1. Suppose the viscosity TJ of a particular composite fluid is such that it is related to the size of the fluid particles, their mean square velocity their mass Tn, and their relaxation time T under some thermal process, through a functional relationship. Which of the following could be a possible form for such an expression?

<img src='./qimages/1677-1.jpg'><br><br>

2. If x denotes the position operator of a quantum mechanical particle, then the eigenfunctions pie for the operator x ad/dx (where a is a constant with appropriate dimensions), having eigenvalues lamda and wave vector k are described by

3. The magnetic field at a distance z above the centre of a circular loop of radius R carrying a steady current I anticlock wise in k is

4. The relation between pressure and bulk modulus B of an electron gas at 0 K is

<img src='./qimages/1677-4.jpg'><br><br>

5. The matrix 3 has 2 independent eigenvectors given by

<img src='./qimages/1677-5.jpg'><br><br>

6. The output voltage of the given circuit (the diodes are silicon diodes) is

<img src='./qimages/1677-6.jpg'><br><br>

A 9.0 V
B 9.3 V
C 8.66 V
D 7.9 V

7. A canonical ensemble provides a model for

A an equilibrium system with fixed volume number of molecules which exchanges energy with the outside world

B an equilibrium isolated system with fixed volume, number of molecules and energy

C an equilibrium system with fixed volume which can exchange energy matter with the surroundings

D a system at constant pressure

8. Two orthogonally polarized light beams traverse through a birefringent mate rial. If during this passage one of the beams acquires an extra phase of pie with respect to the other, then the material is

A Half wave plate
B Quarter wave plate
C Polarizer
D Depolarizer

9. The decay constant of a radioactive sample is lamda . The half-life and mean-life of the sample are respectively given by

<img src='./qimages/1677-9.jpg'><br><br>

10. The possible number of ways that a stick of length 20 units will break into 3 pieces of length at least 2 units (the length of any piece may be ... is

<img src='./qimages/1677-10.jpg'><br><br>

11. To find a root of a transcendental equation, one can use bisection method secant method. One needs to have the value of the function with opposite signs at two points, when using

A as well as
B need not be for
C only not
D neither nor

12. The ratio of Pr(i and of a binomial distribution with n 20 and p 0.3 changes its behavior at i

<img src='./qimages/1677-12.jpg'><br><br>

13. The coefficient of variation for this data is

<img src='./qimages/1677-13.jpg'><br><br>

14. The ratio of the AM and GM of the roots of the polynomial x4 -20x2+64

<img src='./qimages/1677-14.jpg'><br><br>

15. The derivative of the integral

<img src='./qimages/1677-15.jpg'><br><br>

16. The residue of cot z at any of its poles is

<img src='./qimages/1677-16.jpg'><br><br>

17. Let A be an n x n matrix which is both Hermitian and unitary. Then

A A2 1
B A is real
C The eigenvalues of A are 0,1
D The minima and characteristic polynomials are the same

18. A combustion reaction of an organic molecule can be considered as

<img src='./qimages/1677-18.jpg'><br><br>

19. According to the Hess Law of heat-summation, the reaction may take place in several stages, nevertheless, the energy evolved (or observed) from the reaction

<img src='./qimages/1677-19.jpg'><br><br>

20. The product obtained in the following reaction CH3CH2CH2Br AIBRA->

<img src='./qimages/1677-20.jpg'><br><br>

21. Among the following transitions the one that falls in the visible region of electromagnetic spectrum is

<img src='./qimages/1677-21.jpg'><br><br>

22. The metal present in Vitamin B12 is

A zinc

B copper

C nickel

D cobalt

23. Crown ethers have strong affinity towards

A halides

B noble gases

C alkali metal ions

D transition metal ions

24. Solutions of 'the following compounds, all at the same molality, were prepared. Which solution has the lowest freezing point?

A KBr
B AI(N03h
C NaN02
D MgCl2

25. The molecule among the following that does not undergo nitration reaction with the mixture of HN03 and H2S04 is

<img src='./qimages/1677-25.jpg'><br><br>

26. If lamdai denote the eigenvalues of the matrix H

<img src='./qimages/1677-26.jpg'><br><br>

27. A unit normal n to the level curves In(x2 y2) in the plane at the point is

<img src='./qimages/1677-27.jpg'><br><br>

28. <img src='./qimages/1677-28.jpg'><br><br>

29. A material with cubic structure has got a lattice parameter value a 5A. What is the d-spacing between its planes?

<img src='./qimages/1677-29.jpg'><br><br>

30. In the XRD pattern of a cubic crystal, it is found that reflections corresponding to and are missing. Your conclusion is that

<img src='./qimages/1677-30.jpg'><br><br>

31. A square Lead slab of side 50 em, thickness 5 em, is subject to a shearing force (on its narrow face) of magnitude 9 x 104 N. The lower edge is riveted to the floor. If the shear modulus of Pb is 5.6 x 109 Pa, then the upper edge is displaced by

<img src='./qimages/1677-31.jpg'><br><br>

32. The terminal velocity of a copper ball of radius 2.0 mm in falling through a tank of oil at 20 is 6.5cm/s (given the densities of oil copper: poil 1.5 x 10sk9 f m3, p"opp",:8.9 x 703kgf m3). The viscosity of the oil at 20 "C is

<img src='./qimages/1677-32.jpg'><br><br>

33. Consider a state described by a complete set of quantum numbers with energy eigenvalue epsola The energy is found by computing U (kT)2logz/kt where Z is the partition function, T the temperature k Boltzmann's constant. If no more than two particles are characterized by a given set of quantum numbers, the energy is given by

<img src='./qimages/1677-33.jpg'><br><br>

34. The average energy of a system in thermal equilibrium is The mean square deviation of the energy from when Cv is the heat capacity of the entire system at constant volume, is

<img src='./qimages/1677-34.jpg'><br><br>

35. When temperature decreases, the chemical potential of a system of bosons

A increases eventually goes to zero
B decreases eventually goes to zero
C increases becomes negative
D decreases becomes negative

36, Suppose right-handed cirClllarly polarized light (defined to be clockwise as the observer looks toward the oncoming wave) is incident on an absorbing slab. The slab is suspended by a vertical thread. The light is directed upwards and hits the underside of the slab. If the light is of 1 Watt at a wavelength of 620 nm, and if all of this light is absorbed by the slab, what is the torque TO exerted on the slab in dyne-em?

A 3.3 X 10-9

B 3.3 X 10-6

C 6.6 X 10-9

D 9.9 X 10-9

37. A possible means for making an airplane invisible to radar is to coat the plane with an anti-reflective polymer. If the radar waves have a wavelength of 3 cm and refractive index of the polymer is 1.5, how thick should the coating be?

<img src='./qimages/1677-37.jpg'><br><br>

38. A He-Ne laser operates at a frequency of 4.74 x 1014 Hz, with a line width of deltav 1.5 GHz. Light travels between mirrors separated by 30 cm. How many longitudinal modes are possible in this frequency range?

A 5
B 4
C 3
D 2

39. <img src='./qimages/1677-39.jpg'><br><br>

A 208 MeV
B 501 MeV
C 20.8 MeV
D 5.01 MeV

40. The process

<img src='./qimages/1677-40.jpg'><br><br>

A can occur
B cannot occur since L is not conserved
C cannot occur since B is not comserved
D cannot occur since L spin are not conserved

41. <img src='./qimages/1677-41.jpg'><br><br>

42. For the given Op-Amp circuit the output voltage is

<img src='./qimages/1677-41.jpg'><br><br>

A 0.40 V

B 0.45 V

C 0.46 V

D 0.48 V

43. if the potential energy of a particle has a dependence on the radius vector r of the form u being a constant), then using the virial theorem, the average kinetic energy T and the average total energy E of the particle are:

<img src='./qimages/1677-43.jpg'><br><br>

44. <img src='./qimages/1677-44.jpg'><br><br>

45. The energy levels of a one-dimensional harmonic oscillator of electric charge 2e, located in a constant electric field E are given by

<img src='./qimages/1677-45.jpg'><br><br>

46. A 3-d isotropic harmonic oscillator has the energy eigenvalues where 3,..What is the degree of degeneracy of the quantum state

<img src='./qimages/1677-46.jpg'><br><br>

47. Using the Bohr-Sommerfeid quantization rule, if a ball is bouncing elastically in a vertical direction, its energy levels (with m being the mass of the ball, 9 the acceleration due to gravity, h Planck's constant, and nepsola will be

<img src='./qimages/1677-47.jpg'><br><br>

48. The potential of a uniformly charged spherical shell of radius R with surface charge density epsola is

<img src='./qimages/1677-48.jpg'><br><br>

49. A metal sphere of radius a carries a charge Q. It is surrounded out to radius b by a linear dielectric material of permittivity E. Find the potential at the centre

<img src='./qimages/1677-49.jpg'><br><br>

50. A particle of mass m moving with velocity V1 leaves a space in which its potential energy is a constant U1 and enters another in which its P.E. is a different constant U2 . If theta1 and theta2 are the angles between the normal to the plane and the velocities of the particle V1 V2 of the particle before after passing the
plane the change in direction of motion of the particle is given by

56. The estimator provided by Hit or Miss method for a definite integral is an

unbiased estimator

consistent estimator

A B C D
as well as Only not Only not neither not

57. The differential equation is invariant with respect to

Change of scale

Translation

<img src='./qimages/1677-57.jpg'><br><br>

58. Let X be a Geometric random variable with P=0.3. Then the

<img src='./qimages/1677-58.jpg'><br><br>

59. The weighted sum of independent identical random variables Xi's for S=IWiXi is an unbiased estimator for the population mean if SIGMAWI=

<img src='./qimages/1677-59.jpg'><br><br>

6O. Let Band C represent a triangle, and D be point on the plane spanned by ABC. D can be represented as

<img src='./qimages/1677-60.jpg'><br><br>

61. Let PO,P1,P2,P3,....,Pn be n+1 point in points space of d dimensional representation (ie Pi=(xi1,xi2,...,xid) where xij is real number). Consider Vi=Pi-PO for i=1,2....n will

<img src='./qimages/1677-61.jpg'><br><br>

62. A Train of length I km is at a platform of length p km. The engine (which pulls the train) is at the medial of the platform. If the train speed should not cross 10kmph while it is crossing any point of the platform, the time required to run the engine at 10kmph (with the assumption that the train can take any spe.ed instantaneously) is

<img src='./qimages/1677-62.jpg'><br><br>

63. In a chemical reactor the compounds A and B participate in forward reaction and produces compound C. C produces A B in backward reaction. and represents the respective mass of the compounds in the, reactors at time t and forward and backward rate of reactions be kl and k2. A mathematical representation of the process

<img src='./qimages/1677-63.jpg'><br><br>

64. Let X be any continuous univariate Random Variable and represent distribution function then the distribution of

<img src='./qimages/1677-64.jpg'><br><br>

65. The paired t test is useful for testing the hypothesis of

<img src='./qimages/1677-65.jpg'><br><br>

66. Let then

<img src='./qimages/1677-66.jpg'><br><br>

67. The Sturm-Liouville problem:

<img src='./qimages/1677-67.jpg'><br><br>

68. Nontrivial solutions of x>O are

<img src='./qimages/1677-68.jpg'><br><br>

69. The limit of the sum of for k=l to n as n->INFINITY

<img src='./qimages/1677-69.jpg'><br><br>

70. Let G be a group such that a2=e for each a E where e is the identity element of G. Then

<img src='./qimages/1677-70.jpg'><br><br>

71. For the matrix

<img src='./qimages/1677-71.jpg'><br><br>

72. Which of the following statements is false

<img src='./qimages/1677-72.jpg'><br><br>

73. The number of elements of order 5 in symmetric group 55 is

<img src='./qimages/1677-73.jpg'><br><br>

74. The set of all eigen values of the Sturm-Liouville problem is given by

<img src='./qimages/1677-74.jpg'><br><br>

75.The set of linearly independent solutions of the D4y-D2y=0 is

<img src='./qimages/1677-75.jpg'><br><br>

76. The molecule among the following that does not show Raman activity is

A)LI2

B)LiH

HrO

CTI4

77. The well behaved function among the following is

exp

exp

exp

exp

78. The hermitian operator among the following is

d/dx

exp

xd/dx

xd/dx

79. The wave function that mixes most with the ground state wave function of hydrogen atom in the presence of an electric field along the x-direction is

A)2s

B)2pX

2pY

2pz

80. Brillouin condition states thaT

<img src='./qimages/1677-80.jpg'><br><br>

81. Metal to ligand charge transfer occurs in:

Metal in high oxidation state and ligand having low lying acceptor orbitals

Metal in low oxidation state and ligand having low lying acceptor orbitals

Metal in high oxidation state and ligand having non bonding electrons

Metal with low lying empty orbital and ligand having lone pair of higher energy

82. Among the following that possesses maximum spin only magnetic moment in an octahedral environment is

Co3+

Mn2+

cR3+

V2+

83. Ground state term for C02+ ion is:

4F

3F

5D

65

84. The wrong statement regarding Wilkinson's catalyst among the following is

Its formula is (PhrP):RhCl

It acts as catalyst for hydrogenation

It loose chloride ion to form the active species for catalysis

It loose one triphenylphosphine ligand to form the active species for catalysis

85. Which among the following is not true for metal nitrosyl compounds:

Linear nitrosyl acts as three electron donor

Bent nitrosyl act as two electron donor

Bent nitrosyl act as one electroo donor

Metal nitrosyls generally obey 18-electron rule

86. Viscosity co-efficient of gas increasing temperature whereas viscosity co
efficient of liquid increasing temperature. Fill in the blanks from the following:

increases, decreases

decreases, increases

does not change, decreases

increases, does not change

87. The glass transition temperature of polymer is the temperature at which:

Crystalline domains of polymer melts

Amorphous domains of polymer becomes glassy

Crystalline transformation takes place

Both crystalline and amorphous domains of polymer melts

88. The weight average molar mass fur a sample containing 10% by weight of polymer of molar mass 10,000 and 90% by weight of polymer of molar mass 1,00,000 is

A)9.1x102

B)3.6x104

9.1x104

D)1.5X104

89. The repeating unit of Nylon-6,10 polymer is

<img src='./qimages/1677-89.jpg'><br><br>

90. Consider that the tei-nitro toluene is cOOlpletely combusted to form carbon dioxide, water and nitrogen gas, the oxygen balance for the TNT is









91. Product obtained in the following transformation is

<img src='./qimages/1677-91.jpg'><br><br>

92. Product obtained in the following transformation is

<img src='./qimages/1677-92.jpg'><br><br>

93. Product obtained in the following transformation is

<img src='./qimages/1677-93.jpg'><br><br>

94. Product obtained in the following transformation is

<img src='./qimages/1677-94.jpg'><br><br>

95. Product obtained in the following transformation is

<img src='./qimages/1677-95.jpg'><br><br>

96. The crystal field splitting diagram of orbitals in various fields are given below as and (iii). The correct matching of splitting diagram for corresponding crystal fields is

<img src='./qimages/1677-96.jpg'><br><br>

Octahedral field; Tetrahedral field; Square planar field

Tetrahedral field; Octahedral filed; Square planar field

Square planar field; Tetrahedral field; Octahedral filed

Square planar field; Octahedral filed; Tetrahedral field


97. The products X and Y in the following reaction are

<img src='./qimages/1677-97.jpg'><br><br>

98. Nitrogen molecule has fundamental vibrational frequency of 6.985x1013 S·I.The ratio of the v to V 0 population at 800°C is

0.440

0.044

0.404

0.004

99. Calculate EO for the reaction Given EO =0.44 v for 2e and EO= -0.77 v for

0.563 v

0.0367 v

0.850 v

0.33 v

100. CaF2 has a face-centered cubic lattice with and there are eight F-and four Ca2+ ions per unit cell. The density of CaF2 at 20°C is 3.18 g/cm3• The unit cell length of CaF2
crystal at 20°C is

0.546 A

5.46 A

4.56 A

6.54 A