fiitjee aits mains 2013

8/13/2019 fiitjee aits mains 2013

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

FULL TEST II

Time Allotted: 3 Hours Maximum Marks: 360

P lease read the ins t ruct ions careful ly . You are al lot ted 5 minutesspec i f ical ly for th is purpose.

You are not al lowed to leave the Examinat ion 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-Iis Physics, Part-IIis 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 beprovided for rough work.

6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronicdevices, 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 answerson 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 mark for wrong answer.

Name of the Candidate

Enrolment No.

ALLINDIA

TESTSE

RIES

FIITJEE JEE (Main), 2013

FromLongTermC

lassroomProgramsandMedium/

ShortClassroomProgram4

inTop10,10inTop

20,43inTop100,

75in

Top200,159inTop500Ranks&3542

totalselec

tions

in

IIT-JEE

2012


2/23

AITS-FT-II-PCM-JEE(Main)/13


2

Useful Data

PHYSICS

Acceleration due to gravity g = 10 m/s2

Planck constant h = 6.6 1034J-s

Charge of electron e = 1.6 1019 C

Mass of electron me= 9.1 1031kg

Permittivity of free space 0= 8.85 1012 C

2/N-m

2

Density of water water= 103kg/m

3

Atmospheric pressure Pa= 10

5

N/m

2

Gas constant R = 8.314 J K1mol

1

CHEMISTRY

Gas Constant R = 8.314 J K1mol

1

= 0.0821 Lit atm K1mol

1

= 1.987 2 Cal K1 mol1Avogadro's Number Na = 6.023 10

23

Plancks constant h = 6.625 1034 Js= 6.625 1027ergs

1 Faraday = 96500 coulomb

1 calorie = 4.2 joule1 amu = 1.66 1027 kg1 eV = 1.6 1019J

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

PPhhyyssiiccss 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 given LCR series circuit satisfies the condition for resonance with a given AC source. If theangular frequency of the AC source is increased by 100% then in order to establish resonance,without changing the value of inductance, the capacitance must be(A) increased by 100% (B) reduced by 50%(C) increased by 75% (D) reduced by 75%

2. The end A of a ladder AP of length 5 m, kept inclined to a verticalwall is slipping over a horizontal surface with velocity of 2 m/s,when A is at a distance of 3m from the wall. Velocity of centre of

mass at this moment is(A) 1.25 m/s (B) 0 m/s(C) 1 m/s (D) 2 m/s

A O

P

2m/s

3m3. Nine similar resistors of resistance R are connected as shown in

the figure. Equivalent resistance between points A and B is(A) 3/5 R (B) 4/5 R(C) 9/5 R (D) R

A

B

Rough work


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4

4. An isosceles right angle triangle of side d is placed in a horizontal

plane. A point charge q is placed at a distance d vertically abovefrom one of the corner as shown in the figure. Flux of electric fieldpassing through the triangle is

(A)0/ 6q (B) 0/18q

(C) 0/ 24q (D) 0/ 48q d

d

d

+q

5. A cavity is taken out from a uniform conducting sphere. Inside

the cavity a dipole is placed as shown in the figure. Potential atpoint P is

(A)0

cos

4 d

ql

(B) Zero(C) Insufficient information(D) none of these

R

P

d

+q

ql

O

6. In the given LCR circuit, the key is closed at t = 0. The emf

induced in the coil at t = 0 will be(A) zero

(B)

2CR

L

(C) with VA> VB(D) with VA< VB

L

R

C

A B

7. A vertical jet of water coming out of a nozzle with velocity 20m/s supports a plate of mass M stationary at a height

h= 15m, as shown in the figure. If the rate of water flow is 1 litreper second, the mass of the plate is (Assume the collision to beinelastic).(A) 1 kg (B) 1.414 kg(C) 2 kg (D) 10 kg

15 m

M

v= 20 m/s

Rough work


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5

8. The number of significant digits in 0.001001 is(A) 6 (B) 4(C) 7 (D) 2

9. The binding energy of a particle of mass m with a planet, when it is on the planets surface, is

20

1mv

2

. A tunnel is dug along a diameter of the planet and the particle is dropped into it from the

surface, when the body reaches the centre of the planet, its speed is

(A) v0 (B)0v

2

(C) Zero (D) 0v

2

10. Consider the two identical particles shown in the given figure. They arereleased from rest and can move towards each other under the influenceof their mutual gravitation forces. Speed of each particle, when theseparation reduces to half of initial value equals

d

M M

(A)GM

d

(B)2GM

d

(C)GM

2d (D) none of these

11. A gas of adiabatic exponent is supplied heat at a constant pressure. What is the ratio betweendQ, dW and dU in the process

(A)1

: 1:

(B) 1 : 1 : 1

(C) : 1 : 1 (D) : 1 : 1

Rough work


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6

12. Find the value of u so that the ball reaches at point B.

(Take g = 10 m/s2)

(A) 20 m/s (B) 40 m/s

(C) 152 m/s (D) 50 m/s

10m

45

B

A

u

20m

15m

13. Acceleration vs time graph is shown in the figure for a

particle moving along a straight line. The particle is initiallyat rest. Find the time instant(s) when the particle comes torest ?(A) t = 0, 1, 2, 3, 4(B) t = 0, 2, 4(C) t = 1, 3(D) None of these

+2

O

2

1 2 3 4 t(sec)

a(m/s )2

14. A body of mass m is released from rest on an inclined plane in an elevator

(moving up with acceleration a0). Find the time taken by the body to reach thebottom of the inclined plane.

(A)0

L

(a g)sin+ (B)

0

2L

(a g)sin+

(C)0

3L

(a g)sin+ (D)

0

L2

(a g)sin+

Lsmooth

m

a0

15. Find minimum value of the angle so that block of mass m does notmove on rough surface. The coefficient of static friction between the block

and surface is whatever may be the value of applied force F.

F m

( ) Rough Surface

(A) tan1() (B) 1

1tan ( )

2

(C) cot1() (D) 1

1cot ( )

2

Rough work


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7

16. Two infinite long wires each carrying current I lying along x

and y axis respectively. A charged particle having a chargeq and mass m projected with a velocity u along a straightline OP. The kinetic energy of particle as a function of timeis correctly shown by (neglect gravity)

45o

P

I

O I

(A)KE

t

(B)KE

t

(C)KE

t

(D)KE

t

17. A photon of frequency f causes the emission of a photoelectron of maximum kinetic energy EKfrom a metal. If a photon of frequency 3f is incident on the same metal, the maximum kineticenergy of the emitted photoelectron(A) equals 3EK(B) is greater than 3EK(C) is less than 3EK(D) maybe equal to, less than or, greater than 3EK.

18. A proton, within a nucleus, decays into a neutron during a process called +decay, which occursin some unstable nuclei. This process is represented by the equation:

A AZ Z 1 eX Y e

+ + +

Let ( )AZm X represent the mass of an atom of AZ X , and c represent the velocity of light invacuum. Assume that eis massless. The Q value of the process is given by

(A) ( ) ( )A A 2Z Z 1 em X m Y 2m c (B) ( ) ( )A A 2Z Z 1m X m Y c

(C) ( ) ( )A A 2Z Z 1 em X m Y m c (D) ( ) ( )A A 2Z Z 1 em X m Y m c

+

.

Rough work


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8

19. If the behaviour of light rays through a prism lens is as shown in the

following figure, then

(A) 1= 2 (B) 1< 2(C) 1> 2 (D) 12

2

1

2

20. The focal length of a thin convex lens ( = 3/2) in air is 20 cm. When immersed in liquid of

refractive index 1.75 then lens will be(A) Diverging with focal length 70 cm (B) Concave with focal length 70 cm(C) Converging with focal length 20 cm (D) Concave with focal length 20 cm

21. A steel ring of radius r and cross-sectional area A is fitted on to a wooden disc of radiusR(R > r). If Youngs modulus be Y, then the force with which the steel ring is expanded is :

(A)R

AYr

(B)R r

AYr

(C)Y R r

A r

(D)Yr

AR

22. A rod of length 40 cm has the coefficient of linear expansion 1= 6 106

/C. Another rod of

length lhas the coefficient of linear expansion 2= 4 106

/C. If the difference in the lengths ofthe two rods always remain same at all temperatures, then the value of lis(A) 26 cm (B) 60 cm(C) 80 cm (D) 32 cm

23. A small block of mass m is placed on a rough rotating table. Find

maximum angular velocity (0) that can be given to the table so that theparticle does not slip on the table. It is given that the coefficient of friction

between the block and the table is ().

(A)

2 g

d

(B)

3 g

d

(C)g

d

(D)

g2

d

d

0

m

Rough work


9/23



9

24. A body executes simple harmonic motion. The potential energy (PE), kinetic energy (KE) andtotal energy (TE) are measured as a function of displacement x. Which of the followingstatements is true?(A) TE is zero when x = 0 (B) PE is maximum when x = 0(C) KE is maximum when x = 0 (D) KE is maximum when x is maximum

25. A square loop of side 4 cm is lying on a horizontal table. Auniform magnetic field of 0.5 T is directed downwards at anangle of 60 to the vertical as shown in figure. If the fieldincreases from zero to its final value in 0.2 s, the emf inducedin the loop will be(A) 1 mV (B) 2 mV(C) 3 mV (D) 4 mV

60

B

26. A mass m on a frictionless table is attached to a hanging mass by a

spring (of spring constant K and natural length 0

) and a cordthrough a hole in the table. If the hanging mass remains stationary

and the mass m moves on a circular path with angular velocity theradius of its circular path is

(A) 0 (B)2

0

2

m

K m

(C) 02

K

(K m )

(D) 0

2

K

K m+

m

27. A progressive wave is travelling in a medium such that frequency of oscillation and displacementamplitude of the particles of the medium are f and A respectively. The ratio of their accelerationamplitude and velocity amplitude is

(A) 2f (B) f

(C)2 f

A

(D)

f

A

.

Rough work


10/23



10

28. For a particle executing simple harmonic motion, the correct variation of acceleration a withdisplacement x is given by(A)

x

a

O

(B)

x

a

O

(C)

x

a

O

(D)

x

a

O

29. An open organ pipe of length L vibrates in second harmonic mode. The pressure variation ismaximum, (neglect end corrections)(A) at the two ends

(B) at a distanceL

4from either end inside the tube

(C) at the midpoint of the tube(D) none of these.

30. The minimum work done by the agent, in pulling a small particle ofmass m from A to B as shown in figure, is(A) 4 mgR (B) mgR(C) 3mgR (D) 2mgR

BR

m smooth

A

agent

Rough work


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11

CChheemmiissttrryy PART IISECTION 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. The equilibrium constant for the reaction in aq. solution

( )3 3 3 3H BO Glycerine H BO glycerine+ is 0.95. How many moles of glycerin should beadded per litre of 0.1 M H3BO3. So that 80% of the H3BO3is converted to boric acid-glycerinecomplex:(A) 494 (B) 4.29(C) 3.5 (D) 0.08

2. A radioactive substance decays to its daughter element. If R is the number of radioactive atoms

of the parent element remaining and d is the number of atoms of the daughter element formedthen the time of decay t is related to R and d as

(A)1 R

t n 1d

= +

(B)1 d

t n 1R

= +

(C)1 R

t nd

=

(D)d

tR

=

3. When NaOH is titrated with HCl(aq.) the graph of the pH vs volume of NaOH will be:

(A)

vol of NaOH

pH

(B)

vol of NaOH

pH

(C)

vol of NaOH

pH

(D)

vol of NaOH

pH

Rough Work


12/23



12

4. The equilibrium constant for the ionization of aliphatic amine RNH2(g) in water is 8 10-6

at 25oC

( ) ( ) ( ) ( )+ -2 2 3RNH g + H O l RNH aq + OH aq

Concentration of amine at equilibrium is 0.5 M. The pH of the aqueous solution of amine will be

(A) 2.7 (B) 4.7

(C) 11.3 (D) 9.3

5. When two half cell of electrode potential of Eaand Ebare combined to form a cell of electrode

potential E , then(If na, nband nare no. of electron exchanged in 1

st, 2

ndand combined half cell)

(A) b aE E E= (B)a a b bE n E nE

n

=

(C) a a b b2

E n E nE

n

=

(D) a bE E E= +

6. K4[Fe(CN)6] if = 0.7 the value of vant Hoff factor i' is:(A) i 2.3= (B) i 2.8= (C) i 3.8= (D) i 3.4=

7. In a compound atom of element A form ccp lattice and those of element B occupy 2/3rd

of

tetrahedral voids. The formula of the compound will be:

(A) A3B4 (B) A2B4

(C) A3B2 (D) A2B3

8. A current of 4A is passed through a solution of silver nitrate to coat a metal surface of 80 cm2with

0.005 mm thick layer of silver. Molar mass of silver is 108 g mol1

. If the density of silver is 10.8 gcm

3, the time for which the current is passed is

(A) 84.5 sec. (B) 90.5 sec.(C) 96.5 sec. (D) 100.5 sec.

9. A perfect gas undergoes a rev. adiabatic expansion from (300 K, 200 atm) to (90 K, 10 atm). Theatomacity of gas is:(A) 1 (B) 2(C) 3 (D) 4

10. The SO2molecule have

(A) 2 p d bond (B) 1 p p and 1p d bond

(C) 2 p p bond (D) 2 bond 2 bond and 2 lone pair

11. In H2CCl2if C Cl bond length is 235o

A , the distance between atoms in the compound is:(A) 2.07 10

-8cm (B) 4.07 10

-8cm

(C) 4 10-5

cm (D) 2 10-5

cm

Rough Work


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13

12. The oxidizing agent is:(A) Mn(Co)4 (B) Mn(Co)5(C) Mn2(Co)10 (D) Fe(Co)9

13. Which of the following alkene on acid catalysed hydration form 2-methyl propan-2-ol.

(A) (CH3)2C = CH2 (B) CH3 CH = CH2

(C) CH3 CH = CH CH3 (D) CH3 CH2 CH = CH2

14. The Ellingham diagram of ZnO and CO is converting in corresponding oxides is

2Zn O ZnO+

22C O 2CO+

1180

oT in C

600

200( )oG kJ

To make ZnO C Zn CO+ + reduction process

spontaneous, temperature should be:

(A) 1000oC (B) > 1100

oC

(C) < 500oC (D) < 1100

oC

15. 3 2AgNO X Y O + +

3 3 2X HNO AgNO NO H O+ + +

2 2 3Y H O HNO HNO+ +

(A) X = Ag Y = NO

(B) X = Ag2O Y = N2O(C) X = Ag2O Y = N2(D) X = Ag Y = NO2

16. Spiegeleisan is an alloy of(A) Cu, Zn and Ni (B) Mn, Fe and C(C) Ni + Cr + Cu (D) Fe, Cr, Ni

Rough Work


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14

17.

O

O

O

CH3

4NaBH

the major product of reaction is

(A)

OH

O

OH

(B)

O

OH

O

(C)

OH

O

OH

(D)

OH

OH

OH

18.

O

3

2 4

HNO

H SOP,

P is consider only major product

(A) O

NO2

(B) O

NO2

(C) O

O2N

(D) NO2

OH

Rough Work


15/23



15

19. Which of the following is anti-aromatic:

(A) (B)

(C)N OH

(D)O O

20. The Zwitter ion which represents the physiological existence of aspartic acid (pH = 7.3) is:

(A) H3N HC

CH2

COO

CONH2

(B) H3N HC

CH2

COO

COO (C) H3N CH2 COO

(D)

NH

H3N HC

CH2

COO

21.

HOOC

pKa = 4.09

COOH

pKa = 5.09

[1,1,1]bicyclopentanecarboxylic acid

(A)

2-methyl peopanoic acid (B)

so the correct statement is:

(A) A is more acidic than B due to more salvation energy(B) B is more acidic than A due to more salvation energy(C) A is less acidic than B as B has more salvation energy(D) Conjugate base of A has larger area than B

Rough Work


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16

22.

OH

H H

HH

F

OH

H H

FH

H

(1) (2)

The true statement about the two conformer is:

(A) at eqm. conc. 1 = con. 2 (B) conc of 1 > conc of 2(C) both have intramolecular H-bonding (D) transformation of 1 into 2 will be exothermic

23.

KOH

Br2

P of reaction will have:

C

O

NH2

+

C

O

NH2

(14)

(15)

(C = C14

)

(A)

NH2

(14)

(B)

NH2

(15)

(C)

NH2

(15)

(D)

NH2

(15)

Rough Work


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17

24.

O

( )15

pH 4 5

2NH OH +

N OH

15

2 5H O/PCl P Q +

P and Q are :

(A) NH O

+

O

P Q

(B)

NH O

+

NH

O

P Q

(C)

N

H

+

O

P Q

(D) OHOH

+

OH OH

P Q

25. H++

( )1

N

NH2

NH CH3

CNH2

O ( )2( )3

The H+will be attacking on position

(A) 1 (B) 2(C) 3 (D) react equally on all three positions

Rough Work


18/23



18

26. Which of the following will react faster with Ag+?

(A)Cl

(B)Cl

OCH3 (C)

Cl

COOH

(D)Cl

NO2

27. Which among the following ions has maximum covalent character?(A) KCl (B) CuCl(C) RbCl (D) CsCl

28. O

2 5 2 5(i) C H O / C H OH

(ii) R

O

CHO

R would be(A) HCHO (B) CH3CHO

(C) (COOC2H5)2 (D)H C

O

OC2H5

29. Which of the following is biodegradable polymer?(A) Polyethene (B) Cellulose(C) PVC (D) Nylon 6

30. The conductivity of 0.001 M Na2SO4solution is 2.6 10

-4

S cm

-1

and increases to 7 10

-4

S cm

-1

,when the solution is saturated with CaSO4. The molar conductivities of Na+and Ca

+2are 50 and

120 S cm2 mole

-1 respectively. Neglect the conductivity of used water. What is the solubility

product of CaSO4?(A) 4 10

-6 (B) 2.57 10

-3

(C) 3 10-4

(D) 6.46 10-6

Rough Work


19/23


20/23



20

5. An insurance company believes that people can be divided into two classes; those who areaccident prone and those who are not. Their statistics show that an accident prone person will nothave an accident in a yearly period with probability 0.4 whereas this probability is 0.2 for the otherkind. Given that 30% of people are accident prone. The probability that a new policyholder willhave an accident within a year of purchasing a policy is(A) 0.74 (B) 0.28(C) 0.34 (D) 0.66

6. A non-zero vector a

is parallel to the line of intersection of the plane P1determined by i j+ and i 2 j and plane P2determined by vector 2i j+ and 3i 2k+ , then angle between a

and vector

i 2j 2k + is

(A)4

(B)

2

(C)3

(D) none of these

7. If H1, H2, H3, , H2n + 1are in H.P., then2n

i i i 1

i i 1i 1

H H( 1)

H H

+

+=

+

is equal to

(A) 2n 1 (B) 2n + 1(C) 2n (D) 2n + 2

8. If A and B are symmetric matrices of the same order and X = AB + BA and Y = AB BA, then(XY)

Tis equal to

(A) XY (B) YX

(C) YX (D) none of these

9. If p is a prime number (p 2), then the difference ( )p

p 12 5 2 + + is always divisible by (where

[.] denotes the greatest integer function)(A) p + 1 (B) p

(C) 2p (D) 5p

10. Let a, b, c R such that no two of them are equal and satisfy

2a b c

b c 2a 0

c 2a b

= , then equation

24ax2+ 4bx + c = 0 has

(A) atleast one root in [0, 1/2] (B) atleast one root in1

, 02

(C) atleast one root in [1, 2] (D) none of these

Rough work


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21

11. If f(x) = x 1 and g(x) = |f(|x|) 2|, then the area bounded by y = g(x) and the curvex

24y + 8 = 0 is equal to

(A) ( )4 4 2 53

(B) ( )4 4 2 33

(C) ( )8 4 2 33

(D) none of these

12. The all possible values of a such that

( ) ( )2 1 2 1 22 2sin x asin x sin x 10x 26 cos x 10x 26 05 5

+ + + + + =

has atleast one solution

is/are

(A) ( ), 2 2 , (B) ( ( ), 2 ,

(C) ( )2 , 2 (D) none of these

13. Let

13 5 10

8 7 14

z 2i 3i 7i

=

, where is complex cube root of unity then

(A) z is purely real number (B) z is purely imaginary(C) z has equal real and imaginary part (D) none of these

14. Let f : R R satisfy 2f(x) cos x x R, then the number of roots of equation f(x) = 0 in x (0, 10) is(A) exactly 3 (B) exactly 4(C) atleast 4 (D) atleast 2

15. Which of the following is always correct?

(A) if f(x) > 0 x domain, then f(x) cannot be periodic(B) if f(x) < 0 x domain, then f(x) cannot be many one

(C) if |f(x)| is differentiable at x = a then f(x) is also differentiable at x = a(D) if f(x) is continuous at x = a, f(a) = 5 and x = a is the point of local minima of f(x), then [f(x)]is also continuous at x = a (where [.] denotes G.I.F)

16. Consider the graph of y = ax2, a R+and y2 x2= 4y 3 then number of points of intersections

is/are(A) 2 (B) 4(C) 6 (D) 1

Rough work


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22

17. The function f(x) = 2x3+ x2+ x + r where , , r R has local minima at x = 3tand local max at

x = 23t. It

5x

2= is the point of inflection then the possible value of t is/are

(A) 3log 5 (B) 5log 3

(C) 53

log

5

(D) 35

log

3

18. Evaluate 2 2n 2

1log 1

n

=

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

19. Let f(0) = 0 and ( ) ( )

2

f 2t

0

f ' 2t e dt 5= then the value of f(4) is(A) 2 ln 3 (B) ln 10(C) ln 11 (D) 2 ln 2

20. In a ABC angle A =2

3

and BC + AC = 20 and AB + BC = 21, then the length of side BC is

(A) 13 (B) 14(C) 15 (D) 16

21. The function

x

sint

0

1f(x) log sin t dt

2

= + , x (0, 2) is strictly increasing in the interval

(A)5 7

x ,6 6

(B)5

x ,6 6

(C)7 11

x ,

6 6

(D) none of these

22. Let A = {1, 2, 3, ....., n}. If aiis the minimum element of the set Aiwhere AiA such that n(Ai) = 3then sum of all aifor all possible sets Aiis/are

(A) n 2C (B)n 1

4C

(C) n 1 2C+ (D) n 1 4C

+

23. The number of integral order pair (x, y) that satisfy the system of equation|x + y 4| = 5 and |x 3| + |y 1| = 5 is/are(A) 0 (B) 4(C) 8 (D) infinite numbers

Rough work


23/23


24. Let f(x, y) = (2y2+ 1)x

2+ 2(4y

2 1)x + 4(2y

2+ 1) x, y R then least value of f(x, y) is

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

25. The value of n for which the equation 9x4 12x

3+ nx

2 8x + 4 is a perfect square

(A) 16 (B) 18

(C) 8 (D) 24

26. If a, b are odd integers then number of integral root, of equatino x10

+ ax9+ b = 0 is/are

(A) 10 (B) 2(C) 5 (D) none of these

27. The equation of the plane through the intersection of the planes x + 2y + z 1 = 0 and2x + y + 3z 2 = 0 and perpendicular to the plane x + y + z 1 = 0 and x + ky + 3z 1 = 0. Thenthe value of k is

(A)5

2 (B)

3

2

(C)5

2 (D)

3

2

28. Let 1, 1, 2, 3, ..... n 1be n roots of equation xn+ x + = 0 where ijif i j then the

value of ( ) ( )( ) ( )1 2 1 3 1 4 1 n 1..... is

(A) ( ) n 21n n 1 (B) n n z2 1C

(C) ( )n 11n + (D) 0

29. Mr. X has 5 children, and Mr. Y has 3 children. Of the either children it is known that there are 5girls and 3 boys. Then probability that atleast one of the family have only girls as their children

(A)1

56 (B)

9

56

(C)11

56 (D)

10

56

30. Let f(x) is an even, periodic function with period as 2, and that f(x) = x x [0, 1] then f() is(A) (B) (C) 4 (D) 4

Rough work

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fiitjee aits mains 2013