concept recap test mains 6

7/28/2019 Concept Recap Test Mains 6

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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

CONCEPT RECAPITULATION TEST(Set VI)

Time Allotted: 3 Hours Maximum Marks: 360

Please read the inst ruct ions carefu l ly. You are a l lot ted 5 minutesspeci f ica l ly for th is purpose.

You are not a l lowed to leave the Examinat 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 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 yourEnrolment 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


2/22

AITS-CRT(Set-VI)-PCM-JEE(Main)/13


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 = 10

5

N/m

2

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

Plancks constant h = 6.625 1034 Js= 6.625 1027 ergs

1 Faraday = 96500 coulomb

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

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. Determine the region of the electron spectrum which liberates photo-electrons from potassium.Given that the work function of potassium is 2.24 eV.(A) < 5525 (B) > 5525 (C) < 5.43 (D) none of the above

2. The refractive indices for violet and red colour are 1.54 and 1.52 respectively, the angulardispersion of a prism of angle 20 and made of such glass will be(A) 0.4 (B) 0.2(C) 3.06 (D) 30.6

3. In an interference experiment the separation between the 1st and the 11th bright fringe on ascreen is 2.5 mm. The screen is at a distance of 3 m from the interfering sources. If = 5000, Then ratio of intensity at 0.1 mm from central max and maximum intensity is

(A) 24

sin5

(B) 1 cos

5

(C) 1 sin5

(D) 2

2cos

5

4. A ball of mass m, attached to a light wire of length l, is rotated in a horizontal circle. The area ofcross-section of the wire is A and its breaking stress is S then maximum angular velocity is

(A) 1sradml

AS

2

1 (B) 1srad

ml

AS

(C) 1sradml

AS

4

1 (D) 1sradml

AS2

ml

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4

5. A uniform solid cylinder of mass M and radius R is pulled horizontally by a force

F acting at its center of mass from rest. Then indicate the correct direction offriction, assuming that it rolls without sliding on a rough horizontal surface

F

(A)F

f

(B)F

f

(C) F

f=0

(D) cannot be interpreted

6. A small block of mass m, having charge q is placed on frictionlessinclined plane making an angle with the horizontal. There exists auniform magnetic field B parallel to the inclined plane but perpendicularto the length of spring. If m is slightly pulled on the inclined in downwarddirection, the time period of oscillation will be (assume that the blockdoes not leave contact with the plane)

B

(A)m

2K

(B)2m

2K

(C)qB

2 K (D)qB

2 2K .

7. The first over tone of an open organ pipe and the fundamental tone of a closed organ pipe closedorgan give 5 beats per second when sounded together. If the length of the closed pipe is 25 cm,what are the possible lengths of the open organ pipe?(speed of sound in air = 340 m/s):(A) 90 cm and 100 cm (B) 98.5 cm and 101.5 cm(C) 100 cm and 103 cm (D) 102 cm and 105 cm

8. A block of mass m is attached with a spring in its natural length,of spring constant k. The other end A of spring is moved with aconstant acceleration a away from the block as shown in thefigure. Find the maximum extension in the spring. Assume thatinitially block and spring is at rest w.r.t ground frame

mA

a

(A)ma

k(B)

1 ma

2 k

(C)2ma

k(D)

4ma

k.

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5

9. In an A.C. circuit when applied voltage is V = V0 sin (t /4) then resulting current is I = I0 sin(t + /4) then average power developed in the circuit is

(A) 0 0V I 2 (B) V0I0

(C) zero (D) None of the above

10. A balloon of mass M with a light rope having monkey on the rope is in equilibrium.If the monkey starts moving up with acceleration a w.r.t. rope. Then theacceleration of centre of mass of the system is

(A)a(M m)

(M m)

+

(B) Zero

(C) a (D)aM

m.

m

M

11. For what value of R, power developed across 6

resistor is equal to the power developed across 24 resistor?(A) 12 (B) 6 (C) 24 (D) 8

6 i iR

24 12. A cell of emf 2V is connected across a resistance5 . The potential difference between the

terminals of the cell is found to be 1.25 V. The internal resistance is

(A)15

8 (B) 3

(C)10

3 (D) none of these.

13. In a parallel plate capacitor of plate area A, plate separation d and charge Q, the force ofattraction between the plates is F, then

(A) 2F Q (B)2

1F

A

(C) F d (D)1

Fd

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6

14. As arrangement shown in the figure at t = 0 switch S1 isclosed, find current ithrough battery at t = 0

(A)1

v

R

(B)

1 2

v

R R+

(C)2

v

R

(D) None of the above

L

C

+

r

R2

R1

S1

t = 0

15. The time period of a simple pendulum in air is T. The time period of the same simple pendulum inanother medium which offers a Buoyant force on the bob, one third of its weight, is

(A)3

2T (B)

2

3T

(C)3

2T (D)

2

3T

16. A sealed tank containing a liquid of density moves with ahorizontal acceleration a0, as shown in the figure. The difference inpressure between the points A and B is(A) hg (B) la0(C) hg la0 (D) hg + la0

A

Bh a0

A

17. Identify the correct definition of gravitational potential at a point.(A) it is defined in terms of the force required to displace a unit mass from infinity to that point(B) it is defined in terms of the force required to move a unit mass from the surface of earth to

that point(C) it is defined in terms of the force required to displace a unit mass from that point to infinity(D) none of these

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7

18. The density () versus temperature (T) graph of an ideal gasundergoing a process AB is as shown in the figure. Choosethe incorrectoption(A) PAVA= PBVB(B) PB> PA(C) WAB is positive

(D) DUAB= 0

T

A

B

19. An ideal gas of adiabatic exponent is supplied heat at a constant pressure. Then ratiodQ : dW : dU is equal to

(A) : 1 :1

(B) 1 : 1 : 1

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

20. In a thermodynamic process helium gas obeys the law TP2/5 = constant. The heat given to thegas when the temperature of 2 moles of the gas is raised from T to 4T (R is the universal gasconstant) is(A) 9 RT (B) 18 RT(C) Zero (D) Data insufficient

21. A particle moves with a speed v in a circle of radius R . Thex-component of the average velocity of the particle in a half-revolution, as shown in figure, is

(A)

v(B)

2

v

(C)4

v

(D)2

v

60

yinitial

position

x

finalposition

22. One end of a rope is bound to a vertical wall. The other

end is pulled with a horizontal force of 30 N. An additionalforce of 10N is applied to the right at the point A in themiddle of the rope. Which of the following is true abouttensions at points P and Q

QP

10 N

30 NA

(A) TP = TQ = 40N (B) TQ = TP = 20N(C) TP TQ = 10N (D) TQ = 20N TP = 40 N

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8

23. A particle of specific chargeq

m= C/kg is projected from the origin towards positive xaxis with a

velocity of 10 m/s in a uniform magnetic field B 2k= G

T. The velocity vG

of particle after time1

t12

= s will be (in m/s)

(A) 5[ i 3 j+ ] (B) 5(

3 i j+ )

(C) 5[ 3 i j ] (D) 5[ i j+ ]

24. The effective charge experienced by an M( n = 3) electron in an atom of atomic number z is about(z 7.4) e. The frequency of L X-rays of such an element is

(A)( )

23cR z 1

4

(B)

( )2

3cR z

4

(C)( )

25cR z 7.4

18

(D)

( )2

5cR Z 7.4

36

25. Wavelength ofK X-ray of an elementA is 1 and wavelength ofK X-ray element B is 2. 12

is

equal to1

4and Z1 and Z2 are the atomic numbers of elementA and B respectively. Then relation

between Z1 and Z2 are given by(A)

2 12 1Z Z = (B) 2 12 1Z Z =

(C) 2

1

4Z

Z= (D) 1

2

4Z

Z=

26. In Youngs experiment, light of wave length 6000 is used to produce fringes of width 0.32mm. If the whole apparatus is dipped in a liquid of refractive index 1.6 then fringe width will be(A) 0.5 mm (B) 0.6 mm(C) 0.4 mm (D) 0.2 mm

27. A converging lens of focal length 30 cm and aconverging mirror of focal length 40 cm are placed withtheir principal axis at a distance of 40 cm from the lensan object is placed. It is found that final image is formedat focus of lens, then distance between lens and mirroris

/////

/

/

/

/

/

/////////////

S

Object

40cm(A) 160 cm (B) 120 cm(C) 200 cm (D) None of these

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9

28. The point masses m1 and m2 are placed at the twoends of a rigid massless rod of length l. The system isset into rotation with an angular velocity about anaxis which is at a distance x from the mass m1 andperpendicular to rod. The value ofxfor which the workdone in the process is minimum is

m1 m2

l

(A)2l (B) l

2

1

mm

(C)21

1

mm

m

+

l(D)

21

2

mm

m

+

l

29. A block of mass m is connected to two springs of spring constants 2k and 3krespectively, as shown in the diagram, with both the springs being vertical andfixed at their other ends. Both springs are initially unstretched and the mass m isgiven an initial velocity u in the downward direction. The block oscillates. Theamplitude of oscillation of the block is given by

(A)2mu mg

5K 5K+ (B)

mg

5K

2k

3k

m

(C)22mu mg

5K 5K

+

(D)2mu mg

5K 5K

30. In a resonance-column experiment to measure the velocity of sound, the first resonance isobtained at a length l1 and the second resonance at a length l2, (end correction is taken intoconsideration), then(A)

2 13l l>

(B)2 13l l=

(C)2 1

3l l< (D) may be any of the above depending on the frequency of the tuning fork used.

Rough work


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10

CChheemmiissttrryy PART II

SECTION A

Straight Objective Type

This section contains 30 multiple choice questions numbered 1 to 30. Each question has 4 choices (A),(B), (C) and (D), out of which ONLY ONE is correct.

1. Which of the following is the correct IUPAC name of the following compound

C

O

NH CH3Cl

(A) p-acetamido chlorocyclohexane (B) 4-chloro-N-methylcyclohexane carboxamide(C) N-methyl amido chlorocyclohexane (D) None of the above

2. Compare relative stability of the following resonating structure:

(p)

C

O

N

(q) (r)

C

O

N

C

O

N (A) p > q > r (B) q > p > r(C) q > r > p (D) p > r > q

3. How many distinct monochlorinated products (including stereoisomers) may be obtained whenthe alkane shown below is heated in presence of Cl2

(A) 4 (B) 5(C) 6 (D) 8

4. Which of the following statement is incorrect?(A) [NiCl4]

-2 is Ni(CO)4 both are tetrahedral in shape(B) [NiCl4]

-2 is paramagnetic while Ni(CO)4 is diamagnetic(C) [NiCl4]

-2 shows colour while Ni(CO)4 is colourless(D) [NiCl4]

-2 and Ni(CO)4 both contains nickel in +2 oxidation state

Rough Work


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11

5. The E2 product of the following reaction will be?

HBr

CH3

H

NaOH

(A)

HCH3OH

H

(B)

CH3

H

H

OH

(C)

CH3H

(D)

CH3HH

H

6.

O

CHO

COCl

C

O

RO( )A

( )D

( )C

( )B

Find out the reactivity order with LiAlH4 is:

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

7.HI

CH3 O14

( )base A

CH3

H

O

( )OH dilute B

A +

Product B in the above reaction is:(A)

CH3 H

O

14

(B)CH3

CH3 H

Br

C

O

14

(C)

CH3 O14

(D) 14 O

H

Rough Work


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12

8.OH Product of the reaction is

CH3 CH

Et

OAc ( )d dextrorotatory

(A) CH3 CH

Et

OH ( )d (B) CH3 CH

Et

OH ( )A

(C) CH3 CH

Et

OH ( )d & A (D) CH3 C

CH3

CH2

9. Which of the following product will be obtained in the given (consider minor product also)Backmann-type rearrangement?

O

O

Me

O

( )( )

2

5

i NH OH, H Cl

ii PCl ,Products are:

(i)

O

O

N

H

O

Me

(ii)

O

O

N

O

H

Me

(iii) O

ON

Me

(A) (i) and (ii) (B) (ii) and (iii)(C) (i) and (iii) (D) (i), (ii) and (iii)

10. Which of the following will react fastest with sodium?(A)

CH2OH

(B)CH2OH

(C)CH2OH

O

(D) (CH3)3C OH

Rough Work


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13

11. Arrange decreasing order of reactivity of given compounds with NBS (N-Bromosuccinimide)(I) C6H5 CH3 (II) C6H5 CH2 CH2 CH3(III) C6H5 CH2 CH = CH2 (IV) 6 5 2

|

3CH

C H CH CH CH =

Select the correct answer from the codes given below codes:(A) IV, III, I & II (B) IV, III, II & I

(C) I, II, III & IV (D) I, III, II & IV

12. An excited hydrogen atoms returns to the ground state. The wavelength of emitted photon is .The principal quantum number of the excited state will be:

(A)1/2

R

R 1

(B)1/2

R 1

R

+

(C) ( )1/2

R R 1 + (D) ( )

1/2

1

R R 1

+

13. Binding energy per nucleon versus mass number for w, x, y, z are indicated on the curve:

Mass number

5.0

7.5

8.0

8.5

z

y

x

w

Binding energyper nucleon(MeV)

The process that would release energy is:(A) y 2z (B) w x + z(C) w 2y (D) x y + z

14. Figure shows two spherical containers P and Q connected by a tap T. P contains an ideal gas atpressure 5 105 N/m2 and temperature 300 K. Q contains same gas at pressure 2 105 N/m2and temperature 400 K. If the tap is opened the final pressure becomes m 105 N/m2. What isthe value of m? The volume of Q is four time the volume of P:

PQ

T

(A) 1.4 (B) 2.4(C) 1.8 (D) 2.8

15. It is believed that non Stoichiometric compound Fe0.93O formed by dopping of Fe3+ ions in FeO

crystal by replacement of Fe2+. The total no. of cationic vacancies in 0.1 mole of Fe0.93

O are:(A) 0.07 moles (B) 0.007 moles(C) 0.021 moles (D) 0.014 moles

Rough Work


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14

16. Insulin (C6H10O5)n dissolved in a medium shows osmotic pressure at C gm/cm3 concentration

and 300 K temperature. The slope of against C is 4.1 10-3. Molecular mass of insulin is(A) 3 103 (B) 6 106(C) 3 106 (D) 6 103

17. Calculate the cell potential of the following cell:

Pt(s) | H2(g) (0.1 bar) | BOH (0.1 Meq.) || HA(0.1 M) | H2(g) (1 bar) | Pt.Given: Ka (HA) = 10-7

Kb (BOH) = 10-5

(A) 0.39 V (B) 0.93 V(C) 0.36 V (D) 0.63 V

18. According to VSEPR theory, the most stable arrangement is(A)

X

X

(B)X

X

(C)

X

X

(D) X

X

19. ( ) ( ) ( ) ( ) ( )32

2 3 2 3 2AgBr s 2S O aq. Ag S O aq. Br aq.

+ +ZZZXYZZZ

Given: ( ) ( )13 13sp f 2 3K AgBr 5 10 ; K Ag S O 5 10= =

What is the molar solubility of AgBr in 0.1 M Na2S2O3?(A) 0.5 M (B) 0.045 M(C) 0.45 M (D) None of these

20. The heat liberated when 1.89 g of benzoic acid is burnt in a bomb calorimeter at 25oC, increase intemperature of 18.94 g water in calorimeter is 0.632oC. If the specific heat of water is at 25oC is0.998 cal/g deg. The value of heat of combustion of benzoic acid is(A) 881.1 k cal (B) 771.4 k cal(C) 981.1 k cal (D) 871.2 k cal

21. On heating a mixture of SO2Cl2 and CO, two equilibria are simultaneously established:

( ) ( ) ( )2 2 2 2SO Cl g SO g Cl g+ZZZXYZZZ

( ) ( ) ( )2 2CO g Cl g COCl g+ ZZZXYZZZ

On adding more SO2 at equilibrium what will happen?(A) Amount of CO will decrease(B) Amount of SO2Cl2 and COCl2 will increase(C) Amount of CO will remain unaffected(D) Amount of SO2Cl2 and CO will increase

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15

22. The number of isomers possible for disubstituted borazine B3N3H4X2 is(A) 3 (B) 4(C) 6 (D) 5

23. 10 g of bleaching powder on reaction with KI required 50 ml of 2 N hypo solution. Thuspercentage of bleaching powder is:(A) 100 (B) 80(C) 63.5 (D) 35.5

24. Which of the following statement is incorrect:(A) ICl is a good conductor of electricity in fused state(B) Cl2O7 is an anhydride of perchloric acid(C) Melting and boiling points of HBr is more than HCl(D) F2 form stable oxoacids

25. Functionally active form of vitamin D is:(A) Cholecalciferol (B) dehydro cholesterol(C) Ergocalciferol (D) Calcitriol

26. A complex is prepared by mixing CoCl3 and NH3 0.1 M solution of the complex was found to

freeze at 0.372oC. The formula of the complex is (Kf= 1.86oC/m for H2O)(A) [Co(NH3)6]Cl3 (B) [Co(NH3)4Cl2]Cl(C) [Co(NH3)5Cl]Cl2 (D) [Co(NH3)3Cl3]

Rough Work


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16

27. ( ) 4MnO /HA colourless salt A delocalisation of permegnate solution occurs +

( )

2H OHeat

gases

x y z, z 'B' + +

Gas y + B MilkinessGas burns with blue flame. Mark the correct choice.

A x y z B(A) CaCO3 CO CO2 CaO Ca(OH)2(B) CaC2O4 CO CO2 CaO Ca(OH)2(C) CaC2O4 CO2 CO CaO Ca(OH)2(D) CaOCl2 Cl2 O2 CaO Ca(OH)2

28.

CH2CH2NMe3Cl

CH3

O

Wolff ishnerreduction

Product (P)

The structure of (P) is

(A)

CH2CH2NMe3Cl

CH3

(B)CH3

O

CH2

(C)

CH3

CH2

(D)CH3

O

CH2

29. Arrange Ce+3, La+3, Pm+3 and yb+3 in increasing order of their size

(A) yb+3 < Pm+3 < Ce+3 < La+3 (B) Ce+3 < yb+3 < Pm+3 < La+3(C) yb+3 < Pm+3 < La+3 < Ce+3 (D) Pm+3 < La+3 < Ce+3 < yb+3

30. When an impurity in metal has greater affinity for oxygen and is more easily oxidized the metalitself then the metal is refined by:(A) Cupellation (B) Zone refining(C) Poling (D) Electrolytic process

Rough Work


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17

MMaatthheemmaattiiccss PART III

SECTION A

Straight Objective Type

This section contains 30 multiple choice questions numbered 1 to 30. Each question has 4 choices (A),(B), (C) and (D), out of which ONLY ONE is correct.

1. In a very particular language code for a true statement is 2 and for a false statement is 1.(i) Image of the point (2, 3) in the line y + x = 0 is (3, 2)(ii) Maximum distance between the two points lying on the two given circles

x2 + y2 + 2x + 4y + 4 = 0 and 2x2 + 2y2 20x 24y + 59 = 0 is 10(iii) No tangent can be drawn from the (3, 2) to the ellipse 9x2 + 16y2 = 144(iv) Total four circles can be drawn which touch all the sides of a triangle formed by x = 0, y = 0

and 3x + 4y = 42If codes of the above statements are written in the form of a natural number in the sameorder then that number is

(A) 2122 (B) 2112(C) 1221 (D) 1212

2. A function f(x) is given by ( )( ) ( ) ( )

( ) ( ) ( )

2011 4011 60111 1 1

2011 4011 60111 1 1

1 sin x 1 cos x 1 tan xf x

1 cosec x 1 sec x 1 cot x

+ + +=

+ + +

then range of f(x) lies in the internal(A) (0, 26011) (B) [22011, 26011](C) (26011, 28011) (D) [210, 28011]

3. If 2c is the shortest distance between the linesx z

1n

=A

, y = 0 andy z

1m n

+ = , x = 0 then which

of the following is true

(A)2 2 2 21 1 1 1

m n c+ =

A(B)

2 2 2 21 1 1 1

m n c+ + =

A

(C)2

1 1 1 1

m mn n c+ + =

A A(D) 2 2 2 2m n c+ + =A

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18

4. The exhaustive set of conditions on a and b such that the ellipse2 2

2 2

x y1

a b+ = and the hyperbola

2 2x y1

25 16 = have exactly four tangents in common are

(A) a (5, 5) {0}; b R {0}; a b (B) a (5, 5) {0}; b (4, 4) {0}

(C) b (4, 4) {0}; a R {0}; a b (D) a (5, 5); b (4, 4) {0}; a b

5. A system of curves is given by

22 yx

2521

2x y = 82

y 3x

2

. Find the range of values of and such

that the points (1, ) and (, 2) lies in the largest region enclosed by the above system of curves

(A) ( )4 5, 1 and (1, 2) (B) ( )4 6, 1 and (1, 2)

(C) ( )4 6, 1 and (1, 2) (D) ( )4 6, 1 and (1, 2)

6. In how many ways Ram can distribute 40 applies in his six children named A, B, C, D, E and Fsuch that A gets two more than B, C gets 3 more than F and D gets five less than E and any onemust have atleast one fruit(A) 101 (B) 91(C) 96 (D) 136

7. A book is having 500 pages printed back to back numbered from 1 to 1000. The number of sideswhere digit 3 is printed. Exactly once, exactly twice and thrice is respectively(A) 228, 29, 1 (B) 243, 27, 1(C) 233, 28, 1 (D) 300, 26, 1

8. Number of planes containing the two family of linesx 1 y 2 z 1

2 0 k

+= = and

x 3 y 1 z k

1 k 2

+ = =

(A) no such plane (B) exactly one plane(C) exactly two planes (D) exactly three planes

Rough work


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19

9. If y = (sin x + cosec x)2 + (cos x + sec x)2 + (tan x + cot x)2

where x R {x ; x = n, (2n + 1)/2 n I} and minimum value of y = p thenp

3

is where [.]

denotes the greatest function(A) 4 (B) 6(C) 7 (D) 8

10. Let C1 and C2 be two curves on the complex plane defined as

C1 : ( )z z 2 z 1+ = C2 : arg (z + 1 + i) = Where (0, ) such that the curves C1 and C2 touches each other at P(z0) then the value of|z0|

2 is(A) 1 (B) 2(C) 3 (D) 4

11. Roots of a quadratic equation x2 + 5x + 3 = 0 are 4cos2 + a, and 4sin2 + a. Another quadraticequation is given as x2 + px + q = 0 where p, q N and p, q [1, 10]. If roots of second quadraticequation are real then the probability that they are 4cos4 + b and 4sin4 + b is

(A)1

16 (B)3

32

(C)1

32(D)

5

100

12. Let a i 2 j 3k= + G

, b 2i j k= + G

then the vector xG

satisfying a x a b = and a x 0 = is oflength

(A) 10 (B) 5

(C)5

2(D)

5

4

13. Number of integral values of k such that the equation cos1 x + cot1 x = k possesses solution is(A) 5 (B) 10(C) 2 (D) 8

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20

14. If we know that sin A =12

13 and sin B =

15

17but the actual values of A and B are not given, then

how many different values of cos(A B) are possible depending upon the actual values of A andB(A) 1 (B) 2(C) 3 (D) 4

15. For a triangle if inradius is six units and the distance of the vertices of a triangle from the nearest

point of contact of the incircle with the sides be p.q and r respectively thenpqr

p q r+ +is

(A) 36 (B) 6(C) 18 (D) 216

16. If f(x) = 3x9 2x4 + 2x3 3x2 + x + cos x + 5 and g(x) = f1(x) then find the value of g(6)

(A)1

2(B) 1

(C) 2 (D) 4

17. Let ( ) ( )x

0

f x t t dt= + and the mean value theorem says that there must be atleast one c (4, 9)

such that f(c) is equal to the average slope of f(x) on [4, 9] then for this number c, c c+ isequal to

(A)123

30(B)

119

30

(C)63

8(D)

111

35

18. For the following system of equations

2 4 1 x y 9

2 2 1 y = x 5

2 1 0 z 4z 3

+

find the value of

x + y + z = ?(A) 6 (B) 5

(C)9

2(D) 2

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21

19. Let n n n n n nn 0 1 1 2 n 1 nS C C C C ..... C C= + + + where n N ifn 1

n

S 15

S 4+ = the sum of all possible

values of n is(A) 3 (B) 6(C) 7 (D) 5

20. If z be a complex number such that |z 2| + |z 4| = 5 where R+ always represents anellipse then the number of integral values of is(A) 2 (B) 3(C) 4 (D) 5

21. Let z be a nonzero complex number and w ( 1) be a nonreal can be root of unity. If the area oftriangle formed by A(Z), B(wz) and C(w2z) be 48 3 then |z| is(A) 4 (B) 8

(C) 16 (D) 8 3

22. If the coefficient of x7 and x8 in the expansion ofn

x2

3

+

are equal the value of n is

(A) 15 (B) 45(C) 35 (D) 55

23. Let A(z1), B(z2) and C(z3) be the vertices of a triangle ABC such that z3 + iwz2 = (1 + iw)z1 wherew is the cube root of unity not 1, then ABC is

(A) isosceles triangle with A6

= (B) isosceles triangle with A

3

=

(C) right angle isosceles (D) equilateral

24. Givenn 10

nr

r 0

r 3 7.2 2C

r 1 10=

+ = + then value of n is

(A) 3 (B) 6(C) 8 (D) 9

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25. Consider the triangle with sides as a = n + 1, b = n + 2 and c = n with tan C =4

3and n N then

area ABC is(A) 84 (B) 72(C) 64 (D) 50

26. Number of solutions of the equation 2 3 1 3cos x sinx 12 4

++ = +

in the internal [, ] is

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

27. Three vertices of a triangle ABC are given as A(2, 1), B(7, 1), C(3, 4) images of this triangle aretaken in xaxis, yaxis and the line y = x. Now G1, G2 and G3 are the centroids of the three imagetriangles then the area of the G1G2G3 is(A) 10 (B) 11(C) 20 (D) 13

28. For which of the following functionsx 0lim f(x)

exists

(A) ( ){ }

xf x

sinx= (B) ( )

{ }xf x

sinx=

(C) ( )[ ]

xf x

sinx= (D) ( )

[ ]xf x

sinx=

29. If the equation 3 2x bx cx 1 0,+ + + = ( )b c< , has only one real root . Then the value of

( ) ( )1 1 22tan cosec tan 2sin sec + , is

(A) (B)2

(C)

2

(D)

30. Square ABCD is inscribed in a circle point E is on the circle. If AB = 8, then the value ofAE2 + BE2 + CE2 + DE2 is(A) 196 (B) 256(C) 144 (D) 364

Rough work

concept recap test mains 6

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