upkar prakashan, agra-2 - kopykitab · reasoning graphical analysis, analytical and numerical...

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UPKAR PRAKASHAN, AGRA-2

ByDr. Madhusudan Prasad Sinha

Deptt. of PhysicsJagajivan Ram Shramik College, Jamalpur

Munger811214Tilka Manjhi Bhagalpur University,

Bhagalpur812007 (Bihar)&

Manoranjan Kr. SinhaDeptt. of Electronics & Communication

Muzaffarpur Institute of Technology, Muzaffarpur842003Aryabhat Knowledge University, Patna800001 (Bihar)

PARTA + B + C

According to New Syllabus and Pattern

Publishers

Publishers

UPKAR PRAKASHAN2/11A, Swadeshi Bima Nagar, AGRA282 002Phone : 4053333, 2530966, 2531101Fax : (0562) 4053330E-mail : [email protected], Website : www.upkar.in

Branch Offices :4845, Ansari Road, Daryaganj,New Delhi110 002Phone : 01123251844/66

Paras Bhawan(First Floor),Khazanchi Road,Patna800 004Phone : 06122673340

1-8-1/B, R.R. Complex (Near SundaraiahPark, Adjacent to Manasa Enclave Gate),Bagh Lingampally,Hyderabad500 044Phone : 04066753330

28, Chowdhury Lane, ShyamBazar, Near Metro Station,Gate No. 4Kolkata700 004 (W.B.)Phone : 03325551510

B-33, Blunt Square, KanpurTaxi Stand Lane, Mawaiya,Lucknow226 004 (U.P.)Phone : 05224109080

8-310/1, A. K. House,Heeranagar, Haldwani,Distt.Nainital263 139(Uttarakhand)Mob. : 7060421008

1461, Juni Shukrawari,Sakkardara Road,Opp. Hanuman Mandir,Nagpur440 009Phone : 07126564222

The publishers have taken all possible precautions in publishing this book, yet ifany mistake has crept in, the publishers shall not be responsible for the same.

This book or any part thereof may not be reproduced in any form byPhotographic, Mechanical, or any other method, for any use, without writtenpermission from the Publishers.

Only the courts at Agra shall have the jurisdiction for any legal dispute.

ISBN : 978-81-7482-146-1

Price : 41000(Rs. Four Hundred Ten Only)

Code No. 452

Printed at : UPKAR PRAKASHAN (Printing Unit) Bye-pass, AGRA

Preface

It is a matter of pleasure to present this guide (help) book of UPKARS CSIR-UGC : NET/JRF/SET Physical Sciences PartA+B+C for CSIR-UGCNational Eligibility Test (NET) for Lectureship,Junior Research Fellowship (JRF) and State Eligibility Test (SET) for Lectureship. This book has beenprepared for the candidates/students preparing on the basis of the new syllabus and new patternprescribed by University Grant commission (UGC) and CSIR, New Delhi.

The aim of writing this book is to provide a self-oriented study style and covering the differentaspects of examination in Physics for all those candidates/students who do not have the facilities ofextra guidance for the preparation. Selected Multiple Choice Questions and Exercise Model Test Setshave been given in the book. Each chapter has an important review of topics as a help to memory of thestudents.

All the necessary subject matter has been presented in a simple, lucid style and in an elaborateform which will help even a fresher in following the subject with a little effort and in forming clearmental concept. Neat and clear diagrams are used for explanations. It is earnestly hoped that this bookbased on new pattern will be found useful by the candidates/students appearing in CSIR-UGC NET/JRFExaminations.

The author is grateful to Dr. Vijay Kr. Singh Head of the Deptt. of Physics, Tilka ManjhiBhagalpur University, Bhagalpur, Head, Deptt. of Physics, R.D. & D.J. College Munger, Dr. RajmaniPd. Sinha, Ex. V.C., Lalit Narayan Mithila University, Darbhanga present Chairman of B.S.E.B. Patna.Head, Deptt. of Physics, P.U. Patna, Dr. B.P. Sinha, Ex. Head, Deptt. of Physics, B. N. College Patna,Patna University, Patna & late Dr. Nageshwar Prasad, Head Deptt. of Physics, Kisan College Sohsarai,Biharsharif (Nalanda), Magadh University Bodh-Gaya, Gaya (Bihar), who taught me the art of writings.

The author is grateful to his wife Smt. Gaytree Sinha who has relieved him from domesticliabilities.

Possible suggestions from the learned teachers for improvement of this book, are thankfullyinvited.

Above all, the author shows his gratitude to the blessings of his late grandparents, late mother,father, the elders in the family, the love and good wishes of the younger ones.

Our thanks are also due to UPKAR PRAKASHAN for encouraging me to write this book and bywhose interest and efforts this book could be brought out in time.

Dr. M. P. Sinha&

Er. M. K. Sinha

Contents

Previous Years Solved Papers

PartA

1. Numerical Ability & Quantitative Comparison 332

Important Facts & Formulae with Examples 3 Multiple Choice Questions .... 14

2. Numerical Reasoning and Logical Reasoning 3355

Important Facts & Formulae with Examples 33 Multiple Choice Questions .... 43

3. Data Interpretation and Analysis 5662

Important Facts & Formulae with Examples .. 56 Multiple Choice Questions .... 59

4. Puzzle Test 5772

PartB & C1. Mathematical Methods of Physics... 346

Important Facts and Formulae 3 Multiple Choice Questions ....... 36

2. Classical Mechanics..... 4771


3. Electromagnetic Theory... 7298


4. Quantum Mechanics.... 99137


5. Thermodynamics and Statistical Physics... 138168


( v )

6. Electronics and Experimental Methods.... 169326

Important Facts & Formulae 169 Multiple Choice Questions ....... 285

7. Atomic and Molecular Physics... 327364


8. Condensed Matter Physics... 365417


9. Nuclear and Particle Physics... 418457


Nobel Prize Winners in Physics, Table for S. I. Units, Constants &Logarithms 458480

GENERAL INFORMATION

EXAM SCHEMETime : 3 Hours Max. Marks : 200

Single Paper Test having Multiple ChoiceQuestions (MCQs) is divided in three parts.

Part A This part shall carry 20 questions pertaining

to General Aptitude with emphasis on logicalreasoning graphical analysis, analytical andnumerical ability, quantitative comparisons, seriesformation, puzzles etc. The candidates shall berequired to answer any 15 questions. Eachquestion shall be of two marks. The total marksallocated to this section shall be 30 out of 200.

Part BThis part shall contain 25 Multiple Choice

Questions (MCQs) generally covering the topicsgiven in the Part B of syllabus. Candidates arerequired to answer any 20 questions. Eachquestion shall be of 35 marks. The total marksallocated to this section shall be 70 out of 200.

Part CThis part shall contain 30 questions from Part

C & B of the syllabus that are designed to testa candidates knowledge of scientific conceptsand/or application of the scientific concepts. Thequestions shall be of analytical nature where acandidate is expected to apply the scientificknowledge to arrive at the solution to the givenscientific problem. A candidate shall be requiredto answer any 20 questions. Each question shall beof 5 marks. The total marks allocated to thissection shall be 100 out of 200. There will be negative marking @25% for

each wrong answer.

To enable the candidates to go through thequestions, the question paper booklet shall bedistributed 15 minutes before the scheduled

time of the Exam. The answer sheet (OMRsheet) shall be distributed at the scheduledtime of the Exam.

SYLLABUSPart A

This part shall carry 20 questions pertainingto General Aptitude with emphasis on logicalreasoning graphical analysis, analytical andnumerical ability, quantitative comparisons, seriesformation, puzzles etc. The candidates shall berequired to answer any 15 questions. Eachquestion shall be of two marks. The total marksallocated to this section shall be 30 out of 200.

Part BI. Mathematical Methods of Physics

Dimensional analysis. Vector algebra andvector calculus. Linear algebra, matrices, Cayley-Hamilton Theorem. Eigenvalues and eigenvectors.Linear ordinary differential equations of first &second order, Special functions (Hermite, Bessel,Laguerre and Legendre functions). Fourier series,Fourier and Laplace transforms. Elements ofcomplex analysis, analytic functions; Taylor &Laurent series; poles, residues and evaluation ofintegrals. Elementary probability theory, randomvariables, binomial, Poisson and normal distri-butions. Central limit theorem.

II. Classical MechanicsNewtons laws. Dynamical systems, Phase

space dynamics, stability analysis. Central forcemotions. Two body Collisionsscattering inlaboratory and Centre of mass frames. Rigid bodydynamicsmoment of inertia tensor. Non-inertialframes and pseudoforces. Variational principle.Generalized co-ordinates. Lagrangian andHamiltonian formalism and equations of motion.

( vii )

Conservation laws and cyclic co-ordinates.Periodic motion: small oscillations, normalmodes. Special theory of relativityLorentztransformations, relativistic kinematics and massenergy equivalence.

III. Electromagnetic Theory

Electrostatics : Gausss law and its appli-cations, Laplace and Poisson equations, boundaryvalue problems. Magnetostatics: Biot-Savart law,Amperes theorem. Electromagnetic induction.Maxwells equations in free space and linearisotropic media; boundary conditions on the fieldsat interfaces. Scalar and vector potentials, gaugeinvariance. Electromagnetic waves in free space.Dielectrics and conductors. Reflection andrefraction, polarization, Fresnels law, inter-ference, coherence and diffraction. Dynamics ofcharged particles in static and uniform electro-magnetic fields.

IV. Quantum Mechanics

Wave-particle duality. Schrdinger equation(time-dependent and time-independent).Eigenvalue problems (particle in a box, harmonicoscillator, etc.). Tunneling through a barrier.Wave-function in co-ordinate and momentumrepresentations. Commutators and Heisenberguncertainty principle. Dirac notation for statevectors. Motion in a central potential: orbitalangular momentum, angular momentum algebra,spin, addition of angular momenta; Hydrogenatom. Stern-Gerlach experiment. Time-inde-pendent perturbation theory and applications.Variational method. Time dependent perturbationtheory and Fermis golden rule, selection rules.Identical particles, Pauli exclusion principle, spin-statistics connection.

V. Thermodynamic and Statistical Physics

Laws of thermodynamics and their con-sequences. Thermodynamic potentials, Maxwellrelations, chemical potential, phase equilibria.Phase space, micro and macro-states. Micro-canonical, canonical and grand-canonicalensembles and partition functions. Free energyand its connection with thermodynamic quantities.Classical and quantum statistics. Ideal Bose andFermi gases. Principle of detailed balance.Blackbody radiation and Plancks distribution law.

VI. Electronics and Experimental Methods

Semi-conductor devices (diodes, junctions,transistors, field effect devices, homo and hetero-junction devices), device structure, devicecharacteristics, frequency dependence andapplications. Opto-electronic devices (solar cells,photo-detectors, LEDs). Operational amplifiersand their applications. Digital techniques andapplications (registers, counters, comparators andsimilar circuits). A/D and D/A converters.Microprocessor and microcontroller basics. Datainterpretation and analysis. Precision and accuracy.Error analysis, propagation of errors. Leastsquares fitting.

Part C

I. Mathematical Methods of PhysicsGreens function. Partial differential

equations (Laplace, wave and heat equations intwo and three dimensions). Elements ofcomputational techniques: root of functions,interpolation, extrapolation, integration bytrapezoid and Simpsons rule, Solution of firstorder differential equation using Runge-Kuttamethod. Finite difference methods. Tensors.Introductory group theory : SU(2), O(3).

II. Classical MechanicsDynamical systems, Phase space dynamics,

stability analysis. Poisson brackets and canonicaltransformations. Symmetry, invariance andNoethers theorem. Hamilton-Jacobi theory.

III. Electromagnetic TheoryDispersion relations in plasma. Lorentz

invariance of Maxwells equation. Transmissionlines and wave guides. Radiation from movingcharges and dipoles and retarded potentials.

IV. Quantum MechanicsSpin-orbit coupling, fine structure. WKB

approximation. Elementary theory of scattering :phase shifts, partial waves, Born approximation.Relativistic quantum mechanics : Klein-Gordonand Dirac equations. Semi-classical theory ofradiation.

V. Thermodynamic and Statistical PhysicsFirst and second-order phase transitions.

Diamagnetism, paramagnetism and ferromag-netism. Ising model. Bose-Einstein condensation.

( viii )

Diffusion equation. Random walk and Brownianmotion. Introduction to non-equilibrium processes.

VI. Electronics and Experimental MethodsLinear and non-linear curve fitting, chi-square

test. Transducers (temperature, pressure/ vacuum,magnetic fields, vibration, optical and particledetectors). Measurement and control. Signalconditioning and recovery. Impedance matching,amplification (Op-amp based, instrumentationamp, feedback), filtering and noise reduction,shielding and grounding. Fourier transforms, lock-in detector, box-car integrator, modulationtechniques.

High frequency devices (including generatorsand detectors).

VII. Atomic & Molecular PhysicsQuantum states of an electron in an atom.

Electron spin. Spectrum of helium and alkaliatom. Relativistic corrections for energy levels ofhydrogen atom, hyperfine structure and isotopicshift, width of spectrum lines, LS & JJ couplings.Zeeman, Paschen-Bach & Stark effects. Electronspin resonance. Nuclear magnetic resonance,chemical shift. Frank-Condon principle. Born-Oppenheimer approximation. Electronic,rotational, vibrational and Raman spectra ofdiatomic molecules, selection rules. Lasers :spontaneous and stimulated emission, Einstein A& B coefficients. Optical pumping, populationinversion, rate equation. Modes of resonators andcoherence length.

VIII. Condensed Matter PhysicsBravais lattices. Reciprocal lattice. Diffraction

and the structure factor. Bonding of solids. Elastic

properties, phonons, lattice specific heat. Freeelectron theory and electronic specific heat.Response and relaxation phenomena. Drudemodel of electrical and thermal conductivity. Halleffect and thermo-electric power. Electron motionin a periodic potential, band theory of solids :metals, insulators and semi-conductors.Superconductivity : type-I and type-II super-conductors. Josephson junctions. Superfluidity.Defects and dislocations. Ordered phases ofmatter : translational and orientational order,kinds of liquid crystalline order. Quasi crystals.

IX. Nuclear and Particle Physics

Basic nuclear properties : size, shape andcharge distribution, spin and parity. Bindingenergy, semi-empirical mass formula, liquid dropmodel. Nature of the nuclear force, form ofnucleon-nucleon potential, charge-independenceand charge-symmetry of nuclear forces. Deuteronproblem. Evidence of shell structure, single-particle shell model, its validity and limitations.Rotational spectra. Elementary ideas of alpha, betaand gamma decays and their selection rules.Fission and fusion. Nuclear reactions, reactionmechanism, compound nuclei and direct reactions.

Classification of fundamental forces.Elementary particles and their quantum numbers(charge, spin, parity, isospin, strangeness, etc.).Gellmann-Nishijima formula. Quark model,baryons and mesons. C, P, and T invariance.Application of symmetry arguments to particlereactions. Parity non-conservation in weakinteraction. Relativistic kinematics.

CSIR-UGC-NET/JRF Exam. June 2016 Solved PaperPhysical Sciences(Held on 19 June, 2016)

PART A

1. My friend Raju has more than 1000 books,said Ram. Oh no, he has less than 1000books, said Shyam. Well, Raju certainlyhas at least one book, said Geeta. If only oneof these statements is true, how many booksdoes Raju have ?(A) 1 (B) 1000(C) 999 (D) 1001

2. Of the following, which is the odd one out ?(A) Cone (B) Torus(C) Sphere (D) Ellipsoid

3. An infinite number of identical circular discs

each of radius 12 are tightly packed such that

the centres of the discs are at integer values ofcoordinates x and y. The ratio of the area ofthe uncovered patches to the total area is

(A) 1 4

(B)4

(C) 1 (D)

4. It takes 5 days for a steamboat to travel fromA to B along a river. It takes 7 days to returnfrom B to A. How many days will it take for araft to drift from A to B (all speeds stayconstant) ?(A) 13 (B) 35(C) 6 (D) 12

5. N is a four digit number. If the leftmost digitis removed, the resulting three digit number is1/9th of N. How many such N are possible ?(A) 10 (B) 9(C) 8 (D) 7

6. What is the minimum number of movesrequired to transform figure 1 to figure 2 ? Amove is defined as removing a coin andplacing it such that it touches two other coinsin its new position.

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

7.

(A) (B)

(C) (D)

8.

2 | CSIR Physical Sci. (J-16)

Which of the following inferences can bedrawn from the above graph ?(A) The total number of students qualifying

in Physics in 2015 and 2014 is the same(B) The number of students qualifying in

Biology in 2015 is less than that in 2013(C) The number of Chemistry students

qualifying in 2015 must be more than thenumber of students who qualified inBiology in 2014

(D) The number of students qualifying inPhysics in 2015 is equal to the number ofstudents in Biology that qualified in 2014

9. A student appearing for an exam is declaredto have failed the exam if his/her score is lessthan half the median score. This implies(A) 1/4 of the students appearing for the

exam always fail(B) if a student scores less than 1/4 of the

maximum score, he/she always fails(C) if a students scores more than 1/2 of the

maximum score, he/she always passes(D) it is possible that no one fails

10. The relationship among the numbers in eachcorner square is the same as that in the othercorner squares. Find the missing number

(A) 10 (B) 8(C) 6 (D) 12

11. Which one of the following statements islogically incorrect ?(A) I always speak the truth(B) I occasionally lie(C) I occasionally speak the truth(D) I always lie

12. What comes next in the sequence ?

(A) (B)

(C) (D)

13. AB and CD are two chords of a circlesubtending 60 and 120 respectively at thesame point on the circumference of the circle.Then AB : CD is

(A) 3 : 1 (B) 2 : 1

(C) 1 : 1 (D) 3 214. Which of the following best approximates sin

(05) ?

(A) 05 (B) 05 90

(C) 05

180(D) 05

360

15. The set of numbers (5, 6, 7, m, 6, 7, 8, n) hasan arithmetic mean of 6 and mode (mostfrequently occurring number) of 7. Then m n =(A) 18 (B) 35(C) 28 (D) 14

16. Fill in the blank : F2, , D8, C16, B32, A64.(A) C4 (B) E4(C) C2 (D) G16

17. How many times starting at 1:00 pm wouldthe minute and hour hands of a clock make anangle of 40 with each other in the next 6hours ?(A) 6 (B) 7(C) 11 (D) 12

18. A solid contains a spherical cavity. The cavityis filled with a liquid and includes a sphericalbubble of gas. The radii of cavity and gasbubble are 2 mm and 1 mm, respectively.What proportion of the cavity is filled withliquid ?

(A)18

(B)38

(C)58

(D)78

19. The diagram shows a block of marble havingthe shape of a triangular prism. What is themaximum number of slabs of 10 10 5 cm3size that can be cut parallel to the face onwhich the block is resting ?

CSIR Physical Sci. (J-16) | 3

(A) 50 (B) 100

(C) 125 (D) 250

20. Brothers Santa and Chris walk to school fromtheir house. The former takes 40 minuteswhile the latter, 30 minutes. One day Santastarted 5 minutes earlier than Chris. In howmany minutes would Chris overtake Santa ?

(A) 5 (B) 15

(C) 20 (D) 25

PART B

21. Let (x, t) and (x, t) be the coordinate systemsused by the observers O and O, respectively.Observer O moves with a velocity v = calong their common positive x-axis. If x+ = x+ ct and x = x ct are the linear combinationsof the coordinates, the Lorentz transformationrelating O and O takes the form

(A) x+ = x_ x+

1 2 and x =

x+ x

1 2

(B) x+ = 1 + 1

x+ and x = 1 1 +

x

(C) x+ = x+ x

1 2 and x =

x x+

1 2

(D) x+ = 1 1 +

x+ and x = 1 + 1

x

22. Four equal charges of +Q each are kept at thevertices of a square of side R. A particle ofmass m and charge +Q is placed in the planeof the square at a short distance a (


n = 0

a(a + 1) (a + n 1)b(b + 1) (b + n 1)

c(c + 1) (c + n 1)n! zn,

satisfies the recursion relation

(A)ddz

F(a, b, c; z) = cab

F(a 1, b 1, c 1; z)

(B)ddz

F(a, b, c; z) = cab

F(a + 1, b + 1, c + 1; z)

(C)ddz

F(a, b, c; z) = abc

F(a 1, b 1, c 1; z)

(D)ddz

F(a, b, c; z) = abc

F(a + 1, b + 1, c + 1; z)

28. The Hamiltonian of a system with generalizedcoordinate and momentum (q, p) is H = p2q2.A solution of the Hamiltonian equation ofmotion is (in the following A and B areconstants)

(A) p = Be 2At, q = AB

e2At

(B) p = Ae 2At, q = AB

e 2At

(C) p = AeAt, q = AB

e At

(D) p = 2Ae A2t, q =

AB

eA2t

29. The value of the contour integral

12i

OC e4z 1

cosh (z) 2sinh (z) dz

around the unit circle C traversed in the anti-clockwise direction, is

(A) 0 (B) 2

(C) 8

3(D) tanh ( )12

30. The state of a particle of mass m in a one-dimensional rigid box in the interval 0 to L isgiven by the normalised wavefunction (x)

= 2L ( )35 sin ( )2xL + 45 sin ( )4xL . If

its energy is measured, the possibleoutcomes and the average value of energy are,respectively

(A)h2

2mL2,

2h2

mL2 and

7350

h2

mL2

(B)h2

8mL2,

h2

2mL2 and

1940

h2

mL2

(C)h2

2mL2,

2h2

mL2 and

1910

h2

mL2

(D)h2

8mL2,

2h2

mL2 and

73200

h2

mL2

31. A magnetic field B is Bz in the region x > 0and zero elsewhere. A rectangular loop, in thexy-plane, of sides l (along the x-direction) andh (along the y-direction) is inserted into thex > 0 region from the x < 0 region at a

constant velocity v = vx. Which of thefollowing values of l and h will generate thelargest EMF ?(A) l = 8, h = 3 (B) l = 4, h = 6(C) l = 6, h = 4 (D) l = 12, h = 2

32. The x and z-components of a static magneticfield in a region are Bx = B0(x2 y2) and Bz =0, respectively. Which of the followingsolutions for its y-component is consistentwith the Maxwell equations ?(A) By = B0xy(B) By = 2B0xy(C) By = B0 (x2 y2)

(D) By = B0 ( )13 x3 xy233. Suppose that the Coulomb potential of the

hydrogen atom is changed by adding aninverse-square term such that the total

potential is V(r ) =

ze2

r +

gr2

, where g is a

constant. The energy eigenvalues Enlm in themodified potential(A) depend on n and l, but not on m(B) depend on n but not on l and m(C) depend on n and m, but not on l(D) depend explicitly on all three quantum

numbers n, l and m

34. If Lx, Ly and Lz are the components of theangular momentum operator in three dimen-

sions, the commutator [L x, LxLyLz] may besimplified to

(A) i hLx ( )L2z L2y (B) ihLzLyLx(C) ihLx (2L

2z L

2y) (D) 0

35. Two parallel plate capacitors, separated bydistances x and 11x respectively, have adielectric material of dielectric constant 30inserted between the plates, and are connected

CSIR Physical Sci. (J-16) | 5

to a battery of voltage V. The difference incharge on the second capacitor compared tothe first is(A) + 66% (B) + 20%(C) 33% (D) 10%

36. The eigenstates corresponding to eigenvaluesE1 and E2 of a time-independent Hamiltonianare |1 and |2 respectively. If at t = 0, thesystem is in a state |(t = 0) = sin |1 + cos|2 the value of (t) | ( (t) at time t willbe(A) 1

(B)(E1 sin2 + E2 cos2)

E21 + E22(C) eiE1t/h sin + eiE2t/h cos

(D) e iE1t/h sin2 + e iE2t/h cos2

37. The half space regions x > 0 and x < 0 arefilled with dielectric media of dielectricconstants 1 and 2 respectively. There is auniform electric field in each part. In the righthalf, the electric field makes an angle 1 tothe interface. The corresponding angle 2 inthe left half satisfies

(A) 1 sin 2 = 2 sin 1(B) 1 tan 2 = 2 tan 1(C) 1 tan 1 = 2 tan 2(D) 1 sin 1 = 2 sin 2

38. A box of volume V containing N moleculesof an ideal gas, is divided by a wall with ahole into two compartments. If the volume ofthe smaller compartment is V/3, the varianceof the number of particles in it, is

(A)N3

(B)2N9

(C) N (D) N3

39. Given the input voltage Vi, which of thefollowing waveforms correctly represents theoutput voltage V0 in the circuit shown below ?

(A)

(B)

(C)

(D)


40. The intensity distribution of a red LED on anabsorbing layer of material is a Gaussiancentred at the wavelength 0 = 660 nm andwidth 20 nm. If the absorption coefficientvaries with wavelength as 0 K( 0),where 0 and K are positive constants, thelight emerging from the absorber will be(A) blue shifted retaining the Gaussian

intensity distribution(B) blue shifted with an asymmetric intensity

distribution(C) red shifted retaining the Gaussian

intensity distribution(D) red shifted with an asymmetric intensity

distribution

41. The dependence of current I on the voltage Vof a certain device is given by

I = I0 ( )1 VV02

where I0 and V0 are constants. In anexperiment the current I is measured as thevoltage V applied across the device is

increased. The parameters V0 and I0 can begraphically determined as(A) the slope and the y-intercept of the I-V2

graph(B) the negative of the ratio of the y-intercept

and the slope, and the y-intercept of theI-V2 graph

(C) the slope and the y-intercept of the I Vgraph

(D) the negative of the ratio of the y-interceptand the slope, and the y-intercept of the

I V graph42. A gas of non-relativistic classical particles in

one dimension is subjected to a potential V(x)= |x| (where is a constant). The partition

function is ( ) = 1kBT(A)

4m32h2

(B)2m

32h2

(C)8m

3a2h2 (D)

3m32h2

43. In the schematic figure given below, assumethat the propagation delay of each logic gateis tgate.

The propagation delay of the circuit will bemaximum when the logic inputs A and Bmake the transition(A) (0, 1) (1, 1) (B) (1, 1) (0, 1)(C) (0, 0) (1, 1) (D) (0, 0) (0, 1)

44. When an ideal monoatomic gas is expandedadiabatically from an initial volume V0 to3V0, its temperature changes from T0 to T.Then the ratio T/T0 is

(A)13

(B) ( )132/3

(C) ( )131/3

(D) 3

45. The specific heat per molecule of a gas ofdiatomic molecules at high temperatures is(A) 8kB (B) 35 kB(C) 45 kB (D) 3kB

PART C

46. In finding the roots of the polynomial f(x) =3x3 4x 5 using the iterative Newton-Raphson method, the initial guess is taken tobe x = 2. In the next iteration its value isnearest to(A) 1671 (B) 1656(C) 1559 (D) 1551

47. For a particle of energy E and momentum p(in a frame F), the rapidity y is defined as y =

12 ln

E + p3c

E p3c . In a frame F moving with

velocity v = (0, 0, c) with respect to F, therapidity y will be

(A) y = y + 12 ln (1 2)

(B) y = y 12 ln ( )1 + 1

(C) y = y + ln ( )1 + 1 (D) y = y + 2 ln ( )1 + 1

continue

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