JEE (Main)-2019

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com

OPEN TEST

Time Allotted: 3 Hours Maximum Marks: 360 Please r ead the inst ruct ions carefu l l y. You are a l lot ted 5 m inutes

speci f i ca l l y for th is purpose. You are not a l lowed to leave the Exam inat ion Hal l before the end of

the test .

INSTRUCTIONS

A. General Instructions 1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.

2. This question paper contains Three Parts.

3. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics.

4. Each part has only one section: Section-A.

5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be

provided for rough work.

6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic

devices, in any form, are not allowed.

B. Filling of OMR Sheet 1. Ensure matching of OMR sheet with the Question paper before you start marking your answers

on OMR sheet.

2. On the OMR sheet, darken the appropriate bubble with black pen for each character of your

Enrolment No. and write your Name, Test Centre and other details at the designated places.

3. OMR sheet contains alphabets, numerals & special characters for marking answers.

C. Marking Scheme For All Three Parts.

1. Section-A (01 – 30, 31 – 60, 61 – 90) contains 90 multiple choice questions which have only one

correct answer. Each question carries +4 marks for correct answer and –1 mark for wrong

answer.

Name of the Candidate

Enrolment No.

ALL

IND

IA IN

TEG

RA

TED

TE

ST

SE

RIE

S

FIITJEE JEE (Main)-2019

http://www.fiitjee.com

AIITS-OT-PCM-JEE(Main)/19


2

Useful Data

PHYSICS

Acceleration due to gravity g = 10 m/s2

Planck constant h = 6.6 1034 J-s

Charge of electron e = 1.6 1019 C

Mass of electron me = 9.1 1031 kg

Permittivity of free space 0 = 8.85 1012 C2/N-m2

Density of water water = 103 kg/m3

Atmospheric pressure Pa = 105 N/m2

Gas constant R = 8.314 J K1 mol1

CHEMISTRY

Gas Constant R = 8.314 J K1 mol1

= 0.0821 Lit atm K1 mol1

= 1.987 2 Cal K1 mol1

Avogadro's Number Na = 6.023 1023

Planck’s constant h = 6.625 1034 Js

= 6.625 10–27 ergs

1 Faraday = 96500 coulomb

1 calorie = 4.2 joule

1 amu = 1.66 10–27 kg

1 eV = 1.6 10–19 J

Atomic No: H=1, He = 2, Li=3, Be=4, B=5, C=6, N=7, O=8,

N=9, Na=11, Mg=12, Si=14, Al=13, P=15, S=16, Cl=17, Ar=18, K =19, Ca=20, Cr=24, Mn=25, Fe=26, Co=27, Ni=28, Cu = 29, Zn=30, As=33, Br=35, Ag=47, Sn=50, I=53, Xe=54, Ba=56, Pb=82, U=92.

Atomic masses: H=1, He=4, Li=7, Be=9, B=11, 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, Co=59, Ni=58.7, Cu=63.5, Zn=65.4, As=75, Br=80, Ag=108, Sn=118.7, I=127, Xe=131, Ba=137, Pb=207, U=238.




3

PPhhyyssiiccss PART – I

SECTION – A

(One Options Correct Type)

This section contains 30 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE option is correct. 1. Two projectiles are thrown from the same point simultaneously with initial speeds u1 and

u2 at angles 1 and 2 with horizontal respectively If u1 sin 1 = u2 sin 2, then path of one projectile as seen from other will be

(A) A parabola (B) A vertical straight line (C) A horizontal straight line (D) none of above 2. In order to calculate the speed of sound in nitrogen gas at 300 K, you are given that the

gas is diatomic. You will also need to know only the (A) density of the gas at 300 K, and the mass of one mole of the nitrogen (B) pressure of the gas at 300 K (C) molecular weight of nitrogen and the universal gas constant (D) characteristic gas constant for nitrogen 3. A spring of force constant k is cut into two pieces such that one piece is double the

length of the other. Then the long piece will have a force constant of

(A) 2 k3

(B) 3 k2

(C) 3k (D) 6k 4. The bob hanging from a light string is projected horizontally with a

speed u0. In the subsequent upward motion of the bob in vertical plane

(A) A negative amount of work has been done by tension on the bob. (B) A positive amount of work has been done by gravity on the bob. (C) The tension in the string and speed of bob both may become zero

at an instant. (D) None of these.

u0 m

Space for Rough work




4

5. For a system in equilibrium as shown in figure elongation in spring will be

(A) 2mgk

(B) mgk

(C) mg2k

(D) mg3k

k

m 6. A simple pendulum has time period T = 2s in air. If the whole arrangement is placed in a

nonviscous liquid whose density is 12

times the density of bob. The time period of the

simple pendulum in the liquid will be

(A) 2 s2

(B) 4 s

(C) 2 2 s (D) 4 2 s 7. A gas bubble from an explosion under water oscillate with a period T proportional to pa

db Ec where p is the static pressure, d is the density and E is the total energy of explosion. The values of a, b, c are

(A) a = 0, b = 1, c = 2 (B) a = 1, b = 2, c = 1 (C) a = 5/6, b = -1/2, c = ½ (D) a = -5/6, b = 1/2, c = 1/3 8. A heavy disc is thrown on a horizontal surface with an initial linear velocity of v0. It will

start pure rolling when its linear velocity becomes

(A) 0v2

(B) 02v3

(C) 03v5

(D) 05v7





5

9. A string of length 1m and linear mass density 0.01 kg m–1 is stretched to a tension of 100 N. When both ends of the string are fixed, the three lowest frequencies for standing wave are f1, f2 and f3. When only one end of the string is fixed, the three lowest frequencies for standing wave are n1, n2 and n3. Then

(A) n3 = 5n1 = f3 = 125 Hz (B) f3 = 5f1 = n2 = 125 Hz

(C) f3 = n2 = 3f1 = 150 Hz (D) n2 = 1 2f f2 = 75 Hz

10. Two identical blocks each of mass 1 kg are join together

with a compressed spring. The system at any time after releasing is moving with unequal speed in the opposite direction as shown in figure. Choose the correct statement

3ms-1 5ms-1

(A) it is not possible (B) whatever may be the speed of the blocks the centre of mass will remain stationary (C) the centre of mass of the system is moving with a velocity of 2ms-1 (D) the centre of mass of the system is moving with a velocity of 1 ms-1

11. A U tube of uniform cross section is kept in a vertical position. A liquid of mass m and

density d is filled in one of its limbs. This liquid will oscillate in this tube with time period T given by

(A) mT 2gda

(B) maT 2gd

(C) mT 2g

(D) mT 22agd

12. A liquid is filled in a spherical container of radius R till a height

h. At this position the liquid surface at the edges is also horizontal. The contact angle is

(A) 0 (B) 1 R hcosR

(C) 1 h RcosR

(D) 1 R hsinR

h

R R





6

13. A firecracker exploding on the surface of a lake is heard as two sounds a time interval t apart by a man on a boat close to water surface. Sound travels with a speed u in water and a speed v in air. The distance from the exploding firecracker to the boat is (u > v)

(A) uvtu v

(B) t(u v)uv

(C) t(u v)uv (D) uvt

u v

14. A sphere of mass m and radius r slips on a rough horizontal

plane. At some instant it has translational velocity vo and rotational velocity about the centre vo/2r. Find the velocity of bottom most point A of the sphere.

(A) vo/2 in +ve x-direction. (B) vo/2 in ve x-direction. (C) zero. (D) vo in +ve x-direction.

O

=vo/2r

x(ve)

vo

A +x

15. In order to shift a body of mass m from a circular orbit of radius 2R to a higher orbit of

radius 4R around the earth, (Where R is radius and M is mass of earth) the work done on the body is

(A) GMm8R

(B) GMm2R

(C) GMm4R

(D) GMmR

16. For a given process with an enclosed one mole of

monoatomic ideal gas, the variation of its pressure (P) with its volume (V) is as shown in the graph AB. If the temperature of the gas at A is (To )K, then,

(A) the temperature at B = (2To)K (B) the temperature at B = (3To)K (C) the work done by gas from A to B is 1.5 J (D) the change in the internal energy of the gas is 9RTo.

1

2

0 2 1

P (N/m2)

V (m3)

B

A





7

17. A tank with vertical walls is mounted so that its base is at a height H above the horizontal ground. The tank is filled, with water to a depth h. A hole is punched in the side wall of the tank at a depth x below the water surface. To have maximum range of emerging stream, the value of x is (h > H)

(A) H h2 (B) H

2

(C) h2

(D) H h2

18. A boat carrying a number of large stone piece is floating in a water tank. What will

happen to the water level if the stones are unloaded into the water? (A) rises (B) falls (C) remains unchanged (D) rises till half the number of stones are unloaded and then being to fall 19. An open organ pipe of length L vibrates in second harmonic mode. The pressure

vibration is maximum (A) at the two ends (B) at a distance L/4 from either end inside the tube (C) at the mid-point of the tube (D) none of these 20. A body of mass m is falling freely through a height h from the top of a tower. The velocity

just before touching the ground is 3 / 2 gh . The work done by air drag is

(A) mgh4

(B) mgh4

(C) zero (D) none of these





8

21. A man holds an umbrella at 300 with vertical to keep himself dry. He then runs at a speed of 10 ms-1 and find the raindrops are hitting him vertically. Speed of the raindrops wrt earth is

(A) 120ms (B) 110ms (C) 110 3ms (D) 120ms 22. An insect of mass m crawls along the hanging thread with an

acceleration ga2

. The reaction offered by ground on the block of

mass 2 m is:

(A) 3mg2

(B) mg

(C) 2mg (D) mg2

ga 2

2m

m

23. A cubical frame is made by connecting 12 identical uniform

conducting rods as shown in the figure. In the steady state the temperature of junction A is 1000 C while that of the G is

00 C . Then, (A) H will be Hotter than B (B) Temperature of F is 040 C (C) Temperature of D is 066.67 C (D) Temperature of E is 050 C

E F

B A

H

D a C

G

a

00C

24. What change in surface energy will be noticed when a drop of radius R splits up into

1000 droplets of radius r, surface tension of T? (A) 24 R T (B) 27 R T (C) 216 R T (D) 236 R T 25. A train of mass M is moving on a circular track of radius R with constant speed v. The

length of train is half the perimeter of track. The linear momentum of the train will be (A) 0 (B) 2M/ (C) MvR (D) Mv





9

26. The force exerted by a liquid density , on the wall of the dam of width b, as shown in the figure, Atmospheric pressure is P0.

(A) 0ghP bh2

(B) 0P gh bh

(C) 0ghP bh3

(D) 0P gh bh2

h

b

27. A uniform disc of radius R lies in the x – y plane, with its centre at origin moment of

inertia about z – axis is equal to its moment of inertia about line y = x + c. The value of c will be –

(A) R2

(B) R2

(C) R4 (D) – R

28. The velocity of a particle is 2

0 gt ft . If its position is x =0 at t =0, then its displacement after unit time (t =1) is :

(A) 0 g / 2 f (B) 0 2g 3f (C) 0 g / 2 f / 3 (D) 0 g f 29. A car accelerates from rest with a constant acceleration on a straight road. After

gaining a velocity the car moves with the same velocity for some-time. Then the car decelerated to rest with a retardation . If the total distance covered by the car is equal to S, the total time taken for its motion is

(A) S 1 12

(B) S

(C)

(D) S2

30. In order to do work : (A) force must act at any angle to the displacement (B) Force may not act along the same direction as is the displacement (C) must act along the direction of displacement (D) must act normal to the direction of displacement





10

CChheemmiissttrryy PART – II

SECTION – A


This section contains 30 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE option is correct.

31. XeF4 is planar whereas CCl4 is tetrahedral because (A) in XeF4, Xe is sp2 hybridised and C is sp3 hybridised in CCl4. (B) Xe is sp3d2 hybridised in XeF4 but due to the presence of two lone pairs of electrons,

the shape is planar whereas in CCl4, C is sp3 hybridised. (C) in both XeF4 and CCl4, the central atom is sp3 hybridised. (D) Xe is a noble gas whereas C is a non-metal. 32. In an experiment, 50 ml of 0.1M solution of a salt reacted with 25 ml of 0.1 M solution of

sodium sulphite. The half equation for the oxidation of sulphite ion is: 2 2

3(aq) 2 4(aq) (aq)SO H O SO 2H 2e If the oxidation number of the metal in the salt was 3, what would be the new oxidation

number of the metal? (A) 0 (B) 1 (C) 2 (D) 4 33. The compound most likely to decolourise a cold solution of alkaline potassium

permanganate is

(A) 2 2H C CH (B)

(C)

(D) CH3

CH3

CH3





11

34. Which one of the following compounds will give in the presence of peroxide a product different from that obtained in the absence of peroxide?

(A) 1-butene HCl (B) 1-butene, HBr (C) 2-butene, HCl (D) 2-butene, HBr. 35. Of the following transitions in hydrogen atom, the one which gives an absorption line of

lowest frequency is (A) n = 1 to n = 2 (B) n = 3 to n = 8 (C) n = 2 to n = 1 (D) n = 8 to n = 3 36. Each of the following pair contains species with the same geometry EXCEPT (A) P 3

4O , S 24O (B) 4 4NH ,BF

(C) CO2, C2H2 (D) N2O, NO2 37. A reaction mixture containing H2, N2 and NH3 has partial pressures 2 atm, 1 atm and 3

atm respectively at 725 K. If the value of Kp for the reaction, N2(g) + 3H2(g) 2NH3(g) is 4.28 10–5 atm–2 at 725 K, in which direction the net reaction will go ?

(A) Forward (B) Backward (C) No net reaction (D) Direction of reaction cannot be predicted. 38. 10 L of aqueous solution contains 0.1 mole of each of NaCl, CH3COONa and

CH3COOH. What is the pH of the solution? [Ka of CH3COOH = 10–5] (A) 3 (B) 6 (C) 4 (D) 5 39. A solution of HCl is diluted so that its pH changes by 0.3. How does concentration of H+

ion change? (A) 0.5 times of initial value (B) 0.3 times of initial value (C) 10–3 times increases (D) None





12

40. If for two gases of molecular weights MA and MB at temperature TA and TB, TAMB = TBMA, then which property has the same magnitude for both the gases.

(A) density (B) pressure (C) KE per mole (D) Urms

41. Assuming that air is 79% by mole of N2, 20% O2 and 1% Ar, the density of air at 25°C

and 1 atm is (A) 1.18 g/lit (B) 1.08 g/lit (C) 1.28 g/lit (D) 1.0 g/lit. 42. 2SiO HF X Y

HF Z Compound (Z) in the above reaction is: (A) SiF4 (B) H2SiF4 (C) H2SiF6 (D) H2SiF3 43. Pyrosilicate ion is: (A) SiO2

2 B) SiO42

(C) Si2O76 D) Si2O7

7 44. Arrange the following in decreasing order of E2 reaction:

Cl

Cl

Cl

Cl

Cl

Cl

Cl

Cl

Cl

Cl

Cl

Cl

Cl

Cl

Cl

Cl

Cl

Cl

(X ) (Y) (Z)

(A) X > Y > Z (B) X > Z > Y (C) Z > X > Y (D) Y > X> Z





13

45. OH

OH

OH

H P, P is

[info there is interconversion between the given compounds

CH2 ]

(A)

(B)

(C)

(D)

46. For the reaction equilibrium 22NOBr g 2NO g Br g

If 2Br

PP9

at equilibrium and P is total pressure. The ratio PKP

is equal to

(A) 19

(B) 181

(C) 127

(D) 13





14

47. Which of the following is not correct? (A) G is zero for a reversible reaction (B) G is positive for a spontaneous reaction (C) G is negative for a spontaneous reaction (D) G is positive for a non-spontaneous reaction 48. The first ionisation enthalpies of Na, Mg, Al and Si are in the order: (A) Na < Mg > Al < Si (B) Na > Mg > Al > Si (C) Na < Mg < Al < Si (D) Na > Mg > Al < Si 49. The types of hybrid orbitals of nitrogen in 2 3 4NO ,NO and NH respectively are expected to

be (A) sp, sp3 and sp2 (B) sp, sp2 and sp3 (C) sp2, sp and sp3 (D) sp2, sp3 and sp 50. Which molecule/ion out of the following does not contain unpaired electrons? (A) 2N (B) O2

(C) 22O (D) B2

51. In each of the following total pressure set-up at equilibrium is assumed to be equal and

is 1 atm. With equilibrium constants Kp given as K1, K2 & K3 for I, II & III equilibria respectively, which of the following is correct ?

I. CaCO3(s) CaO(s) + CO2(g), K1

II. NH4HS(s) NH3(g) + H2S(g), K2

III. NH2CO2NH4(s) 2NH3(g) + CO2(g), K3 (A) K1 = K2 = K3 (B) K1 < K2 < K3 (C) K3 < K2 < K1 (D) None of these





15

52. Under the same reaction conditions, initial concentration of 1.386 mol. dm–3 of a substance becomes half in 40 seconds and 20 seconds through first order and zero

order kinetics, respectively. Ratio 1

0

[K ][K ]

of the rate constants for first order (K1) and zero

order (K0) of the reaction is : (A) 0.5 mol–1 dm3 (B) 1.0 mol. dm–3 (C) 1.5 mol. dm–3 (D) 2.0 mol–1. dm3

53. Solubility of AgCl in water, 0.01M CaCl2, 0.01M NaCl and 0.05M AgNO3 are S1, S2, S3

and S4 respectively then. (A) S1 S2 S3 < S4 (B) S1 > S3 > S2 > S4 (C) S1 > S2 = S3 > S4 (D) S1 > S3 > S4 < S2

54. 2 32 Na COH O Heat4 HeatSiCl (A) (B) (C). The compound (C) is;

(A) SiO2 (B) Si (C) SiC (D) Na2SiO3 55. Aluminium chloride exists as a dimmer, Al2Cl6, in solid state as well as in solution of non-

polar solvents such as benzene. When dissolved in water, it gives :

(A) 3Al 3Cl (B) 3

2 6Al H O 3Cl

(C) 3

6Al OH 3HCl

(D) 2 3Al O 6HCl

56. Borax is used as a cleaning agent because on dissolving in water, it gives; (A) alkaline solution (B) acidic solution (C) bleaching solution (D) neutral solution 57. A mixture of two gases is formed when an organic acid heated with conc.H2SO4. When

the gaseous mixture is passed through KOH solution, one gas is absorbed. The unabsorbed gas combines with chlorine and forms a poisonous gas. The organic acid and the two gases evolved with conc. H2SO4 are respectively:

(A) CH3COOH, CO2, CO (B) oxalic acid, CO2, CO (C) HCOOH, CO, H2O (D) none of these





16

58. An inorganic compound (A) made of two most occurring elements in the earth’s crust and used in building construction when made to react with carbon, forms a poisonous gas (B) which is most stable hetero diatomic molecule. Compounds (A) and (B) are

(A) SiO2, CO2 (B) SiO2, CO (C) SiO2, N2 (D) CaO, CO2

59. A reaction, 2A 3B takes place according to first order kinetics. The time in which the

concentration of reactant and product become equal is (k = 4.6 × 10–2 min–1), (log 5 = 0.7; log 3 = 0.48; log 2 = 0.3)

(A) 11 min (B) 15 min (C) 9 min (D) 25 min 60. A vessel contains H2 and H2S gases at a partial pressures of 1 and 2 atm respectively at

certain temperature then the reaction, 8 H2S (g) 8H2(g) + S8(s) occurs. It is found

that 2 2

2 2

H H S

H S Hat equilibrium at time,t 0

n nn n

(n represents no of moles). Then identify the correct

value of the given property : (A) KP = 1/256 (B) KP = 256 (C) At equilibrium the volume of the gaseous mixture is doubled when provided with

frictionless piston (D) KP = KC = 320





17

MMaatthheemmaattiiccss PART – III

SECTION – A


This section contains 30 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE option is correct. 61. Find number of integral values of a for which equation 2

e elog x 5x log x a 3 has exactly one solution

(A) 4 (B) 5 (C) 6 (D) 1 62. If a and b are real number such that 3a 4b 25 then the minimum value of 2 2a b is

equal to (A) 1 (B) 5 (C) 25 (D) not defined

63. Equation of a circle is 2 2 2x y r which has two chords y 0 and xy3

. In smaller

sector between chords a circle of radius unity touches the chords and the circle internally, then r is

(A) 1 2 6 (B) 2 3 (C) 1 2 6 (D) 1 2 6 64. In parabola 2y 4x, two shortest normal chords are diagonals of a quadrilateral, then

area of quadrilateral is (A) 24 2 (B) 18 2 (C) 72 2 (D) 36 2





18

65. Equation of an ellipse 1E2 2x y 1,

16 9 then equation of ellipse 2E whose foci are ends of

minor axis of 1E and which passes through foci of 1E is

(A) 2 2x y 1

7 16 (B)

2 2x y 116 7

(C) 2 2x y 1

9 16 (D)

2 2x y 17 9

66. A circle passes through (3, 4) and (10, 11) then length of tangent to this circle from (2, 3)

is (A) Variable (B) 8 (C) 4 2 (D) 4

67. Let P(x, y) be a variable point such that 2 2 2 2x 1 y 2 x 5 y 5 4

represent a hyperbola then eccentricities of conjugate hyperbola is

(A) 54

(B) 43

(C) 53

(D) 32

68. If , are roots of 2x 5x 8 0 and n nnt then 6 4

5

t 8t5t is

(A) 5 (B) 4 (C) 8 (D) 1 69. If 2 24x y 45 and 2 2x 4y 5 are orthogonal then the value of is

(A) 19

(B) 13

(C) 9 (D) 18





19

70. The value of 3 o 3 o 3 osin 10 sin 50 sin 70 is equal to

(A) 32 (B) 3

4

(C) 34 (D) 3

8

71. The number of solution of the equation 5 516 sin x cos x 11 sin x cos x in the

interval 0, 2 is (A) 6 (B) 7 (C) 8 (D) 9

72. If 1 2 20H ,H ,....H are 20 harmonic means between 2 and 3 then 201

1 20

H 3H 2H 2 H 3

(A) 20 (B) 21 (C) 40 (D) 38 73. The coefficient of rx 0 r n 1 in the expansion of

n 1 n 2 n 3 2 n 1x 3 x 3 x 2 x 3 x 2 ...... x 2 is

(A) n n nrC 3 2 (B) n n r n r

rC 3 2

(C) n r n rrC 3 2 (D) None of these

74. If z lies on the circle z 2i 2 2 then the value of z 2argz 2

is equal to

(A) 3 (B)

4

(C) 6 (D)

2





20

75. If z 2 i z sin argz4

then locus of z is

(A) a pair of straight lines (B) circle (C) parabola (D) ellipse 76. In a decagon find number of points of intersection of diagonals which will lie inside the

decagon if no three diagonals are concurrent (A) 35

2C (B) 10 82 2C C

(C) 96C (D) 10

4C 77. Let y be an element of the set A 1,2,3,5,6,10,15,30 and 1 2 3x ,x ,x be positive integer

such that 1 2 3x x x y then the number of positive integral solutions of 1 2 3x .x .x y is (A) 64 (B) 27 (C) 81 (D) none of these 78. 7 people leave their bag outside the temple and returning after working the deity picked

one bag each at random. In how many ways at least one and at most three of them get their correct bags?

(A) 3 7 73 5 1C .9 C .44 C .265 (B) 7 7 7

6 3 5C .265 C .9 C .44 (C) 7 7 7

5 2 1C .9 C .44 C .265 (D) none of these

79. If 12a 3c 2b5

and a, b, c, > 0 then maximum value of term independent of x in the

expansion of 2511

32abx cx

is

(A) 2510C (B) 2525

15C 35

(C) 35

2515

1C35

(D) 35

2510

1C25





21

80. If 2 2 24a b 2c 4ab 6ac 3bc 0 , then family of lines ax by c 0 is concurrent at one or the other of the two points whose coordinate are

(A) 11,2

or 2, 1 (B) 1, 1 or 12,2

(C) 2, 2 or 1, 12

(D) (1, 2) or 1, 12

81. The sum of the infinite series 2 21 1 1 1 11 1 1 .....2 3 2 2 3

is

(A) 125

(B) 95

(C) 85

(D) 53

82. The inverse of the compound proposition p q r q p is

(A) ~ p q ~ r ~ q ~ p (B) ~ p ~ q ~ r ~ q ~ p

(C) ~ p ~ q r ~ q ~ p (D) ~ p ~ q ~ r ~ q ~ p 83. A lamp post standing at a point A on a circular path of radius ‘r’ subtends an angle at

some point B on the path and AB subtends an angle of o45 at any other point on the path, the height of the lamp post is

(A) r tan2

(B) 2r tan

(C) 2 r cot (D) r cot2





22

84. By mathematical induction n 2 2n 111 12 is divisible by (A) 132 (B) 133 (C) 233 (D) 11 85. If , , are roots of 3 2x 2x 3x 4 0 then the value of 2 2 2 2 2 2 is (A) –7 (B) –5 (C) –3 (D) 0 86. If 1 2 2na,a ,a ,.....a ,b are in A.P and 1 2 2ng,g ,g ,........g ,b are in G.P. and h is the H.M. of a

and b, then 1 2n 2 2n 1 n n 1

1 2n 2 2n 1 n n 1

a a a a a a.....g g g g g g

is equal to

(A) nh (B) nh

(C) 2nh (D) 2nh

87. Normals are drawn from a point P to 2y 4x . The slopes of the normals are 1 2 3m ,m ,m .

If locus of P with 1 2m m is part of 2y 4x , then is (A) 2 (B) 1 (C) 4 (D) none of these 88. If e and 1e are the eccentricities of the curves xy 2y 3x 2 0 and

2 2x y 6x 4y 1 0 respectively then 2 21e e is

(A) 1 (B) 4 (C) 6 (D) 9





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89. If n5 2 6 I f, n,I N and 0 f 1, then I is

(A) 1 ff (B) 1 f

1 f

(C) 1 f1 f

(D) 1 f1 f

90. If 1 2 1 3 1 4S sin sin sin sin ..........3 2 3 3 3 4 3

then S =

(A) 0 (B) 3

(C) 2 (D)

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