill produce two isomer of the product?(1) Facial (2) Meridional(3) Both (4) None

41. Which of the following will give compoundwith fruity order when treated with aceticacid in presence of Conc. H2SO4?(1) CH3CH2–OH (2) HCOOH

(3) CH3CHO (4)

O

CH – C – CH3 3

42. Which of the following is a non-narcoticanalgesic?(1) Morphine (2) Heroin(3) Aspirin (4) Codeine

43. The rate constant, Arrhenius constant(pre-exponential factor) of the chemicalreaction and the activation energy of achemical reaction at 25ºC are 4 × 10–4 sec–1 ,16 × 1014 sec–1 and 200 kJ/mol respectively.The value of rate constant at T ® ¥ is.(1) 2 × 1018 sec–1

(2) 16 × 1014 sec–1

(3) Infinity(4) 4 × 10–4 sec–1

44. Two liquids A and B have, PA0 and

PB0 = 1 : 3 at a certain temperature. Assume

A and B form an ideal solution, and theratio of mole of A to B in the liquid phaseare 1 : 3, then mole fraction of A in vapourphase in equilibrium with the solution -(1) 0.1 (2) 0.2(3) 0.5 (4) 1.0

45. In which of the following cases backbonding direction is from central(underlined) atom to surrounding atom.(1) [(CN)3C]– (2) :CCl2

(3) B(NH2)3 (4) NF3

46. Choose the incorrect order for the propertyindicated in the given options.

(1) 2N+ > N+ : E. A. order

(2) N > NO > O : I.E. order(3) K > Ga : E. A. order(4) Sn > P : E.A. order

47. Which one of the following will produceoptically active monohalogen derivative

(1) (2)

(3) (4)

0000CJA103118009E-10/16



48. Which of the following can produce 2°alcohol when treated with suitable RMgXfollowed by NH4Cl?

(1)

O

H – C – H (2) CH3CH2–OH

(3) O2 (4) CH – C – CH3 3

O

49. The value of m¥L for HCl, NaCl and

CH3COONa are 426.1, 126.5 and91 Scm2mol–1 respectively. Calculate the

value of m¥L for acetic acid -

(1) 390.6 Scm2mol–1 (2) 195.3 Scm2mol–1

(3) 35.5 Scm2mol–1 (4) 336.1 Scm2mol–1

50. When anion leaves the normal lattice siteand electron occupies interstitial sites inits crystal lattice, the defect generated iscalled -(1) Schottkey defect(2) Frenkel defect(3) Metal excess defect(4) Stoichiometric defect

51. If Pauli exclusion principle allows threeelectron is an orbital, and other rules areremaining same then find the block numberof Co (Z = 27)(1) d (2) p(3) s (4) can't be predicted

52. When chromite ore is heated with Na2CO3strongly followed by cooling and washingwith water, then brown residue obtainedwhich is of(1) Fe2O3 (2) Fe2O3.FeO(3) Na2CrO4 (4) FeO.Cr2O3

53.

NH2

Ac O2

Pyridine A (1) HNO3

(2) H O3B + C

(Major)

+ H SO2 4

B is :

(1)

NH2

NH2

(2)

NH2

NO2

(3) H2N NH–C–CH3

O

(4)

NH2

NH2


E-11/160000CJA103118009


54. Which of the following compounds willshow stereoisomerism :

(1)

CH3

CH

OHCH3

(2)

CH3HH

HHMe

(3) (4)

55. The concentration of CH3COO – in asolution prepared by adding 0.1 mole ofCH3COOAg(s) in 1 litre of 0.1 M - HClsolution is-(Given:Ka(CH3COOH) = 10–5M ;Ksp(AgCl) = 10–10M2 ;Ksp(CH3COOAg) = 10–8M2)(1) 10–3M (2) 10–2M (3) 10–1M (4) 1M

56. Given the following bond enthalpies :B.E.(N º N) = 942 kJ/mol ;BE(H–H) = 436 kJ/molBE(N–N) = 163 kJ/mol,BE(N –H) = 390 kJ/mole.Determine enthalpy change for thefollowing polymerisation reaction per moleof N2(g) consumed -nN2(g) + nH2(g) ® –(–NH –NH –)n–(1) 272 kJ (2) 136 kJ (3) 435 kJ (4) 200 kJ

57. Highly polluted water could have BODvalue of :-(1) 5 ppm (2) » 0 ppm(3) less than 7 ppm (4) 17 ppm or more

58. In portland cement, which of the followingcompounds are mainly present.(I) Dicalcium silicate. (II) Tricalcium silicate(III) Tricalcium aluminate(1) (I) only (2) (II) and (III) only(3) (I) and (III) only (4) (I), (II) and (III)

59. Amongst the compounds given, the onethat would form a brilliant coloured dye ontreatment with NaNO2 in dil. HCl followedby addition to an alkaline solution ofb-naphthol is -

(1) N(CH )3 2 (2)

NHCH3

(3)NH2

H C3(4)

CH NH2 2

60. Polymer MonomerA. Nylon-6

B. Natural RubberC. StarchD. Orlon

P. Acrylo nitrile

Q. Glucose

R. CaprolactumS. Isoprene

Select CORRECT option?A B C D

(1) P Q R S(2) Q P S R(3) R S Q P(4) S R P Q

0000CJA103118009E-12/16



PART C - MATHEMATICS

61. The integral 2

2 2(sin2x cos x)dx

1 sin x(sin 2x cos x)+

+ -ò is

equal to(1) tan–1(tan2x – tanx) + c(2) tan–1(tan2x + tanx) + c(3) cot–1(tan2x – tanx) + c(4) cot–1(tan2x + tanx) + c(Where c is constant of integration)

62. The locus of a point P(a, b) moving underthe condition that the line y = ax + b is atangent to the ellipse 2x2 + y2 = b2, is(1) a hyperbola (2) a parabola(3) an ellipse (4) a circle

63. Let a, b, c, d be non-zero numbers. If pointof intersection of 6ax + 2ay + c = 0 and5bx + 3by + d = 0 lies in second quadrantsuch that its distance from x-axis is twiceits distance from y-axis then(1) 7bc + 10ad = 0 (2) bc + 2ad = 0(3) 7ad + 10bc = 0 (4) bc – 2ad = 0

64. If ˆˆ ˆa i j k= - + +r and ˆˆb 2i k= +

r

, then findz-component of a vector rr which is coplanarwith ar and b

r

, r.b 0=rr and r.a 7=

r r .

(1) 0 (2) 3 (3) 6 (4) 52

65. Let 4 6p p

- < q < - suppose a1 and b1 are

roots of the equation x2 + 2xcosecq + 1 = 0and a2 and b2 are roots of the equationx2 + 2xcotq – 1 = 0. If a1 < b1 and a2 > b2

then a1 + b2 equals(1) –2cotq (2) –2cosecq(3) 0 (4) none of these

66. If ƒ : R ® R is defined by ƒ(x) = x – [x] + 14

,

where [x] is the greatest integer not

exceeding x, then { }1x R : ƒ(x)4

Î = is equal

to(1) Q, the set of all rational numbers(2) N, the set of all natural numbers(3) N0, the set of all whole numbers

(4) Z, the set of all integers

67. If (1 – y)35(1 + y)45 = A0 + A1y + A2y2 + A3y

3

+ ..... + A80y80, then

(1) 21

A 2A

> (2) A1 = A2

(3) 21

A 1A

< (4) 21

A1 2A

< <


E-13/160000CJA103118009


68. Three numbers whose sum is 18 are in A.P.

If they are added by 6, 92 and 3

respectively, then the are in G.P. Then sumof square of numbers is

(1) 379

4 (2) 4454

(3) 225

2 (4) 992

69. Find the standard deviation of 10observations 111, 211, 311, ....., 1011.

(1) 100 3 (2) 250

(3) 300 (4) 50 3370. A vertical lamp-post of height 10 m stands

at the corner of a rectangular field. Theangle of elevation of its top from thefarthest corner is 30°, while from one ofthe other two corners it is 45°. The area ofthe field is

(1) 2100 2 m (2) 210 2 m

(3) 2100 3 m (4) 210 3 m71. The number of subsets R of P = {1, 2, 3, ....., 9}

which satisfies the property. "There existintegers a < b < c with a Î R, b Ï R, c Î R" is(1) 512 (2) 466(3) 467 (4) None of these

72. A committee of 6 is to be chosen from10 men and 7 women so as to containatleast 3 men and 2 women. The number ofdifferent ways in which this can be done iftwo particular women refuse to serve onthe same committee

(1) is less than 7000

(2) lies between 7000 and 8000

(3) lies between 8000 and 9000

(4) is more than 9000

73. If a particle moves along a line by

S 1 t= + then its acceleration isproportional to __________ of its velocityat any instant 't'

(1) Square (2) Cube

(3) Double (4) Triple

74. The value of 4x 01 cos(1 cos2x)lim

x®

- - is

(1) 4 (2) 2 (3) 1 (4) 12

75. The value of 2

2x0

dx2 4+ò is

(1) 14 (2)

12 (3) 2 (4) 1

0000CJA103118009E-14/16



76. A bag contain 5 blue and 7 green balls. Aballs is drawn at random from the bag, itscolour is observed and this ball along withthree additional balls of same colour andone additional ball of other colour arereturned to the bag. If now a ball is drawnat random from the bag, then probabilitythat this ball is blue, is

(1) 5596 (2)

2548

(3) 1724 (4)

4196

77. Find the length of a line segment whoselength of projections on coordinate planesare 1, 2 and 2

(1) 32 (2) 3 2

(3) 3 (4) 678. If A, B, C are angle of a triangle ABC and

tanAtanC = 3; tanBtanC = 6; then which ofthe following is incorrect ?

(1) A4p

= (2) tanAtanB = 2

(3) tan A 3tanC

= (4) tanB = 2tanA

79. Distance of point A(1, 2) measuredparallel to the line 3x – y = 10 from theline x + y + 5 = 0, is(1) 2 5 (2) 2 10

(3) 4 5 (4) 4 1080. Let A be the sum of the first 20 terms and

B be the sum of the first 40 terms of theseries 13 + 2.23 + 33 + 2.43 + 53 + 2.63 + .....If B – 2A = 600l, then l is equal to -(1) 1281 (2) 1381(3) 1024 (4) 1481

81. If ƒ(x) = sin–1x and3

1 1x x2 2

lim ƒ(3x 4x ) a 3 lim ƒ(x)+ +

® ®

- = -

the find [a]where [a] is the greatest integer notexceeding a(1) 1 (2) 0 (3) 3 (4) 2

82. If S, S1, S2 be the circles of radii 5, 3, 2respectively. If S1 and S2 touch externallyand they touch internally with S. Theradius of circle S3 which touches externallywith S1 and S2 and internally with S is

(1) 3019 (2)

127

(3) 54 (4) can't be determined


E-15/160000CJA103118009


83. If set of real numbers is an universal setand set A = {t Î R :ƒ(x) = (x – 1)|x2 – 3x + 2| + sin|x – 1|, is

differentiable at x = t}, then n(A) is equal to(where n(B) denotes number of elementsin set B)(1) 0 (2) 1 (3) 2 (4) 3

84. If 1 2A1 1é ù

= ê úë û

and f(x) = (1 + x)(1 – x)–1 then

find f(A)(1) A (2) –A (3) A2 (4) A–1

85. ~(p ® ~q) is equivalent to(1) ~p ^ ~q (2) ~p ^ q(3) p ^ q (4) None of these

86. Two sets P and Q are as underP = {(a,b) Î R × R : |a – 5| < 1 and |b – 5| < 1}Q = {(a,b) Î R × R : 4a2 + 9b2 – 48a – 90b + 330 = 0}(1) P Ç Q = f (an empty set)(2) P Ç Q is singleton set(3) P Ì Q(4) Q Ì P

87. If system of equation 2x – y + z = 0,x – 2y + z = 0 and 2lx – y + 2z = 0 has infinitemany solution, then l is equal to-

(1) 5 (2) 52 (3)

32-

(4) –6

88. Let y = y(x) be the solution of the

differential equation 2 dy(1 x ) xy 1dx

- - = ,

x Î (–1, 1). If y(0) = 0, then 1y2

æ öç ÷è ø

is equal to

(1) 3 3p (2) 3

p (3) 6p

(4) 3p

89. Let = + + + l +r

1 ˆˆ ˆ ˆ ˆL : r (i j k) (i j) , l Î ¡

2 ˆˆ ˆL : i (µ 1)j (µ 1)k+ + + + , m Î ¡

are two lines intersecting at point 'A'.Through point B(3, 3, 1) a line in drawnmaking an angle of 60° with L2 andintersecting it at point 'C'. Then area ofDABC is

(1) 2 2 (2) 3 2

(3) 2 3 (4) 3 3

90. If area bounded by curve

1 1y cos (sin x) cos (cosx)2

- -p= + - ,

x-axis and x2p£ £ p is equal to p

2

k(where k Î I), then k is(1) 12 (2) 8 (3) 4 (4) 2

Note :On 03-01-2019 (Thursday) JEE Main FULL SYLLABUSTest is introduced for Both Enthusiast and Leader Course.

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(Academic Session : 2018 - 2019) & COURSE

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