JEE-ADVANCED_Part Test 1_Paper II-2013

7/29/2019 JEE-ADVANCED_Part Test 1_Paper II-2013

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CODE - B

JEE-ADVANCED(2013)PART TEST - 1 (Pap er II )

Time: 3 Hours Maximum Marks: 198

S y l la bus Covered

Physics: Unit and dimension, Error Analysis, Kinematics, Laws of Motion and friction, Work, Energy and PowerChemistry: Some Basic Concept, Atomic Structure, Chemical Bonding and Molecular Structure, States of Matter (Gaseous & liquid)

Mathematics: Functions, Limits, Continuity and Differentiability, Application of Derivatives, Indefinite Integration

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

INSTRUCTIONS

A. General:

1. This booklet is your Question Paper containing 60 questions.

2. The Test ID is printed on the right hand top corner of this booklet. This should be entered on the OMR sheet.

3. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers, and electronic gadgets in any form arenot allowed to be carried inside the examination hall.

4. The answer sheet, a machinereadable Optical mark recognition sheet (OMR Sheet), is provided separately.

5. DO NOT TAMPER WITH / MUTILATE THE OMR SHEET OR THE BOOKLET.B. Question paper format:

6. The question paper consists of 3 parts (Part I: Physics, Part II: Chemistry, Part III: Mathematics). Each part has3 sections.

7. Section Icontains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), for its answer, out of whichonly one is correct.

8. Section II contains 3 paragraphs each describing theory, experiment, data etc. There are 6 multiple choice questionsrelating to three paragraphs with 2 questions on each paragraph. Each question of a particular paragraph has four choices(A), (B), (C) and (D) out of whichONLY ONE is correct.

9. Section IIIcontains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), for its answer, out ofwhichone or more is/are correct.

C. Marking Scheme:

10. For each question inSection I, you will beawarded 3 marksif you darken the bubble corresponding to the correct answerandzero markif no bubble is darkened. In case of bubbling of incorrect answer, minus one (1) markwill be awarded.

11. For each question inSection II, you will beawarded 3 marksif you darken the bubble corresponding to the correct answer,andzero markif no bubble is darkened. In all other cases, minus one (1) markwill be awarded.

12. For each question in Section III, you will be awarded 4 marks if you darken the bubble(s) corresponding to the correctchoice(s) for the answer, andzero markif no bubble is darkened. No negative marks will be awarded for incorrect answersin this Section.

TEST ID 00043390


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JEE-ADVANCED Part Test 1 (Paper II) B

1

PHYSICS

SECTION ISingle Correct Choice Type

This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer,

out of which ONLY ONE is correct.

1. If the Plancks constant h, velocity of light C and time T are taken as fundamental units, then thedimension of force in the new system will be(A) hc1 T1 (B) hc1 T2 (C) hc1 T2 (D) h1 c1 T2

2. Twelve persons are initially at the twelve corners of a regular polygon of twelve sides of side a.Each person now moves with uniform speed V in such a manner that 1 is always directed towards2, 2 towards 3, 3 towards 4 and so on. The distance travelled by each person before they meet is

(A) 2a2 3+

(B) 2a2 3

(C) 2a3

(D) a2 3+

3. If coefficient of friction between all surfaces is 0.4, then the minimumforce F to have the equilibrium of the system will be, (takeg = 10 m/s2)

(A) 31.25 N (B) 150 N

(C) 135 N (D) 50 N

4. For the situation shown in the figure, the block is stationary w.r.t.inclined fixed in an elevator. The elevator is having an acceleration of

5 a0 whose components are shown in the figure. The surface isrough and coefficient of static friction between the incline and block iss. Determine the magnitude of force exerted by incline on the block.

(take 0 ga ,2= = 37, s = 0.6)(A)

mg10

(B)3mg

4125

(C)9mg25

(D)13mg

2

5. A particle moves with a constant speed u along the curve y = sin x. The magnitude of accelerationat the point corresponding to x = /2 is :

(A)2u

2(B)

2u

2(C) u2 (D) 22u

6. In the situation as shown in figure if acceleration of B is a thenfind the acceleration of A

(A) a sin (B) a cot

(C) 2a tan (D) 2a cos


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JEE-ADVANCED Part Test 1 (Paper II)B

2

7. For the system shown in the figure, a small block of mass m and smooth irregular shaped block ofmass M, both free to move are placed on a smooth horizontal plane. The minimum velocity Voimparted to block so that it will overcome the highest point of M is

(A) 2gh (B)m

2 1 ghM

+

(C)2m

ghM

(D)M

2 1 ghm

+

8. If error in the measurement of mass is 0.8% and in volume it is 0.4%, then error in themeasurement of density is

(A) 1.2 % (B) 0.4 % (C) 0.8 % (D) 1%

SECTION II

Comprehension TypeThis section contains 3 groups of questions. Each group has 2 multiple choice questions based on a paragraph. Each

question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE is correct.

Paragraph for Questions Nos. 9 to 10

A particle initially (i.e. at time t = 0) moving with a velocity u is subjected to a retarding force, asa result of which it decelerates at a rate a k= where is the instantaneous velocity and k isa positive constant.

9. The particle comes to rest in a time(A)

2 uk

(B)u

k(C) 2k u (D) k u

10. The distance covered by the particle before coming to rest is

(A)3/ 2uk

(B)3/22u

k(C)

3/ 23u2k

(D)3/22u

3k


A string of length l is fixed at one end and carries a mass m at the other end. The string makes2/ rps around a vertical axis through the fixed end so that the mass moves in the horizontal circle(Figure)

M

T


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3

11. The tension in string is(A) ml (B) 16 ml (C) 4 ml (D) 2 ml

12. The angle of inclination of the string with vertical is

(A) 1cos gl

(B) 1cos 16g

l

(C) 1cos 4gl

(D) 1cos 8gl


A block of mass 3M attached by one end of string of length L fixed by other end is justtouching smooth horizontal surface as shown in fig.

If block of mass M moving with velocity 0 3 5V gL= collides perfectly elastically with blockof mass 3M block and mass 3M looses contact from string at peak point of its vertical circularpath.

13. The range obtained by 3M block from Q point is

(A) 29L (B) 37 L (C) 5L (D) 4 2 L

14. The tension in string, when string makes an angle 060 with vertical is

(A)

1294 Mg (B)

174Mg

(C)

638Mg

(D)

52Mg

SECTION IIIMultiple Correct Choice Type


out of which ONE OR MORE is/are correct.

15. Mark the correct statement(s).(A) Work-energy theorem is valid only for particles(B) Work-energy theorem is an invariant law of physics

(C) Work-energy theorem is valid only in inertial frames of reference(D) Work-energy theorem can be applied in non-inertial frames of reference too

16. If Sand Vare one main scale and one varnier scale and n 1 divisions on the main scale areequivalent to n divisions of the vernier, then

(A) Least count isS

n

(B) Vernier constant isS

n

(C) The same vernier constant can be used for circular verniers also(D) The same vernier constant cannot be used for circular verniers


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17. A small ball starts moving from A over a fixed track as shown infigure. Surface AB has friction. From A to B the ball rolls withoutslipping. Surface BC is frictionless. KA, KB and KC are kineticenergies of the ball at A, B and C, respectively. Then

(A) hA > hC; KB > KC (B) hA > hC; KC > KA(C) hA = hC; KB = KC (D) hA < hC; KB > KC

18. In the figure, a man of true mass M is standing on a weighing machineplaced in a cabin. The cabin is joined by a string with a body of mass m.Assuming no friction, and negligible mass of cabin and weighingmachine, then

m

(A) measured mass of man is Mm(M m)+

(B) acceleration of man is mg(M m)+

(C) acceleration of man isMg

(M m)+(D) measured mass of man is M

19. A particle travels in a straight line such that its position with respect to origin varies with time (t)

as 2180332 23 ++= tttx . Then correct statements are(A) the acceleration of the particle at t= 5s is 6m/s2

(B) minimum speed of particle is at2

11=t s

(C) the particle is retarded in the interval 0=t s to 5.5=t s(D) the particle is retarded in the interval 0=t s to 5=t s and from t= 5.5 s to t= 6 s20. A car has total mass 50 kg (including fuel). Gases are ejected backwards with a velocity 20 m/s

with respect to car. The rate of ejection of gas is 2 kg/s. If the mass of fuel is 20 kg and the carstarts from rest. If the coefficient of friction between car and road is = 0.1. Which of the

following statements is/are correct ( 210 m/sg = and4

ln 0.283

=

)

(A) maximum speed of car will be 0.6 m/s(B) car will start moving after time t = 5 sec(C) car will stop after t = 10.6 sec(D) maximum speed of car will be 1 m/s

hA hC

B

A


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CHEMISTRY




21. In O2F2, which of the following statement is incorrect?(A) O-F bond length in O2F2 is longer than O-F bond length in OF2(B) The O.N. of oxygen in O2F2 is +1.(C) The OO bond length in O2F2 is shorter than OO bond length in H2O2.(D) None of these

22. Virial equation of state for real gas 2 3B C DZ 1 ...V V V= + + +

Where B = IInd virial coefficientC = IIIrd virial coefficientD = IVth virial coefficient

Find out the value ofBZ

at Boyles temperature.

(A) 0 (B) 1 (C)a

bRT

(D)a

bR

23. Equal masses of methane and hydrogen are mixed in an empty container at 25oC. The fraction of

total pressure exerted by hydrogen is:

(A)12

(B)89

(C)19

(D)1617

24. A mixture of 3 ( )NH g and 2 4 ( )N H g is placed in a sealed container at 300K.The total pressureof the gaseous mixture is 0.5atm . The container is heated to 1200 K at which both 3NH and

2 4N H decomposed completely according to the following equation .

3 2 22 ( ) ( ) 3 ( )NH g N g H g +

2 4 2 2( ) ( ) 2 ( )N H g N g H g +

After decomposition is complete , the total pressure at 1200 K is found to be 4.5 atm. The mole %

of 2 4N H in the initial mixture at 300 K was(A) 20% (B) 25% (C) 50% (D) 75%

25. The Bohr orbit radius for the hydrogen atom (n = 1) is approximately 0.530. The radius for thefirst excited state (n = 2) orbit is(A) 0.13 (B) 1.06 (C) 4.77 (D) 2.12

26. When a certain metal was irradiated with light of frequency 3.2 1016 Hz, photoelectrons emittedhad twice the kinetic energy as did photoelectrons emitted when the same metal was irradiatedwith light of frequency 2.0 1016 Hz. Hence, threshold frequency is(A) 0.8 1015 Hz (B) 8.0 1015 Hz(C) 0.8 1014 Hz (D) 6.4 1016 Hz


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27. 10 g sample of zinc was dissolved in 200 ml of 0.1 N KMnO4 solution acidified with H2SO4. TheKMnO4 solution is totally discharged. It was found that a gas was produced which when allowedreacting with the requisite amount of oxygen and sparked and condensed showed a total volumecontraction of 1500 ml at STP, then the mass percent of zinc in the sample is

(A) 35.5% (B) 45.5 % (C) 50.5% (D) 40.5%28. Two flasks of equal volume connected by a narrow tube of negligible volume are at 27C and

contain Cl2 at 1 atm pressure and Cl2O at 1.5 atm pressures respectively. The two gases wereallowed to mix and heated to react as given below:

Cl2O Cl2 + 1/2 O2

after the reaction, one of the vessel was kept in a water bath maintained at 27C while the othervessel was kept in another water bath maintained at 52C, then the pressure in both the vessels atthis temperature is

(A) 2.7 atm (B) 1. 7 atm (C) 2.5atm (D) 1.5 Atm

SECTION II




A water is said to be a soft water if it produces sufficient foam with the soap and water that doesnot produce foam with soap is known as hard water.Temporary hardness is due to presence of calcium and magnesium bicarbonate. It is simplyremoved by boiling as

( )3 3 2 22Ca HCO CaCO CO H O + +

Temporary hardness can also be removed by addition of slaked lime, Ca(OH) 2

( ) ( )3 3 22 2Ca HCO Ca OH 2CaCO 2H O+ +

Permanent hardness is due to presence of sulphate and chlorides of Ca, Mg etc. It is removed as

2 2 3 3CaCl Na CO CaCO 2NaCl+ +

4 2 3 3 2 4CaSO Na CO CaCO Na SO+ +

The degree of hardness is measured in terms of ppm of CaCO 3. 100 ppm means 100 gm of CaCO3

is present in 106 gm of H2O. If any water contain 120 ppm of MgSO4 its hardness in terms ofCaCO3 = 100 ppm.

29. A sample of drinking water was found to be contaminated with chloroform. The level ofcontamination was 15 ppm. The molality of chloroform in the water sample is

(A) 3.42 104 (B) 5.21 106 (C) 1.25 104 (D) 1.25 10630. The weight of Ca(OH)2 required for 10 litre of water to remove the temporary hardness of

100 ppm due to Ca(HCO3)2 ?(A) 16.6 g (B) 1.66 g (C) 0.74 g (D) 7.4 g


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de-Broglie proposed dual nature of particle by giving an equation =h

mv

whereas Heisenberg proposed uncertainty principle as hx p4

.

On the contrary particle nature of electron was established on the basis of photoelectric effect.When a photon strikes the metal surface it gives up its energy to the electron. Part of this energy(say W) is used by the electrons to escape from the metal and the remaining imparts the KE

21 mv2

to the photoelectron. The potential applied on the surface to reduce the velocity of

photoelectron to zero is known as stopping potential; the stopping potential is plotted against1/ of incident radiation for two different metals as:

1/ (m-1

)

Vo

(volts)

Metal I Metal II

Work function of metal I is 0.24 eV.31. Select the incorrect statement.

(A) KE of photo-electron does not depend upon the wavelength of incident radiation.(B) Photoelectric current depends on intensity of incident radiation and not on frequency.(C) Stopping potential depends on frequency of radiation and not on intensity.(D) None of these

32. Energy required to stop the ejection of electrons from Cu plate is 0.24 eV. Calculate the workfunction when radiations of wavelength 253.7 nm strikes the plate.(A) 24.3 eV (B) 24 eV (C) 4.95 eV (D) 4.65 eV


Lewis concept of covalency of an element involved octet rule. Later on it was found that manyelements in their compounds e.g. BeF2, BF3 etc. have incomplete octet whereas PCl5, SF6 etc.have expanded octet. This classical concept also failed in predicting the geometry of molecules.Modern concept of covalence was proposed in terms of valence bond theory. Hybridizationconcept along with V.B. Theory successfully explained the geometry of various molecules butfailed in many molecules. The geometry of such molecules was explained by VSEPR concept.Finally molecular orbital theory was proposed to explain many other molecules.

33. Which are true statements among the following?(I) p - p bonds are present in SO2(II) SeF4 and CH4 has same shape(III) XeF2 and CO2 has same shape(IV) SF4 is sea-saw structure whereas ICl3 is T-shaped.(A) I, IV (B) I, II, III(C) I, III (D) I, II, III, IV

34. The bond angles2

NO+ , NO2 and 2NO

are respectively:(A) 180, 134, 115 (B) 134, 180, 115(C) 115, 134, 180 (D) 115, 180, 130


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35. Which of the following statement is incorrect :(A) O2 is paramagnetic, O3 is also paramagnetic

(B) O2 is paramagnetic2

2N+ is also paramagnetic

(C) B2 is paramagnetic, C2 is also paramagnetic(D) Different observation is found in their bond length when NO NO+ and CO CO+

36. Which of the following statements is incorrect?(A) All CO bonds in 23CO

are equal but not in 2 3H CO

(B) All CO bonds in HCO2H are equal but not in 2HCO

(C) CO bond length in 2HCO is longer than CO bond length in 23CO

(D) CO bond length in 2HCO and CO bond length in 23CO

are equal.

37. Which of the following represents schrodinger equations

(A)2 2 2 2

2 2 2 2

8[ ] 0

mE V

x y z h

+ + + =

(B) H E =

(C) ( )T V E+ =

(D)

( ) 1T H+ = 38. A sample of metal contains 2.516 1023 atoms and has a mass of 82.29 g. Select correct

statements for this case:

(A) Atomic mass of the metal is 197

(B) Number of moles present in the given amount is 0.42

(C) The probable metal is coin metal

(D) It is natural occurring metal

39. In which of the following pairs of species the central atom has same hybridization?

(A) (ClF4O) , (XeOF4) (B) (ClF2O)

+, (ClF4O)

(C) ClF3, ClF3O (D) ClF3O, ClF3O2

40. Chlorine gas is prepared in laboratory by the reaction:

2 2 7 3 2 2K Cr O HCl KCl CrCl Cl H O+ + + +

If a 61.3 g sample of 96% K2Cr2O7 is allowed to react with 320 ml of hydrochloric acid solutionhaving density 1.15 g/mol and containing 30% HCl by mass. Now select the correct statement (s)among the following:

(A) The mass of Cl2 generated is 55.5 g (B) Equivalent weight of K2Cr2O7 is 49 g

(C) Equivalent weight of HCl is 85.16 g (D) The stoichiometric coefficient of HCl is 14.


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MATHEMATICS




41. The domain of the function f(x) = ( )(sin x cos x )log | cos x | cos x , 0 x+ + is

(A) (0, ) (B) 0,2

(C) 0,3

(D) none of these

42. If the positive numbers x and y are connected by the relation x2 xy + y2 = 12, then maximumvalue of 2x + 3y, is

(A) 2019

(B) 7419

(C) 6719

(D) 7619

43.( )

2

7 2 7

1 7cos x f (x)dx C,

sin x cos x sinx

= + then f(x) is equal to

(A) sin x (B) cos x (C) tan x (D) cot x

44. Let f(x) = (x + 1) (x + 2) (x + 3) . . . (x + 100) and g(x) = f(x). ( )2f (x) f (x) , then

g(x) = 0, has(A) no solution (B) exactly one solution(C) exactly two solutions (D) minimum three solutions

45. Let 20, x 0

f(x) x , x 0


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SECTION II




Among several applications of maxima and minima one is finding the largest term of a sequence.

Let be a sequence. Consider f(x) obtained by replacing x by n in an e.g. for nn

an 1

=+

considerx

f(x)x 1

=+

on [1, ).

49. The largest term of 2 3na n / (n 200)= + is

(A) 29/453 (B) 49/543 (C) 43/543 (D) 41/451

50. The largest term of the sequence 2na n / (n 10)= + is

(A) 3/19 (B) 2/13 (C) 1 (D) 1/7


If f is a continuous function on [a, b] and f(a) f(b) < 0, then there exists a point c in (a, b) such thatf(c) = 0 equivalently if f is continuous on [a, b] and x R is such that f(a) < x < f(b) then there isc (a, b) such that x = f(c). It follows from the above result that the image of a closed intervalunder a continuous function is a closed interval.

51. Suppose that f(1/2) = 1 and f is continuous on [0, 1] assuming only rational value in the entireinterval. The number of such function(s) is(A) infinite (B) 2 (C) 4 (D) 1

52. Let f be a continuous function on [1, 1] satisfying (f(x))2 + x2 = 1 for all x [1, 1]. The numberof such functions is(A) 2 (B) 1 (C) 4 (D) infinitely many


If f(A) = g(A) = 0 or f(A) = g(A) = , f(x), g(x) exists at x = a thenx a x a

f (x) f (x)Lt Lt

g(x) g (x)

=

. The

existence of RHS is only sufficient for the existence of LHS. But it is not necessary. Answer the

following questions.53.

tanx

x 0

1Lt

x

is

(A) e (B)1e

(C)e

1e

e

(D) 1

54.x aLt x a

cosx. log(x a)

log(e e )

is

(A) cos a (B)1e

cos a (C) e cos a (D) none of these


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55. If composite function f1 (f2 (f3 (......(fn (x))))) n times is an increasing function and if r of fi s aredecreasing function while rest are increasing, then maximum value of r(n r) is

(A)2n 1

,4

when n is an even number (B)2n

,4

when n is an odd number

(C)2n 1

,4

when n is an odd number (D)2n

,4

when n is even number

56. A curve g (x) = 27 2 6 2(1 ) (6 5 4)d+ + + +x x x x x x is passing through origin, then

(A)

7

3g(1) 7= (B)

7

2g(1) 7= (C) 1g( 1) 7 = (D)

7

3g( 1) 14 =

57. Given a real-valued functionfsuch that

2

2 2

tan { },for

( [ ] )

( ) 1 , for 0, where [ ] is the integral

{ }cot{x}, for x < 0

= =

xx > 0

x x

f x x x

x

part and {x}is the fractional part ofx, then

(A) lim ( ) 10

=+

f xx

(B)0

lim ( ) cot1x

f x

=

(C)2

1

0cot lim ( ) 1

= x

f x (D) 10

tan lim ( )4x

f x+

=

58. Let f(x) = Ax2 + Bx + C, where A, B, C are real numbers. If f(x) is an integer whenever x is aninteger, then(A) A is an integer (B) B is an integer(C) C is an integer (D) A + B is an integer

59. If 1 2x

x 1lim 4x tan y 4y 5

4 x 2

+ = + + +

, then y can be equal to

(A) 1 (B) 1 (C) 4 (D) 3

60. Let L =0

limx

22 2

42

xa a x

x

, a > 0. If L is finite, then

(A) a = 1 (B) a = 2 (C)18

=L (D) 116=L


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JEE-ADVANCED PART TEST - 1

ANSWERS

Paper II

PHYSICS CHEMISTRY MATHEMATICS

1. (C)

2. (B)

3. (A)

4. (D)

5. (C)

6. (D)

7. (B)

8. (A)

9. (A)

10. (D)

11. (B)

12. (B)

13. (A)

14. (A)

15. (A), (B), (D)

16. (A), (B), (C)

17. (A), (D)

18. (A), (C)

19. (A), (D)

20. (A), (B), (C)

21. (D)

22. (A)

23. (B)

24. (B)

25. (D)

26. (B)

27. (A)

28. (B)

29. (C)

30. (C)

31. (A)

32. (D)

33. (D)

34. (A)

35. (A), (C) (D)

36. (B), (C), (D)

37. (A), (B), (C)

38. (A), (B), (C), (D)

39. (A), (C), (D)

40. (B), (C), (D)

41. (D)

42. (D)

43. (C)

44. (A)

45. (C)

46. (A)

47. (B)

48. (B)

49. (B)

50. (A)

51. (D)

52. (A)

53. (D)

54. (A)

55. (C), (D)

56. (A), (C)

57. (A), (B), (C), (D)

58. (C), (D)

59. (B), (D)

60. (A), (C)

B

JEE-ADVANCED_Part Test 1_Paper II-2013

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