paper fiitjee jee main sample paper

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

FULL TEST – IV

Time Allotted: 3 Hours Maximum Marks: 432

P lease read the instruct ions careful ly. You are al lot ted 5 minutesspeci f ical ly for th is purpose.

You are not al lowed to leave the Exami nation Hal l before the end ofthe 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 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 03 and 10 to 12) contains 6 multiple choice questions which have only onecorrect answer. Each question carries +8 marks for correct answer and – 2 mark for wrong

answer.

Section-A (04 to 09 and 13 to 30) contains 24 multiple choice questions which have only onecorrect answer. Each question carries +4 marks for correct answer and – 1 mark 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 .


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


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 10

23

Planck’s constant h = 6.625 1034 Js= 6.625 10 –27 ergs

1 Faraday = 96500 coulomb1 calorie = 4.2 joule

1 amu = 1.66 10 –27 kg1 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

Physics

PART – I

SECTION – A

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. Four particles each of mass M, are orbiting in a circle of radius r in the same sense of rotationdue to their mutual gravitational force of attraction. The time period of revolution is

(A)

3r T 2

GM 1 2 2

(B)

3r T 4

GM 1 2 2

(C)

32r T

GM 1 2 2

(D)

32r T 2

GM 1 2

2. For a silver atom, energy corresponding to K transition is 21.75 KeV. Also minimum energy of a

striking electron so as to produce L X-rays is 3.56 KeV. Now, if electron with an energy of 23KeV strike a silver target the characteristic X-rays spectrum will have :

(A) Only K and L X-rays (B) Only L X-rays

(C) K and L X-rays (D) Only K X-rays

3. In n, 2n, 3n are the fundamental frequencies of the three segments into which a string is dividedby placing required number of bridges below it. If n0 is the fundamental frequency of the string,then(A) n0 = 3n (B) n0 = 6n

(C) 03n

n5

(D) 06n

n11

4. Two SHMs are represented by equations 1 2y 6cos 6 t / 6 , y 3 3 sin3 t cos3 t (A) Ratio of their amplitudes is 1 (B) Ratio of their amplitudes is 1/2(C) Ratio of their maximum velocities is 1 (D) Ratio of their maximum velocities is 1/2

Space for Rough work


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4

5. From the following transistor characteristics, what can beinferred?

(A)1 2 3CE CE CE

V V V

(B) 1 32

CE CE

CE

V VV

2

(C)2 1 2CE CE CE

V V V

(D)3 2 1CE CE CE

V V V

(mA)

1CEV

2CEV

3CEV

BEV (V)

IB

6. A particle is dropped to move along the axis of a concave mirror of focallength f from a height f/2 as shown in the figure. The acceleration due togravity is g. Find the maximum speed of the image.

(A)3fg

16 (B)

27fg

16

(C)3

fg4

(D)fg

16

f

f

2

7. A spherical metal ball of radius ‘r’ is lying at the bottom ofa stationary container containing liquid of density as

shown in the figure. Find the force exerted on the upperhemispherical portion of the sphere due to gauge

pressure ( 0P atmospheric pressure)

r4r

(A) 2

0

r 3P 7r g

3

(B)

2

0

r 3P 7r g

2

(C) 2 0r 3P 7r g (D) 2

02 r 3P 7r g

8. A spring mass system executes damped harmonic oscillations given by the equation

bt2my Ae sin ' t

where

2

2

k b'

m 4m

where the symbols have their usual meanings.If a 2 kg mass (m) is attached to a spring of force constant (K) 1250 N/m, the period of the

oscillation is / 12 s . The damping constant ‘b’ has the value.(A) 9.8 kg/s (B) 2.8 kg/s(C) 98 kg/s (D) 28 kg/s



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5

9. White light (wavelength 4000-7000 Ao) is incident normally on a glass plate of thickness one

micron and refractive index 1.5. Number of strongly reflected wavelengths by the plate is(A) 1 (B) 2(C) 3 (D) 4

10. Electromagnetic radiations fall on a metallic body whose work function is 2eV. For a particular

radiation of frequency v, the maximum kinetic energy of the photoelectrons is found to be 4 eV.

What would be the maximum kinetic energy of photoelectrons for the radiation of frequency5v

3?

(A) 6 eV (B)14

eV3

(C) 8 eV (D)10

eV3

11. In the figure shown A and B are two thin

transparent slabs of refractive indices 1 and

2 2 1 and there is no gap between A

and B. A beam of light of wavelength fallson A normally. A part of it reflects at upperface and a part reflect at the interface of A andB and then come back to the previousmedium. The phase difference between tworeflected waves at a particular point at anytime t is

t1

t2

A

B

air

air

1

2

(A)

2

1

t

4

(B)

1

2

t

4

(C) 1 12

t

(D) 1 14

t



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6

12. A capacitor is connected across an inductor. At time t = 0 charge on the capacitor is equal to1

2

qmax, where qmax is the maximum charge on the capacitor. The time t, at which the energy storedin the capacitor is equal to the energy stored in the inductor is(The inductance of the inductor is L and capacitance of the capacitor is C. Resistance of thecircuit is zero)

(A) 2 LC (B)1

LC2

(C)LC

2

(D)

1

2 LC

13. A long horizontal rod has a bead which can slide along its length, the bead initially at a distance Lfrom end A of the rod. The rod is set in angular motion in the horizontal plane about end A withconstant angular acceleration . If the coefficient of friction between rod and the bead is , andgravity is neglected then graph between frictional force acting on bead and the time is

t / time

f

t / 2 time

f

t / time

f

t / 2 time

f

(A) (B)

(C) (D)



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7

14. A block of mass 4 m and a conducting square loop of mass m (with a cell of emf E and resistanceR) are connected by a light insulating string passing over a frictionless pulley as shown in thefigure. The plane of the loop (initially at rest) is perpendicular to magnetic field. As the system isreleased

x x x x

x x x x

x x x

xx

x xx x x x

E

4m0

R g

x

y

z

(A) the block does not move(B) the loop starts rotating about y-axis.(C) the loop moves down with constant velocity(D) the acceleration of the block is constant but not zero

15. A conductor of (area A) having charge density is placedperpendicularly to a uniform electric field E and is connected to a spring(of spring constant k) whose other end is fixed. Now the spring isreplaced by similar spring having length one third of the original spring.The extension of spring in this position is

E

k

E

(A)2E A

k

(B)

2E A

3k

(C)E A

3k

(D)

2E A

4k

16. A uniform rope of mass m and length L hangs from the ceiling. A small wavepulse is created at bottom, then which of following is correct regarding wavepulse.(1) Rate of change of speed with respect to time varies(2) Rate of change of speed with respect to time is constant(3) Rate of change of speed with respect to time is zero(4) Wave speed varies(A) 1, 3 (B) 1, 4(C) 2, 4 (D) 3, 4



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8

17. A conducting rod of length l is rotating with constant angularvelocity about point O in a uniform magnetic field B as shownin the figure. The emf induced between ends P and Q will be

(A) 21

B4

l (B) 25

B10

l

(C) zero (D) 21B2

l

3l /4l /4

P OQ

x

x x x x

x

x

xx x x x

x

18. A solid sphere of mass M and radius R is placed vertically on arough horizontal surface. If a horizontal force F is applied at adistance R/6 below the centre line parallel to the diameter of thesphere, the direction of frictional force will be(A) forward(B) backward(C) depends upon value of F(D) insufficient information

R/6F

R

M

19. In a potentiometer experiment, two cells connected in series get balanced at 9 cm length on thewire. Now the connections of terminals of the cell of lower emf are reversed, then the balancinglength is obtained at 3 cm. The ratio of emf’s of two cells will be(A) 1 : 2 (B) 2 : 1(C) 1 : 4 (D) 4 : 1

20. One mole of a monoatomic ideal gas undergoes the process A B as indicated in the given P-V diagram. The molar heatcapacity for the process is(A) 3R/2(B) 13 R/6(C) 5R/2

(D) 2R V0

A

5V0

B

P

6P0

3P0



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9

21. If l 1 and l 2 (> l 1) are the lengths of an air column for the first and second resonance when a tuningfork of frequency n is sounded on a resonance tube, then the minimum distance of the anti-nodefrom the top end of the resonance tube is

(A) 2 12 l l (B) 1 21

22

l l

(C)2 13

2

l l (D)

2 1

2

l l

22. A thin convex lens is split into two halves. One of thehalves is shifted along the optical axis. The separationbetween fixed luminous point object O and fixedscreen is D = 180 cm. The magnification of imageformed by one of the half lens is m = 2. It follows that(A) The separation between the lens is 90 cm(B) The separation between the lens is 60 cm(C) The focal length of the lens is 45 cm(D) The focal length of the lens is 60 cm

180 cm

Oscreen

23. A block of mass 1 kg is placed on a smooth horizontal surface asshown. Its center is tied to a string of length l = 10 m and other end ofthe string is connected of ball of same mass. Ball B is released fromthe position shown. It falls under gravity and the string becomes taut.The kinetic energy of block and ball of the bodies just after string is

taut are K.Eb and KEp respectively. Then

p

b

K.E

K.E is equal to

(g = 9.8 m/s2)

(A) 12 (B) 13(C) 14 (D) 15

l

30o m

m



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10

24. Calculate the moment of inertia of uniform thin hemispherical shell

of mass M and radius R about axis X - X' shown in figure.

(A) 25

MR3

(B) 27

MR6

(C)

22

MR3 (D) None of these 3

X

X'

25. A small particle of mass M is released from rest frompoint A inside a frictionless fixed hemispherical bowl asshown. The graph between the ratio(r) of magnitude ofcentripetal force and normal reaction on the particle atany point on the bowl as a function of cos is

R

r

1 +1 cos

r

r r

1

1 1

+1

+1 +1

cos

cos cos

(A) (B)

(C) (D)

26. In a certain region of space there exists a constant and uniform magneticfield of induction B. The width of the magnetic field is a. A charge particle

having charge q is projected perpendicular to B

and along the width of thefield. If deflection produced by the field perpendicular to width is d, themagnetic of the momentum of the particle is

(A)2 2d a

qB2d

(B)2

2

aqB

2d

(C)

24dqB

a d (D)

2a dqB

2d

a

x x x x

x x xx x x x

x x x x

d



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11

27. If two uniform spherical drops of a liquid same mass, radius, and falling freely with a terminal

velocity of 3 16 m/s. Coalesce to form bigger drop, then the terminal velocity with which the

bigger drop fall is(A) 8 m/s (B) 4 m/s(C) 10 m/s (D) None of these

28. Binding energy of A = X MeV, B = Y MeV, C = Z MeV [X > Y > Z]. A person in a lab tries to breakeach nucleus into its constituents with the help of energy S MeV [y < S < x], then which of thefollowing nuclei may break?(A) B and C (B) C and A(C) A and B (D) Only C

29. A mono chromatic light is used in Young’s double slit experiment when one of slits is covered by

a transparent sheet of thickness 51.8 10 m, made of material of refractive index 1 no. of fringes

which shift is 18. When another sheet of thickness 53.6 10 m made of material of refractiveindex 2 is used; no. of fringes which shift is 9. Relation between 1 2and is given by

(A) 2 14 3 (B) 1 14 3

(C) 2 13 4 (D) 1 22 4

30. In the circuit shown in the figure, K1 is open. The chargeon capacitor C in steady state is q1. Now key is closedand at steady state charge on C is q2. The ratio ofcharges q1 and q2 is(A) 5/3 (B) 3/5(C) 1 (D) 2/3

E C

1R 2

2R 3



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12

hemistry

PART – II

SECTION – A



1. Picric acid isOH

NO2

NO2O2N

OH

NO2

NO2

O2N

NO2

NO2

O2N

C O H

OOH

Br Br

Br

(A) (B)

(C)(D)

2.

C6H5 O CO

CH3

AlCl3 anhy

O

C

O

CH3

H

+

O

C

CH3

O

H

Above reaction involves

(A) Fries rearrangement (B) Curtius rearrangement

(C) Hofmann rearrangement (D) Beckman rearrangement



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13

3. The heats of neutralization of four acids A, B, C and D are –13.7, –9.4, –11.2 and –12.4 kcal

respectively, when they are neutralized by a common base. The acidic character obeys the

order:

(A) A > B > C > D (B) A > D > C > B

(C) D > C > B > A (D) D > B > C > A

4. At constant volume and at 27oC, the heat of combustion of 7.8 g of benzene is 327 kJ. What will

be the heat of combustion of benzene at constant pressure (R = 8.3 J/mol-K)

(A) 3273 kJ (B) 3278 J(C) 327.3 kJ (D) 32.73 kJ

5.

i BuBr 1. Li

2. CuI(b)

Ph C

O

Cl(c)

(a)

(b) & (c) are -

PhCO &

CuLi

PhCO &

CuLi

CuLi

2

&PhCO

2

None of these

(A)

(D)(C)

(B)

6. Identify ‘D’ in the following reactions:-

MeCl2 + FeCl3

dark

(A)NBS

(B)Mg

Ether (C)

1. Epoxide

(D)2. H3O

+

Cl OH Cl

OH

Br OH Br OH

(A) (B)

(C) (D)



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14

7. PCC is a mild oxidizing agent. It is a mixture of

(A) Pyridine + CrO3 + HCl (B) Pyridine + CrO3 + H2O

(C) Pyridine + CrO3 (D) CrO3 + H2SO4

8.

COO + CH3+ A

Identify ‘A’.

COOCH3 COO CH3

COO

CH3

COO

CH3

(A) (B)

(C) (D)

9.Me3C Cl

AlCl3X

CH3CH2CH2 Cl

AlCl3Y

KMnO4

OH, Z

Z is

CMe3

COOH

COOH

CH2 CH2 CH3

CMe3

CMe3

COOH

COOH

(A) (B)

(C) (D)



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15

10. A compound D (C8H10O) upon treatment with alkaline solution of iodine gives a yellow ppt. The

filtrate on acidification gives a white solid E (C7H6O2). The structure of ‘D’ is

CH CH3

OH

CH2 CH2 OH

COOH CH2CH3

(A) (B)

(C) (D)

11. In which of the following reaction the final product is neither acid nor an acid salt?

Ph CHOTollen's reagent

CH3 CH2 CH3KMnO4/OH

Ph CHOFehling solution

Ph CH2 OHK2Cr 2O7/H

+

(A) (B)

(C) (D)

12. Which optically active compound on reaction with LiAlH4 will give optically inactive compound?

CH3 CH COOH

OCH3

CH3 CH2 CH COOH

OH

CH3 CH2 CH COOH

CH2OH

CH3 CH CH2 COOH

OH

(A) (B)

(C) (D)

13.

CO ClNaN3

X1.

2. OHProduct

The product is -

NC NH2

CONH2 COOH

(A) (B)

(C) (D)



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16

14. If the electronic velocity is 61.09 10 m/s, then electron may be revolving in the(A) 1

st orbit of hydrogen (B) 1

st orbit of helium

(C) 2nd

orbit of hydrogen (D) 2nd

orbit of helium

15. The amount of current which produces hydrogen gas at the rate of 1 cc. per second under

standard conditions -(A) 17.22 ampere (B) 8.61 ampere

(C) 25.83 ampere (D) 4.30 ampere

16. If the density of a mixture of O2 & N2 at NTP is 1.3 g/l, then

(A) partial pressure of O2 will be 0.28 atm (B) partial pressure of O2 will be 29.12 atm

(C) partial pressure of O2 will be 1 atm (D) partial pressure of O2 will be 0.72 atm

17. The rms speed of oxygen molecule is 24.92 10 m/sec. then(A) the temperature of the oxygen molecule is 310

oC

(B) the temperature of the oxygen molecule is 37oC

(C) the temperature of the oxygen molecule is 37 K

(D) the temperature of the oxygen molecule is 370 K

18. What is the density of Na2O having antifluorite-type crystal structure, if the edge lengh of cube is

100 pm and what is the effect on density by 0.05% Frankel defect?

(A) 823.5 g/cm3, density decreases (B) 414.16 g/cm

3, density decreases

(C) 823.5 g/cm3, density remains same (D) 414.16 g/cm

3, density remains same

19. Mole fraction of component A in vapour phase is 1 and that of A in liquid phase is 1 , then

o o A BP vapour pressure of A, P vapour pressure of pure B . The total pressure of liquid is

(A) o 2 A1

P .

(B) o 1 A2

P .

(C) o 1B2

P .

(D) o 2B

1

P .



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17

20. The vapour pressure of 1 molal glucose solution at 100oC will be

(A) 760 mmHg (B) 76.0 mmHg

(C) 1 atm (D) 746.32 mmHg

21. The standard free energy of formation of AgCl (s) at 25oC is 109.7 kJ/mol and H Cl (aq)

is 131.2 kJ/mol. Find oE of a cell made up with standard hydrogen electrode, and

Cl / Ag / AgCl s

(A) 0.446 V (B) 0.669 V

(C) 0.1115 V (D) 0.223 V

22. For the elimentary reaction1

2

K

K2A B , the rate of disappearance of A is equal to

(A) 21

2

2K A

K (B)

2

1 22K A 2K B

(C)

2

1 22K A 2K B (D) 1 22K K A

23. In an experiment, 200 ml of 0.5 m oxalic acid is shaken with 10 g of activated charcoal & filtered.

The concentration of the filtrate is reduced to 0.4 m. The amount of adsorption is

(A) 0.9 (B) 1.8

(C) 0.18 (D) 0.09

24. a f A B, H 10 kJ/mol, E 50 kJ/mol, then Ea of B A will be

(A) 40 kJ/mol (B) 50 kJ/mol

(C) 50 kJ/mol (D) 60 kJ/mol

25. In the reaction, 3 2 22Cu NO CuO NO O . On balancing

(A) 1 mole Cu (NO3)2 gives 1 mole of O2 (B) 1 mole Cu (NO3)2 gives 2 moles of O2

(C) 1 mole Cu (NO3)2 gives 1/2 moles of O2 (D) 1 mole Cu (NO3)2 gives 3 moles of O2



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18

26. If the pH of the half-equivalence point of an amino acid is 2.286 with HCl & 9.719 with NaOH

then, the pH of isoelectric point will be

(A) 6.003 (B) 7.002

(C) 5. 004 (D) 6.010

27. Which of the following match is incorrect?(I) XeOF2 T-shaped

(II) XeO2F2 Square planar

(III) XeO3 Pyramidal

(IV) XeF6 Distorted octahedron(A) (I) (B) (II)

(C) (III) (D) (IV)

28. The structure of glycine at isoelectric point is

(A) 2 2H N CH COOH (B) 2 2H N CH COO

(C) 3 2H N CH COOH (D) 3 2H N CH COO

29. Correct statement is(A) [Co(NH3)6]

3+ has hybridization d

2sp

3 & octahedral shape

(B) [Ni(CN)4]2 has hybridization dsp

2 & square planar shape

(C) [Ni(CO)4] has hybridization sp3 & tetrahedral shape

(D) All are correct

30. Correct statement is :

(A) During extraction of Mg, MgCl2 + NaCl is electrolysed

(B) During extraction of Pb, NaCN removes ZnS & PbS during floatation

(C) During electrolytic refining of Zn, electrolyte is ZnSO4 + H2SO4

(D) All are correct



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19

athematics

PART – III

SECTION – A



1. Px 2y 1 is normal to parabola 2y 4ax for:

(A) no value of P (B) exactly one value of P

(C) exactly two values of P (D) exactly three values of P

2. The number of solutions of the matrix equation 21 1

X2 3

is

(A) more than 2 (B) 2

(C) 0 (D) 1

3. If2

x

2

d xy sinx e ,then

dy

(A) x 1( sinx e ) (B)x

x 2

sinx e

(cos x e )

(C)x

x 3

sinx e

(cos x e )

(D)

x

x 3

sinx e

(cos x e )

4. The line 2x y 1 0 is tangent to the circle at the point (2,5) and the centre of the circles lies on

x 2y 4. The radius of the circle is:

(A) 3 5 (B) 5 3

(C) 2 5 (D) 5 2



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20

5. The expression

8

1 sin i cos8 8

1 sin i cos8 8

(A) 1 (B) -1

(C) i (D) –i

6. If n1

t n 2 n 3 for n=1,2,3,.......4

then1 2 3 2003

1 1 1 1............

t t t t

(A)4006

3006 (B)

4003

3007

(C)4006

3008 (D)

4006

3009

7.(x 2)(x 1)

f(x) , x 3.(x 3)

The minimum value of f(x) is equal to

(A) 3 2 2 (B) 3 2 3

(C) 3 2 2 (D) 3 2 2

8. Let A and B be two events. Suppose P(A)=0.4, P(B)=p and P A B =0.7. The value of p for

which A and B are independent is

(A) 1/3 (B) 1/4

(C) 1/2 (D) 1/5

9. Range of 1 1 1f(x) sin x tan x sec x is

(A)

3

,4 4

(B)3

,4 4

(C)3

,4 4

(D) none of these



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21

10. The area bounded by the two branches of curve 2 3(y x) x and straight line x=1 is

(A) 1/5 sq. units (B) 3/5 sq. units

(C) 4/5 sq. units (D) 8/4 sq. units

11. The population of a country increases at a rate proportional to the number of inhabitants. If the

population doubles in 30 years, then the population will triple in approximately(A) 30 years (B) 45 years

(C) 48 years (D) 54 years

12. If z1 is a root of the equationn n 1

o 1 n 1 n ia z a z .......a z a 3,where a 2for i=0,1,......,n. Then

(A) 11

z3

(B) 11

z4

(C)1

1z

4 (D)

1z

3

13. The ratio of the area of a regular polygon of n sides inscribed in a circle to that of the polygon ofsame number of sides circumscribing the same circle is 3:4. Then the value of n is

(A) 6 (B) 4

(C) 8 (D) 12

14. Differential equation of the family of circles touching the line y= 2 at (0,2) is

(A) 2 2dy

x (y 2) (y 2) 0dx

(B) 2dx

x (y 2) 2 2x y 0dy

(C) 2 2dx

x (y 2) y 2 y 2 0dy

(D) None of these

15. Two vertices of a triangle are (5,-1) and (-2,3). If orthocentre of the triangle is origin, then the co-

ordinates of third vertex is

(A) (4,7) (B) (3,7)

(C) (-4,-7) (D) (4,-7)



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22

16. If P( ) and Q2

are two points on the ellipse2 2

2 2

x y1,

a b then locus of midpoint of PQ is:

(A)2 2

2 2

x y 1

2a b (B)

2 2

2 2

x y2

a b

(C)

2 2

2 2

x y

4a b (D)

2 2

2 2

x y

8a b

17. Given that matrix

x 3 2

A 1 y 4 .

2 2 z

If xyz =60 and 8x+4y+3z=20. Then A(adj A) is equal to

(A)

64 0 0

0 64 0

0 0 64

(B)

88 0 0

0 88 0

0 0 88

(C)

68 0 0

0 68 0

0 0 68

(D)

34 0 0

0 34 0

0 0 34

18. The probability that a teacher will give an unannounced test during any class is 1/5. If a student is

absent twice, then the probability that the student will miss at least one test is

(A) 4/5 (B) 2/5

(C) 7/25 (D) 9/25

19. If x

1

1

1f(x) 1 f(t)dt, then the value of f(e )

x is

(A) 1 (B) 0

(C) -1 (D) None of these

20. The area of the region containing the points (x,y) satisfying 2 24 x y 2( x y ) is

(A) 8 sq. units (B) 2 sq. units

(C) 4 sq. units (D) 2 sq. units



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23

21. If4 5 6

n n n

1 1 1

C C C , then n

(A) 2 (B) 3(C) 4 (D) None of these

22. If2 0 0

A 2 2 0

2 2 2

, then adj adj A is equal to

(A) 83 (B) 6

3

(C) 323 (D) 64

3

23.n

1 1 1 1lim ......

n 1 n 2 n 3 n n

is

(A) ln2 (B) ln3

(C) ln4 (D) ln5

24. Slope of common tangent to the circles

2 2

1C : x y 2x 0 and2 2

2C x y 6x 0 is(A) 0 (B)

1

3

(C) 3 (D) None of these

25. If 2f x f 1 x 2 , then 1

20

f x dx

1 x is equal to

(A) 0 (B)2

(C) (D) 2

26. If e1 and e2 are eccentricities of hyperbolas 2xy c and 2 2 2x y a , then 2 21 2e e (A) 1 (B) 2(C) 4 (D) 8



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24

27. The line of intersection of planes ˆ ˆ ˆr . i 2 j 3k 0 and ˆ ˆ ˆr . 3i 3 j k 0 is equally inclined toˆ ˆi & k and angle with ̂j is , then 2sin is

(A)1

3 (B)

2

3

(C) 12

(D) 14

28. If a x, a, a x are the lengths of the sides of an obtuse angled triangle, then x lies in

(A)a

, a2

(B)a 3a

,3 4

(C)a

, a4

(D)a

, a3

29. A seven digit number without repetition and divisible by 9 is to be formed by using 7 digits out of1, 2, 3, 4, 5, 6, 7, 8, 9. The number of ways in which this can be done is

(A) 9 (B) 2 7

(C) 4 7 (D) None of these

30. The linesx 1 y z

2 1 2

and x y z 2 0 x 3z 5 are coplanar for

(A)97

11 (B)

43

5

(C)73

9 (D)

31

7


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