aiot jee adv testpaper 1 eng code 0-05-05 2013

PAPER - 1INSTRUCTIONSA. General :

1. This Question Paper contains 66 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 gadgetsin 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, darkenthe 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 Three

Sections.

16. For each question in SectionI, you will be awarded 4 marks if you darken the bubble(s) corresponding tothe 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 3 marks if you darken the bubble corresponding to thecorrect answer and zero marks if no bubble is darkened. In case of bubbling of incorrect answer, minusone (1) mark will be awarded.

18. For each question in SectionIII, you will be awarded 3 marks if you darken the bubble corresponding tothe correct choice for the answer and zero mark if no bubbled is darkened. There is no negative markingfor 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 : 05-05-2013 Duration : 3 Hours Max. Marks : 228

CODE 0ALL INDIA OPEN TEST (AIOT) JEE ADVANCED

TARGET : JEE (ADVANCED)-2013 COURSE : JP, JF, JR & JCC

RESONANCE P1AIOT050513C0-1

PHYSICS

Space for Rough Work

PART- I - PHYSICS

SECTION - IStraight Objective Type

This section contains 10 multiple choice questions. Each question has choices (A), (B), (C), (D) and(E) out of which ONLY ONE is correct.

1. A block of mass m is connected to a spring ( spring constant k ) . Initially the block isat rest and the spring is in its natural length. Now the system is released in gravitationalfield and a variable force F is applied on the upper end of the spring such that thedownward acceleration of the block is given as a = g t, where t is time elapses and = 1 m/s3 , the velocity of the point of application of the force is :

(A) 2tgt

km 2

(B)

2tgt

km 2

(C)

2tgt

km 2

(D) 2tgtkm

(E) zero

2. A rod P of length 1m, is hinged at one end A and there is a ring attached to the other end. Another long rodQ is hinged at B and it passes through the ring. The rod P is rotated about an axis which is perpendicular toplane in which both rods are present and the variations between the angles and are plotted as shown.Thedistance between the hinges A and B is:

(A) 3m (B) 1m (C) 2 m(D) 3 m (E) 22 m



PHYSICS



3. STATEMENT-1 : In photoelectric experiment the ejected electrons have same kinetic energy.STATEMENT-2 : According to Einstein kinetic energy of every ejected electron is the difference in the energyof a photon and the work function of the metal.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 is False, Statement-2 is True.(E) Statement-1 is False, Statement-2 is False.

4. A force given by kfjfifF zyx

acts on a particle which moves from (a,b,c) to (d,e,f) . The work done bythe force F is : (Here A1 , A2, A3 are magnitude of area bounded)

(A) A1 + A2 + A3 (B) A1 A2 A3 (C) A1 + A2 A3(D) A1 A2 + A3 (E) A1 A2 A3

5. In a box of liquid of density , there is a fixed sphere of density 2. Fromthe point P the center of the sphere is 3m while the height of the box is 4m.The mass of the liquid is 5 kg while that of the sphere is 2 kg. The height ofthe center of mass of the liquid and the sphere system, with respect to thepoint P is :

(A) 12/7 m (B) 15/7 m (C) 16/7 m(D) 2 m (E) None of these


PHYSICS


6. A disc of mass m and radius R, is placed on a smooth fixed surface. Point A is the geometrical center of discwhile point B is the center of mass of the disc.The moment of inertia of the disc about an axis through itscenter of mass and perpendicular to the plane of the figure is . A constant force F is applied on the top of thedisc. The acceleration of the center A of the disc at the instant B is below A (on same vertical line) will be :

(A) m

F (B) I4

FR3m

F 2 (C)

I4FR

m

F 2

(D) I

FR3m

F 2 (E)

2FRm

F

7. A trolley is moving with a velocity v. There is a smooth circular tube fixed inthe trolley having a small sphere resting at the bottom. Now the trolley isuniformly decelerated until it comes to stop. During the deceleration thesphere moves by an angle and acquires sufficient speed so that it justcompletes the vertical circle in the tube. The magnitude of the decelerationof the trolley is :

(A)sin

g (B) 2sin

g (C)cos

g2

(D) sin

g2 (E) 2cos

g


PHYSICS


8. A steel rod is projecting out of a rigid wall. The shearing strength of steel is345 MN/m2.The dimensions AB = 5 cm , BC = BE = 2 cm . The maximum load thatcan be put on the face ABCD is:(neglect bending of the rod) (g = 10 m/s2)

A B

CDE

F

(A) 3450 Kg(B) 1380 Kg(C) 13800Kg(D) 345 Kg(E) None of these

9. 4 moles of H2 at 500 K is kept in an adiabatic rigid container. After some time it was found that 1 mole of thegas dissociated into H atoms . The dissociation energy per mole of H2 gas is 2000 cal,Let the new temperatureof the gas be 100T. The integral value of T is : (Use R= 2cal/mole-K)(A) 3 (B) 4 (C) 5(D) 6 (E) 2

10. Electric field in a region is given as k3jy2ixE in this region point A(3,3,1) and point B (4,2,1) arethere.The magnitude of work done by the electric field, if 2 coulomb charge is moved from A to B. All valuesgiven and asked are in SI units.(A) 3 (B) 4 (C) 5(D) 6 (E) 2

SECTION - IIComprehension Type

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


PHYSICS


Paragraph for Question Nos. 11 to 12

In the ac circuit shown, XL=7 ,R = 4 and XC= 4 .The reading of the ideal voltmeter V2 is 28 .

11. The reading of the ideal ammeter will be:

(A)1 A (B)2A (C) 2 A (D) 21

A

12. The reading of idea voltmeter V1 will be :(A) 20 volt (B) 7 volt (C) 8 volt (D) 10 volt


PHYSICS



See the adjoining circuit .Mark the correct options.

13. The current through the cell just after closing the switch S is :

(A) R (B) R

2 (C) R3 (D) R2

14. The current through the cell long after closing the switch S is :

(A) R53 (B) R5

(C) R3 (D) R


PHYSICS



Two coherent point sound sources S1 and S2 are placed as shown in the figure. Both are emitting sound offrequency 165 Hz. S1 is ahead of S2 in phase by -radian. (Speed of sound is 330 m/s)

15. How many times maximum sound can be observed on line AB :(A) 7 (B) 6 (C) 5 (D) 11

16. If power of sources are same and equal to 7200 watt. Resultant intensity (in watt/m2) at point B will be :(A) 2)1850( (B) 2)1830( (C) 2)1850( (D) None of these

SECTION - IIIInteger Answer Type

This section contains 6 questions. The answer to each of the questions isa single digit integer, ranging from 0 to 9. The appropriate bubble below therespective question number in the ORS have to be darkened.


PHYSICS


17. An electric dipole (dipole moment = p) is placed in a uniform electric field in stable equilibrium position atrest. Now it is rotated by a small angle and released . The time after which it comes to the equilibrium

position again (for first time) is t. If the moment of inertia of the dipole about the axis of rotation is 22pEt

x

,

then find the value of x.

18. Monochromatic light of wavelengthpasses through a pair of slits S1 and S2 ,separated by a distance equal

to fringe width . There is a screen placed at a distance D in which two parallel slits 1S and

2S are cut at

the positions of 3rd and 4th maxima. Again there is a screen at a distance D. P is a point at a distance of 2

from the central line of the first pair of slits S1 and S2 ,, while Q is on the central line of the second pair of slits

1S and

2S . All slits are of same widths.If the intensity of light at the point P is and the intensity at Q is

4x

, then find the value of x.


PHYSICS


19. A scale (=10-3/0C ) gives correct reading at 00C. It is used at a different temperature 150C.The scale is usedto measure length of 1m. If the value of the difference in the measured length and the actual length is 3x mmthen calculate x.

20. m gm of steam at 1000C is mixed with 31.50 gm ice at 200C.Take sice= ssteam= 0.5 cal/gm0C ,s

water= 1cal/gm0C and the latent heat of fusion and vaporization as 80cal/gm and 540 cal/gm respectively.Thefinal temperature is found to be 100C . Find the value of m.

21. A 1kg ball is suspended in a uniform electric field with the help of a string fixed to a point.The ball is given acharge 5 coulomb and the string makes an angle 370 with the vertical in equilibrium position.In the equilibriumposition the tension is double the weight of the ball. Find the magnitude of the electric field in N/Coul.

22. A sphere P(emissivity = 1) of radius 2R and and another sphere Q(emissivity = 1/2) of radius R are placed invacuum at some distance.There are no other objects. The temperature of the sphere Q is maintained at200 K by the means of a heater. A fraction 1/32 of the power emitted by the sphere Q falls on the sphere P.If the equilibrium temperature of the sphere P is 10 T, find the value of T.


RESONANCE

CHEMISTRY

P1AIOT050513C0-10

PART II : CHEMISTRY

SECTION - IStraight Objective Type

This section contains 10 questions. Each question has 5 choices (A), (B), (C), (D) and (E) for its answer, outof which ONLY ONE is correct.

23. If enthalpy of formation of CH3CH3 (g), CH3CH2CH3 (g) and CH3CH2CH2CH3 (g) are 20 kcal / mole,25 kcal / mol and 30 kcal/mol respectively, then enthalpy of formation of CH3CH2CH2CH2CH2CH3(g) is:(A) 50 kcal/mol (B) 40 kcal/mol(C) 45 kcal/mol (D) 35 kcal/mol (E) 55 kcal/mol

24. Which is incorrect order of basic strength ?(A) NH2 > PH2 (B) H2O > H2S

(C) CH3 > (D) > (E) CO32 > HCO3

25. S1 : The intercept of a graph of PVm along Y-axis vs P along X-axis is equal to 1 for any real gas.S2 : Equal volumes of real gases contain equal number of molecules under a given condtion of temperatureand pressure.

S3 : The rate of diffusion of CH4 is 54

times rate of diffusion of CD4 under identical conditions.

Which of the following is Correct ?(A) FFF (B) FTF (C) TFF (D) TTT (E) FFT


RESONANCE

CHEMISTRY

P1AIOT050513C0-11


26. When 12g of carbon reacted with oxygen to form CO and CO2 at 25C and constant pressure, 77.5 Kcal ofheat was liberated and no carbon was left. Calculate the mass of oxygen which reacted.

fH (CO) = 25 Kcal/mol.fH (CO2) = 95 Kcal/mol.(A) 32g (B) 2g (C) 24g (D) 40g (E) 28g

27. A current of 19.3 mA is passed for 9375 sec. through 500 ml of 2 mM ZnSO4 solution. If final molarity of Zn2+is 0.5 mM, then the current efficiency of the source is : (Assume volume remains constant during thisprocess).(A) 80% (B) 75%(C) 72% (D) 65% (E) None of these

28. On the basis of following reactions, identify the correct matchingA(aq) + Al heat (B)(gas). (Colorless combustible gas which is lightest)A(aq) + C heat PH3(gas).A(aq) + NH4Cl heat (D)(gas) . (turns red litmus blue)(A) A = NaOH, C = P4 (B) A = CH3COOH, B = CH4(C) A = KOH, D = NH3, C = H3PO4 (D) A = HCl, B - H2, C = H3PO4(E) A = H2SO4, D = HCl, C = P4

29.

)I(OH|

HCCCHC)CH( 33 ionisomerisatH

)II(oductPr

The correct statement is :(A) (I) and (II) give positive tests with Tollen's reagent.(B) (I) and (II) give positive tests with Fehling solution.(C) (I) and (II) both react with Lucas reagent.(D) (I) and (II) both liberate H2 gas with sodium metal.(E) (I) and (II) both give yellow ppt. with 2, 4 DNP.

RESONANCE

CHEMISTRY

P1AIOT050513C0-12


30. Diasteromers are possible for structural formula :

(A) C3FClBrI (alkynes) (B) C2FClBrI (C) (D)

(E) C2H4BrCl

31. Which of the following is a disacchharide which is ;(I) not a reducing sugar(II) having -(1,2) glycosidic linkage.

(A) (B)

(C) (D)

(E)

RESONANCE

CHEMISTRY

P1AIOT050513C0-13


32. The following benzyl alcohols are reacted with HBr. The least reactive and the most reactive are respectively:

(A) 1, 4 (B) 2, 3 (C) 2, 4 (D) 1, 3 (E) 1, 2


This section contains 3 paragraphs. Based upon each paragraph, there are 2 questions. Each question has4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.


dS = Tdqrev dq

rev = TdS

qrev

= TdSHence q is the area under the curve in S vs T diagram projected on S axis.

RESONANCE

CHEMISTRY

P1AIOT050513C0-14

33.

Consider the cyclic process ABCDEFGA. The area of the two circles are equal. The net work done duringABCDEFGA is :(A) positive(B) negative(C) Zero(D) work cannot be determined in a cyclic process from S vs T diagram.

34.

Which of the following is correct regarding the cycle ABCD ?(A) S

surr >

0 along process BC and DA(B) The process AB is isothermal expansion(C) The process BC is adiabatic expansion(D) S

surr 6

, J < 6

(C) I < 6

, J > 6 (D) I > 6

, J > 6

(E) I = J = 6

50. Vectors 3a 5b

and 2a b

are mutually perpendicular. If a 4b

and b a

are also mutually perpendicular,,then cosine of the angle between a

and b

is equal to

(A) 195 43 (B) 19

3 43 (C) 19

2 45 (D) 19

6 43 (E) 19

5 45

51. Mr. A and Mr. B have a competition. Initially, each player has one attempt at hitting a target. If one player hitsthe target and other does not then the successful player wins. If both players hits the target, or if both playersmiss the target, then each has another attempt, with same rules applying. If the probability of Mr. A hitting the

target is always 54

and the probability of Mr. B hitting the target is always 32

, then the probability Mr. A winsthe competition is

(A) 154 (B) 11

4 (C) 134 (D) 3

2 (E) 1352. The equation of the curve satisfying the differential equation y2 (x2 + 1) = 2xy1 passing through the point(0, 1) and having slope of tangent at x = 0 is 3, is

(A) y = x2 + 3x + 2 (B) y2 = x2 + 3x + 1 (C) y = x3 + 3x + 1 (D) y = x3 3x + 1(E) y2 = x2 3x + 1

RESONANCE

MATHEMATICS

P1AIOT050513C0-20


53. The equation x + cosx = a has exactly one positive root. Complete set of values of 'a' is(A) (0, 1) (B) (, 1) (C) (1, 1) (D) (1, ) (E) (0, )

54. If is a imaginary cube root of unity then the value of

10

1r)r)(r(

225cos

is

(A) 1 (B) 21 (C) 2

1 (D) 1 (E) 0


This section contains 3 paragraphs. Based upon each paragraph, there are 2 questions. Each question has4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Paragraph for Question Nos. 55 to 56Consider a general equation of degree 2, as

x2 10xy + 12y2 + 5x 16y 3 = 055. The value of for which the given equation represents a pair of straight lines is

(A) 1 (B) 2 (C) 3/2 (D) 356. For the value of obtained in above question, if L1 = 0 and L2 = 0 are the lines denoted by the given equation,

then the product of the abscissa and ordinate of their point of intersection is(A) 18 (B) 28 (C) 35 (D) 25

Paragraph for Question Nos. 57 to 58Let f(n) denote the nth term of the sequence 3, 6, 11, 18, 27............. and g(n) denote the nth term of thesequence 3, 7, 13, 21, .............. let F(n) and G(n) denote the sum of n-terms of the above sequencesrespectively.

57. )n(G)n(Flim

n

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

58.nn

n n

F(n) f(n)lim lim =G(n) g(n)

(A) e3/2 e (B) e3/2 e1 (C) e3/2 (D) e1

RESONANCE

MATHEMATICS

P1AIOT050513C0-21


Paragraph for Question Nos. 59 to 60Let ABCDE be a regular pyramid with square base ABCD and sidesAB = BC = CD = AD = AE = BE = CE = DE = 2.

59. Shortest distance between line through AB and DE

(A) 32

(B) 322 (C) 3

22 (D) 32

60. Acute angle between faces ADE and ABE is

(A) cos1

41 (B) cos1

31 (C) cos1

32 (D) cos1

54

SECTION - IIIInteger Answer Type

This section contains 6 questions. The answer to each of the questions isa single digit integer, ranging from 0 to 9. The appropriate bubble below therespective question number in the ORS have to be darkened.

61. A line with positive direction cosines passes through the point P(2, 1, 2) and makes equal angles with thecoordinate axes. The line meets the plane 2x + y + z = 9 at point Q. If the length of the line segment

PQ is , then value of 2 is

RESONANCE

MATHEMATICS

P1AIOT050513C0-22


62. Consider a triangle ABC and let a, b and c denote the lengths of the sides opposite to vertices A,B and Crespectively. If a,b,c (in order) are in arithmetic progression such that x2 + 3x + 5 = 0 and 3x2 + ax + c = 0have a common root, then find the radius of the incircle of triangle ABC.

63. If the co-efficients of three consecutive terms in the expansion of (1 + x)n, n N are in the ratio 1 : 7 : 35, then

find 43n

.

64. Let f(x) be a non-constant thrice differentiable function defined on x R such that f(x) = f(6 x), x R andf (0) = f (2) = f (5) = 0. If p is the minimum number of zeros of (x) = (f(x))2 + f(x) f(x) in the interval[0, 6], then the value of 3

p is

65. Find the number of ordered triplets (x y, y z, z x), where x,y,z satisfyx(x 1) + 2yz = y(y 1) + 2zx = z(z 1) + 2xy.

66. If a0 is the value of a (0, 1] for which the area bounded by the graph of the function y = xb + 3xc(where b > 1, c > 1) and the lines x = 0, x = 1, y = ab + 3ac is greatest, then evaluate 7a0 .

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