Resonance AIOT for JEE Advanced

CODE

0

ALL INDIA OPEN TEST (AIOT) JEE ADVANCED TARGET : JEE (ADVANCED)-2013 Date : 05-05-2013

Duration : 3 Hours

COURSE : JP, JF, JR & JCC Max. Marks : 228

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

PAPER - 1 INSTRUCTIONS 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 ORS in 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 ball point pen. 11. If student does not fill his/her roll no. and paper code correctly and properly, then his/her marks will not be displayed 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 while darken 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 not scribble, smudge, cut, tear, or wrinkle the ORS. Do not put any stray marks or whitener anywhere on the ORS. 14. If there is any discrepancy between the written data and the bubbled data in your ORS, the bubbled data will be 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 Section–I, you will be awarded 4 marks if you darken the bubble(s) corresponding to the correct choice for the answer and zero mark if no bubbled is darkened. In case of bubbling of incorrect answer, minus one (–1) mark will be awarded. 17. For each question in Section–II, you will be awarded 3 marks if you darken the bubble corresponding to the correct answer and zero marks if no bubble is darkened. In case of bubbling of incorrect answer, minus one (–1) mark will be awarded. 18. For each question in Section–III, 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. There is no negative marking for incorrect answer(s) in this section.

DO NOT BREAK THE SEALS WITHOUT BEING INSTRUCTED TO DO SO BY THE INVIGILATOR

A. General : 1. This Question Paper contains 66 questions.

PHYSICS

PART- I - PHYSICS SECTION - I Straight 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.

2.

A block of mass m is connected to a spring ( spring constant k ) . Initially the block is at rest and the spring is in its natural length. Now the system is released in gravitational field and a variable force F is applied on the upper end of the spring such that the downward 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)

m t 2  gt  k 2

(B)

m t 2  gt  k 2

(D)

m  gt  t 2 k

(E) zero

(C)

m t 2  gt  k 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 rod Q is hinged at B and it passes through the ring. The rod P is rotated about an axis which is perpendicular to plane in which both rods are present and the variations between the angles  and are plotted as shown.The distance between the hinges A and B is:

(A) 3m Space for Rough (D) 3Work m

(B) 1m

(C) 2 m

(E) 2 2 m

Space for Rough Work

RESONANCE

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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 energy of 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 F  fx ˆi  fy ˆj  fzkˆ acts on a particle which moves from (a,b,c) to (d,e,f) . The work done by the force F is : (Here A1 , A2, A3 are magnitude of area bounded)

5.

(A) A1 + A2 + A3

(B) A1 – A2 – A3

(D) A1 – A2 + A3

(E) –A1 – A2 – A3

(C) –A1 + A2 – A3

In a box of liquid of density  , there is a fixed sphere of density 2. From the 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 of the center of mass of the liquid and the sphere system, with respect to the point P is : (A) 12/7 m

(B) 15/7 m

(D) 2 m

(E) None of these

Space for Rough Work

(C) 16/7 m

Space for Rough Work

RESONANCE

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PHYSICS

6.

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

(A)

F m

F 3FR 2  (D) m I 7.

(B)

F 3FR 2  m 4I

(E)

F FR2   m

(C)

F FR 2  m 4I

A trolley is moving with a velocity v. There is a smooth circular tube fixed in the trolley having a small sphere resting at the bottom. Now the trolley is uniformly decelerated until it comes to stop. During the deceleration the sphere moves by an angle  and acquires sufficient speed so that it just completes the vertical circle in the tube. The magnitude of the deceleration of the trolley is : (A)

(D)

g sin  2g sin 

(B)

(E)

g sin2 

(C)

2g cos 

g cos 2 

Space for Rough Work

RESONANCE

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PHYSICS

8.

A steel rod is projecting out of a rigid wall. The shearing strength of steel is 345 MN/m2.The dimensions AB = 5 cm , BC = BE = 2 cm . The maximum load that can be put on the face ABCD is:(neglect bending of the rod) (g = 10 m/s2) (A) 3450 Kg A

(B) 1380 Kg

D

(C) 13800Kg

B C

E

F

(D) 345 Kg (E) None of these

9.

10.

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

(B) 4

(D) 6

(E) 2

(C) 5

Electric field in a region is given as E  x ˆi  2yˆj  3kˆ in this region point A(3,3,1) and point B (4,2,1) are there.The magnitude of work done by the electric field, if 2 coulomb charge is moved from A to B. All values given and asked are in SI units. (A) 3

(B) 4

(D) 6

(E) 2

(C) 5

SECTION - II

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

RESONANCE

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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

11.

The reading of the ideal ammeter will be: (A)1 A

12.

8 2.

(B)2A

The reading of idea voltmeter V1 will be : (A) 20 volt (B) 7 volt

(C)

2

A

(C) 8 volt

(D)

1 A 2

(D) 10 volt

Space for Rough Work

RESONANCE

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PHYSICS

Paragraph for Question Nos. 13 to 14 See the adjoining circuit .Mark the correct options.

13.

The current through the cell just after closing the switch S is : (A)

14.

 R

(B)

2 R

(C)

 3R

(D)

 2R

(D)

 R

The current through the cell long after closing the switch S is : (A)

3 5R

(B)

 5R

(C)

3 R

Space for Rough Work

RESONANCE

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PHYSICS

Paragraph for Question Nos. 15 to 16 Two coherent point sound sources S1 and S2 are placed as shown in the figure. Both are emitting sound of frequency 165 Hz. S1 is ahead of S2 in phase by -radian. (Speed of sound is 330 m/s)

15.

16.

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

(D) 11

If power of sources are same and equal to 7200  watt. Resultant intensity (in watt/m2) at point B will be : (A) ( 50  18 )2

(B) ( 30  18 )2

(C) ( 50  18 )2

(D) None of these

SECTION - III

Integer Answer Type This section contains 6 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. The appropriate bubble below the respective question number in the ORS have to be darkened.

Space for Rough Work

RESONANCE

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PHYSICS

17.

An electric dipole (dipole moment = p) is placed in a uniform electric field in stable equilibrium position at rest. 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 x

t 2 pE , 2

then find the value of x. 18.

Monochromatic light of wavelengthpasses 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 S 1 ’ and S 2  are cut at

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

  S1 ’ and S 2 . All slits are of same widths.If the intensity of light at the point P is  and the intensity at Q is

x , then find the value of x. 4

Space for Rough Work

RESONANCE

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PHYSICS

19.

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

20.

m gm of steam at 1000C is mixed with 31.50 gm ice at –200C.Take sice= ssteam= 0.5 cal/gm 0C , s water= 1cal/gm0C and the latent heat of fusion and vaporization as 80cal/gm and 540 cal/gm respectively.The final 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 a charge

5 coulomb and the string makes an angle 370 with the vertical in equilibrium position.In the equilibrium

position 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 in vacuum at some distance.There are no other objects. The temperature of the sphere Q is maintained at 200 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.

Space for Rough Work

Space for Rough Work

RESONANCE

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CHEMISTRY

PART II : CHEMISTRY SECTION - I

Straight Objective Type This section contains 10 questions. Each question has 5 choices (A), (B), (C), (D) and (E) for its answer, out of which ONLY ONE is correct. 23.

If enthalpy of formation of CH3–CH3 (g), CH3–CH2–CH3 (g) and CH3–CH2–CH2–CH3 (g) are –20 kcal / mole, –25 kcal / mol and –30 kcal/mol respectively, then enthalpy of formation of CH3–CH2–CH2––CH2–CH2–CH3 (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– >

25.

(D)

(E) CO32– > HCO3–

>

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 temperature and pressure. S3 : The rate of diffusion of CH4 is Which of the following is Correct ? (A) FFF (B) FTF

4 times rate of diffusion of CD4 under identical conditions. 5

(C) TFF

(D) TTT

(E) FFT

Space for Rough Work

RESONANCE

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CHEMISTRY

26.

When 12g of carbon reacted with oxygen to form CO and CO2 at 25C and constant pressure, 77.5 Kcal of heat 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 this process). (A) 80% (B) 75% (C) 72% (D) 65% (E) None of these

28.

On the basis of following reactions, identify the correct matching heat A(aq) + Al   (B)(gas). (Colorless combustible gas which is lightest) heat A(aq) + C   PH3(gas). heat A(aq) + NH4Cl   (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.

H (CH3 )3 C – CH – C  C – H     Pr oduct isomerisat ion | OH (II)

(I)

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. Space for Rough Work

RESONANCE

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CHEMISTRY

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)

Space for Rough Work

RESONANCE

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CHEMISTRY

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

SECTION - II

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

Paragraph for Question Nos. 33 to 34

dS =

dqrev T



dqrev = TdS

qrev =  TdS Hence q is the area under the curve in S vs T diagram projected on S axis. Space for Rough Work

RESONANCE

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CHEMISTRY

33.

Consider the cyclic process ABCDEFGA. The area of the two circles are equal. The net work done during ABCDEFGA 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) Ssurr > 0 along process BC and DA (B) The process AB is isothermal expansion (C) The process BC is adiabatic expansion (D) Ssurr < 0 in the complete cyclic process ABCDA. Space for Rough Work

RESONANCE

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CHEMISTRY

Paragraph for Question Nos. 35 to 36 An ore found in nature contain two elements A and B from 4th period of periodic table. Also both of these elements belong to the same group in the list of basic radicals analysis. An orange compound of element A on reacting with KCl and concentrated H2SO4 produce deep red vapors. These deep red vapors on passing through aqueous H2SO4 solution acquire orange color. If Barium chloride is added to this solution along with Baryta water, a yellow ppt is obtained. On the basis of this information, answer the following questions. 35.

36.

The element B can be : (A) Ca (B) Fe

(C) Hg

(D) Al

The element B in its stable high oxidation state gives blue color with excess of : (A) NH3 (B) K3 [Fe(CN)6] (C) K4 [Fe(CN)6] (D) NaSCN

Paragraph for Question Nos. 37 to 38

37.

Compound (P) may be :

(A)

(B)

(C)

(D)

Space for Rough Work

RESONANCE

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CHEMISTRY

38.

Which is not correct statement ? (A) Q is the recemic mixture. (B) Total four stereoisomers are possible with (R). (C) S will reacts with cold dil. KMnO4 & decolourises pink colour solution. (D) LiAlH4 reacts with S to give

SECTION - III

Integer Answer Type This section contains 6 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. The appropriate bubble below the respective question number in the ORS have to be darkened.

39.

Coordination number of underlined or mentioned atom is greater than or equal to 4 in how many of the following ? (i) Na2 SiF6 (ii) Silica (Silicon) (iii) CaSiO3 (where the silicate unit is cyclic trisilicate) (iv) Silicon (v) [Ag(S2O3)2]3– (vi) SO32– (vii) H3PO3 (viii) N2O5 (ix) B2H6 (x) PH4Cl

Space for Rough Work

RESONANCE

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CHEMISTRY

40.

How many of the following oxides are anhydrides of dibasic oxy-acid ? (i) SO2 (ii) P4O10 (iii) NO2 (iv) CO2 (v) Li2O (vi) CO (vii) ClO2 (viii) Cl2O (ix) I2O5

41.

2 moles of a mixture of O2 and O3 is reacted with excess of acidified solution of KI. The iodine liberated require 1L of 2M hypo solution for complete reaction. The weight % of O3 in the initial sample is x. Find

x . 10

42.

The number of completely filled orbitals in 29Cu which have atleast two nodes is/are :

43.

C4H8 (unsaturated hydrocarbons)

44.

An aromatic hydrocarbon has molecular formula C10H14, on oxidation with boiling alkaline KMnO4 followed by acidification yields benzene dicarboxylic acid. Calculate total isomers for C10H14.

Total number of products formed :

Space for Rough Work

RESONANCE

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MATHEMATICS

PART- III - MATHEMATICS

SECTION - I

Straight Objective Type This section contains 10 questions. Each question has 5 choices (A), (B), (C), (D) and (E) for its answer, out of which ONLY ONE is correct. 2

45.

 sec A cos ecA   is  If A = 5º then the value of  2 2   (1 – 4 sin A ) ( 4 cos A – 1)  (A) 6 (B) 8 (C) 16

(D) 24

(E) 28

(D) 1433

(E) 1534

(D) 936

(E) 1008

10

46.

The value of

 2

r –1



 8r – 3 is equal to

r 1

(A) 1343 47.

48.

(B) 1234

(C) 1334

How many perfect squares are divisors of the product 1! . 2! . 3! ....9! ? (A) 504 (B) 672 (C) 864

 x3 x  y     , where [.] denotes the greatest integer The area of the smaller region in which the curve  100 50  2

2

function, divides the circle  x  2   y  1  4, is equal to (A)

2  3 3 sq. units 3

(B)

3 3  sq. units 3

(C)

4  3 3 sq. units 3

(D)

5  3 3 sq. units 3

(E)

4  3 3 sq. unit 6

Space for Rough Work

RESONANCE

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MATHEMATICS /6

49.

Let I =

 0

(A) I <

cos x dx, J  x

  , J< 6 6

(E) I = J = 50.

/3

cos x dx . Which of the following is CORRECT ? x

(B) I >

  , J< 6 6

(C) I <

  , J> 6 6

  , J> 6 6

(D) I >

 6

19 5 43

(B)

19 3 43

(C)

19 2 45

(D)

19 6 43

19

(E)

5 45

Mr. A and Mr. B have a competition. Initially, each player has one attempt at hitting a target. If one player hits the target and other does not then the successful player wins. If both players hits the target, or if both players miss the target, then each has another attempt, with same rules applying. If the probability of Mr. A hitting the 4 2 target is always and the probability of Mr. B hitting the target is always , then the probability Mr. A wins 5 3 the competition is (A)

52.



        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)

51.

/2

4 15

(B)

4 11

(C)

4 13

(D)

2 3

(E)

1 3

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 2 2 (E) y = x – 3x + 1

Space for Rough Work

RESONANCE

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MATHEMATICS

53.

54.

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, ) If  is a imaginary cube root of unity then the value of cos (A) –1

(B) –

1 2

(C)

 225

(E) (0, )

10

 (r – )(r –  ) is r 1

1 2

(D) 1

(E) 0

SECTION - II

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

Paragraph for Question Nos. 55 to 56 Consider a general equation of degree 2, as x2 – 10xy + 12y2 + 5x – 16y – 3 = 0 55.

The value of  for which the given equation represents a pair of straight lines is (A) 1 (B) 2 (C) 3/2 (D) 3

56.

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 58 Let f(n) denote the nth term of the sequence 3, 6, 11, 18, 27............. and g(n) denote the nth term of the sequence 3, 7, 13, 21, .............. let F(n) and G(n) denote the sum of n-terms of the above sequences respectively. 57.

lim

n 

F(n) G (n)

(A) 2

(B) 1 n

58.

(C) 0

(D) 

(C) e3/2

(D) e–1

n

 f(n)   F(n)  lim    =   nlim n  G(n)  g(n)     (A) e3/2 – e (B) e–3/2 – e–1

Space for Rough Work

RESONANCE

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MATHEMATICS

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

Shortest distance between line through AB and DE

2 (A)

60.

3

(B)

2 2 3

(C)

2 2 3

(D)

2 3

Acute angle between faces ADE and ABE is  1 (A) cos–1   4

 1 (B) cos–1   3

2 (C) cos–1   3

4 (D) cos–1   5

SECTION - III

Integer Answer Type This section contains 6 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. The appropriate bubble below the respective 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 the coordinate 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

Space for Rough Work

RESONANCE

P1AIOT050513C0-21

MATHEMATICS

62.

Consider a triangle ABC and let a, b and c denote the lengths of the sides opposite to vertices A,B and C respectively. If a,b,c (in order) are in arithmetic progression such that x2 + 3x + 5 = 0 and 3x2 + ax + c = 0 have 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

n–3 . 4

64.

Let f(x) be a non-constant thrice differentiable function defined on x  R such that f(x) = f(6 – x), x  R and f (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 p [0, 6], then the value of is 3

65.

Find the number of ordered triplets (x – y, y – z, z –x), where x,y,z satisfy x(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 = x b + 3x c (where b > 1, c > 1) and the lines x = 0, x = 1, y = ab + 3ac is greatest, then evaluate 7a0 .

Space for Rough Work

RESONANCE

P1AIOT050513C0-22

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(Space for rough work)