CODE MAJOR TEST-2 (MT-2) TARGET : IIT-JEE 2011 0 · Determine the sum of fully filled and half filled orbitals, which have number of radial nodes less than the number of angular nodes,

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

Date : 09-01-2011 Duration : 3 Hours Max. Marks : 243

PAPER - 1

CODE

0COURSE : VIJETA (P) & VISHWAAS (F)

MAJOR TEST-2 (MT-2)TARGET : IIT-JEE 2011

INSTRUCTIONSA. General :

1. This Question Paper contains 75 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 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 bottom-half of the ORS :

9. The ORS has CODE printed on its lower and upper Parts.

10. Make sure the CODE on the ORS is the same as that on this booklet. If the Codes do not match, ask for a

change of the Booklet.

11. Write your Roll No., Name and Name of centre and sig with pen in appropriate boxes. Do not write these

anywhere else.

12. Darken the appropriate bubbles below your registration number with HB Pencil.

C. Question paper format and Marking scheme :

13. The question paper consists of 3 parts (Chemistry, Mathematics & Physics). Each part consists of Four Sections.

14. For each question in Section�I , you will be awarded 3 marks if you darken the bubble corresponding to the

correct answer and zero marks if no bubble is darkened. There is no negative marking for incorrect

answer(s) for this this section.

15. For each question in Section�II , you will be awarded 3 marks if you darken the bubble(s) corresponding

to the correct choice(s) 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.

16. For each question in Section�III , you will be awarded 2 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.

17. For each question in Section�IV, you will be awarded 3 marks if you darken only the bubble corresponding

to the correct answer and zero mark if no bubble is darkened. In case of bubbling of incorrect answer,

minus one (�1) mark will be awarded.

DO

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RESONANCE P1MT2XI090111C0-1

(SPACE FOR ROUGH WORK)

PART�IAtomic 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]

SECTION - IStraight Objective Type

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

1. The standard molar enthalpies of formation of cyclohexane () and benzene () at 25ºC are � 37 and +11.5

Kcal/mol respectively. The standard enthalpy of hydrogenation of cyclohexene () at 25ºC is � 28.5 Kcal/mol.

From the given data, calculate the magnitude of resonance energy of benzene :

(A) 37 Kcal/mol (B) 134 Kcal/mol (C) 54 Kcal/mol

(D) 157 Kcal/mol (E) 35 Kcal/mol

2. If two moles of a hypothetical real gas X occupy a volume of 4L at 10 atm pressure and 300 K, then which ofthe following statement is correct :

(A) Gas X is less compressible with respect to an ideal gas, since attractive tendencies are dominant amonggas molecules.

(B) On applying greater pressure, the gas X will respond by increasing its volume, since repulsive tendenciesare dominant among gas molecules.

(C) As the pressure is lowered and temperature is increased, the gas X will show greater deviation from idealbehaviour.

(D) Assuming the attractive / repulsive tendencies of gas X to be the same even at STP conditions, 1 mole ofgas X occupies a volume of 22.4 L at a pressure lower than that at STP (keeping temperature constant).

(E) The value of compressibility factor (Z) will be greater than 1 for the real gas X under the conditions givenin the question.



3. Which of the following statements is INCORRECT regarding caustic potash, KOH :(A) It is prepared by the electrolysis of an aqueous solution of KCl.(B) It is used for the absorption of gases like CO

2, SO

2 etc. in eudiometry.

(C) White phosphorus undergoes disproportionation reaction with its aqueous solution, when boiled.(D) Commercially, it can be prepared by Le-Blanc process, but not by Solvay�s process.

(E) Its 2 moles absorb 4 moles of NO forming KNO2 , N

2O and H

2O.

4. A proton beam can undergo diffraction by crystals. Through what potential (in volts) should a beam of protonsbe accelerated so that its wavelength becomes equal to 14.3 pm :(Given : Mass of a proton = 1.66 × 10�27

Kg)

(A) 1 V (B) 4 V (C) 9 V

(D) 16 V (E) 25 V

5. The solubility of Fe(OH)3 in a buffer solution of pH = 6 is 4.32 × 10�2 mol/L. How many times is this solubility

greater than its solubility in pure water. (Ignoring the hydrolysis of Fe3+ ions)

(A) 1000 (B) 216 (C) 10

(D) 432 (E) 216000




6. The density of a mixture of O2 and N

2 at NTP is 1.4 g/L. Then the partial pressure of O

2 is :

(A) 0.84 atm (B) 0.68 atm (C) 0.52 atm

(D) 0.36 atm (E) 0.2 atm

7. Which of the following compounds of Xenon have non-zero dipole moment ?

(A) XeF4

(B) XeO3F

2(C) XeO

2F

2

(D) XeO4

(E) XeF2

8. In which of the following processes on an ideal gas, there occurs an increase in entropy of the surroundings:

(A) Reversible Isothermal expansion.

(B) Irreversible adiabatic process.

(C) Isothermal free expansion (against vacuum)

(D) Adiabatic free expansion (against vacuum)

(E) None of these




9. Total number of geometrical isomers in the given compound is :

(A) 3 (B) 6 (C) 8

(D) 16 (E) 4

10. The total number of isomers for the alkyne with molecular formula C3HDClBr is :

(A) 4 (B) 6 (C) 8

(D) 5 (E) 7

SECTION - IIComprehension Type

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

Paragraph for Question Nos. 11 to 12

A 7 mole mixture of Cu2S and CuS was treated with 10 L of 1 M KMnO

4 solution in acidic medium producing

Cu2+, SO2 and Mn2+. The SO

2 gas produced was boiled off and the excess KMnO

4 was titrated with 6 L of 1

M FeSO4 solution.

Now answer the following questions :

11. What percentage of total KMnO4 is being consumed by FeSO

4 solution :

(A) 60% (B) 12% (C) 30% (D) 24%

12. In what molar ratio, is KMnO4 getting consumed by Cu

2S and CuS respectively :

(A) 4 : 3 (B) 8 : 15 (C) 2 : 9 (D) 1 : 1





A mixture containing 2 moles of an ideal gas A ( = 4/3) and 4 moles of an ideal gas B ( = 5/3) is expandedfrom 2 L to 8 L by a process, for which the graph of log T (y-axis) vs log V (x-axis) is a straight line with slope

�21

. The initial temperature of gas mixture is 320 K. Assuming the gas mixture to behave ideally,answer the

following questions :

13. Work done by the gas mixture in the above process is : (R = Gas constant)(A) 1920 R (B) 2000 R (C) 1840 R (D) 1760 R

14. What can be said about the value of Ssystem

for the above process :(A) will be greater than zero. (B) will be less than zero.(C) will be equal to zero. (D) nothing can be said with certainty.


There are three beakers labelled as A, B and C containing aqueous solutions of CH3COOH, NaOH and KOH

respectively.

A student performs some experiments :(a) When solution 'A' and 'B' are mixed completely, then it form buffer of pH = 4.7(b) When 'A' and 'C' solutions are mixed completely, then the resultant solution is basic.(log 2 = 0.3, log 5 = 0.7)

15. What would be the ionisation constant (Ka) of CH

3COOH ?

(A) 2 10�5 (B) 10�5 (C) 2 10�6 (D) 5 10�6

16. What will be the pH of solution, when 'A' and 'C' solutions are mixed completely ?(A) 9.5 (B) 5 (C) 10.15 (D) 8.85



SECTION - IIITrue & False Type

This Section Contains 4 questions. Each statement is either true (T) or false (F).

17. The number of electrons, having anticlokwise spin present in Zn2+ having n = 3, m = 1 values, is 3.

18. NCl3 does not undergo reaction with water due to non-availability of d-orbitals on N-atom.

19. Under identical conditions, a gas with lower molecular mass diffuses faster as compared to another gas withhigher molecular mass.

20. Epoxyethane and methoxymethane are functional isomers.




SECTION - IVInteger Answer Type

This section contains 5 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.

21. Determine the sum of fully filled and half filled orbitals, which have number of radial nodes less than thenumber of angular nodes, in ground state of Mn2+ ion.

22. Determine the sum of number of d-p bonds and number of peroxy linkages in one molecule each of Caro'sacid (H

2SO

5) and Marshall's acid (H

2S

2O

8).




23. Calculate the difference between enthalpy change (H) and internal energy change (E) in Kcal for thecombustion of 1 mole of heptane () at 27ºC. Give your answer in terms of magnitude, rounding it off to

nearest whole number.

24. How many of the following compounds do not impart characteristic colour to the Bunsen flame :

NaCl , BeCl2 , KOH , BaSO

4 , MgCl

2 , CsCl , Na

2SO

4 , Mg(OH)

2 , K

2CO

3

25. Write the total geometrical isomers (only cyclic) of C3H

3Br

2Cl.




PART- II



26. The complete range of k for which the inequality kcos2x � kcosx + 1 0, x (�, ), is

(A) k < � 21

(B) k > 4 (C) � 21

k 4 (D) 0 k 4

(E) �21 k

21

27. If the equation 2x2 + 4xy + 7y2 � 12x � 2y + t = 0, where t is a parameter has exactly one real solution of

the form (x, y). Then value of (x + y) is equal to

(A) 3 (B) 5 (C) �5 (D) �3

(E) 0

28. If z is a complex number satisfying the equation |z � (1 + i)|2 = 2 and = z2

, then the locus traced by in

complex plane is

(A) x � 2y � 1 = 0 (B) x + y � 1 = 0 (C) x � y + 1 = 0 (D) x + y + 1 = 0

(E) x � y � 1 = 0





29. If Sn =

n

1r234 rr2r

1r2, then S10 is equal to

(A) 121120

(B) 120121

(C) 120119

(D) 122121

(E) 119120

30. If a, b, c, d, e are positive integers and matrix A =

e0d

cba such that a + b + c + d + e = abcde, then

number of matrices A is equal to

(A) 16 (B) 24 (C) 40 (D) 60

(E) 48

31. BC is latus rectum of a parabola y2 = 4ax and A is its vertex. The minimum length of projection of BC on atangent drawn in portion of BAC is

(A) a2 (B) a22 (C) 2a (D) a23

(E) a24




32. If , and be the eccentric angles of point where a circle cuts an ellipse, then cos( + + + ) is equalto

(A) 1 (B) �1 (C) 0 (D) �21

(E) 21

33. The locus of P(x, y) such that 16y8yx 22 � 9x6�yx 22 = 5 is

(A) hyperbola (B) ellipse (C) circle (D) infinite ray

(E) finite line segment

34. If sin(sinx + cosx) = cos(cosx � sinx), then the largest possible value of sinx, is

(A) 2

1(B) 1 (C)

4�16 2

(D) 4

(E) 21




35. Number of 9 lettered words that can be formed using all the letters of the word 'MEENANSHU' if alike lettersare never adjacent, is k(7!). Then k lies in the interval.

(A) [1, 5] (B) (5, 10] (C) (10, 15] (D) (15, 20]

(E) (20, 25]




a, b, c are the sides of ABC satisfying log

ac

1 + loga � logb = log2. Also the quadratic equation

a (1 � x2) + 2bx + c (1 + x2) = 0 has two equal roots.

36. a, b, c are in

(A) A.P. (B) G.P. (C) H.P. (D) none of these

37. Measure of angle C is

(A) 30º (B) 45º (C) 60º (D) 90º





The line x + 2y + a = 0 intersects the circle x2 + y2 = 4 at two distinct points A and B. Another line12x � 6y � 41 = 0 intersects the circle x2 + y2 � 4x � 2y + 1 = 0 at two distinct points C and D.

38. The values of 'a' lies in the interval

(A) )52,52(� (B) )52,0( (C) )5,5(� (D) )52�,0(

39. The equation of circle passing through the points A, B, C and D is

(A) 5x2 + 5y2 � 8x � 16y � 36 = 0 (B) 5x2 + 5y2 + 8x � 16y � 36 = 0

(C) 5x2 + 5y2 + 8x + 16y � 36 = 0 (D) 5x2 + 5y2 � 8x � 16y + 36 = 0


Let S be the set of first 18 natural numbers. The number of ways of selecting three numbers from S suchthat

40. They are all consecutive or none of them are consecutive is

(A) 536 (B) 560 (C) 576 (D) 640

41. They form an A.P. is

(A) 54 (B) 60 (C) 64 (D) 72





This Section Contains 4 questions. Each statement is either true (T) or false (F).

42. Number of ways in which 4 identical balls can be kept in 7 different boxes if each box can have atmost oneball is 35.

43. Number of ways in which 5 balls can be selected from a bag containing 5 identical and 5 different balls,is 32.

44. Equation x4 � 2x2 sin2 2x

+ 1 = 0 has only one real solution.

45. Equation tan

6x = 2 tanx has no real solution.





This section contains 5 questions. The answer to each of the questionsis a single digit integer, ranging from 0 to 9. The appropriate bubble belowthe respective question number in the ORS have to be darkened.

46. If the variable line 3x � 4y + k = 0 lies between the circles x2 + y2 � 2x � 2y + 1 = 0 and

x2 + y2 � 16x � 2y + 61 = 0 without intersecting or touching either circle, then the range of k is (a, b) where

a, b . Find the value of (b � a).

47. If the sum of all the solutions of the equation 3 cot2 + 10 cot + 3 = 0 in [0, 2] is k where k , then findthe value of k.

48. If is the imaginary cube root of unity, then find the number of ordered pairs of integers (a, b) such that|a + b| = 1.




49. The line 3x + 6y = k intersect the curve 2x2 + 2xy + 3y2 = 1 at two distinct points A and B. The circle on ABas diameter passes through the origin. The sum of possible values of k is

50. Let A be the set of all 3 × 3 skew symmetric matrices whose entries are either �1, 0 or 1. If there are exactly

three 0's three 1's and three (�1)'s, then the number of such matrices, is



PART - III



51. A tube of length open at only one end is cut into two equal halves. The sixth overtone frequency of piececlosed at one end equals to sixth overtone frequency of piece open at both ends. The radius of cross�section of tube is :

(A) 12

(B) 725

(C) 24

(D) 245

(E) 485

52. In given figure, speed of A & D is 85

m/sec as shown and speed of

B with respect to A is 1 m/sec., find speed of c in vertical direction.(assume strings remains tight)

(A) 3 m/sec. (B) 5

19m/sec. (C)

2065

m/sec.

(D) 2 m/sec. (E) None of these




53. A non�uniform rope of length hangs from a ceiling. Mass per unit length of rope () changes as = 0ey,

where y is the distance along the string from its lowest point. Then graph between square of velocity of waveand y will be best represented as :

(A) (B) (C)

(D) (E)

54. A cubical box is filled 50% with water and is open from upper part then it isfixed on a moving cart with an acceleration 'a' on an fixed inclined as shownin figure. Value of a for which water will not come out from cube:

(A) 2g

(B) g (C) 2g

(D) 3g (E) All of these




55. A monkey of mass 'm' climbs�up on a rope with relative acceleration

2g

upward. Rope is wrapped on a uniform circular ring of mass 8m and

there is no slipping between ground and ring. If initial distance betweenmonkey and pulley is then how much time it will take to reach to thepulley. (Assume ring is sufficiently far from pulley) : (Neglect size of monkeyfor calculation, pulley and rope are ideal)

(A) g2

(B) g5

(C) g10

(D) g2

(E) None of these

56. A metal block of area 0.10 m2 is connected to a 0.020 kg mass via a string thatpasses over an ideal pulley as shown in figure. A liquid with a film thickness of0.30 mm is placed between the block and the table. When system is releasedthe block moves to the right with a small constant speed of 0.090 ms�1, thencoefficient of visocity of liquid is :

(A) 3

10× 10�3 Pa s (B)

320

× 10�3 Pa s (C) 10�2 Pa s

(D) 3

40× 10�3 Pa s (E) 6 × 10�3 Pa s

57. Extension in a uniform rod of length l, mass m, cross section radius r and young�smodulus Y when is suspended at one of its end.

(A) Yr3

gm2

(B) Yr

gm22

(C) Yr

gm2

(D) Yr2

gm2

(E) Yr2

gm52




58. 0.056 kg of nitrogen is enclosed in a vessel at a temperature of 27ºC. How much heat has to be transferred

to the gas to double the most probable speed of its molecules. (R = 2 cal/mol.k)(A) 4500 cal (B) 9000 cal (C) 18000 cal(D) 5000 cal (E) None of these

59. A gas has molar heat capacity C = 24.9 J mol�1 k�1 in the process P2T = constant. Then (R = 8.3 J/mol k)(A) Gas is monoatomic (B) Gas is diatomic (C) Gas is triatomic(D) Atomicity of gas is 4 (E) Data insufficient

60. A small ball of mass m is released from height h on a wedge having circulartrack as shown in figure. Find the normal force on ball due to wedge just afterit enters in circular track.(Assume it enters at point P tangentially and allsurfaces are smooth)

(A) R

mgh2(B)

Rmgh

34

(C) R

mgh4

(D) R2

mgh(E) zero




A driver is riding a car with velocity vC between two vertical walls on a horizontal surface as shown in figure.

A source of sound of frequency 'f' is situated on the car. (vc << v, where v is the speed of sound in air)




61. Beat frequency observed by the driver corresponding to sound waves reflected from wall-1 and wall-2 (reflectedwaves corresponding to waves directly coming from source) :

(A) fv

vc (B) fv

v2 c (C) fv2

vc (D) fv

v4 c

62. Consider the sound wave observed by the driver directly from car has a wavelength 1 and the sound wave

after reflection from wall-1 observed by the driver has wavelength 2 then

21

21

is :

(A) v

vc (B) v

v2 c (C) v4

vc (D) v

v4 c


A uniform disc of mass m is imparted an impulse at a height 2R3

from AB (as shown) where R is the radius

of the disc. Surface AB is smooth while BC and CD is sufficiently rough to prevent slipping.

63. Minimum value of impulse P so that disc climbs up on the surface CD without loosing contact at point C :

(A) gR23

m (B) gR23

m2 (C) gR21

m (D) gRm

64. Find the friction force on sphere just after minimum impulse is imparted in previous question :

(A) 3

mg(B)

32

mg(C)

3

mg2(D) mg3




Consider one mole of an ideal monoatomic gas is inside a fixed, perfectly insulating cylindrical vessel attemperature T and piston is at equilibrium initially as shown in figure. Now a particle of mass m strikeshorizontally to piston of same mass at mid�point of piston and sticks to piston. Initially temperature

T = R

mv2

, where R is universal gas constant) (Neglect heat loss through piston, assume that velocity is so

small that change in the the temperature of gas due to motion of piston is simultaneous in whole volume)(friction is absent everywhere)

65. Ratio of maximum temperature and minimum temperature of gas during motion of piston :(A) 1 (B) 7 : 6 (C) 7 : 5 (D) 6 : 7

66. Assume whole system is placed in gravity free room, and in previous question, particle strikes elasticallythen find ratio of maximum temperature to minimum temperature during motion of piston :(A) 4 : 3 (B) 3 : 4 (C) 2 : 1 (D) 1 : 2






This Section Contains 4 questions. Each question is either true (T) or false (F).

67. More heat is required to change temperature of an ideal gas, at constant pressure than at constant volumeby same amount.

68. A rigid body rolls up inclined plane without sliding. The friction force on it may be downwards.

69. A string is carrying sinusoidal wave. Consider a small segment of string then total energy of this smallsegment is conserved.

70. When a ball strikes a fixed horizontal surface at angle with vertical and rebounds at with same angle withvertical then it must be an elastic collision.


This section contains 5 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.

71. A uniform string of length , fixed at both ends is vibrating in its 2nd overtone. The maximum amplitudeis 'a' and tension in string is 'T', if the energy of virbation contained between two consecutive nodes is

8K

Ta 22

then 'K' is :




72. A tall glass jar has a small hole of radius 0.06 mm at its bottom, xis the approximate depth upto which the jar can be lowered vertically

in water before water enters into it through the hole. Find10x

in cm.

(Surface Tension of water = 0.06 N/m) (g = 10 m/s2 , density ofwater = 1000 kg/m3) (Assume drop of water becomeshemispherical before water enters in jar)

73. 4 gms of steam at 100°C is added to 20 gms of water at 46°C in a container of negligible mass.

Assuming no heat is lost to surrounding, If the mass of water in container at thermal equilibrium is 5.5x(in gms) then 'x' is : Latent heat of vaporisation = 540 cal/gm. Specific heat of water = 1 cal/gm-°C.

74. A uniform rectangular plate of mass 1 kg is performing combinedrotational motion and translational motion with constant angular speed2 rad./sec (as shown in figure). Speed of centre of mass of plate is1m/sec. If the kinetic energy of plate with respect to a point A (point A

is on the plate) is 3K

Joule then 'K' is :




75. Initially a small block is in equilibrium and at a height 10m from ground as shown. At t = 0, block explodes intwo equal parts. One part collides with the ground at t = 1 sec and sticks to ground at the position just belowthe initial equilibrium position and another part remains held with spring, then find the amplitude of oscillationsof the block held by spring.

(Space for rough work)

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Documents

CODE MAJOR TEST-2 (MT-2) TARGET : IIT-JEE 2011 0 · Determine the sum of fully filled and half filled orbitals, which have number of radial nodes less than the number of angular nodes,