JEE-MAIN_Part Test - 1_Paper

7/27/2019 JEE-MAIN_Part Test - 1_Paper

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JEE-MAIN Part Test 1

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PART A: CHEMISTRY

1. Arrange in increasing order of O O bondlength in the following compounds O

2,

O2[SbF6], Rb[O2] using ground stateconfiguration of dioxygen in thesecompounds.

(a) O2 [SbF6].< 2O < Rb[O2]

(b) 2O < Rb[O2] < O2 [SbF6]

(c) O2 [SbF6].< Rb[O2] < O2

(d) 2O < O2 [SbF6] < Rb[O2]

2. Number of unpaired electrons in [V(H2O)6]3+

is

(a) 2 (b) 3

(c) 4 (d) 5

3. Nitric acid can be produced from NH3 inthree steps process

(I) 4NH3 (g) + 5O2 (g)

4NO (g) + 6H2O (g)

(II) 2NO (g) + O2 (g) 2NO2 (g)

(III) 3NO2 (g) + H2O (l) 2HNO3 (aq) +

NO (g)

% yield of Ist, IInd and IIIrd are 50%, 60% and80% respectively then what volume ofNH3(g) at 1 atm and 0C is required toproduce 1575 g of HNO3

(a) 156.25 L (b) 350 L

(c) 3500 L (d) 35 L

4. The molecular weight of haemoglobin isabout 65,000 g/mol. Haemoglobin contains0.35% Fe by mass. How many iron atomsare there in a haemoglobin molecule?

(a) 1 (b) 2(c) 3 (d) 4

5. Gastric juice contains about 3.0g of HCl perlitre. If a person produces about 2.5 litre ofgastric juice per day, how many antacidtablets each containing 400 mg of Al(OH)3are needed to neutralise all the HClproduced in one day.

(a) 10 (b) 14.8

(c) 13.5 (d) 16

6. Two oxides of certain metal were separatelyheated in a current of hydrogen untilconstant weights were obtained. The waterproduced in each oxide was carefullycollected and weighted. It was found that 1 gof each oxide gave 0.1254g and 0.2263 g ofwater respectively. The given data supportsthe law of(a) Reciprocal proportions(b) Multiple proportions(c) Conservation of mass(d) Law of gaseous volume

7. x gram of KClO3 is thermally decomposedat NTP giving as much oxygen, which issufficient for combustion of 3.12 g ofacetylene gas. What is the value of x ?(Given molecular mass of KClO3 = 122.5)(a) 12.25 g (b) 24.5 g(c) 49 g (d) 2.25 g

8. The spin multiplicity for the orbital electronis 2s + 1 where s is total electron spin. Thespin multiplicity for stage (I), (II) and (III)are respectively

hv change of

spin

(I) (II) (III)

(a) 1, 1, 1 (b) 1, 2, 3(c) 1, 1, 3 (d) 1, 3, 1

9. In Bohrs model of atom when an electronjumps from n = 1 to n = 3, how much energywill be emitted or absorbed

(a) 2.15 1011

erg(b) 0.1911 1010erg(c) 2.389 1012erg(d) 0.239 1010erg

10. An iron nail increases 10% of its mass dueto partial rusting into Fe2O3. The percentageof total iron that has rusted is(a) 10% (b) 23.3%(c) 20% (d) unpredictable.

11. Which of the following statement(s) is/arecorrect ?


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(I) The removal of one electron fromNa+(g) ion requires more energy thanthat from Mg+(g)

(II) The extent of hydration of Na+ ion is

more than that of K+

ion.(III) Ionic radii follows the order for three

elements (X, Y, Z) of same periodbelonging to group 1, 2 and 3 (i.e. I A, IIA and III A) in the periodic table isX+ > Y2+ > Z3+.

(IV) With the increasing electronegativity(which increases with increasingpositive charge), the basic strength ofany elemental oxide decreases.

(a) (I) and (II) are correct(b) (I) and (III) are correct(c) (I), (II) and (III) are correct(d) (I), (II), (III) and (IV) are correct

12. The energy level of 4sorbital is less than3dorbital because(a) 4sorbital is more near to nucleus than

3dorbital.(b) 4sorbital penetrates more into the

nucleus than 3dorbital.(c) 4sorbital can have only two electrons

whereas 3d can have 10 electrons

(d) 4sorbital is spherical and 3dorbital isdouble dumb bell.13. A photon of 400 nm is absorbed by a gas

and re-emits two photons. One re-emittedphoton has wavelength 500 nm the otherphoton has wavelength of(a) 2000 (b) 200(c) 5000 (d) 20000

14. If uncertainty in the measurements ofposition and velocity of electron are equal,then minimum uncertainty in its velocitywill be

(a)1 h

2m (b)

1 h2 m

(c)h

2 m(d)

h2 m

15. An electron diffraction experiment wasperformed with a beam of electronsaccelerated by a potential difference of 10.0KV. What is the wavelength of electronbeam. (1 KV = 1000 eV for electrons).

(a) 0.246 (b) 1.23(c) 0.062 (d) 0.123

16. The bond order for CO+ is,(a) 3 (b) 2.5(c) 3.5 (d) 2

17. Select correct statement(s).(a) Acidic strength of HBr > HCl but reverse

is true for their reducing property.(b) Basic strength of PH3 > AsH3 but

reverse is true for their bond angle.(c) Dipole moment of CH3Cl > CH3F but

reverse is true for their HCH bond angle.(d) Ka1 of fumaric acid is higher than maleic

acid but reverse is true for their Ka2.

18. The hybrid state of B-atom in boron-hydrideis sp2, while in its dimer it has sp3 hybridstate because(a) one of the empty orbitals of boron takes

part in hybridisation(b) overlapping between s and p-orbitals of

H and B forms a bond(c) B2H6 is an electron rich compound(d) B2H6 is less stable than BH3

19. Arrange NO2, 2NO+ and 2NO

in order of

decreasing bond angle?(a) 2 2 2NO NO NO

+ > >

(b) 2 2 2NO NO NO +> >

(c) 2 2 2NO NO NO +> >

(d) 2 2 2NO NO NO +> >

20. A 4 : 1 molar mixture of He and CH4 iscontained in a vessel at 20 bar pressure. Dueto a hole in the vessel the gas mixture leaksout. The composition of the mixture effusing

out initially is(a) 8 : 1 (b) 1 : 8(c) 1 : 2 (d) 2 : 3

21. A vessel has nitrogen gas and water vapourat a total pressure of 1 atm. The partialpressure of water vapour is 0.3 atm. Whenthe contents of this vessel are transformed toanother vessel having one third of thecapacity of original vessel, completely at thesame temperature, the total pressure of thesystem in the new vessel is


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(a) 3.0 atm (b) 1 atm

(c) 3.33 atm (d) 2.4 atm

22. The behaviour of a real gas is usuallydepicted by plotting compressibility factor Zversus P at a constant temperature. At hightemperature and high pressure, Z is usuallymore than one. This fact can be explained byvander Waals equations when

(a) The constant a is negligible and not b.

(b) The constant b is negligible and not a.

(c) Both the constants a and b arenegligible.

(d) Both the constant a and b are notnegligible.

23. For two gases, A and B with molecularweights MA and MB, it is observed that at acertain temperature, T, the mean speed of Ais equal to the root mean square speed of B.Thus the mean speed of A can be madeequal to the mean speed of B, if

(a) A is at temperature T and B at T, T > T

(b) A is lowered to a temperature T2 = T38

while B is at T

(c) Both A and B are raised to a highertemperature

(d) Both A and B are placed at lowertemperature

24. Which of the following statement is correct?

(a) Ionic hydrides have low melting points.

(b) Ionic hydrides have high melting points

(c) Ionic hydrides conduct electricity in thesolid state

(d) Ionic hydrides are bad conductors of

electricity in the molten state25. The first ionisation energy of Ar is less than

that of Ne. An explanation of this fact is that

(a) The effective nuclear chargeexperienced by a valence electron in Aris much smaller than in Ne.

(b) The effective nuclear chargeexperienced by a valence electron in Aris much larger than in Ne.

(c) The atomic radius of Ar is larger than

that of Ne.(d) The atomic radius of Ar is smaller

26. Which of the following sets of elementshave almost same atomic radii.(a) Fe, Co, Ni, Cu (b) He, Ne, Ar, Xe

(c) Be, Mg, Ca, Sr (d) Cl, Br, I27. Which of the following has least Ionic radii

(a) N3 (b) Mg2+

(c) Na2+ (d) Al3+28. Select the correct statement from the

following?(a) Covalent hydrides are formed by s-block

elements.

(b) The stability of covalent hydridesdecreases in a period from left to right

(c) Co-valent hydrides have low meltingand boiling points

(d) Co-valent compounds are goodconductor of electricity.

29. The energy of a I, II and III energy levels of

a certain atom are E, 4E3

and 2E

respectively. A photon of wavelength isemitted during a transition from III to I.What will be the wavelength of emission fortransition II to I?

(a) /2 (b)

(c) 2 (d) 3

30. N0/2 atoms of X(g) are converted into X+ (g)

by energy E1. N0/2 atoms of X(g) areconverted into X (g) by energy E2. Hence,

ionization potential and electron affinity ofX(g) are:

(a)( )1 21

0 0

2 E E2E,

N N(b) 1 2

0 0

2E 2E,

N N

(c)( )1 2 2

0 0

E E 2E,

N N(d) none is correct


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PART B: PHYSICS

31. In the system shown in the figure the massm moves in a circular arc of angularamplitude 60 and mass 4 m is stationary.Then choose the incorrect statement.

4mT

m

60

B

A

(a) the minimum value of coefficient of

friction between the mass 4 m and thesurface of the table is 0.25.

(b) the work done by gravitational force onthe block m is positive when it movesfrom A to B.

(c) the power delivered by the tension whenm moves fromA to B is zero.

(d) the kinetic energy of m in position Bequals the work done by gravitationalforce on the block when it moves fromposition A to position B.

32. Width of a river is 60 m. A swimmer wantsto cross the river such that he reaches fromA to B directly. Point B is 45 m ahead ofline AC (perpendicular to river). Assumespeed of river and speed of swimmer asequal. Swimmer must try to swim at angle with line AC. Value of is (assume that

3sin37

5 = )

A

BC

River Flow

(a) 37 (b) 53(c) 30 (d) 16

33. If the energy, E = Gphqcr, where G is theuniversal gravitational constant, h is thePlancks constant and c is the velocity oflight, then the values of p, q and r are,respectively

(a) 12 , 12 and 52 (b) 12 , 12 and 52

(c)12

,12

and32

(d)12

,12

and32

34. One centimeter on the main scale of avernier calipers is divided into 10 equalparts. If 10 divisions of vernier coincidewith 8 small division of the main scale, theleast count of calipers is(a) 0.01 cm (b) 0.02 cm(c) 0.05 cm (d) 0.005 cm

35. Find minimum value of the angle so thatblock of mass m does not move on roughsurface. The coefficient of static frictionbetween the block and surface whatever maybe the value of applied force F.

F m

( ) Rough Surface

(a) tan1() (b) ( )11

tan2

(c) cot1() (d) ( )11 cot2

36. In the given figure, the angle of inclinationof the inclined plane is 30. Find thehorizontal velocity V0 so that the particlehits the inclined plane perpendicularly.

90

H

3090

V0

(a) 02gH

V5

= (b) 02gH

V7

=

(c) 0gH

V5

= (d) 0gH

V7

=

37. Two equal masses hang on either side of apulley at the same height from the ground.The mass on the right is given a horizontalspeed. After some time


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v

Ground

(a) The mass on the left will be nearer toground

(b) The mass on the right will be nearer toground

(c) Both the masses will be at equal distance

from the ground.(d) Nothing can be said regarding their

positions.38. If retardation produced by air resistance to

the projectile is one tenth of acceleration dueto gravity, the time to return from themaximum height(a) increases by 9% (b) decreases by 9%(c) increases by 11% (d) decreases by 11%

39. The position of a particle moving alongxaxis is given by x = 3t2 t3 where x is in

m and t is in s. consider the followingstatements :(i) Displacement of the particle after 4 is 16

m.(ii) Distance traveled by the particle upto 4 s

is 24 m.(iii) Displacement of the particle after 4 s is

16 m.(iv) Distance covered by the particle upto 4 s

is 22 m.Select the correct alternative

(a) statements (i) and (ii) only are correct.(b) statement (ii) and (iii) only are correct.(c) statements (i) and (iii) only are correct.(d) none of these

40. A rubber bead of mass 5 gm falls from aheight of 100 cm and rebounds to half theheight. The impulse imparted by floor isapproximately(a) 38 N-s (b) 3.8 N-s(c) 0.038 N-s (d) 0.38 N-s

41. A formula is given as3b k. .t

P 1a m.a

= +

where P = pressure

k = Boltzmanns constant; = Temperature; t = Timea and b are constants. Dimensionalformula of b is same as(a) Moment of inertia(b) Linear momentum(c) Angular momentum(d) Torque.

42. A block of 1 kg is kept on a rough surface ofan elevator moving up with constantvelocity of 5 m/s. In 10 seconds work doneby normal reaction (the block does not slideon the inclined surface)

1kg

37

5m/s

(i) from ground frame is 320 J(ii) is equal to work done by friction force

in elevator frame

(iii) is equal to work done by friction inground frameOf the three statements given above, theones that are true is given by the choice(a) (i) (b) (ii), (iii)(c) (i), (ii) (d) only (iii)

43. Read the following statements(i) 12300 has only 3 significant digits(ii) 1.2300 104 has only 5 significant digits(iii) 0.012300 106 has only 3 significant digits(iv) all trailing zeroes are non significant digitsCorrect statements are(a) (i), (ii) (b) (iii), (iv)(c) only (iv) (d) (i) and (iv)

44. A small spherical ball is suspended througha string of length l. The whole arrangementis placed in a vehicle which is moving withvelocity v. Now suddenly the vehicle stopsand ball starts moving along a circular path.If tension in the string at the highest point istwice the weight of the ball then


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(a) v = 5gl

(b) v = 10gl

(c) velocity of the ball at highest point

is gl

(d) velocity of the ball at the highest point

is 3gl

45. The force acting on a particle of mass 1 kg,starting from rest from the origin, is shownin the figure. The velocity of the particle at

x = 2 m is

2

F(N)

1 2 x(m)

(a) 2 2 m/s (b) 6 m/s

(c) 2 m/s (d) 3 m/s46. Several particles are projected from a point

in various direction but with same initialspeed vo. At any subsequent time t.

(a) All of them lie on a paraboloid

(b) All of them lie on a sphere(c) All of them lie in one plane

(d) All of them lie along a straight line

47. Two particles each of mass m are moving onx-axis and y-axis with velocities 4 m/s and6m/s respectively. Velocity of their centre ofmass is

(a) 13m / s (b) 5 m / s

(c) 52 m / s (d) 10m / s

48. A bullet is fired at a plank of wood with a

speed of 200 ms1. After passing through theplank, its speed reduces to 180 ms1.Another bullet, of the same mass and sizebut moving with a speed of 100 ms1 is firedat the same plank. What would be the speedof this bullet after passing through theplank? Assume that the resistance offered bythe plank is the same for both the bullets?

(a) 48 ms1 (b) 49 ms1

(c) 50 ms1 (d) 51 ms1

49. An athletes coach told his team that muscletimes speed equals power. What dimensionsdoes he view for muscle?(a) MLT2 (b) ML2 T2

(c) MLT2 (d) L50. A bowler throws a ball horizontally along

east direction with speed of 144 km/hr. Thebatsman hits the ball such that it deviatesfrom its initial direction of motion by 74north of east direction, without changing itsspeed. If mass of the ball is 1/3 kg and timeof contact between bat and ball is 0.02 s.Average force applied by batsman on ball is(a) 800 N, 53 East of North(b) 800 N, 53 North of East

(c) 800 N, 53 North of West(d) 800 N, 53 West of North.51. Six particles are placed on the corners of a

regular hexagon of side 4 m. Each startsfrom rest with a constant speed of 10 m/ssuch that direction of motion of each isalways pointing towards the next in order.They finally converge. The distance coveredby each particle before they converge is(a) 4 m (b) 8 m (c) 12 m (d) 16 m

52. Two blocks of masses m1 and m2 are

connected through a massless inextensiblestring. Block of mass m1 is placed at thefixed rigid inclined surface while the blockof mass m2 is hanging at the other end of thestring, which is passing through a fixedmassless frictionless pulley shown in figure.The coefficient of static friction between theblock and the inclined plane is 0.8. The systemof masses m1 and m2 is released from rest.

m =4kg1 m =2kg2

30 Fixed

g=10m/s2

=0.8

(a) the tension in the string is 20 N after

releasing the system(b) the contact force by the inclined surface

on the block is along normal to theinclined surface

(c) the magnitude of contact force by theinclined surface on the block m1 is

20 3N (d) All are correct


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53. A smooth hoop lies on a smooth horizontaltable and is fixed. A particle is projected onthe table from a point A on the innercircumference of the hoop at angle with

radius vector. If e be the coefficient ofrestitution and the particle returns to thepoint of projection after two successiveimpacts. The final angle made by velocityvector with radius of hoop is

A

(a)2

2

etan ' tan

(1 e ) =

+

(b) 2tan ' e tan =

(c)2

tantan '

e

=

(d)tan

tan 'e

=

54. Choose the wrong statement

(a) Zero velocity of a particle does notnecessarily mean that its acceleration iszero.

(b) Zero acceleration of a particle does notnecessarily mean that its velocity iszero.

(c) If speed of a particle is constant, itsacceleration must be zero.

(d) none of these55. You lift a suitcase from the floor and keep it

on a table. The work done by you on thesuitcase does not depend on

(a) the path taken by the suitcase(b) the tame taken by you in doing so

(c) your weight

(d) all of these56. A particle is projected in vertical plane from

horizontal surface, with speed of projectionu and angle of projection above thehorizontal.

u

Range

STATEMENT 1The horizontal range must be the farthestdisplacement of the particle from point ofprojection along the horizontal.

becauseSTATEMENT 2

The projectile is farthest distance from thepoint of projection, when its instantaneousvelocity vector and position vector (w.r.t.point of projection) are mutually perpendicular.

(a) Statement 1 is True, Statement 2 isTrue; Statement 2 is a correctexplanation for Statement 1.

(b) Statement 1 is True, Statement 2 isTrue; Statement 2 is NOT a correctexplanation for Statement 1.

(c) Statement 1 is True, Statement 2 isFalse.

(d) Statement 1 is False, Statement 2 isTrue.

57. A man of mass 80 kg pushes a box of mass

20 kg horizontally. The man moves the boxwith a constant acceleration of 2 m/s2 but hisfoot does not slip on the ground. There is nofriction between the box and the ground,whereas there is sufficient friction betweenthe mans foot and the ground to preventhim from slipping.

80kg

20kg

STATEMENT 1The force applied by the man on the box isequal and opposite to the force applied bythe box on the man.

because

STATEMENT 2

Friction force applied by the ground on theman is 200 N.


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(a) Statement 1 is True, Statement 2 isTrue; Statement 2 is a correctexplanation for Statement 1.

(b) Statement 1 is True, Statement 2 is

True; Statement 2 is NOT a correctexplanation for Statement 1.

(c) Statement 1 is True, Statement 2 isFalse.

(d) Statement 1 is False, Statement 2 isTrue.

58. A body falling freely from a given height Hhits an inclined plane in its path at a heighth. As a result of this impact the direction ofthe velocity of the body becomes horizontal.Then the value of (h/H) the body will take

maximum time to reach the ground is(a)

12

(b)18

(c)38

(d)5

12

59. The potential energy of a particle isdetermined by the expression U = (x2 + y2),where is a positive constant. The particlebegins to move from a point with thecoordinates (3, 3) (m), only under the actionof potential field force. Then its kinetic

energy T at the instant when the particle is ata point with the coordinates (1, 1) (m) is

(a) 8 (b) 24

(c) 16 (d) zero

60. Choose the correct statement (s) of the

following :(a) force acting on a particle for equal timeintervals can produce the same changein momentum but different change inkinetic energy

(b) force acting on a particle for equal timeintervals can produce different change inmomentum but same change in kineticenergy

(c) force acting on a particle for equaldisplacements can produce different

change in kinetic energy but samechange in momentum

(d) None of these

PART C: MATHEMATICS

61. For what values of a ; a cos + 5 sin 7for all real values of

(a) [ 2 6, 2 6] (b) [2 6, )

(c) ( , 2 6] (d) none of these62. If sin cos =

1

2 , then for real values of

and , the expression cos sin will lie in

(a)1 1

,4 4

(b)1 1

,2 2

(c)1 1

,8 8

(d) none of these

63. The number of non-congruent right angledtriangles having integral sides andhypotenuse 65 unit is(a) Three (b) Two

(c) Four (d) Six64. The value of 4 4cos sin

24 24

will be

(a)2 6

4

+(b)

2 63

+

(c)2 6

2

(d) none of these

65. If { }2 2cos sin sin sin ,k + + thenthe value of k is ( R)


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(a) 21 cos+ (b) 21 sin+

(c) 22 sin+ (d) 22 cos+

66. If is a root of 25 cos2 + 5 cos 12 = 0,

/2 < < , then sin 2 is equal to(a) 24/25 (b) 24/25(c) 13/18 (d) 13/18

67. The value of sin10o.sin50o.sin70o will be

(a)18

(b)14

(c)12

(d) none of these

68. In a ABC, if cosA = cosB . cosC then cotB.cotC will be

(a) 12

(b) 1

(c)3

2(d) none of these

69. A solution (x, y) of x2 + 2x sin xy + 1 = 0 is(a) (1, 0) (b) (1, 0)

(c)3

1,2

(d)3

1,2

70. Let o o0 45< < and tan1t (tan )= , t2 =

(tan)

cot

, t3 = (cot)

tan

, and t4 = (cot)

cot

,then(a) t1 > t2 > t3 > t4 (b) t2 < t1 < t3 < t4(c) t1 > t2 > t4 > t3 (d) t1 < t2 < t4 < t3

71. An observer finds that the angular elevationof a tower is A, on advancing 3 m towardsthe tower the elevation is 45o, and onadvancing 2m further, the elevation is 90oA, the height of the tower is(a) 1m (b) 6m(c) 5m (d) 8m

72. If (1 + tan1o

) . (1 + tan2o

) . (1 + tan3o

) (1 + tan44o) = 2n, then n will be(a) 44 (b) 22(c) 11 (d) none of these

73. The least positive value of for whichcos3 + sin5 = 0 is

(a)3

4

(b)

3

16

(c)38

(d) none of these

74. The number of positive values of tan(x/2)for which 3 sinx + 4 cosx = 5 is(a) 2 (b) 3(c) 1 (d) none of these

75. If sin + cos = x, then sin6 + cos6 =2 21 [4 3( 1) ]

4x for

(a) All real x (b) x2 2(c) x2 2 (d) None of these

76. The value of x for which 4 sin1x + cos1x =, will be

(a)13

(b)23

(c)12 (d) none of these

77. The value of

1 1 11 3 1tan cos sin2 23

+ +

will be

(a)6

(b)

56

(c)3

(d) none of these

78. The value of1 1sin(2 tan (1 / 3)) cos(tan 2 2) + is

(a)13

15(b)

11

15

(c)1415

(d) none of these

79. Two angles of a triangle are 11

sin5

and

1 1sin10

, then third angle will be

(a)6

(b)

3

4

(c)

3

(d)

5

6

80. If tan + tan 2 + 3 tan tan 2 = 3 ,then(a) (6 1) /18,n n I = +

(b) (6 1) / 9,n n I = +

(c) (3 1) / 9,n n I = +

(d) None of these


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81. A person observes the angle of elevation of abuilding as 30. The person proceedstowards the building with a speed of

( )25 3 1 m/hour.

After 2hours, he

observes the angle of elevation as 45. Theheight of the building (in meter) is

(a) 100 (b) 50

(c) ( )50 3 1+ (d) ( )50 3 1

82. The minimum positive value of forwhich 32 tan8 = 2 cos2 3 cos and 3cos2 = 1 is

(a)3

(b)

23

(c)43

(d) none of these

83. The value of 12

n 1

1tan

n n 1

=

+ + is

(a)4

(b)

2

(c)3

(d) none of these

84. The summation of

1 1 11 1 1tan tan tan1 2 1 2(3) 1 3(4)

+ + ++ + +

1 11 1tan ....... tan1 4(5) 1 n(n 1)

+ ++ + +

, will

be

(a) 1n

tann 2

+(b) 1

ntan

n 1

+

(c) 1n 1

tann 2

+

+(d) 1

n 1tan

n 2

+

85. The expression

4 2 4 2sin 4cos cos 4sin + + for allreal values of, will be equal to

(a) cos (b) cos2

(c) sin (d) sin286. The expression (4 cos2 9o 3) (4 cos2 27o 3)

will be equal to(a) cot 9o (b) sin 9o

(c) cos 9o (d) tan 9o

87. A tower subtends an angle at a point A onthe ground, and the angle of depression of itsfoot from a point B just above A and at adistance b from A is . The height of thetower is

(a) b tan cot (b) b tan tan(c) b cot cot (d) b cot tan

88. If2 2

1

2 2

1 t 1 ttan

1 t 1 t

+ = + +

then t2 will be

(a) cos 2 (b) sin 2

(c) sin (d) cos

89. If( )

1 1 1

2

3tan cos sin

101

yx

y

+ =+

and

both x and y are positive and integers, then(x, y) is(a) (1, 2) and (2, 7) (b) (1, 2) and (1, 7)(c) (1, 7) and (2, 7) (d) (1, 7) and (2, 1)

90. The equation 3sin2x + 10cosx 6 = 0 issatisfied for n I , if

(a) 1x n cos (1 / 3)= +

(b) 1x 2n cos (1/ 3)=

(c) 1x n cos (1 / 3)=

(d) none of these

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JEE-MAIN_Part Test - 1_Paper

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