apt2_tes

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IMPORTANT INSTRUCTIONS

1. Immediately fill the particulars on this page of the Test Booklet with Blue / Black Ball Point Pen.Use of pencil is strictly prohibited.

2. The Test Booklet consists of100questions.

3. There are three parts in the question paper. The distribution of marks subjectwise in each part is as under for each correctresponse.

PART A PHYSICS (144 marks)Question No.1 to 18 & 25 to 30consist ofFOUR (4)marks and 19 to 24 consist ofEIGHT (8)marks for each correctresponse.

PART B CHEMISTRY (144 marks)Question No.31 to 54 consist ofFOUR (4) marks and Question No.55 to 60 consist ofEight (8) marks for each correctresponse.

PART C MATHEMATICS (144 marks)Question No.61 to 65, 67, 68 & 70 to 90 consist ofThree (3) marks, 92 to 100 consist ofFour (4) marks and66, 69, 91consist ofEIGHT (8) marks for each correct response.

4. Candidates will be awarded marks as stated above in Instructions No. 3 for correct response of each question. (one fourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total scorewill be made if no response is indicated for an item in the Answer sheet.

5. No candidate is allowed to carry any textual material, printed or written, bits of papers, paper, mobile phone, any electronicdevice, etc., except the Admit Card inside the examination hall/room.

6. Rough work is to be done on the space provided for this purpose in the Test Booklet only. This space is given at the bottomof each page.

7. On completion of the test, the candiate must hand over the Answer Sheet to the Invigilator on duty in the Room/Hall. However,the candidates are allowed to take away this Test Booklet with them.

8. Make sure that the CODE printed of the Answer Sheet is the same c as that on this booklet. In case of discrepancy, thecondidate should immediately report the matter to the Invigilator fo replacement of both the Test Booklet and the Answer Sheet.

9. Do not fold or make any stray marks on the Answer Sheet.

Date : 18-04-2011 Duration : 3 Hours Max. Marks : 432

AIEEE PREPARATORY TEST-2 (APT-2)TARGET : AIEEE 2011 0

CODE

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

D O N O T B R E A K T H E S E A L S W I T H O U T B E I N G

I N S T R U C T E D T O D O S O B

Y T H E I N V I G I L A T O R

Name of the Candidate Roll Number

I have read all the instructions and

shall abide by them.

-------------------------------- Signature of the Invigilator

I have verified all the information

filled in by the Candidate.

-------------------------------- Signature of the Candidate

CLASS - XII / XIII

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(SPACE FOR ROUGH WORK)

P RT

SECTION - IStraight Objective Type

This section contains 18 multiple choice questions. Each question has 4 choices (1), (2), (3) and (4) for itsanswer, out of which ONLY ONE is correct.

1. A convex lens forms a real image 9 cm long on a screen. Without altering the position of the object andthe screen, the lens is displaced and we get again a real image 4 cm long on the screen. Then the lengthof the object is-(1) 9 cm (2) 4 cm (3) 6 cm (4) 36 cm

2. As shown in the fig. the uniform magnetic field between the two identical plates is B. There is a holein the plate. If through this hole a particle of charge q, mass m and kinetic energy E enters themagnetic field, then the particle will not collide with the upper plate provided

B d

d v

(1)2mE

Bqd

! (2)2mE

Bqd

! (3)2mE

Bqd

" (4)2mE

Bqd

"

3. Copper and silver voltameters are connected in series. If 0.8 gm of copper is deposited in copper voltameter,then the amount of silver deposited in silver voltameter will be(Chemical equivalents of copper and silver are 32 and 108 respectively)(1) 0.27 kg (2) 2.7 kg (3) 27 gm (4) 2.7 gm


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4. Figure shows the intensity-wavelength relations of X-rays coming from two different Coolidge tubes.The solid curve represents the relation for the tube A in which the potential difference between thetarget and the filament is V A and the atomic number of the target material is Z A. These quantities are V Band Z B for the other tube. Then,

(1) VA > VB, ZA > Z B (2) VA > VB, ZA < Z B (3) VA < VB, ZA > Z B (4) VA < VB, ZA < Z B

5. The potential energy of a particle in a certain field is given by 2a b

Urr

# $ , where a and b are positiveconstants and r is the distance from the centre of the field. The distance of particle in the stable equilibriumposition is

(1)ab

(2)ab

$ (3)2ab

(4)2ab

$

6. A playground merry-go-round is at rest, pivoted about a frictionless axis. A child of mass m runs on theground along the path tangential to the rim with speed v and jumps on to merry-go-round. If R be theradius of merry-go-round and I is the moment of inertia, then the angular velocity of the merry-go-roundand the child is :

(1) 2mvR

mR I% (2)mvR

I(3)

2mR ImvR

%(4)

ImvR

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7. A microscope consists of an objective with a focal length 2 mm and an eye piece with a focal length 40 mm.The distance between the foci (which are between the lenses) of objective and eyepiece is 18 cm. The totalmagnification of the microscope is (Consider normal adjustment and take D = 25 cm)(1) 562.5 (2) 625 (3) 265 (4) 62.5

8. The value of g at a particular point is 9.8 ms 2. Suppose the earth suddently shrinks uniformly to half itspresent size without losing any mass. The value of g at the same point (distance of the point from thecentre of earth does not change) will now be :

(1) 29.8ms $ (2) 24.9ms $ (3) 219.6ms $ (4) 239.2ms $

9. Assuming that the junction diode is ideal, the current in the arrangement shown in the figure is :

R=100 &1V 2V

(1) 0 mA (2) 2 mA (3) 10 mA (4) 30 mA

10. Two junction diodes one of Germanium (Ge) and other of silicon (Si) are connected as shown in figure to a

battery of emf 12 V and a load resistance 10 k & . The germanium diode conducts at 0.3 V and silicon diode

at 0.7 V. When a current flows in the circuit, the potential of terminal Y will be

10 k &

Y

12 V

Ge

Si

(1) 12 V (2) 11 V (3) 11.3 V (4) 11.7 V

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11. A semiconductor X is made by doping a germanium crystal with arsenic (Z = 33). A second semiconductorY is made by doping germanium with indium (Z = 49). The two are joined end to end and connected to abattery as shwon. Which of the following statements is correct?

X Y

(1) X is p-type, Y is n-type and the junction is forward biased(2) X is n-type, Y is p-type and the junction is forward biased(3) X is p-type, Y is n-type and the junction is reverse biased(4) X is n-type, Y is p-type and the junction is reverse biased

12. A block of ice at 100C is slowly heated and converted to steam at 100 0C. Which of the following curvesrepresents the phenomenon qualitatively

(1) T e m p

Heat supplied

(2) T e m p

Heat supplied

(3) T e m p

Heat supplied

(4) T e m p

Heat supplied

13. A potential barrier of 0.4 V exists across a p-n junction. A constant electric field of magnitude 10 6 V/mexists in the depletion region. The width of depletion region is(1) 4 10 7 m (2) 0.1 m (3) 5 10 7 m (4) None of these

14. If energy(E), velocity(V) and force(F) be taken as fundamental quantity, then what are the dimension of mass(1) EV 2 (2) EV 2 (3) FV 1 (4) FV 2

15. The expression y = a sin bx sin ' t represents a stationary wave. The distance between two consecutivenodes is -

(1) b(

(2) b2(

(3) b2(

(4) b1

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16. In an interference pattern the (n + 4) th blue bright fringe and nth red bright fringe are formed at the same spot.If red and blue light have the wavelength of 7800 and 5200 then value of n should be -(1) 2 (2) 4 (3) 6 (4) 8

17. When the number of nucleons in nuclei increase, the binding energy per nucleon(1) increases continuously with mass number(2) decreases continuously with mass number(3) remains constant with mass number

(4) first increases and then decreases with increase of mass number18. Potential difference between the points P and Q in the electric circuit shown is -

i=1.5A

R =12c &R =6D &

R =2A & R =4B &

3 &

P

Q

(1) 4.5 V (2) 1.2 V (3) 2.4 V (4) 2.88 V

SECTION - IIStraight Objective Type

This section contains 6 multiple choice questions. Each question has 4 choices (1), (2), (3) and (4) for itsanswer, out of which ONLY ONE is correct.


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19. Flux ) (in webers) in a closed circuit of resistance 10 ohm varies with time t (in seconds) accordingto the equation ) = 6t 2 5t + 1. What is the magnitude of the induced current in 0.25 second-(1) 0.8 A (2) 1.2 A (3) 0.6 A (4) 0.2 A

20. A flywheel is in the form of a uniform circular disc of radius 1 m and mass 2 kg. The work which mustbedone on it to increase its frequency of rotation from 5 revs -1 to 10 revs -1 is approximately

(1) 21.5 10 J+ (2) 23.0 10 J+ (3) 31.5 10 J+ (4) 33.0 10 J+

21. When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied whichincreases the internal energy of the gas is

(1)25

, -. /0 1 (2)

35

, -. /0 1 (3)

37

, -. /0 1 (4)

57

, -. /0 1

22. The fundamental frequency of a string stretched with a weight of 4kg is 256 Hz. The weight required toproduce its octave is -(1) 4 kg wt (2)12 kg wt (3) 16 kg wt (4) 24 kg wt

23. The rectangular surface of area 8 cm x 4 cm of a black body at a temperature of 127 0C emits energy at therate of E per second. If the length and breadth of the surface are each reduced to half of its initial value, andthe temperature is raised to 327 0C, the rate of emission of energy will become

(1)3

E8

(2)81

E16

(3)9

E16

(4)81

E64

24. A thin spherical conducting shell of radius R has a charge q. Another charge Q is placed at the centre of theshell. The electrostatic potential at a point P at a distance R/2 from the centre of the shell is :

(1) R4Q2

0(2 (2) R4q2

R4Q2

00 (2$

(2 (3) R4q

R4Q2

00 (2%

(2 (4) R4)Qq(

0(2%

R2


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SECTION - IIIComprehension Type

This section contains 2 paragraphs. Based open each paragraph, there are 3 multiple choice questions.Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Paragraph for Question Nos. 25 to 27

The bob of a pendulum of mass of m and length ! and a charge of q is in the rest position in a uniformhorizontal electric field of E.

25. The tension in the string of the pendulum is :

(1) mg (2) qE (3) 3 42 / 122 )qE()mg( % (4) 3 44 / 122 )qE()mg( %

26. Find out the angle 5 made by string from vertical in equilibrium positon :

(1) //

1

-..

0

, $qEmg

tan 1 (2) //

1

-..

0

, $qEmg

sin 1 (3) //

1

-..

0

, $qEmg

cos 1 (4) // 1 -

..0 , $

mgqE

tan 1

27. Find out time period of small oscillations from mean position :

(1) g2

!( (2) g2

1 !

( (3) 2 / 122

mqE

g

2

// 1

-..0

, / 1 -.

0 , %

( !

(4) 2 / 122

mqE

g21

// 1

-..0

, / 1 -.

0 , %

(!


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In the Young's double slit experiment a point source of 6 = 5000 is placed slightly off the central axis asshown in the figure.

28. Find the nature and order of the interference at the point P :

(1) 70 th maxima (2) 70 th minima (3) 60 th maxima (4) 60 th minima

29. Find the nature and order of the interference at O :(1) 20 th minima (2) 20 th maxima (3) 10 th maxima (4) 10 th minima

30. Where should we place a film of refractive 7 = 1.5 and what should be its thickness so that maxima of zeroorder is obtained at O.

(1) Infront of S 1, 20 7m (2) Infront of S 2, 20 7m(3) Infront of S 1, 10 7m (4) Infront of S 2, 10 7m


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P RT B

Atomic 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]


This section contains 24 multiple choice questions. Each question has choices (1), (2), (3) and (4),out of which ONLY ONE is correct.

31. Which of the following has the minimum bond length ?(1) O 2

+ (2) O 2 (3) O 2

2 (4) O 2

32. Name the type of the structure of silicate in which one oxygen atom of [SiO 4]4 is shared ?

(1) Linear chain silicate (2) Sheet silicate(3) Pyrosilicate (4) Three dimensional silicate

33. Two gases A and B having the same volume diffuse through a porous partition in 20 and 10 secondsrespectively. The molecular mass of A is 49 u. Molecular mass of B will be :(1) 50.00 u (2) 12.25 u (3) 6.50 u (4) 25.00 u

34. The energies E 1 and E 2 of two radiations are 25 eV and 50 eV respectively. The relation between theirwavelengths i.e. ! 1 and ! 2 will be :

(1) ! 1 = ! 2 (2) ! 1 = 2 ! 2 (3) ! 1 = 4 ! 2 (4) ! 1 = 21

!2

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35. A gaseous mixture was prepared by taking equal mole of CO and N 2. If the total pressure of the mixturewas found 1 atmosphere, the partial pressure of the nitrogen (N 2) in the mixture is :(1) 0.5 atm (2) 0.8 atm (3) 0.9 atm (4) 1 atm

36. The complexes [Co(NH 3)6] [Cr(CN) 6] and [Cr(NH 3)6] [Co(CN) 6] are the examples of which type of isomerism?(1) Linkage isomerism (2) Ionization isomerism(3) Coordination isomerism (4) Geometrical isomerism

37. Which of the following pairs of metals is purified by van Arkel method ?(1) Ga and "n (2) Zr and Ti (3) Ag and Au (4) Ni and Fe

38. In the reactionA(s) + B(g) + Heat 2C(s) + 2D(g)

equilibrium is established. The pressure of D is increased and found be doubled when equilibriium isrestablished. The factor by which B is changed is(1) 2 (2) 3 (3) 4 (4) 3

39. For the reaction NO 2 + CO # CO 2 + NO the experimental rate expression is dt

dc = k[NO 2]2 the number

of molecules of CO involves in the slowest step will be -(1) 0 (2) 1 (3) 2 (4) 3

40. Which of the following will have maximum electron affinity :(1) 1s 2 2s 2 2p 5 (2) 1s 2 2s 2 2p 6

(3) 1s 2 2s 2 2p 6 3s 2 3p 5 (4) 1s 2 2s 2 2p 6 3s 2 3p 6

41. The IUPAC name of [Pt(NH 3)4 (NO 2)Cl]SO 4 is(1) tetramminechloronitroplatinum ( "") sulphate (2) tetramminechloronitroplatinum ( "V) sulphate(3) chlorotetramminenitroplatinum ( "V) sulphate (4) chloronitrotetrammineplatinum ( "V) sulphate

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42. Which one of the following statements is correct:(1) Brownian movement is more pronounced for smaller particles than for bigger ones(2) Sols of metal sulphides are lyophilic(3) Schulze-Hardy law states, the bigger the size of the ion, the greater is its coagulating power(4) One would expect charcoal to adsorb hydrogen gas more strongly than chlorine.

43. Nessler s reagent is a mixture of (1) HgCl

2 and K " (excess) (2) HgCl

2, K" (excess) and liquor ammonia

(3) HgCl 2, K" (excess) and KOH (4) K 2 [Hg"4] and K "

44. Critical temperature of a gas is ______ its Boyle temperature .(1) higher than (2) equal to (3) lower than (4) no relation

45. Which of the following statement is wrong.(1) Resonance effect operates through $ bonds.(2) All resonating structure of carboxylate ion are equivalent.(3) Resonance and inductive effect are permanent in nature.(4) Resonance and inductive effect are distance dependent.

46. % % % % # % 42 CCl / Br (Y) % % % % % # % & / NaNH 2 (Z)

The correct statement is :

(1) Compounds W and Z are same. (2) Compounds X and Z are same.(3) Compounds X and W are same. (4) None of the compounds (X, Y, Z and W) are same.

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47. B % % % % % % % % % ' 2H / catalystLindlar R C ( C R % % % % # % 3NH / Na A, A and B are geometrical isomers. (R CH=CH R).(1) A is cis, B is trans (2) A is trans, B is cis(3) A and B both are cis (4) A and B both are trans.

48. Which of the following is a nonreducing sugar ?

(1)

O||

OHCH)CHOH(COHCH 232 ))) (2)

(3) (4)

49. In which of the following reaction, the stereo chemistry of the product has been correctly shown

(1) % % # % "3P (2) % % % % % # % Ether / SOCl 2

(3) % % # % HBr (4) % % % % % % # % Pyridine / SOCl 2

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50. What is the acidity order of the following compounds

I

COOH

II

COOH

CH 3 III

COOH

CH3 IV

COOH

CH 3

V

COOH

CH 3CH 3

(1) I > II > III > IV > V (2) II > III > IV > V > I(3) V > III > I > II > IV (4) V > III > II > I > IV

51. Which of the following is polyamide molecule?(1) Terylene (2) Rayon (3) Nylon 6 (4) Polystyrene

52. 3HC ( CH % % % % % % # % tionPolymerisa X42

3

SOH.conc

HNO.conc % % % % % # % YY % % % % # % HCl / Sn Z)C5 0(

HCl,2NaNO!

% % % % % # %

NaOHdil

Phenol % % % # % W

Product W can be :

(1) (2)

(3) (4)

53. Which statement is INCORRECT .(1) Phenol has smaller dipolemoment than methanol.(2) Haloarenes are insoluble in water but are soluble in benzene.(3) Chloroform contains chlorine but gives no reaction with AgNO 3 solution.(4) Ethanol has much lower pka value than phenol.

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54. C 6H12 % % % % % # % * O2HZn,3O (y)

OH2NH % % # % (z)

4SO2H % % # %

(x)Compound x in the above reaction will be

(1) (2)

(3) (4)

SECTION - IIStraight Objective Type

This section contains 6 multiple choice questions. Each question has choices (1), (2), (3) and (4), outof which ONLY ONE is correct.

55. The number of hydroxide ions in 10 ml of an aquesous solution with pOH = 13 is(1) 10 13 (2) 6.023 x 10 8 (3) 6.023 x 10 13 (4) 6.023 x 10 10

56. The volume occupied by atoms in a simple cubic unit cell is : (edge length = a)

(1) a 3 (2)3a4 3$

(3)6a 3$

(4)83 $

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P RT C


This section contains 30 questions. Each question has 4 choices (1), (2), (3) and (4) for its answer, out ofwhich ONLY ONE is correct.

61. If a!

, b!

, c!

are unit vectors, then the maximum value of 2|b3 a2|!!

+ 2|c3 b2|!!

+ 2|a3 c2|!!

is

(1) 27 (2) 39 (3) 51 (4) 57

62. If the curves 2

2

a

x + 2

2

by

= 1 and 22x

! 2

2y" = 1 cut each other orthogonally, then

(1) a 2 + b 2 = ! 2 + " 2 (2) a 2 b 2 = ! 2 " 2(3) a 2 b 2 = ! 2 + " 2 (4) a 2 + b 2 = ! 2 " 2

63. If A = {(x, y): y = e x, x # R}, B = {(x, y): y = x , x # R}, then(1) AB $ (2) BA $ (3) BA % = & (4) BA ' = AA

64. The area bounded by the function f(x) = x 2 : R + ( R+ and its inverse function is

(1)21

sq. units (2) 31

sq. unit (3) 32

sq. units (4) 61

sq. units

65. The greatest value of the function f(x) = 2sin x + sin 2x on the interval )*+

,-. /

23

,0 is

(1)2

33(2) 3 (3)

23

(4) none of these

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66. Find the radius of largest circle in the following figure if all the three small circles are identical of radius r

(1) r132

00 1

2334

5 6 (2) r1

3

200 1 2

334 5

(3) 00 1 2

334 5 61

3

2r (4) r13

200 1

2334

5 6

67. If ! , " be the roots of x 2 + x + 2 = 0 and 7, 8 be the roots of x 2 + 3x + 4 = 0 then ( ! + 7)(! + 8)(" + 7)(" + 8)is equal to(1) 18 (2) 18 (3) 24 (4) 44

68. ABCD is a square taken in anticlockwise direction with A as (1 2i) and the point of intersection of diagonalsis E (6 i) then vertex D is(1) 7 6i (2) 5 4i (3) 5 + 4i (4) none of these

69. For real numbers x and y, we write x R y 9 x y + 2 is an irrational number. Then the relation R is(1) reflexive only (2) symmetric only (3) transitive only (4) equivalence relation

70. The value of 3cosxlim

( [cos 1 x] where [ : ] denotes greatest integer function is

(1) 2 (2) 3 (3) 3 (4) Limit does not exist

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71. Which of the following transformation reduces the differential equation dxdz

+xz

" nz = 2xz

( " nz) 2 into the

form dxdu

+ P(x) u = Q(x) ? Where P(x) and Q(x) are function of x

(1) u = " nz (2) u = e z (3) u = ( " nz) 1 (4) u = ( " nz) 2

72. If (1 + 3x + 3x2

)20

= a 0 + a 1x + a 2x2

+ a 3x3

+ a 4x4

+ a 5x5

+ ....... + a 40 x40

, then find the value of2a 2

6a 3 + 12a 4 20a 5 ......... + 1560a 40

(1) 3450 (2) 3350 (3) 3540 (4) 2150

73. If g = f 1 then [f(g(x))] ;; equals

(1) 3)]x(g[)x(g

;;;

(2) 0 (3) )x(g1;; (4) 3)]x(g[

1

;

74. A is a region such that4z

andz4

have their real and imaginary parts s # (0, 1). If P = area of region A then [P]

equals ([x] represents greatest integer x)(1) 0 (2) 3 (3) 5 (4) 4

75. In how many ways 4 mangoes, 1 orange, 1 banana, 1 watermelon can be arranged in a row so that none ofthe mangoes is together. Assume that fruits of same kind are identical

(1) 144 (2) 288 (3)!4!12

(4) none of these

76. The negation of the compound proposition p < (~ p < q) is(1) p = q (2) t (3) f (4) (p = q) = ? p

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77. In a quadrilateral ABCD if sin 0 1 23

4 5 6

2BA

cos 0 1 23

4 5

2B A

+ sin 0 1 23

4 5 6

2DC

cos 0 1 23

4 5

2D C

= 2 then @ 2A

cos cos2B

is equal to(1) 0 (2) 6 (3) 3 (4) 2

78. If 4n! = / , then the numerical value of tan ! . tan2 ! . tan3 ! .....tan(2n 1) ! is equal to(1) 1 (2) 0 (3) 1 (4) 2

79. If head means one and tail means two then coefficients of quadratic equation ax 2 + bx + c = 0 are chosenby tossing three fair coins. The probability that roots of the equation are imaginary is

(1) 85

(2) 83

(3) 87

(4) 81

80. |tanx + secx| = |tanx| |secx|, x # [0, 2 / ], if and only if x belongs to the interval

(1) [0, / ) (2) 0 1 2

,-. /

2,0 ' )*

+34 5 // ,

2

(3) 0 1

2,-

. //2

3, ' )

*

+34

5 // 2,2

3(4) none of these

81. Matrix A such that A 2 = 2A I , where I is the identity matrix. Then for n A 2, A n is equal to(1) nA (n 1) I (2) nA I (3) 2 n 1 A (n 1) I (4) 2 n 1 A I

82. y = f(x) be a function such that f(x) = min B C)x2(,)x2(x DD then the area bounded by y = f(x) and x-axis isequal to

(1)41

26/ (2)

41

46/ (3)

21

46/ (4)

21

26/

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APT-2 180411C0-20


83. If p(x) be polynomial satisfying the identity p(x 2) + 2x 2 + 10x = 2x p(x + 1) + 3, then function p(x) is(1) one-one (2) many-one (3) periodic (4) even

84. For all positive integers n, P(n) is true E 2n 2 > 3n then which of the following is true.(1) P(3) is true. (2) P(5) is true.(3) If P(m) is true then P(m + 1) is also true. (4) If P(m) is true then P(m + 1) is not true.

85. The reflection of the point A(1,0,0) in the line2

1 x= 3

2y 6 = 20 z is

(1) (3, 4, 2) (2) (5, 10, 38) (3) (1, 1, 10) (4) (2, 3, 8)

86. The top of a pole, placed against a wall at an angle ! with the horizon just touches the coping and when itsfoot is moved a meter away from the wall and its angle of inclination is " , it rests on the sill of a window, thevertical distance of the sill from the coping is

(1) a sin 0 1 23

4 5 "6!

2 (2) a cot 0 1

234 5 "6!

2 (3) a cot0 1 23

4 5 "6!

2 (4) a tan0 1 23

4 5 "6!

2

87. 0 1 23

4 5

)*+

,-. 66D66

F(1nn1nnlim 22

n where [ ] denotes the greatest integer function is

(1) 0 (2) 1/2 (3) 2/3 (4) 1/4

88. Two sides of a rhombus are parallel to the lines y = x + 2 and y = 7x + 3. If the diagonals of the rhombusintersect at point (1, 2) and vertex A lies on y-axis then coordinates of A are

(1) (0, 1) (2) (0, 1) (3) (0, 2) (4) 0 1 23

4 5

25

,0

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APT-2 180411C0-21


89. If f(x) = ! n + " n and)4(f1)3(f1)2(f1)3(f1)2(f1)1(f1)2(f1)1(f13

66666666

= k (1 ! )2 (1 " )2 (! " )2, then k is equal to

(1) 1 (2) 1 (3) !" (4) !"7

90. Let x 1, x 2 ,........x n be n observations such that 400x2

i G@ and 80x i G@ . Then a possible value of n

among the following is(1) 9 (2) 12 (3) 15 (4) 18

SECTION - IIMultiple Correct Answer Type

This section contains 7 questions. Each question has 4 choices (1), (2), (3) and (4) for its answer, out ofwhich ONE OR MORE is/are correct.

91. If a, b, c are distinct numbers in arithmetic progression and roots of the quadratic equation(a + 2b 3c)x 2 + (b + 2c 3a)x + (c + 2a 3b) = 0 are ! and " then both ! and " belong to domain of(1) sin 1x (2) sec 1(secx) (3) sec(sec 1x) (4) tan 1x

92. If the sum of the products taken two at a time of the numbers 1, 2, 3, 4, ......., 10 is N then 220N

(1) is a prime number (2) is a composite number(3) has two proper divisors (4) has 18 as sum of its divisors

93. The slope of the tangent to the hyperbola25x2

16y 2

= 1 which passes through the point (1, 4) is

(1) 1 (2) 34

(3) 2 (4) 1

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APT-2 180411C0-22


94. If f(x) = HI

HJK

LM6/6

N6

0x,4lnxxsine

0x,x

12 4 8

x

2

xxxx

is continuous at x = 0, then M is a

(1) rational number (2) irrational number (3) natural number (4) complex number

95.

Odx|x|n|x| " equals (x P 0)

(1)2

x2|x|n"

4x 2

+ c , x P 0 (2)21

|x|n|x|x " 41

|x|x + c, x P 0

(3) 2

x 2|x|n" +

4x 2

+ c, x < 0 (4)2

x2|x|n"

4x 2

+ c , x > 0

96. A letter is selected from each of the words MATHEMATICS and STATISTICS the probability that the same

letters is selected is ba

then a + b + 3 (where a and b are co-prime) is divisible by

(1) 3 (2) 5 (3) 7 (4) 13

97. If P(A) denotes power set of set A, then(1) P(A) % A = A (2) P(A) % A = & (3) P(A) % {A} = A (4) P(A) ' A = P(A)

SECTION - IIIComprehension Type

This section contains 1 paragraphs. Based open each paragraph, there are 3 questions. Each question has4 choices (1), (2), (3) and (4), out of which ONLY ONE is correct.

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Definite integral of any discontinuous function is normally solved by the property Ob

a

dx)x(f = Oc

a

dx)x(f +

O

b

c

dx)x(f , where c # (a, b) is the point of discontinuity of f(x).

98. The value of O2

2

1 )xec(coseccos dx is

(1) 1 (2) 0 (3) 4 (4) 2

99. The value B = O100

1

1 ]x[sec dx (where [.] denotes greatest integer funciton) is equal to

(1) sec1 (2) 100 sec1 (3) 99 sec1 (4) sec 1 100

100. The value of O/

0

1 dx)x(sincos is

(1)4

3 2/(2)

2

2/(3)

4

2/(4) 0

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