Aits 2016 Ft II Jeem Jeea Main Questions Paper

8/19/2019 Aits 2016 Ft II Jeem Jeea Main Questions Paper

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FULL TEST – II

Time Allotted: 3 Hours Maximum Marks: 360

P lease read the instruct ions careful ly . You are al lot t ed 5 minutesspecif ical ly for th is purpose.

You are not a l lowed to leave the Examinat ion Hal l before the end ofthe test.

INSTRUCTIONS

A. General Instruct ions1. 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. Fill ing o f OMR Sheet1. 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.

(i) Section-A (01 to 30) contains 30 multiple choice questions which have only one correct answer.

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

Name of the Candidate

Enrolment No.

A L L

I N D I A

T E S T

S E R

I E S

FIITJEE JEE (Main)-2016

F I I T J E E

S t u d e n t s F r o m C

l a s s r o o m /

I n t e g r a t e d S c h o o l P r o g r a m s

h a v e s e c u r e d t o 2 Z o n a l , 6 S t a t e &

1 8 C i t y T o p p e

r R a n k s .

3 3 i n T o p 1 0 0 ,

7 8 i n T o p 2 0 0 a n d 2 0 5 i n T o p 5 0 0 A l l I n d i a

R a n k s b a g g e d b y F I I T J E E S t u d e n t s f r o m A

l l P r o g r a m s h a v e q u a l i f i e d i n

J E E ( A d v a n c e d ) , 2 0 1 5 .


2/24

AITS-FT-II-PCM-JEE(Main)/16

FIITJEE L t d . , F I I T JEE Hou se, 2 9 -A , Ka l u Sa r a i , Sa r va p r i y a V i h a r , New De l h i -1 1 00 16 , Ph 461 06000 , 2 65694 93 , Fa x 265139 42

websi t e : w ww . f i i t j e e .c om

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 C

2/N-m

2

Density of water water = 103 kg/m

3

Atmospheric pressure Pa = 105N/m

2

Gas constant R = 8.314 J K1 mol

1

CHEMISTRY

Gas Constant R = 8.314 J K1 mol

1

= 0.0821 Lit atm K1mol

1

= 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.


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3

P P h h y y s s i i c c s s PART – I

SECTION – A

Single Correct Choice Type

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

1. A bent wire AB carrying a current I is placed in a region of uniform

magnetic field B

. The force on the wire AB is

(A) BIL (B)3

2 BIL

(C) Zero (D)2

BIL

A

B

2

L B

L

2. A conductor AB carries a current i in a magnetic field B

. If AB r

and the force on the conductor

is F

. Then:(A) F r B i

(B) F i B r

(C) F i r B

(D) F

is the resultant effect of the electric forces on the electrons in the conductor.

3. A copper rod of length L and mass m is sliding down a smooth inclined

plane of inclination with a constant speed . A current I is flowing inperpendicular to the plane of diagram inwards. A vertically upward

magnetic field B

exists in this region. The magnitude of the required

magnetic field B

is

B P

Q

(A) sinmg

IL (B) cos

mg

IL

(C) tanmg

IL (D)

sin

mg

IL

Space for Rough work


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4

4. An equilateral triangular loop ADC of side l carries a current i in the

direction shown in figure. The loop is kept in a uniform horizontal

magnetic field B

as shown in figure. Net force on the loop is(A) Zero

(B)2

3ilB , parallel to the plane of the loop

(C)2

3ilB , perpendicular to the plane of loop, inwards

(D) 3 ilB , perpendicular to the plane of loop

i

A

C D

B

i i

5. An iron wire of length l is magnetized have a magnetic moment m . If it is bent into a semicircle of

radius r , its magnetic moment is.

(A) m (B)2m

(C)m

(D)

1m

r

6. A magnet is suspended horizontally in the earth’s magnetic field. When slightly displaced, itoscillates in the horizontal plane with a period T . If a piece of wood having the same moment ofinertia as the magnet is attached to the magnet, the new period of oscillation is

(A)2

T (B)

2

T

(C) 2 T (D) 2T

7. An air core solenoid has1000 turns and is one metre long. Its cross- sectional area is 2

10 cm . its

self- inductance is(A) 2.56 mH (B) 1.92 mH

(C) 1.26 mH (D) 2.78 mH



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5

8. A capacitor of 10 F and an inductor of 1 H are joined in series. An ac of 50 Hz is applied to this

combination. The impedance of the combination is(A) 5.67 (B) 4.16

(C) 7.02 (D) 3.21

9. A light ray is incident an angle 45 with the normal to a 2 cm thick transparent plate 2n . Thelateral shift of the light as it emerges out from the plate is

[Given: Lateral shift, sin

cos L

t i r S

r

]

(A) 7 1

7cm

(B) 7 1 cm

(C)

7 1

7 1cm

(D)

2 1

2cm

10. A fish is rising up vertically inside a pond with a velocity 1

4 cm s

, notices a bird, which is divingdownwards. The velocity of the bird appears to be 116 cm s to the fish. The actual velocity of the

diving bird is(refractive index of water is 4

3)

(A) 12 /cm s (B) 9 /cm s

(C) 8 /cm s (D) 7.5 /cm s

11. Two surfaces AB and CD of a thick lens have radii of

curvature 2 R and R respectively. Thickness at the centre is 3 R .

Refractive index of the material of the lens is 1.5 . The image of a

point object placed on the axis of the lens at a distance 4 R from

the surface of smaller radius of curvature and to its left is formedat

O

A C

B D

3 R4 R

(A)4

3

RfromCD to its right (B)

4

3

Rfrom CD to its left

(C)8

3

Rfrom CD to its right (D)

8

3

Rfrom CD to its left



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6

12. Two convergent lenses A and B (erect) of focal

lengths30 50cm and cm are separated by d cm apart co- axially.

An erect object of height2 cm is kept in front of I lens

at 40 cm from it. The real image is formed at100

3

cm to the right

of II lens (see figure). The value of d is

d

40 cm100

3 cm

A B

I O

(A) 20 cm (B) 15 cm

(C) 10 cm (D) 25 cm

13. Radius of gyration of a body about an axis at a distance 6 cm from its centre of mass is 10 cm . its

radius of gyration about a parallel axis through its centre of mass is(A) 6 cm (B) 8 cm

(C) 10 cm (D) 12 cm

14. Moment of inertia of uniform rod of mass m and length l is 217

12ml about a line perpendicular to the

rod. The distance of this line from the middle point of the rod is

(A) l (B)2 3

l

(C)2

l (D)

2

3l

15. Two particles of masses 2m and m moving in opposite directions collide elastically with

velocities 2and respectively. The velocity of 2 m after collision is:

(A) (B) 1.5

(C) Zero (D) 1.1



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16. Two blocks of masses 3 6kg and kg are placed on a smooth

horizontal surface. They are connected by a light spring of

force constant, 1200k Nm .Initially the spring isunstretched. The indicated velocities are imparted to theblocks. The maximum extension of the spring is

(A) 10 cm (B) 15 cm (C) 20 cm (D) 30 cm

3 kg 6 kg

11ms12 ms

Smooth

17. A block is released from rest at the top of an inclined plane which latercurves into a circular track of radius r as shown in figure. Find theminimum height h form where it should be released so that it is able to

complete the circle.(A) 2.5 r (B) 3 r

(C) 2 r (D) 3.5 r

18. A body of mass m , having momentum p , is moving on a rough horizontal surface. If it is stopped

in a distance x , the coefficient of friction between the body and the surface is given by:

(A)2

22

p

gm x (B)

2

2

p

gmx

(C)2

p

gmx (D)

22

p

gm x

19. Two equal masses are attached to the two ends of a spring of spring constant k . The masses are

pulled apart symmetrically to stretch the spring by a length x over its natural length. The work

done by the spring on each mass is:

(A) 21

2kx (B) 2

1

2kx

(C) 21

4kx (D) 2

1

4kx



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8

20. A net force of 200 N gives a body of mass 1m an acceleration of 2

80 ms and a body of mass 2m , an

acceleration of 2240 ms . The acceleration that this force caused when the masses combine

together is

(A) 250 ms (B) 260 ms

(C) 2120 ms (D) 2100 ms

21. The force- time graph for the motion of a body is shown in thefollowing figure. The change in momentum of the body

between 0 20and s is

(A) 120 kg ms (B) 125 kg ms

(C) 130 kg ms (D) 135 kg ms 2

10

F N

10

20 t s

22. A vessel contains oil (density= 30.8 g cm ) over mercury (density= 313.6 g cm ). A homogeneous

sphere floats with half its volume immersed in mercury and the other half in oil. The density of the

material of the sphere in3

g cm

is:(A) 3.3 (B) 6.4(C) 7.2 (D) 12.8

23. A cubical block is floating in a liquid with half of its volume immersed in the liquid. When the

whole system accelerates upwards with a net acceleration of / 3g , the fraction of its volume

immersed in the liquid is

(A) 1 / 2 (B) 3 / 8

(C) 2 / 3 (D) 3 / 4



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9

24. The time period of a simple pendulum is T . The pendulum is oscillated with its bob immersed in aliquid of density . If the density of the bob is p and viscous effect is neglected, the time period of

the pendulum will be

(A)

1/ 2

pT

p

(B)

1/ 2

T p

(C)1/ 2 p

T

(D)1/ 2

T p

25. For hydrogen gas p v

C C x and for oxygen gas p v

C C y where p v

C and C are molar specific

heats. Then the relation between x and y is

(A) 16 x y (B) 16 y x

(C) 4 x y (D) x y

26. Two moles of helium gas are taken over the cycle12341 , as shown in

the p T diagram. Assuming the gas to be ideal the work done on the

gas in taking it from1 2to is

(A) 200 R (B) 300 R

(C) 400 R (D) 500 R 500300

3

2

P Pa

52 10

510

T k

27. A small spherical monoatomic ideal gas bubble 5

3

is trapped

inside a liquid of density L

p Assume that the bubble does not exchange

any heat with the liquid. The bubble contains n moles of gas. The

temperature of the gas when the bubble is at bottom is 0T . The height

of the liquid is H and the atmospheric pressure is 0P . Neglect surface

tension. As the bubble moves upwards, besides the buoyancy force

the forces acting on it are besides the buoyancy force the forces actingon it are

Liquid

H

y

0P

(A) Only the force of gravity(B) The force due to gravity and force due to pressure of the liquid(C) The force due to gravity, the force due to pressure of the liquid and force due to viscosity of

the liquid(D) The force due to gravity and the force due to viscosity of the liquid



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28. A knife edge of mass M is dropped from a height h on a wooden floor with its tip pointing of

downward. If the blade penetrates a distance S into the wood the average resistance offered by

the wood to the blade is

(A) Mg (B) 1 h

Mgs

(C) 1 h Mgs

(D)

2

1 h Mgs

29. A uniform rope of mass M and length L is pulled along a frictionless inclined plane of angle(by

appling a force F Mg )parallel to incline. Tension in the chain at a distance x from the end at

which force is applied is

(A) sin x x

F Mg L L

(B) 1 x

F L

(C) 1 sin x x

F Mg L L

(D) None of these

30. Two Conducting spherical shells having radii a and b chargedto 1 2&q q respectively. Find the potential difference between 1& 2

(A) 1

0

1 1

4

q

a b

(B) 2

0

1 1

4

q

a b

(C) 1 2

0

1 1

4

q q

a b

(D) 1

04

q

a

2q

2

1

1q

a

b



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11

C C h h e e m m i i s s t t r r y y PART – II

SECTION – A



1. 112 mL of 2 NO at NTP was liquefied, the density of the liquid being11.15 g mL . The volume of

the liquid is:(A) 0.1 mL (B) 0.2 mL

(C) 128.8 mL (D) 1.15 mL

2. A mixture of HCOOH and 2 2 4 H C O is heated with conc. 2 4 H SO . The gaseous mixture thus

produced is collected and passed through NaOH solution. The volume of the gaseous mixture

decreases by1

6

th

. The molar ratio of HCOOH and 2 2 4 H C O in the mixture of acids is:

(A)1

4 (B) 6

(C) 4 (D)1

6

3. Equal volumes of ethanoic acid and KOH are mixed, the heat evolved is:

(A) equal to heat of formation of water from H and OH

(B) less than the heat of formation of water from H and OH

(C) equal to heat of formation of water from 2 H and 2O in gaseous state

(D) equal to enthalpy of neutralization of KOH and HCl

4. Consider the following reaction,

2 A g B g

The rate constant for this reaction is 2 12.303 10 min . The time in which the molar ratio of A to B

becomes 3 : 2 is equal to:

(A) 12.5 min (B) 2.303 min

(C) 5.12 min (D) 80 min



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12

5. Consider the following gaseous phase equilibrium, 2 A g B g . The degree of dissociation

of A is1

3 and

2

3 at 1P and 2P pressures respectively. The ratio of 1P and 2P is:

(A)7

4 (B)

7

32

(C)8

32 (D)

32

5

6. The pH of a 2 4 H SO solution is 2. The pH of this solution, if equal volume of 0.2 M NaCl

solution is added to it, will be:(A) 1.7 (B) 2.3

(C) 3.2 (D) 2

7. In a crystal structure of an element, atoms are present in ccp arrangement and tetrahedral voids,

which of the following relation between the atomic radius and edge length is correct for the unitcell which is formed in this arrangement? (a is the edge length and R is the radius of atom):

(A) 2 4a R (B) 3 8a R (C) 3 4a R (D) 2a R

8. 1000 g of 1 molal aqueous solution of sucrose is cooled and maintained at 3.534 C . What is

the amount of ice separated out 2 1.86 f K for H O i s :(A) 353 g (B) 220 g

(C) 150 g (D) 510 g

9. Acidified water is electrolysed using inert electrodes. The total volume of gases collected atcathode and anode is V mL at STP . The amount of charge passed in the electrolytic cell is equal

to:

(A) 35.74 10 V C (B) 96500 C (C) 31.72 10 V C (D) 31.72 10 C



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13

10. The charge on 2 3 As S may be due to the adsorption of:

(A) H (B) OH

(C)2

O (D) 2S

11. The magnetic moment of xCr is 15 BM . The ratio of number of paired e and unpaired e in x

Cr is equal to:

(A) seven (B) six(C) five (D) four

12. Find H in terms of KJ for the following reaction from the given data

22 2 M g X g M g X g

11

705 IE of M g KJ mol

12

1151 IE of M g KJ mol

11

328 IA of X g KJ mol

(A) 120 KJ (B) 512 KJ

(C) 1200 KJ (D) 110 KJ

13. Which of the following is not three dimensional network structures?

(A) 2SiO (B) 2CO

(C) diamond (D) graphite

14. A 1g sample of 2 2 H O solution containing % x 2 2 H O by weight required x mL of 4KMnO for

complete oxidation in acidic medium. The normality of 4KMnO solution is approximately:

(A) 0.1 (B) 0.4

(C) 0.6 (D) 1.2



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14

15. Consider the following statements about the structure of borax:(i) number of B O B bonds is x(ii) number of B B bonds is y(iii) number of 2sp hybridized B atoms is z

The value of x y z is equal to

(A) 3 (B) 4 (C) 6 (D) 7

16. Which of the following has maximum dipole moment?(A) O

(B) O

(C) O

(D) All have equal value

17.X

Y

Z 2 / H O H A

KCN

/ Mg Ether

R Cl

What is ' '? A

(A)

R C NH2

O

(B)R CHO

(C)

R C O

R

(D)

C

R

R

N

OH



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15

18. Which of the following will not convert R C N to R CHO ?

(A) 2 /i SnCl HCl (B) 2 /i RMgX ii H O H

(C) 4 2 /i LiAlH ii H O (D) 22 /i AlH i Bu ii H O

19. O

COOC2H5 3 ..........i H O ii

The major product is:

(A) O

(B) O

O

(C) O

(D)

O C

CH2

O

20.

3

2

/

/ ; thecompound' ' :

O KOH

Zn H O X Y Y is

(A)

CHO

(B)CHO

x

(C)CHO

(D)

CHO

OH



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16

21.

OH

CH3

O

/ Zn Hg HCl Product

(A)

Cl

CH3

(B)

Cl

CCH3

O

(C)

OH

CH3

(D)

Cl

CH2

22.

CHO 3 ......

EtO Al

The major product is:

(A)

CH2OH

(B)

CH2

CH3 (C)

C

O CH2

O

(D) No reaction



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17

23. Strongest base is:(A)

NH2 CNH2

NH

(B)

C

H2N

H2N

NH2

(C)C

H2N

H2N

O

(D)C

H2N

H2N

OH

24.NH2

2. , is :aq NaNO HCl

P P

(A)Cl

(B)CH

+

Cl

(C)

OH

(D) None of these

25.

N

O

O

H 22 3

1. , 1. ,

2. 2.

K NH DM F KOH

PhCH Br H O A B

The end product B of the above reaction is:

(A)Ph NH2

(B)PhPh N H

(C)

NPh

O

H

Ph

(D)N

PhPh

H



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18

26. Marshall’s acid is:

(A) 2 2 5 H S O (B) 2 2 8 H S O

(C) 2 4 H SO (D) 2 2 7 H S O

27. The correct order of S O bond in 22 3 4, , I SO II SO III SO is:

(A) I II III (B) III I II (C) II III I (D) I III II

28. The following acids have been arranged in the order of increasing acid strength. Identify thecorrect order:

I ClOH II BrOH

III IOH

(A) I II III (B) III II I (C) II I III (D) III I II

29. The correct order of oxidizing power is:

(A) 2 3 HOCl HOClO HOClO HOClO (B) 3 2 HOClO HOClO HOClO HOCl

(C) 2 3 HOClO HOClO HOCl HOClO (D) 2 3 HOCl HOClO HOClO HOClO

30. Shape of 4 XeOF is:

(A) Trigonal bipyramid with lp at axial position

(B) Square pyramid with lp at axial position

(C) Distorted square pyramid with lp at axial position

(D) Square pyramid with lp at square plane.



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19

M M a a t t h h e e m m a a t t i i c c s s PART – III

SECTION – A



1. The number of ordered pairs , x y of real numbers satisfying 2 24 4 2 sin x x y and 2 2 3 x y

is equal to(A) 0 (B) 2(C) 4 (D) 8

2. sin 47 sin 25 sin 61 sin 11 (A) cos7 (B) sin 7 (C) 2cos7 (D) 2 sin 7

3. The tangent to the hyperbola2

xy c at the point P intersects the x-axis at T and the y-axis at T’.The normal to the hyperbola at P intersects the x-axis at N and the y-axis at N’. The areas of the

triangles PNT and PN’T’ are and ’ respectively , then1 1

'

is

(A) equal to 1 (B) depends on t(C) depends on c (D) equal to 2

4. The normal at P to a hyperbola of eccentricity e, intersects its transverse and conjugate axes at Land M respectively. If locus of the mid-point of LM is hyperbola, then eccentricity of the hyperbolais:

(A)1

1

e

e

(B)

2 1e

e

(C) e (D) None of these



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20

5. Area of the triangle formed by the lines 0, 0 x y x y and any tangent to the hyperbola2 2 2 x y a is:

(A) a (B)1

2a

(C)

2a

(D)

21

2a

6. A rectangular hyperbola whose centre is C is cut by any circle of radius r in four points , ,P Q R

and S . Then 2 2 2 2CP CQ CR CS is equal to:

(A) 2r (B) 22r

(C) 23r (D) 24r

7. The point, at shortest distance from the line 7 x y and lying on an ellipse 2 22 6 x y , has co-ordinates:

(A) 2, 2 (B) 0, 3

(C) 2,1 (D) 15,2

8. Locus of the foot of perpendicular drawn from origin to any tangent to the ellipse2

2 12

x y is:

(A) 2

2 2 2 22 x y x y (B)

22 2 2 2

2 x y x y

(C) 2

2 2 2 22 x y x y (D) None of these

9. The line 5 3 8 2 x y is a normal to the ellipse22

125 9

y x . If be the eccentric angle of the

foot of this normal, then ' ' is equal to:

(A)6 (B)

3

(C)4

(D) None of these



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21

10. For parabola 2 2 2 6 2 3 0 x y xy x y , then focus is:

(A) 1, 1 (B) 1,1

(C) 3,1 (D) None of these

11. The triangle formed by the tangent to the parabola 2 y x at the point whose abscissa

is 0 0 1, 2 x x , the y-axis and the straight line 2

0 y x has the greatest area if 0 x is equal to:

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

12. The condition that the parabola 2 24 4 y c x d and y ax have a common normal other than

x- axis 0, 0a c is:

(A) 2 2a c d (B) 2 2c a d (C) 2 2d a c (D) 2 2d c a

13. The point 1 ,P P , (where . denotes the greatest integer function) lying inside the region

bounded by the circle 2 2 2 22 15 0 2 7 0 x y x and x y x then:

(A) 1, 0 0,1 1, 2 p (B) 1, 2 0,1 p

(C) 1, 2 p (D) None of the above

14. If the distance from the origin of the centres of three, circles 2 2 22 0, 1, 2, 3i x y x c i are in

GP. then the lengths of the tangents drawn to them from any point on the circle 2 2 2 x y c are in:

(A) A. P (B) G. P(C) H.P (D) None of these



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22

15. The values of k for which the circle 2 2 2 21 4 8 0 x y and x y x have two common tangents

is:

(A)9 9

,4 4

(B)9 9

, ,4 4

(C)9

,4

9,

4

(D) None of these

16. The equation of image of pair of lines 1 y x in y- axis is:

(A) 2 2 2 1 0 x y x (B) 2 2 2 1 0 x y x

(C) 2 2 2 1 0 x y x (D) None of these

17. If 2 2, 0 4 4 1 0and and ax xy y p x y represent a pair of straight lines, then:

(A) p (B) p

(C) p (D) p or p

18. If 2 2 4 2 ,1!9! 3!7 ! 5!5! !

m

n then orthocentre of the triangle having

sides 1 0, 3 0 2 5 2 0 x y x y and x y is:

(A) 2 2 ,m n m n (B) 2 2 ,m n n m

(C) 2 ,m n m n (D) 2 ,m n m n

19. In ABC , if tan cot tan cot2 2 2 2

B C B C C A C A p q

and tan cot

2 2

A B A Br

then

p :(A) 1 (B) pq (C) pqr (D) None of these



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23

20. In the triangle ABC the medians from B and C are perpendicular. The value of cot cot B C cannot be:

(A)1

3 (B)

2

3

(C)4

3

(D)5

3

21. If ABCD be a cyclic quadrilateral inscribed in a circle of radius 2 unit such that 2 3 BD ; 1 AB then AD :

(A)1 3 5

2

(B)

3 5 1

2

(C)5 1

2

(D) None of these

22. If I be the incentre of ABC and ,P Q are feet of perpendicular from A to , BI CI respectively.

Then : AQ CI : AP BI :

(A) cot2

A B

(B) cot2

B C

(C) cot2

C A

(D) tan2

B C

23. Number of roots of the equation 2 3 1 3

cos sin 1 02 4

x x

which lie in the interval ,

is:(A) 2 (B) 4 (C) 6 (D) 8

24. The number of solutions of tan 5 cos cot 5 sin for 0, 2 is:(A) 28 (B) 14

(C) 4 (D) 2



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24

25. Number of solutions of the equation 2 2 2 24 sin tan cot cos 6 x x x ec x in 0, is:(A) 0 (B) 2

(C) 8 (D) 4

26. The equation 2 2 1 1 cos x n x has (where n is a positive integer):

(A) infinity many real roots (B) exactly one real root(C) exactly 2 2n real roots (D) exactly 2 3n real roots

27. A vertical tower standing at O has marks P, Q, R, S at heights of 1m, 2m, 3m, and 4m from thefoot O and A is a point on the horizontal plane through O. If PQ and RS subtend angles and

respectively at A where OA = 2 m then cos :

(A) 5 / 26 (B) 24 / 650

(C) 23/ 650 (D) 1 / 26

28. , , A B C are three points on a horizontal line through the base O of a pillar OP, such that OA, OB,

OC are in A. P. If , , the angles of elevation of the top of the pillar at , , A B C respectively are

also in A. P. then sin ,s in ,s in are in:(A) A. P. (B) G. P.(C) H. P. (D) None of these

29. If ,n N then 2 3 3 17 2 .3n n n is always divisible by:

(A) 25 (B) 35

(C) 45 (D) None of these

30. Let P n denotes the statement that 2n n is odd. It is seen that 1 . nP n P n P is true for

all:(A) 1n (B) n N (C) 2n (D) None of these


Aits 2016 Ft II Jeem Jeea Main Questions Paper

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