Aiot Main Xi 27 Jan 13 Eng

8/12/2019 Aiot Main Xi 27 Jan 13 Eng

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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 of90 questions.

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 (120 marks)Question No.1 to 30 consist ofFour (4) marks for each correct response.

PART B CHEMISTRY (120 marks)Question No.31 to 60 consist ofFour (4) marks for each correct response.

PART C MATHEMATICS (120 marks)Question No.61 to 90 consist ofFour (4) marks for each correct response.

4. Candidates will be awarded marks as stated above in Instructions No. 3 for correct response of each question. 1/4 (minus one fourth) marks will be deducted for indicating incorrect response of each question. No deduction from the

total score will 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.

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.

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I have verified all the information

filled in by the Candidate.

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

Date : 27-01-2013 Duration : 3 Hours Max. Marks : 360

O E

0

ALL INDIA OPEN TEST (AIOT) JEE MAINCLASS-XI | TARGET : JEE (IITs) 2014 | COURSE : ALL INDIA TEST SERIES (VIKALP)


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(SPACE FOR ROUGH WORK)

PART- A

SECTION - I

Straight Objective Type This sect ion contains 27 mult iple choicequestions. Each question has choices (1), (2),(3) and (4) out of which ONLY ONE is correct.

1. The pressure at the bottom of a tank of water is 3P,where P is the atmospheric pressure . If the wateris drawn out to lower the level of water by one fifththen, the pressure at the bottom of the tank will be:

(1) 2P (2) (13/5) P

(3) (8/5) P (4) (4/5)P

2. A slab of 40 kg is lying on a frictionless floor and ablock of 10 kg rests on the slab as shown in thefigure. The coefficients of static and kinetic frictionbetween the slab and the block are 0.6 and 0.4respectively. If a force of 100 N is applied on theblock, then the acceleration of the slab will be-(g = 10 m/s 2)

40 kg10kg100 N

Frictionless Floor

(1) 15.5 m/s 2 (2) 155 m/s 2

(3) 0.155 m/s 2 (4) 1 m/s 2

3. A rigid ring of mass M and radius R is rotating witha uniform angular speed ! . Now if a small part ofthe ring breaks and fly off, then the radius of gyrationof the remaining part

(1) Increases

(2) Decreases(3) Remains same

(4) Nothing can be predicted

4. The maximum value of m(in kg) so that thearrangement shown in the figure is in equilibriumis (friction coefficient between block and wedge is0.1 and between wedge and ground is 0.4)

(1) 2

(2) 2.5

(3) 3

(4) 3.5

5. Consider a ring performing pure rolling then on afixed rough surface. There is a point A marked on

the circumference of it. If velocity of centre of ringis uniform, then this point will move in a cycloidalpath as shown.

Now, if the ring is perfoming pure rolling with uniformacceleration what will be the path followed by thispoint.

(1)

increasing size of cycloid

(2) v

decreasing size of cycloid.

(3) It will depend on direction of acceleration whetherit is in the direction of velocity of centre or opposite.

(4) No change in path will occur.


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6. A monoatomic ideal gas undergoes a process givenby 2dU + 3dW = 0, then the process is:(1) isobaric(2) adiabatic(3) isothermal(4) none of these

7. The correct shape of a water drop enclosedbetween two glass plates in gravity free space willbe -

(1) (2)

(3) (4)

8. Three consecutive resonant frequencies of stringare 90, 150 and 210Hz. If the length of the string is80cm what is the speed of the transverse wave inthe string.(1) 45 m/s

(2) 96 m/s

(3) 48 m/s

(4) 80 m/s

9. A thin metal rod of length L 0 is shaped into a ringwith a small gap x as shown. On heating the system

(1) x decreases, r and d increase

(2) x and r increase, d decreases

(3) x, r and d all increase

(4) Data insufficient to arrive at a conclusion

10. In a given process on an ideal gas, dW = 0 and dQ< 0 Then for the gas

(1) The temperature will decreases

(2) The volume will increases

(3) The pressure will remain constant

(4) The temperature will increase

11. When a sound wave of frequency 300 Hz passesthrough a medium, maximum displacement of theparticle of the medium is 0.1 cm. The maximumvelocity of the particle will be :

(1) 60 m/s

(2) 30 m/s

(3) 30"

cm/s(4) 60 " cm/s


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12. A mass m is suspended from a massless pulley,which itself is suspended by a massless string anda spring as shown in figure. What will be the timeperiod of osillations of the mass. The force constantof spring is K-

(1)K2

m2"

(2)K

m2 "

(3)Km

"

(4)K2

m"

13. The radius of a wheel is R and its radius of gyrationabout its axis passing through its centre andperpendicular to its plane is K. If the wheel is rollingwithout slipping, the ratio of its rotational kineticenergy to its translational kinetic energy is

(1) 2

2

RK

(2) 2

2

KR

(3) 22

2

KR

R#

(4) 22

2

KR

K#

14. A ball of relative density 0.8 falls into water from aheight of 2m above the surface of water. The depthinside water upto which the ball will sink is (neglectviscous forces):

(1) 8 m (2) 2 m

(3) 6 m (4) 4 m

15. A uniform rope having uniformly distributed masshanges vertically from a rigid support. A transversewave pulse is produced at the lower end. The speed(v) of the wave pulse varies with height (h) fromthe lower end as:

(1) (2)

(3) (4)

16. A wheel of radius r rolls without slipping with a speedv on a horizontal road. When it is at a point A onthe road, a small lump of mud separates from thewheel at its highest point B and drops at point C onthe road. The distance AC will be

B

CA

v

(1) v gr

(2) 2v gr

(3) 4v gr (4) g

r3


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17. A solid cylinder of mass M is attached to a lightspring of spring constant k. It can roll without slippingalong a horizontal surface. The period of oscillationmade by the cylinder is

M

k

(1) k3M2

2 "

(2) k3M

2 "

(3)kM3

2"

(4)k2M3

2"

18. A particle is projected from the ground with an initialspeed v at an angle $ with the horizontal. Themagnitude of average velocity of the particlebetween its point of projection and the highest pointis

(1) $# 2cos212v

(2) $# 2cos12v

(3) $# 2cos312v

(4) v cos $

19. Displacement time graph of particle moving in onedimension is shown. The distance time graph ofgiven particle will be

(1) (2)

(3) (4) Not possible to draw.

20. A body moving with a constant speed describes acircular path whose radius vector is given by

% & jtsinitcos15r !#!'! m, where ! is in rad/sec,and t is in sec. Then its centripetal acceleration is :

(1) 45 ! 2 m/s 2

(2) 5 ! 2 m/s 2

(3) 15 ! m/s 2

(4) 15 ! 2 m/s 2


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21. A source of sound and listener are approachingeach other, with a speed of 40 m/s each. Theapparent frequency of note produced by thesource is 400 cps. Then, its true frequency (incps) is (velocity of sound in air = 360 m/s).

(1) 420

(2) 360

(3) 400

(4) 320

22. Two particles execute SHM on same straight linewith same mean position, same time period6 second and same amplitude 5 cm. Both theparticles start SHM from their mean position (insame direction) with a time gap of 1 second. Findthe maximum separation between the two particles

during their motion :(1) 2 cm

(2) 3 cm

(3) 4 cm

(4) 5 cm

23. A simple pendulum 50 cm long is suspended fromthe roof of a cart accelerating in the horizontal

direction with constant acceleration 3 g m/s 2.

The period of small oscillations of the pendulumabout its equilibrium position is (g = " 2 m/s 2) :

(1) 1.0 sec

(2) 2 sec

(3) 1.53 sec(4) 1.68 sec

24. A uniform ring and a uniform disc of same massand radius are rotating with same angular speed. Ifa constant force is applied tangentially on the ringin opposite direction, it stops after n revolution. Ifthe same force is applied on disc in opposing sensetangentially then the number of revolution made byit before it stops, are :

(1) n/2

(2) n

(3) 2n

(4) 4n

25. A particle moving with a velocity v!

= i

2 + j

3 k

4

strikes a smooth fixed wall placed in x-y plane.Assuming the collision to be inelastic, the velocityof the particle just after the collision may be(1) i

2 + j

3 + k

3

(2) i

2 + j

3 + k

4(3) i

2 + j

3 + k

5

(4) i

2 j

3 k

4

26. In the figure shown find out the distance of centreof mass of a system of a uniform circular plateof radius 3 R from O in which a hole of radius Ris cut whose centre is at 2R distance from centreof large circular plate.

(1) R/4

(2) R/5

(3) R/2

(4) none of these


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27. A block is placed on a rough horizontal planeattached with an elastic spring as shown in figure.

Initially spring is unstretched. If the plane is nowslowly lifted from $ = 0 to $ = 90 , then the graphshowing extension in the spring (x) versus angle($ ) is

(1)

x

y

90

1

00

(2)

x

90

(3)

x

90

(4)

x

90

SECTION - II

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

28. STATEMENT-1 : Steady flow can be maintainedin compressible liquids.STATEMENT-2 : Steady flow means all physicalparameters related to the flow being constant withtime though they may vary with 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

29. STATEMENT-1 : Burns sustained from steam at100 oC are usually more serious than those

sustained by boiling water (at 100 oC)STATEMENT-2 : To convert 1gm of water at 100 oCto 1 gm of steam at 100 oC, 540 calories of heat isto be supplied. Hence 1gm of steam at 100 oC has

more heat content than 1 gm of water at 100o

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




30. STATEMENT-1 : Gas ejected from rocket will neverexert thrust on the rocket if the ejected gas and therocket move in the same direction.STATEMENT-2 : To exert thrust on rocket in itsdirection of motion, the ejected gas ( w.r.t. rocket)must move opposite to velocity of rocket (w.r.t.ground)

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





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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]

Straight Objective Type

This section contains 30 questions. Each question has 4 choices (1), (2), (3) and (4) for its answer, out of which

ONLY ONE is correct.

31. The increasing order of acidic nature of Li 2O, BeO,B2O3, CuO is :

(1) Li2O < BeO < CuO < B 2O3

(2) BeO < CuO < B 2O3 < Li2O

(3) Li2O < CuO < BeO < B 2O3

(4) B 2O3 < CuO < BeO < Li 2O

32. When CO 2 is bubbled through NaOH, it initially gives

(1) CO

(2) Na 2CO 3

(3) NaHCO 3

(4) Both Na 2CO 3 and NaHCO 3 in equimolar ratio

33. Greater polarisation in case of AgCl compared toKCl is due to :

(1) larger size of cation.

(2) smaller size of cation.

(3) inert gas configuration of cation.

(4) pseudo inert gas configuration of cation.

34. If the wavelength of photon emitted from anelectron jump n = 4 to n = 2 in a H-like species is1216 , then the species is :

(1) H-atom

(2) He + ion

(3) Li2+ ion

(4) Be 3+ ion

35. S 1 : O 2 , O 2 and O 3

All are paramagnetic species.

S 2 : Among the alkali metals, Cs behaves as thebest reducing agent in aqueous medium.

S 3 : Dimethyl ether is a weaker lewis base than Disilylether.

(1) T F T

(2) F T F

(3) F F T

(4) T F F


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36. Consider 2HCO 3 (aq.) H 2CO 3 + CO 3

2 (aq.).When CuSO 4 is added to NaHCO 3 (aq.) ,precipitation of CuCO 3 begins. As precipitationreaction starts :

(1) Bubbles of CO 2 are released

(2) More HCO 3 ions are formed

(3) H 2SO 4 is formed

(4) [2CuSO 4 .CuCO 3] begins to precipitate

37. Find the atomic number of element belonging to 4thperiod and 17th group in Modern periodic table :

(1) 17

(2) 25

(3) 59

(4) 35

38. The smallest bond angle among PF 3 , PCl 3 , PH 3and P I 3 is in :

(1) PF 3

(2) PCl 3

(3) PH 3

(4) P I 3

39. Use the given bond enthalpies and other data todetermine ! H for the formation of hydrazine, N2H4(g)from nitrogen and hydrogen in standard stateaccording to the equation : N 2 (g) + 2H 2 (g) "# "

N2H4 (g)

Bond Bond enthalpies

NN 159 kJ mol 1

418 kJ mol 1

HN 389 kJ mol 1

Enthalpy of dissociation of nitrogen = 941 kJ/mol

Enthalpy of atomisation of hydrogen = 218 kJ/mol

(1) ! H = 338 kJ

(2) ! H = 98 kJ

(3) ! H = + 98 kJ

(4) ! H = + 338 kJ

40. Nodal plane(s) for d x2 y2 orbital is/are :

(1) YZ plane

(2) ZX plane

(3) Both (1) and (2)

(4) None of these


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41. A cylindrical container with a movable piston initiallyholds 1.5 moles of an ideal gas at a pressure of 4atm and a volume of 2.5 L. If the piston is moved tomake volume 5 L, while simultaneously withdrawing0.75 mole of gas, what is the final pressure in atm ?(Assume temperature to remain constant)

(1) 1

(2) 4

(3) 3

(4) 2

42. Select the INCORRECT statement :

(1) In a reversible adiabatic compression of an idealgas, there is no change in entropy of gas.

(2) In a reversible isothermal expansion of an idealgas, there is no change in internal energy of gas.

(3) There is always no change in entropy of gas,when an ideal gas undergoes a cyclic process.

(4) During isothermal reversible evaporation of waterat 100 C, ! E = 0.

43. Molecule XCl 2 in gaseous state is observed to benon-polar in nature. Then X can be :

(1) O

(2) Be

(3) S

(4) Both (1) and (3)

44. Which of the following is INCORRECT about criticalconditions of real gas following Vander waal's equa-tion of state :

(1) At critical point, there is no distinction betweenliquid and vapour state, hence density of liquid be-come equal to density of vapour.

(2) At critical point , bothTV

P $ % &

'( )

**

andT

2

2

V

P$$

%

&''

(

)

*

* are

equal to zero.

(3) Z < 1 at T = T C

(4) a + C

2C

P

T and b +

C

CTP

(where symbols have their

usual meanings)

45. 300 ml of 3.0 M NaCl is added to 200 ml of 4.0 MBaCl 2 solution. The concentration of Cl

ions in theresulting solution is :

(1) 4.5 M

(2) 3.4 M

(3) 6 M

(4) 5 M


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46. For the redox reaction MnO 4 + C 2O42

+ H + "# "

Mn2+ + CO 2 + H 2O,

the correct whole number stoichiometric coefficients

of MnO 4 , C2O42

and H + are respectively :

(1) 2, 5, 16

(2) 5, 2, 8

(3) 2, 5, 8

(4) 5, 2, 16

47. aA + bB cC + dD ; ! H

In above gaseous phase reaction, high pressure and

low temperature shift the equilibrium in backwarddirection. So correct set is :

(1) (a + b) > (c + d), ! H > 0

(2) (a + b) < (c + d), ! H > 0

(3) (a + b) < (c + d), ! H < 0

(4) (a + b) > (c + d), ! H < 0

48. The oxide, which is not a reducing agent is :

(1) CO 2

(2) CO

(3) SO 2

(4) Both (1) & (3)

49. Which of the following will not release H 2 onreaction with H 2O ?

(1) LiAlH4

(2) B 2H6

(3) Ca 3N2

(4) CaH 2

50. In which species, sulphur atom has differenthybridisation than others :

(1) SO 42

(2) SO 3

(3) SF 2

(4) H 2SO 3

51. IUPAC name of the following compound is :

(1) 1,2-Dibromo-3-chlorocycloprop-1-ene


(3) 1,2 Dibromo-3-chlorocycloprop-2-ene



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52.

Compound 'X' is :

(1) 1,4-Dimethylcyclohexa-1,4-diene



(4) None of these

53.

Which alkyl groups is not attached directly to the

cyclohexane ring in this compound ?

(1) Isobutyl

(2) sec-Butyl

(3) t-Butyl

(4) Neopentyl

54. In the following compound ;

Which of the following R 1 and R 2 groups will change

the word root ?

(1) COOH and CH3

(2) SO3H and OCH3

(3) OH and CH2 CH3

(4) CH=CH2 and COOH

55. Select the incorrect statement :

(1) Mesomeric effect is premanent and is observedonly in conjugated systems.

(2) Resonance is not possible in CH 2=C=O.

(3) Hyperconjugation involves , -- orbital overlapping

(4) (CH 3)3C. has better hyperconjugation than

(CD3)C.

56. and are :

(1) Functional isomers

(2) Metamers

(3) Chain isomers

(4) Homologus


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57. Number of cyclic structural isomers represented bymolecular formula C 5H8O2 which have highest priorityfunctional group in IUPAC system.

(1) 2

(2) 3

(3) 4

(4) 5

58. The increasing order of m effect of the following is :

(I) CONH2

(II) COOH

(III) CHO

(IV) SO2R

(1) II < I < III < IV

(2) I < III < II < IV

(3) III < II < I < IV

(4) I < II < III < IV

59. Which species is Aromatic :

(1)

(2)

(3)

(4)

60. An alkene give two moles of HCHO, one mole of

CO 2 and one mole of on

ozonolysis. What is its structure?

(1)

(2)

(3)

(4)


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PART- C

SECTION - I

Straight Objective Type

This section contains 25 questions. Each questionhas 4 choices (1), (2), (3) and (4) for its answer, out

of which ONLY ONE is correct.

61. If tan ! 1, tan ! 2, tan ! 3 are real roots of

" # " #3 2x a 1 x b a x b 0,$ % % $ $ & a + 1 ' b, where! 1 + ! 2 + ! 3 ( (0, ) ), then ! 1 + ! 2 + ! 3 is equal to

(1)2

)(2)

4

)

(3)4

3)(4) 3

2)

62. A normal to the hyperbola1

y 4

x 22= 1 has equal

intercepts on positive x and y - axis. If normal touches

the ellipse 1by

ax

2

2

2

2

&% , then a 2 + b 2 =

(1) 5 (2) 25

(3) 16 (4) 325

63. The three roots of the equationx672x273x

= 0 are

(1) 9, 2, 7 (2) 9, 2, 7

(3) 9, 2, 7 (4) 9, 2, 7

64. Set of real values of k for which the lines

x + 3y + 1 = 0, kx + 2y 2 = 0 and 2x y + 3 = 0

form a triangle is

(1) R *+,

-./

4 ,32

(2) R *+,

-./ $

56

,4 ,32

(3) R 2

4,3

/ ,$. +- *

(4) R

65. The equation of the hyperbola passing through the

point (1, 1) and having asymptotes x + 2y + 3 = 0

and 3x + 4y + 5 = 0 is

(1) 3x 2 + 8y 2 + 10xy + 14x + 22y = 0

(2) 3x 2 + 8y 2 + 10xy + 4x + 22y + 7 = 0

(3) 3x 2 + 8y 2 + xy + 14x + 22y + 7 = 0

(4) 3x 2 + 8y 2 + 10xy + 14x + 22y + 7 = 0

66. If the letters of the word SACHIN are arranged in all

possible ways and these words are written out as

in dictionary, then the word SACHIN appears at serialnumber

(1) 602

(2) 603

(3) 600

(4) 601


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67. If a, b, c denote the lengths of the sides of a triangle

opposite to angles A,B,C respectively of a 0ABC,then the correct relation among a, b, c, A, B and C

is given by

(1) (b + c) sinB C

2

%1 23 45 6

= a2

Acos

(2) (b c)2A

cos = 2a sin 4 6 23

5 1

2C B

(3) (b c) sinB C

2$1 2

3 45 6= a 2A

cos

(4) a cosB C

2$1 2

3 45 6

= (b + c) sin2

A

68. The probability that a leap year selected at random

will contain 53 Sundays, is

(1) 3/7

(2) 1/7

(3) 0

(4) 2/7

69.0x

lim7

2 2

21 2x 1 2x

x

% $ $ is equal to

(1) 0

(2) 1

(3) 2

(4) 4

70. Let (y 8)2 = 4(x 9) be a parabola with x = 1 asdirectrix. If 2y = 4x + 11 is tangent then 8 =

(1) 1

(2) 2

(3) 2

(4) 1

71. Let A, B, C be events of a random experiment. If

P(A) = 0.7, P((A : B) C) = 0.3, P((A : C) B) = 0.2,P(A : B : C) = 0.1, then the value ofP(A : C) + P(A (A : B)) is equal to

(1) 0.6

(2) 0.7

(3) 0.8

(4) 0.9

72. A straight line is draw through the point P(3, 4)

meeting the positive direction of co-ordinate axes

at the points A and B. If 'O' is the origin, thenminimum area of triangle OAB is equal to

(1) 12

(2) 6

(3) 24

(4) 48


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73. If in a given frequency distribution, the mean and

median are 21 and 22 respectively, then its mode

is approximately.

(1) 21

(2) 21.5

(3) 22

(4) 24

74. Consider quadratic polynomial

f(x) = x 2 4ax + 5a 2 6a.

Let p : denotes smallest positive integral value of

'a' for which f(x) is positive for every real x and

q : denotes largest distance between the roots ofthe equation f(x) = 0, then the value of p + q is

(1) 9

(2) 11

(3) 13

(4) 15

75. Sum of all possible integral values of x satisfying

the equation 11 x6 8x1 x4 3x &%%%

is

(1) 45

(2) 47

(3) 50

(4) 53

76. The side of a regular hexagon is 2 cm. The ratio of

the radius of circumscribed circle to the radius of

inscribed circle is

(1)23

(2) 21

(3) 2

(4)3

2

77. If A1, A2,..., A 100 are sets such that n(A i) = i + 2,

100321 A........AAA


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79. General solution of 8 sin x cos 5x 8 sin 5x cos x = 1,

is

(1) n ) + ( 1)n 24)

, n ( =

(2)4

n) + ( 1)n 24) , n ( =

(3)4

n) + ( 1)n 6

), n ( =

(4) n ) + ( 1)n 6)

, n ( =

80.If an ellipse slides between two perpendicular straightlines, then the locus of its centre is

(assuming length of axes of ellipse are constant)

(1) a parabola

(2) an ellipse

(3) a hyperbola

(4) a circle

81. Asymptotes of a hyperbola are represented by

2x 2 + 3xy 2y 2 + 2x y = 0. The eccentricity of

hyperbola can be

(1)23

(2) 35

(3)2

(4) indeterminate

82. For two data sets, each of size 5, the variance are

given to be 4 and 5 and the corresponding means

are given to be 2 and 4, respectively. The double of

the variance of the combined data set is

(1) 10

(2) 11

(3) 12

(4) 13

83. Consider the following statements

P : Suman is brilliant

Q : Suman is rich

R : Suman is honest

The negation of the statement Suman is brilliant

and dishonest if and only if Suman is rich can be

expressed as

(1) ((Q > R) ? ~ P)) (2) (Q ? (P > ~ R))(3) Q ? ~ (P > ~ R) (4) ~ ((Q > R) ? P))

84. The circle x 2 + y2 4x 4y + 4 = 0 is inscribed in

a triangle which has two of its sides along the

co-ordinate axes. The locus of the circumcentre ofthe triangle is

(1) (x 2 + y 2) = xy x y

(2) 2 22 yx % = xy x y

(3) 22 yx % = 2(xy x y)

(4) 22 yx % = xy x y


18/20



85. Tangents are drawn to the curve y 2 = 4x from the

point (2, 3). If the product of slopes of the tangents

is a, then the value of |6a| is

(1) 3 (2) 6

(3) 9 (4) 12

SECTION - II

Reasoning Type

This section contains 5 reasoning type questions.

Each question has 4 choices (1), (2), (3) and (4),

out of which ONLY ONE is correct.

86. STATEMENT-1 : If n is an odd prime then

" #@ABCDE % n25 2 n+1 is not divisible by 20 n,where [.] denotes greatest integer function.

STATEMENT-2 : If n is prime thennC 1,

nC2, ......nCn 1 must be divisible by n.

(1) STATEMENT-1 is True, STATEMENT-2 is True;

STATEMENT-2 is a correct explanation for

STATEMENT-1


STATEMENT-2 is NOT a correct explanation

for STATEMENT-1

(3) STATEMENT-1 is True, STATEMENT-2 is

False

(4) STATEMENT-1 is False, STATEMENT-2 is

True

87. STATEMENT-1 : The perpendicular bisector of the

line segment joining the point ( a, 2at) and (a, 0)

is tangent to the parabola y 2 = 4ax, where t ( RSTATEMENT-2 : Number of parabolas with a given

point as vertex and length of latus rectum equal

to 4, is 2.



STATEMENT-1



for STATEMENT-1


False


True

88. STATEMENT -1 : The number of non negative

integral solutions of equation x 1 + x 2 + x 3 = 10 is12 C2 .

STATEMENT-2 : The number of ways of selecting

10 integers out of 12 different non negative integers

is 12C2.



STATEMENT-1



for STATEMENT-1


False


True


19/20



89. STATEMENT - 1 : Locus of mid point of chords of

circle x 2 + y 2 = 4 which subtends angle of 2)

at

origin is x 2 + y 2 = 1.

STATEMENT - 2 : If any chord of circle x 2 + y2 = r2

subtends an angle ! at centre, then its mid point

always lies on x 2 + y 2 = r 2 cos 2 4 6 235 1 !2



STATEMENT-1



for STATEMENT-1

(3) STATEMENT-1 is True, STATEMENT-2 isFalse


True

90. STATEMENT-1 : If ab 2c3 , a 2b3c4, a 3b4c 5 are in A.P.

(a, b, c > 0), then the minimum value of a + b + c

is 3.

STATEMENT-2 : Arithmetic mean of any two

numbers is greater than geometric mean of the

numbers.



STATEMENT-1



for STATEMENT-1


False(4) STATEMENT-1 is False, STATEMENT-2 is

True


20/20

Name of the Candidate Roll Number

I have read all the instructions andshall abide by them.

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

I have verified all the informationfilled in by the Candidate.

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

DLPD TEST CENTERS :

TEST CODE TEST CENTRE TEST CODE TEST CENTRE TEST CODE TEST CENTRE

01 AGARTALA 02 AGRA 03 AHMEDABAD

04 AJMER 05 BHAGALPUR 06 BHAGALPUR

07 BHATINDA 08 BHILAI 09 BHOPAL10 BHUBNESHWAR 11 BIKANER 12 BOKARO13 CHANDIGARH 14 DEOGARH (RANCHI IC) 15 DHANBAD16 GWALIOR 17 HARIDWAR 18 INDORE19 JAMSHEDPUR 20 JAIPUR 21 JAMMU & KASHMIR (J&K)22 JODHPUR 23 KANPUR 24 KOLKATA25 KOTA 26 LUCKNOW 27 MATHURA28 MENGALURU 29 MUMBAI 30 NAGPUR31 NEW DELHI 32 PATNA 33 RAIPUR34 RANCHI 35 SRI GANGANAGAR 36 UDAIPUR37 VARANASI 38 SAMASTIPUR

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