jp-jf_jee main (mt-1)_26-12-2012_code-0

INSTRUCTIONSA. General :

1. This Question Paper contains 87 questions.2. The question paper CODE is printed on the right hand top corner on this sheet of this booklet.3. No additional sheets will be provided for rough work.4. Blank paper, clipboard, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets

in any form are not allowed.5. The answer sheet, a machine-gradable Objective Response Sheet (ORS), is provided separately.6. Do not Tamper / mutilate the ORS or this booklet.7. Do not break the seals of the question-paper booklet before instructed to do so by the invigilators.8. Write your Name, Roll No. and Sign in the space provide on the back page of this booklet.

B. Filling the Top-half of the ORS :Use only Black ball point pen only for filling the ORS. Do not use Gel / Ink / Felt pen as it might smudge the

ORS.9. Write your Roll no. in the boxes given at the top left corner of your ORS with black ball point pen. Also, darken

the corresponding bubbles with Black ball point pen only. Also fill your roll no on the back side of your ORSin the space provided (if the ORS is both side printed).

10. Fill your Paper Code as mentioned on the Test Paper and darken the corresponding bubble with Black ballpoint pen.

11. If student does not fill his/her roll no. and paper code correctly and properly, then his/her marks will not bedisplayed and 5 marks will be deducted (paper wise) from the total.

12. Since it is not possible to erase and correct pen filled bubble, you are advised to be extremely careful whiledarken the bubble corresponding to your answer.

13. Neither try to erase / rub / scratch the option nor make the Cross (X) mark on the option once filled. Do notscribble, smudge, cut, tear, or wrinkle the ORS. Do not put any stray marks or whitener anywhere on theORS.

14. If there is any discrepancy between the written data and the bubbled data in your ORS, the bubbled data willbe taken as final.

C. Question paper format and Marking scheme :15. The question paper consists of 3 parts (Physics, Chemistry & Mathematics). Each part consists of Four

Sections.16. For each question in SectionI, you will be awarded 3 marks if you darken the bubble corresponding to the

correct choice for the answer and zero mark if no bubbled is darkened. In case of bubbling of incorrectanswer, minus one (1) mark will be awarded.

17. For each question in SectionII, you will be awarded 4 marks if you darken the bubble(s) correspondingto the correct choice for the answer and zero mark if no bubbled is darkened. There is no negativemarking for incorrect answer(s) in this section.

18. For each question in SectionIII, you will be awarded 4 marks if you darken the bubble(s) correspondingto the correct choice for the answer and zero mark if no bubbled is darkened. There is no negativemarking for incorrect answer(s) in this section.

19. For each question in SectionIV, you will be awarded 3 marks if you darken the bubble(s) correspondingto the correct choice for the answer and zero mark if no bubbled is darkened. There is no negativemarking for incorrect answer(s) in this section.

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Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

Date : 26-12-2012 Duration : 3 Hours Max. Marks : 300

CODE 0MAJOR TEST-1 (MT-1) (JEE MAIN)

TARGET : JEE (IITs) 2013 COURSE : VIJETA (JP) & VISHWAAS (JF)

RESONANCE JPJEEMAINSXII261212C0-1

(SPACE FOR ROUGH WORK)

PART-A

SECTION - I

Straight Objective TypeThis section contains 12 mult iple choicequestions. Each question has choices (1), (2),(3) and (4) out of which ONLY ONE is correct.

1. Area of each conducting plates 1, 2, 3, 4, 5 and 6 isA. The system is kept in air. Then the capacitancebetween A and B is : (1 & 4, 2 & 5 and 3 & 6 are pairof parallel plates).

(1) dA3 0

(2) 32

dA0

(3) 23

dA0

(4) d3A0

2. The current through 15 V battery is :

(1) 1A(2) 2A(3) 3A(4) 4A

3. Two circular plates of radius R are kept at distanceh to make a parallel plate capacitor as shown infigure. Then the capacitance of this capacitor is.

(1) hR20

(2) hR20

(3) h

R22 20

(4) None of these



4. The direction of force on electron at point O due todipole P is.

(1)

(2)

(3)

(4)

5. The equalent resistance between A and B is.

(1) R (2) 2R

(3) 2R (4) None of these

6. A plane mirror is moving in a circle in front of astationary point object O as shown in fig. Then pathof image of object is.

(1) circle (2) straight line(3) ellipse (4) parabolic

7. A beam of electrons striking a copper targetproduces X-rays.Its spectrum is as shown. Keepingthe voltage same if the copper target is replacedwith a different metal, the cut-off wavelength andcharacteristic lines of the new spectrum will changein comparision with old as :

(1) Cut-off wavelength will remain unchanged whilecharacteristic lines will be different.

(2) Both cut-off wavelength and characteristic lineswill remain unchanged.

(3) Both cut-off wavelength and characteristic lineswill be different.

(4) Cut-off wavelength will be different whilecharacteristic lines will remain unchanged.



8. Consider the circuit containing resistors and anideal battery. Potential difference V

a Vb is equal

to (where points 'a' and 'b' are as shown)

10

11

205 15

32V

a b

(1) 5V (2) 10 V(3) 12.5 V (4) 5 V

9. Two large oppositely charged insulated plates havea uniform electric field between them as shown.The distance between the plates is increased by asmall amount. Which of the following statementsis/are correct.

Statement(i) The electric field strength decreases.

Statement(ii) The electrostatic force of attractionbetween the plates increases.

Statement(iii) The potential difference between theplates increases.

(1) (i) only (2) (ii) only(3) (iii) only (4) (i) and (iii) only

10. In a series LR circuit, the voltage drop acrossinductor is 8 volt and across resistor is 6 volt. Thenvoltage applied and power factor of circuitrespectively are:

(1) 14 V, 0.8 (2) 10 V, 0.8(3) 10 V, 0.6 (4) 14 V, 0.6

11. A current i in a circular loop of radius b producesa magnetic field. At a fixed point far from the loop(on its axis) the magnetic field is proportional towhich of the following combinations of i and b ?

(1) ib(2) ib2(3) i2b(4) i/b2

12. A negative charge is given to a loop and the loop isrotated in the plane of paper about its centre asshown. The magnetic field produced by the ringaffects a small magnet placed above the ring inthe same plane of paper.

(1) the magnet does not rotate(2) the magnet rotates clockwise as seen byobserver from below

(3) the magnet rotates anti-clockwise as seen frombelow

(4) none of the above



SECTION - IIStraight Objective Type

This section contains 5 multiple choice questions.Each question has choices (1), (2), (3), (4) and(5) out of which ONLY ONE is correct.

13. Figure shows a hemisphere of charge Q and radiusR and a sphere of charge 2Q and radius R. Thetotal potential energy of hemisphere is UH and thatthe sphere is US. Then.

(1) 2UH = US (2) 2UH < US(3) 2UH > US (4) UH = US(5) Data insefficient

14. Refractive indices of 2 different media withseparating boundary at the diagonal of rectangularglass slab are shown. Total angle of deviation ofthe ray as shown in the figure, when it emerges inair is :

(1) 120 (2) 90(3) 60 (4) 45(5) 30

15. A negative test charge is moving near a longstraight current carrying wire . A force will act onthe test charge in a direction parallel to thedirection of the current, if the motion of the chargeis in a direction:

(1) towards wire(2) the same as that of current(3) opposite to that of current(4) perpendicular to both the direction of currentand the direction towards wire.

(5) None of these

16. In the circuit shown, cells are of equal emf E but ofdifferent internal resistances r1 = 6 and r2 = 4 .Reading of the ideal voltmeter connected acrosscell 1 is zero. Value of the external resistance R inohm is equal to-

Cell1

E E

Cell2

r1

R

r2

V

(1) 2 (2) 2.4(3) 10 (4) 24(5) zero



17. The negatively and uniformly chargednonconducting disc as shown, is rotatedclockwise. The direction of the magnetic field atpoint A in the plane of the disc is :

(1) into the page (2) out of the page(3) up (4) down(5) zero

SECTION - III

Multiple Correct Answers TypeThis sect ion contains 8 multiple correctanswer(s) type questions. Each question has 4choices (1), (2), (3) and (4), out of which ONEOR MORE is/are correct.

18. Path of charged particle, if only magnetic force actson it can be.

(1) circle(2) helix with constant pitch(3) helix with variable pitch(4) cycloid

19. Which of the following converges themonochromatic parallel beam of light incidenting onit. (all are kept in air)

(1) (2)

(3) (4) None of these

20. Figure shows a LCR 'circuit connected with a dcbattery of emf and internal resistance R. After along time (initially the capacitor was uncharged):

(1) Current through the inductor is R8

(2) Charge stored in the capacitor is 4C

(3) Charge stored in the capacitor is 2C

(4) Potential difference across the terminals of

battery is 4



21. Which of the following statements is/are correct foran x-ray tube ?

(1) On increasing potential difference betweenfilament and target, photon flux of x-rays increases

(2) On increasing potential difference betweenfilament and target, frequency of x-rays increases

(3) On increasing filament current, cutoffwavelength increases

(4) On increasing filament current intensity of x-rays increases

22. In standard Young double slit experiment, visiblelight ( ( 390 nm, 700 nm)) is used in both theslits. Distance between the slits is 2 mm, anddistance of screen from the slits is 1 m. A thin glassslab ( = 1.5) of thickness 6 m is placed in front ofslit S2. Light of which wavelength (s) is missing at

point P, which is directly in front of slit S2. (Neglectdispersion of light)

(1) 400 nm (2) 500 nm

(3) 32000

nm (4) 31600

nm

23. In the circuit shown the capacitor and inductor do

not have energy initially. Then

(1) the current flowing through the battery at t = 0is /2R

(2) The current flowing through the battery at t = 0is 2/3R

(3) The current flowing through the battery at t = is 2/5R

(4) The current flowing through the battery at t = is /2R

24. Pick up the correct statements :

(1) The changing (with time) magnetic field neednot be in existence at the location of induced electricfield.

(2) A uniform magnetic field increasing at constantrate, induces an electric field which is constant andnon conservative.

(3) Non zero force exerted by uniform and constantmagnetic field on a moving charged particle doesno work but always changes momentum of theparticle.

(4) All the above statements are wrong.



25. In a co-ordinate system shown, non-uniform

magnetic induction B = k|x|B0 exist, where B0 is

a positive constant, x- is x-coordinate of point in

shown space and k is unit vector in positive z-

direction. A square coil placed in this system isrotated with uniform angular speed about y axis.The coil may be placed in four ways as shown. IfeI, eII eIII and eIV are the rms emfs induced in thesefour cases, which of the following will be correct.

(1) eI = eII (2) eIII < eI(3) eIII > eIV (4) eII > eI

SECTION - IV

Reasoning TypeThis sect ion contains 4 reasoning typequestions. Each question has 4 choices (1), (2),(3) and (4), out of which ONLY ONE is correct.

26. STATEMENT-1 : For the situation shown in thefigure two monochromatic identical coherent lightsources produce interference pattern on the screen.The intensity of minima nearest to S1 is not exactlyzero.

STATEMENT-2 : Minimum intensity is zero wheninterfering waves have same intensity at the locationof super position.

(1) Statement-1 is True, Statement-2 is True;Statement-2 is a correct explanation forStatement-1.

(2) Statement-1 is True, Statement-2 is True;Statement-2 is NOT a correct explanation forStatement-1

(3) Statement-1 is True, Statement-2 is False(4) Statement-1 is False, Statement-2 is True



27. STATEMENT-1 : In alpha decay of differentradioactive nuclides, energies of alpha particles hasbeen compared. It is found that as energy of alphaparticle increases the half life of the decaydecreases.

STATEMENT-2 : More is the energy in any decayprocess, more is the probability of decaying thenuclide which leads to faster rate of decay.




28. STATEMENT-1 : Although the surface of goggleslenses are curved, it does not have any opticalpower.

STATEMENT-2 : In case of goggles both the curvedsurfaces have equal radii of curvature and havecentre of curvature same side.




29. STATEMENT-1 : Heavy nuclides tend to havemore number of neutrons than protons.

STATEMENT-2 : In heavy nuclei, as there iscoloumbic repulsion between protons, so excessof neutrons are preferable.

(1) Statement-1 is True, Statement-2 is True;Statement-2 is a correct explanation forStatement-1


(3) Statement-1 is True, Statement-2 is False(4) Statement-1 is False, Statement-2 is True.



30. A hydrogen electrode is immersed in a solutionwith pH = 0 (HCl). By how much will the potential(reduction) change if an equivalent amount of NaOHis added to the solution.

(Take 2Hp = 1 atm) T = 298 K.

(1) increase by 0.41 V

(2) increase by 59 mV

(3) decrease by 0.41 V

(4) decrease by 59 mV

31. Equal volume of two solution having pH = 2 andpH = 10 are mixed together at 90C. Then pH ofresulting solution is : (Take Kw at 90C = 1012)

(1) 2 + log 2

(2) 10 log 2

(3) 7

(4) 6

32. The incorrect statement is :

(1) Vapour pressure of a liquid always increasesby increasing temperature.

(2) Vapour pressure only depends on temperatureand not on the nature of substance.

(3) Vapour pressure does not depend on thequantity of the liquid taken and the surfacearea of the liquid.

(4) Vapour pressure is not a colligative property& is independent of the concentration of theliquid.

33. When borax is dissolved in water :

(1) B(OH)3 is formed only

(2) [B(OH)4] is formed only

(3) both B(OH)3 and [B(OH)4] are formed

(4) [B3O3(OH)4] is formed only

PART- BAtomic masses : [H = 1, D = 2, Li = 7, 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, Cu = 63.5,Zn = 65, As = 75, Br = 80, Ag = 108, I = 127, Ba = 137, Hg = 200, Pb = 207]

SECTION - IStraight Objective Type

This section contains 12 questions. Each question has 4 choices (1), (2), (3) and (4) for its answer, out of whichONLY ONE is correct.



34. Which one of the following statements is correct:

(1) Brownian movement is more pronounced forsmaller particles than for bigger ones

(2) Sols of metal sulphides are lyophilic

(3) Schulze-Hardy law states, the bigger the sizeof the ion, the greater is its coagulating power

(4) None of these

35. Sodium nitroprusside when added to an alkalinesolution of sulphide ions produces purplecolouration due to the formation of :

(1) Na[Fe(H2O)5NOS]

(2) Na4[Fe(CN)5NOS]

(3) Na3[Fe(CN)5NOS]

(4) Na4[Fe(H2O5)NOS)]

36. Which of the following are bidentate monoanionligands ?

(1) Acetylacetonato

(2) Oxalato ion

(3) Dimethylglyoximato

Select the correct answer using the codes givenbelow :

(1) 1 only

(2) 1 and 3 only

(3) 3 only

(4) 2 and 3 only

37. Ammonia gas is not prepared by :

(1) reduction of sodium nitrite or sodium nitrateby the reaction of zinc dust and sodiumhydroxide.

(2) hydrolysis of calcium cyanamide.

(3) heating ammonium chloride with slaked lime.

(4) heating of (NH4)2Cr2O7

38. Write the basicity order of the following :

CH3 CH2 NH2 (CH3)2NH 23 NHCCH||O

(I) (II) (III) (IV)

(1) (II) > (I) > (III) > (IV)

(2) (I) > (III) > (II) > (IV)

(3) (III) > (I) > (II) > (IV)

(4) (I) > (II) > (III) > (IV)



39.

,NaOH

%50

/H

product

Product is :

(1)

(2)

(3)

(4)

40. /NaOH ; the major product is

(1)

(2)

(3)

(4)

41. A neutral type amino acid migrates at anode at

(1) pH > pI

(2) pH < pI

(3) pH = pI

(4) it depends on structure of amino acid



SECTION - II

Straight Objective TypeThis section contains 5 questions. Each questionhas 5 choices (1), (2), (3), (4) and (5) for its answer,out of which ONLY ONE is correct.

42. Among the following, the species that is bothparamagnetic and coloured is :

(1) [MnO4]2

(2) [TiCl6]2

(3) [VO4]3

(4) CrO2Cl2(5) [MnO4]

43. Which one of the following statements isincorrect?

(1) In the aluminothermite process, aluminiumacts as reducing agent.

(2) Lead is extracted form its chief ore by bothcarbon reduction and self reduction.

(3) Zinc is extracted from its chief ore by carbonreduction.

(4) Extraction of gold involves the leaching of orewith cyanide solution followed by reductionwith zinc.

(5) In Hall-Heroult process, the electrolyte usedis a molten mixture of alumina, sodiumhydroxide and cryolite.

44. Ionisation constant of each HA (weak acid) andBOH (weak base) are 3.0 x 107 each at 298K.The percentage degree of hydrolysis of BA at thedilution of 10L is :

(1) 25

(2) 50

(3) 75

(4) 40

(5) Data is insufficient

45. Identify final product in the following :

.)eq2(H/HOBr

(1) C CHBr2

||O

(2) C CH Br2

||O

(3) (4) CH CHO

Br

(5)



46. The following compound on hydrolysis will give :

(1) A pair of anomers

(2) A pair of enantiomeris

(3) A pair of epimers

(4) A pair of chain isomers

(5) A pair of molecules having common tautomer

SECTION - III

Multiple Correct Answer Type

This section contains 8 questions. Each questionhas 4 choices (1), (2), (3) and (4) for its answer,out of which ONE OR MORE is/are correct.

47. In the fluorite structure if the radius ratio is

1

23

,

how many ions does each cation touch ?

(1) 4 anions

(2) 12 cations

(3) 8 anions

(4) No cations

48. A solution containing Br ions is treated with eachof the following. Which of these will not liberatebromine gas (in acidic medium) ?

(1) Cl2(2) HI

(3) I2(4) SO3

49. The ozone layer in the earth's upper atmosphereis important in shielding the earth from veryharmful ultraviolet radiation. The ozone, O3,decomposes according to the equation 2O3(g) 3O2(g). The mechanism of the reaction is thoughtto proceed through an initial fast, reversible stepand then a slow second step.

Step 1: Fast, reversible O3(g) O2(g) +O(g)

Step 2: Slow O3(g) + O(g) 2O2(g)

The which of the following is correct ?

(1) Step 2 is rate determining step

(2) The rate expression for step 2 is ddt O[ ]3= k[O3][O]

(3) For Step 1 , molecularity is 1

(4) For Step 2 , molecularity is 2



50. Which of the following complexes is(are)paramagnetic ?

(1) [Mn(CN6)]3

(2) [Cr(NH3)6]3+

(3) [Fe(CN)6]4

(4) [Co(CN)6]3

51. Consider the reactions shown below ;

Which of the following statement (s) is/are correct?

(1) [X] is a yellow coloured precipitate.

(2) [X] is soluble in ammonia solution.

(3) [Y] gives green coloured solution with excessof sodium hydroxide solution.

(4) The conversion of Cr2O72 to [Y] is an redoxreaction.

52. Identify a reagent from the following list which caneasily distinguish between 1-butyne and 2-butyne.

(1) Na metal

(2) H2, Lindlar catalyst

(3) dilute H2SO4, HgSO4

(4) ammonical Cu2Cl2 solution

53. The correct order of leaving group ability is/are :

(1) >

(2) >

(3) >

(4) >

54. RX + Mg Ether RMgX OHCH3 n-Butane

What can be R in the above reaction sequence ?

(1) n-Butyl

(2) sec-Butyl

(3) n-Propyl

(4) Isopropyl



SECTION - IV

Reasoning TypeThis section contains 4 reasoning type questions.Each question has 4 choices (1), (2), (3) and(4), out of which ONLY ONE is correct.

55. Statement-1 : In water, orthoboric acid behavesas a weak monobasic Lewis acid.

Statement-2 : In water, orthoboric acid acts as aproton donor.



(3) Statement-1 is True, Statement-2 is False

(4) Statement-1 is False, Statement-2 is True

56. Statement-1 : On increasing dilution, the specificconductance keep on increasing.

Statement-2 : On increasing dilution, degree ofionization of weak electrolyte increases andmobility of ions also increases.


(2) Statement-1 is True, Statement-2 is True;Statement-2 is NOT a correct explanation forStatement-1.

(3) Statement-1 is True, Statement-2 is False.

(4) Statement-1 is False, Statement-2 is True.

57. Statement : 1 Enantiomers arenonsuperimposable on each other.

Statement : 2 All isomers are nonidenticalcompounds.



(3) Statement-1 is True, Statement-2 is False

(4) Statement-1 is False, Statement-2 is True

58. Statement 1 : The reactivity order is :

for Br2/KOH reagent

Statement 2 : Presence of OMe groupincreases rate of Hofmann bromamide reactionby increasing electron density in migratingphenyl group.


(2) Statement-1 is True, Statement-2 is True;Statement-2 is NOT a correct explanation forStatement-1.

(3) Statement-1 is True, Statement-2 is False.

(4) Statement-1 is False, Statement-2 is True.



PART- C

SECTION - IStraight Objective Type

This section contains 12 questions. Each questionhas 4 choices (1), (2), (3) and (4) for its answer, outof which ONLY ONE is correct.

59. The maximum value of f(x) = cosx on the set of realnumbers satisfying x4 + 36 13x2 is

(1) cos2 (2) cos3

(3) 1 (4) cos1

60.

4

222

2

)9x6x(n)xx1881(n)xx1881(n

dx =

(1) 2 (2) 1

(3) 2n21 (4) 3n2

1

61. If the determinant 11xcos1xsin

xcosx6cos2xsinxcos1x4cosx2cos3

34

22

3

expressed in terms of powers of cosx then the valueof constant term is

(1) 4 (2) 3

(3) 9 (4) 8

62. If nf x 4 x ,n N and rf 0 represents the rth

derivative of f(x) at x = 0, then the value of r

r 0

(f 0 )r!

is equal to

(1) 2n

(2) en

(3) 5n

(4) 4n

63. A person while dialing a telephone number, forgetsthe last three digits of the number but remembersthat exactly two of them are same. He dials thenumber randomly. The probability that he dialed thecorrect number, is equal to

(1) 1135

(2) 127

(3) 154

(4) 1270

64. If A,B,C are set then A (B C) is equal to(1) A (B C)(2) A B C(3) A (B C)

(4) none of these



65. If I = 1

0

2dxxcos then

(1) I

21

,

31

(2) I < 23

(3) I < cos1

(4) I

81

cos,1sin 2

66. If the mean of x in distribution

Variate X 1 2 3 4 5

Frequency of X 4 5 k 1 2

is 2.6, then the value of k is

(1) 8(2) 10(3) 12(4) 18

67. Let a relation R in the set N of natural numbers bedefined as (x, y) x2 4xy + 3y2 = 0 for allx, y N. The relation R is

(1) reflexive(2) symmetric(3) transitive(4) an equivalence relation.

68. Let p,q be statements. Negation of statementp ~ q, is

(1) ~ q p

(2) ~ p q

(3) p q

(4) p q

69. x im x

2

2

3xx3x5x

is equal to

(1) e4

(2) e2

(3) e3

(4) e

70. A curve passes through the point (2a, a) and issuch that sum of subtangent and abscissa isequal to a. Its equation is

(1) (x a) y2 = a3

(2) (x a)2 y = a3

(3) (x a) y = a2

(4) (x + a) y = a2



SECTION - IIStraight Objective Type

This section contains 5 questions. Each questionhas 5 choices (1), (2), (3), (4) and (5) for its answer,out of which ONLY ONE is correct.

71. If x1, x2, x3, x4 are the roots of the equation x4 x3sin 2

+ x2 cos2 x cos

sin

= 0, where

(0, ). Then

4

1iixtan

1 is equal to

(1) 2

(2) 2

+

(3)

(4)

(5) +

72. If a i 2 j k , b j k , then the point of

intersection of lines abar

and babr

is

(1) i j k

(2) i 3 j

(3) i j 2k

(4) 3i j k

(5) i j 2k

73. Let f(x) = 2

cosec1 21x

. Then

(1) 1x

lim f(x) = 0

(2) 1x

lim

f(x) = 2

(3) 3x

lim f(x) = 1

(4) 3x

lim

f(x) = 1

(5) 3x

lim

f(x) = 2

74. The contents of urn and are as follows,Urn : 4 white and 5 black ballsUrn : 3 white and 6 black balls

One urn is chosen at random and a ball is drawnand its colour is noted and replaced back to theurn. Again a ball is drawn from the same urn,colour is noted and replaced. The process isrepeated 4 times and as a result one ball of whitecolour and 3 of black colour are noted. Theprobability that the chosen urn was is

(1) 287125

(2) 12764

(3) 28725

(4) 19279

(5) 49250



75. Area of the region bounded by the curve y = x2 andy = sec1 [sin2x] (where [ . ] denotes the greatestinteger function) is

(1) 3

(2) 32

(3) 34

(4) 36

(5) 32

SECTION - IIIMultiple Correct Answer Type

This section contains 8 questions. Each questionhas 4 choices (1), (2), (3) and (4) for its answer, outof which ONE OR MORE is/are correct.

76. If f(x) is real valued continuous and differentiable

function satisfying (f(x))2 = x

022 ))t('f()t(f

dt + 2013

then which of following are possible.

(1) f(x) = 2013 ex

(2) f(x) = 2013 ex(3) f(x). f(x)= (f(x))2

(4) f(x) = 2013 + 2x

77. A normal is drawn at a point P(x, y) of a curve. Itmeets the x-axis and y-axis at points A and B

respectively such that OA2

+ OB3

= 1, O being

origin. Equation of such curve passing through point(1, 1) can be

(1) x2 + y2 4x 6y + 8 = 0

(2) x2 + y2 2x 3y + 3 = 0

(3) 2x2 + 2y2 x y 2 = 0

(4) x2 + y2 4x + 6y 4 = 0

78. If f(x) = x2, 1 x 4, g(x) = sec1x, x 1 then

(1) Domain of gof(x) is [1, 4] {1}

(2) Domain of gof(x) is [1, 4]

(3) Range of gof(x) is [0, sec1 16]

(4) Range of fog(x) is

4

,02

79. If f(x) = 0 for x < 0 and f(x) is differentiable at x = 0,then for x > 0, f(x) may be

(1) x2

(2) x

(3) sin x

(4) x3/2



80. If G is the centroid and O is the circumcentre of thetriangle with vertices (1, 2, 0), (0, 0, 2) and(2, 1, 1), then equation/s of line OG is/are

(1) x = y = z

(2) y = 1, z = 1

(3) 12x

= 12y

= 12z

(4) 11x

= 11y

= 11z

81. If p, q, r are any three statements and t is a tautologythen which of the following is/are CORRECT ?

(1) p (q r) = (p

q) (p

r)

(2) p (~ p) = t

(3) ~ (p q) = (~p) (~ q)

(4) ~ (p q) = (p ~ q) (~ p q)

82. If c is an arbitrary constant then solution ofdifferential equation x2dy y2dx xy2(x y) dy = 0can be

(1) c2y

yxxy

n2

(2) c2y

xyyx

n2

(3) cxye)yx( 2y2

(4) cxye)yx( 2y

2

83. Two equat ions 11 qn.r

and 22 qn.r

represent two perpendicular planes, where 1n

and 2n

are two unit vectors. One of these plane

is rotated through an angle 45 about line ofintersection of two given planes then equationof plane in new position can be

(1) 21 nn.r

= q1 q2

(2) 21 nn.r

= q1 + q2

(3) 21 nn.r

= q1 + q2

(4) 21 nn.r

= q1 q2

SECTION - IVReasoning Type

This section contains 4 reasoning type questions.Each question has 4 choices (1), (2), (3) and (4),out of which ONLY ONE is correct.

84. STATEMENT-1 : If A =

a000a000a

, then |adj A| = a6

and |adj (adj A) | = a9.STATEMENT-2 : Let A be a square matrix of order

n, then |adj A| = |A|n 1 and |adj (adj A)| = 2)1n(|A| (1) Statement-1 is True, Statement-2 is True;

Statement-2 is a correct explanation forStatement-1.





85. STATEMENT-1 : Number of solutions for the

equation 2x + 3x + 5x = 1001

is equal to one.

STATEMENT-2 : Let f(x) be a strictly increasingfunction and g(x) be a constant function. Thennumber of solutions for f(x) = g(x) is always equalto one.(1) Statement-1 is True, Statement-2 is True;

Statement-2 is a correct explanation forStatement-1.



86. Let c be arbitrary constantSTATEMENT-1 :

xcos1xsin1

ex dx = ex cot 2x

+ c

STATEMENT-2 :

))x(f)x(f(ex dx = ex f(x) + c




87. STATEMENT-1 : If c,b,a

are non coplanar unit

vectors equally inclined to one another at an angle , then there will exist three scalar p, q, r such that

ba

+ cb

= ap

+ bq

+ cr

.

STATEMENT-2 : ba

is a vector perpendicular to

plane containing a

and b

and cb

is a vector

perpendicular to plane containing b

and c

so

ba

+ cb

will be non-zero only if c,b,a

are

coplanar.




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