Part-A. State Eligibility Test Physical Sciences. (Model Answer Key) Q1 : A 1 B -1/ D 1/ Q2 :

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1 State Eligibility Test 2017 Physical Sciences (Model nswer Key) Part- Q1 If f=tan -1 (y/x) then div(grad f ) is equal to य द f=tan -1 (y/x) ह त div(grad f ) क म न ह ग 1 1-1/ -1/ 0 0 1/ 1/ nswer Key Q2 What will be the cylindrical co ordinates of the vector field एक स दश वभव क ब लन क र नद श क nswer Key

2 Q3 What will be the Eigen value of the given matrix दय गय म स क अ भल णक म न बत ऐ 0, 0, 3 0, 0, 3 1, 1, 1 1, 1, 1-1, 2, 3-1, 2, 3 1, 0, 3 1, 0, 3 nswer Key Q4 The differential equation dy/dt = y 2 with the initial condition y(0)=1.2t, will expand as t tends to एक वभ दक सम करण dy/dt = y 2 जसक र भक दश y(0)=1.2t, ह त इसक t क कस म न क लय फ ल व ह ग? /2 1/2 nswer Key Q5 Inverse Laplace transform of will be e 2t sinh5t क तल म ल पल स प तर ह ग

3 e 2t sinh5t e-2t cosh5t e -2t cosh5t e-2t sinh5t e -2t sinh5t e2t cos5t e 2t cos5t nswer Key Q6 If x, y, z are non zero Hermitian operators which of the following relation must be false? य द x, y, z एक श य तर हरम शयन स क रक ह त इनम स क न स स ब ध गलत ह ग? xy + yx = z xy + yx = z xyz = z xyz = z [x.y] = z [x.y] = z x + y = z x + y = z nswer Key Q7 What is the Fourier cosine transform of e -t2? e -t2 क फ रयर क स ईन प तर य ह? e-s2 e -s2 e-s2/2 e -s2/2 e-s2/4 e -s2/4 e -s2/4 e -s2/4 nswer Key

4 Q8 particle of mass M moves on a plane in the field of force radial unit vector. The angular momentum of the particle about its origin will be? एक कण जसक म M ह एक समतल म बल स, जह य इक ई स दश ह, चल रह ह इस कण क क ण य स व ग म ल बन द पर य ह ग? Stationary थर onserved स र Not-conserved स र नह None of these are correct क ई वक प सह नह nswer Key Q9 particle moving under a central force describes the path r = a(1 cos ), then the force is inversely propositional to एक कण क य बल क अ तग त r = a(1 cos ) क पथ पर चल रह ह, त यह बल कसक तल म आन प तक ह ग r2 r 2 r3 r 3 r4 r 4 r5 r 5 nswer Key Q10 The Hamilton's canonical equation of motion in terms of Poisson rackets are प यसन क ट क पद म ग त क ह म टन क न नकल सम मरण ह ग

5 nswer Key Q11 2d2 2d 2 6d 6d The number of degree of freedom of a rigid body in space dimension is एक ढ़ प ड क सम ट वम म कतन वत त क क ट ह ग d(d+1)/2 d(d+1)/2 d(d+1)/d-1 d(d+1)/d-1 nswer Key Q12 The Largrangian of a particle moving in plane under the influence of central potential is given by. The generalized momentum corresponding to r and are एक समतल म चलत ह ऐ कण क ल गर जयन ज एक क य वभव क अ तग त, दय गय ह इसक य प क त स व ग r एव क अन क ल ह ग

6 nswer Key Q13 What will be Hamiltonian corresponding to Lagrangian ल गर जयन क स गत ह मलट नयन य ह ग is nswer Key Q14 n electron has kinetic energy equal to its rest energy. If the momentum of a photon is equal to this electron, what will be the energy of this photon?(you may need E 0 =m e c 2 ) एक इल न क ग तज ऊज उसक वर म ऊज क बर बर ह य द एक फ ट न क स व ग इस इल न क बर बर ह त इस फ ट न क ऊज य ह ग? ( दय गय ह E 0 =m e c 2 ) E 0 E 0 E 0 E 0 E 0 E 0

7 nswer Key Q15 Two particles are travel long in opposite direction with speed 0.9c relative to the laboratory. Their relative speed will be द कण वपर त दश ओ म 0.9 स क ग त स चल यम न ह उनक स प ग त बत ऐ 0.948c 0.948स c स.98c.98स 0.995c 0.995स nswer Key Q16 n electron falls from rest through a potential difference of 100 V. What is its de roglie wave length? एक इल न 100 V क वभव म वर म स न च गरत ह इसक ड गल तर गध य ह ग 12.3 nm 12.3 nm 11.3 o 11.3 o 12.3 o 12.3 o nm nm nswer Key Q17 Which one will be the quantum mechanical operator of a particle moving in one dimension? एक कण एक वम म चल रह ह, त उसक व नटम य क च लक ह ग

8 nswer Key Q18 tanx tanx cosecx cosecx cotx cotx sinx sinx Which are the following wave functions acceptable in quantum mechanics? व टम म क न स म व क त तर ग फलक ह ग nswer Key Q19 particle of mass m is confined in the ground state of a one dimensional box extending from x = -2L to x = +2L. The wave function of the particle in this state is where is constant. The energy of eigen value corresponding to this state is एक m म क कण प र ह ज एक व मय ब स म अपन नर तर अव थ म x = -2L स x = +2L म चल रह ह इस कण क तर ग फलन एक थर क ह ह त उसक इस दश क अ भल णक म न बत ऐ, य द

9 nswer Key Q20 e-a e -a e-2a e -2a 1 - e-a 1 - e -a 1 - e-2a 1 - e -2a particle is described by a wave function that it will be found in the region? in one dimension. What is the probability एक कण क एक वम य दश म तर ग फलक दय गय ह त उसक म यकत ह ग? nswer Key Q21 What is the degeneracy of H - atom in state n = 3? n = 3 दश म H - अण क अप टत ह ग

10 nswer Key Q22 [,] [,] [,-1 ] [, -1 ] [-1,] [ -1,] If and are two operators, then -1 [,] -1 will be य द और द च लक ह त -1 [,] -1 क म न ह ग [-1, -1 ] [ -1, -1 ] nswer Key Q23 2i 2i 2i 2i 2i 2i The commutator of [x 2, p 2 ] is [x 2, p 2 ] क कमय ट टर ह ग (xp + px) (xp + px) (xp - px) (xp - px) px px 2i (px2 + xp 2 ) 2i (px 2 + xp 2 ) nswer Key

11 Q24 The average value of p x, for the box normalized wave function, is एक ब स क स म नय क त तर ग फलन. ह त उसक p x क औसत म न ह ग 0 0 nswer Key Q25 Magnetic dipole of dipole moment is placed in a non-uniform magnetic field. If the position vector of the dipole is, the torque acting on the dipole about the origin is एक आघ ण क च बक य अघ ण ह, उस एक असम न च बक य म रख गय ह य द इसक थत स दश ह त इस पर लगन व ल बल आघ ण क म न बत ऐ

12 nswer Key Q26 Which one of the law provides the displacement current न न नयम म स क न स व थ पन ध र बतल त ह Gauss Law Gauss Law Faraday s Law Faraday s Law mpere Law mpere Law iot Savart Law iot Savart Law nswer Key Q27 If the magnetic monopole exists, which law is to be modified? य द च बक य एक व अ त व म ह त न न म क न स नयम म बदल व ल न ह ग nswer Key

13 Q28 If coulomb gauze is य द क ल ब ग ज, then Lorentz gauze is given by ह त ल र ज ग ज य ह ग nswer Key Q29 For a magnetic vector potential, what will be its current density? एक च बक स दश वभव ह त उसक ध र घन व य ह ग

14 nswer Key Q30 t the interface of two non-conducting medium, the reflection coefficient for normal incidence is given by द क च लक म यम क अ तर प ठ पर, अ भल ब आपतन क लय त ब ब थर क ह ग nswer Key Q31 If is the guide wavelength, is cut off wave length and is the free space wave length, then what is the rectangular wave equation? य द पथ नध रत तर गध य, अ तक य तर गध य तथ म त आक श तर गध य ह त एक आय त क र तर गपथक क लए सम करण ह ग

15 nswer Key Q32 n air filled rectangular wave guide has dimension 6 x 4 cm. What is it guide wave length in TE 10 mode if incident frequency is 3 GHz? एक आय त क र 6 x 4 cm क तर ग पथक हव स भर ह य द आप तत त रग क आव त 3 GHz ह त TE 10 वध म पथक तर ग द ध य ह ग 28 cm 28 cm 19.8 cm 19.8 cm 19 cm 19 cm 10 cm 10 cm nswer Key Q33 Scalar potential (r,t) of an electromagnetic wave satisfies एक व य त च बक य तर ग क अ दश वभव (r,t) न न म स कस स त ट ह ग

16 nswer Key Q34 Which one of the following is correct for a common collector configuration of a transistor? एक ज टर क उभय न ठ स ह व य स क लय न न म य सह ह Low voltage gain, High output impedance, Low input impedance कम वभव ल भ, अ धक नग म तब ध, कम नव श, आगम तब ध Unity voltage gain, High input impedance, Low output impedance एक क वभव ल भ, अ धक नग म तब ध, कम नग म तब ध Very high voltage gain, Moderate input impedance, Low output impedance बह त अ धक वभव ल भ, स म य नव श तब ध, कम नग म तब ध Moderate high voltage gain, Low input impedance and High output impedance स म य स अ धक वभव ल भ, कम नव श तब ध, अ धक नग म तब ध, nswer Key Q % 82.4 % 21.2 % 21.2 % 42.4 % 42.4 % 63.6 % 63.6 % alculate the efficiency of arnot engine working between 227 o and 15 o एक क रन ट जन क 227 o और 15 o क ब च क य रत द त नक ल nswer Key

17 Q36 The boiling point of a liquid कस य क उब ल ब द ecreases with increase of pressure दब व क बढ़न क स थ कम ह त ह Increases with increases of pressure दब व बढ़न क स थ बढ़त ह No change with pressure दब व स क ई प रवत न नह ह त First increases then decreases पहल बढ़त ह और फर कम ह त ह nswer Key Q37 Entropy of the substance remains constant when the substance under goes एक पद थ क ए प य द थर ह त इसक मतलब पद थ म न न म स क न स प रवत न ह ग Isothermal change समत प प रवत न diabatic change म प रवत न Pressure change दब व प रवत न Volume change आयतन प रवत न nswer Key Q38 If the number density of a free electron gas in three dimension is increased eight times, its Fermi temperature will be य द एक म त इल न ग स क नमबर घन व त न वभ य दश म आठ ग न बढ़ ज य त इसक फम त प ह ग Increase by a factor of 4 4 क ग णक म बढ़ ग ecrease by a factor of 4

18 4 क ग णक स घट ग Increase by a factor of 8 8 क ग णक म बढ़ ग ecrease by a factor of 8 8 क ग णक स घट ग nswer Key Q39 Let W be the work done in a quasi static reversible thermodynamic process. Which of the following statement about W is correct? एक थ कक प उ मण य ऊ म ग तक म म W क क य कय गय W क लय न न म स क न स स य ह W is a perfect differential if this process is isothermal य द म समत प य ह त W एक यथ तय अवकल ह W is a perfect differential if the process is adiabatic य द म म ह त W एक यथ तय अवकल ह W is always a perfect differential W हम श एक यथ तय अवकल ह ग W cannot be a perfect differential W कभ भ यथ तय अवकल नह ह ग nswer Key Q40 25o K 25 o K 33o K 33 o K 22o K 22 o K 11o K 11 o K t what temperature will the average speed of hydrogen molecule be the same as that of Nitrogen molecule at 35 o. You may need molecular weight of N 2 = 28 gm/mol and H 2 = 2 gm/mol. एक ह इ जन अण क औसत ग त, 35 o पर न इ जन क अण क औसत ग त क बर बर कस त पम न पर ह ग. आपक दय गय ह आण वक भ र N 2 = 28 gm/mol, H 2 = 2 gm/mol ह

19 nswer Key Q41 The ensemble which allows the subsystems to exchange of energy as well as number of particles with a reservoir is called. एक सम चय ज उपत क ऊज तथ कण क व नमय क क ड क स थ अन म त करन द त ह उस न न म स य कह ग anonical ensemble क न नकल सम चय Micro canonical ensemble म इ क ल न कल सम चय Grand canonical ensemble व हत व हत सम चय Pressure ensemble द ब सम चय nswer Key Q42 For a strongly degenerate Fermi gas, the specific heat is एक मजब त अपभ टत फम ग स क व शषट उ म ह ग Proportional to absolute temperature नरप त पम न क आन प तक Proportional to square of absolute temperature नरप त पम न क वग क अन प तक Proportional to cube of absolute temperature नरप त पम न क घन क अन प तक Independent of temperature त पम न पर नभ र नह nswer Key Q43 JEFT always operates with the below process एक JEFT हम श न न म स कस य क स थ क य करत ह Gate to source p-n junction reverse bias ग ट और स स प -एन स ध क स थ य म वध म

20 Gate to source p-n junction forward bias ग ट और स स प -एन स ध क स थ अ द शक वध म Gate to drain is grounded ग ट और न क उ ड स ज ड़ ज त ह Gate is left open for building field to effect transistor functioning ग ट क ख ल रखत ह त क वभव स रत ज टर क म कर nswer Key Q44 If the following program is run on an 8085 microprocessor, what will be value of and registers? LX1H, 4031 PUSH H PUSH L POP POP HLT य द न न म क एक 8085 म इ स सर पर चल य ज य त और र ज टर क म न य ह ग?? LX1H, 4031 PUSH H PUSH L POP POP HLT 31 and एव and एव and एव 31

21 40 and एव 40 nswer Key Q45 n / converter consists of एक / प रवत क म न न म स कस स बनत ह / converter, amplifier / प रवत क, ए पल फ यर omparator, counter and other gates त ल न, ग ण तथ अ य ग ट omparator, clock, / convertor and counter त ल न, घड़, / प रवत क और ग णत lock, amplifier, oscillator and comparator घड़, ए पय फ यर, द लक तथ त ल न nswer Key Q46 23EF H 23EF H 2FFF H 2FFF H 20FF H 20FF H 4FFF H 4FFF H In a 8085 microprocessor, if the starting address of a 4 K memory is 2000 H, what will be the last address? एक 8085 म इ स सर म 4 K क म म र क थम पत 2000 H म ह त उसक अ तम पत क य ह ग nswer Key Q47 small increases in collector reverse bias, will cause एक स ह य म वध म थ ड़ स बढ न पर ह ग Large increase in emitter current उ सज क ध र म य द बढ़ तर

22 large increase in collector current स ह ध र म य द बढ़ तर Very large decrease in collector voltage स ह वभव म बह त य द कम Very small change in collector reverse saturation current स ह य कम स त त ध र म बह त थ ड़ प रवत न nswer Key Q48 In the ose - Einstein condensates the particles ब स - आइ सट न कण क न न म कस म स स घ नत करत ह Have inter particle attraction जनम कण तर आकष ण ह ondense in real space व त वक सम ट म स ध नत Have overlapping wave functions अ त य प तर ग फलन ह Have large and positive chemical potential य द और धन मक रस य नक वभव ह nswer Key Q49 n ideal op-amp is used to make an inverting amplifier. The two input terminals of the op-amp are at the same potential because एक आदश ऑप-ए प क तल म ए पल फ यर क प म य ग कय ज त ह उसक द न नव श एक सम न वभव पर ह त ह य क - Two input terminals are directly shorted internally द न नव श क सर अ दर स लघ प थत कय ज त ह Input impedance of the op-amp is infinity नव श तव ध अ न त ह त ह Open drop again and MRR are infinity ख ल प श ल ध और स एमआरआर अन त ह Slew rate is very small

23 सलय र ट बह त कम ह nswer Key Q50 The effect of doping intrinsic semi conductor is to एक न ज अध च लक म य द ड प ग क ज य त य भ व ह ग Move Fermi level towards the centre of forbidden band फम ल वल क क व ज त प क तरफ खसक Move the Fermi level away from the centre of the forbidden band फम ल वल क क व ज त प स द र खसक hange the crystal structure of the semiconductor अध च लक क स रचन म प रवत न Keep the Fermi level at the middle of the forbidden band फम ल वल क क व ज त प क ब च म रखन क लय nswer Key Part- Q1 To solve Laplace equation in spherical coordinate system when it is symmetric about z-axis, one of the following methods can be used. Which is/are true? I. ssociated Legendre's Function II. Legendre's Polynomial III. essel Function एक ग ल य नद ष क म ल पल स सभ करण क हल करन क लय, ज z-axis स अ य सम मत ह, न न म स क न स तर क सह ह ग I. सहच र Legendre's फलन II. Legendre's बह पद III. essel फलन Only I and III क वल I और III only II क वल II Only III

24 क वल III II and III II और III nswer Key Q2 With which boundary conditions, the ordinary Green's function does not exist for the differential equation. क न स प रस म तब ध क लय एक स ध रण न फलन क अवकलन क लय नह ह ग nswer Key Q3 a-iv,b-iii,c-i,d-ii

25 ए-iv,ब -iii,स -i,ड -ii a-iii,b-iv,c-i,d-ii ए-iii,ब -iv,स -i,ड -ii a-ii,b-iv,c-iii,d-i ए-ii,ब -iv,स -iii,ड -i a-i,b-ii,c-iv,d-iii ए-i,ब -ii,स -iv,ड -iii nswer Key Q4 What is the order of error in Simpson's 3/8 rule of numerical integration? स पसन क 3/8 क नयम स सम कलन म कस क ट क गलत ह O (h2 ) O (h 2 ) O (h3 ) O (h 3 ) O (h4 ) O (h 4 ) O (h5 ) O (h 5 ) nswer Key Q5 To group of order less than 4 is 4 स कम क ट क सम ह lways cyclic हम श च य lways non-cyclic हम श अच य May or may not be cyclic ह सकत य नह च य yclic under some conditions च य कस ख स दश म nswer Key

26 Q6 If the components of a tensor are zero in one coordinate system, then which of the following observations is/are true? I. omponents are not zero in any system II. omponents are zero in only one - coordinate system III. omponents are zero in all coordinate system य द एक नद श क म एक दश क अ श श य ह त न न म स क न स स य ह I. कस म भ स टम म अ श श य नह ह II. अ श क वल एक नद श क म श य ह III. सभ नद श क म अ श श य ह Statement I and II III और II कथन Statement III only III कथन Statement II only II कथन Statement II and III II और III कथन nswer Key Q7 The canonical transformation Q = p, P = -q is generated by the generating function व हत प तर Q = p, P = -q क जनक फलन क व र उ प दत कय ज त ह त F = qp F = qp F = qq F = qq F = pq F = pq F = pp F = pp nswer Key Q8 Which of the following is/are false? न न म स क न स गलत ह

27 The Poisson bracket of momentum, conjugate to a cyclic coordinate with Hamiltonian vanishes प यसन कट स व ग ह म ट नयन क स थ ज च य नद ष क क स थ स य मत ह,ख म ह ज त ह Lagrangian bracket is in varied under anonical transformation व हत प तर क अ तग त ल गर जयन कट न चर ह Poisson bracket changes sign under communication of concerned dynamical variables प यसन कट, द प रवत न क ग हकचर क अ तरगत अपन च ह बदल ल त ह Lagrangian bracket is commutative with respect to concerned dynamical variables ल गर जयन कट ग तकचर क अ तरगत द प रवत न ह nswer Key Q9 If {l x, x} is the vanishing Poisson bracket, tell which of the following relation/relations is/are false for Poisson bracket? (I) [l x, l y ] = -l z (II) [l x, l z ] = -l y (III) [l z, l y ] = -l x य द {l x, x} एक ल त प यसन कट ह त न न म स क न स प यसन कट गलत ह (I) [l x, l y ] = -l z (II) [l x, l z ] = -l y (III) [l z, l y ] = -l x I and II I और II Only II क वल II Only II and III II और III Only I क वल I nswer Key Q10 Hamilton's canonical equations of motions are ह म टन क ग त क व हत सम करण य ह ग

28 nswer Key Q11 a-iv,b-iii,c-ii,d-i ए-iv,ब -iii,स -ii,ड -i a-iii,b-ii,c-iv,d-i ए-iii,ब -ii,स -iv,ड -i a-iv,b-i,c-ii,d-iii

29 ए-iv,ब -i,स -ii,ड -iii a-i,b-ii,c-iv,d-iii ए-i,ब -ii,स -iv,ड -iii nswer Key Q12 What will be the normal frequencies of normal modes of vibration of the system characterized by the Lagrangian ल गर जयन कपन क स म य आव त य ह ग व र अ भल णक स टम स म य वध क nswer Key Q13 Which statements are true for normal dispersion in a electromagnetic wave? (I) Refractive Index increases as wavelength increase (II) Refraction index decrease as wavelength increase (III) Slope of the curve is greater at shorter wavelength. (IV) Normal ispersion is given by एक व य त च बक प तर ग क लय स म य प र पण क लय क न स कथन स य ह I. तर गद ध य बढ़न पर अपवत न क बढ़त ह II. तर गद ध य बढ़न पर अपवत न क घटत ह

30 III. व ड ढ़ ल न जय द ह त ह,छ ट तर गद ध य पर IV. स म य प र पण I, II and III I,II और III II and IV II और IV II and III II और III II, III and IV II III और IV nswer Key Q14 Which one of the following remains invariant under Lorentz transformations? ल र ज प नतरण क अ त गत क न स अप रवत न य ह nswer Key Q15 The potential which exhibits the dependence of potentials on the velocity of the particle is known as क न स वभव ग त पर नभ र करत ह Scalar Potential अ दश वभव

31 Vector Potential स दश वभव Retarded Potential म दत वभव Lienard - Wiechort Potential ल न ड - वच ट वभव nswer Key Q16 Which statements are true for the boundary conditions in a waveguide? (I) Normal derivative of magnetic field at the surface is zero (II) Tangential component of electric field is not zero. (III) Normal derivative of magnetic field at the surface (IV) Tangential component of electric Field is zero तर ग पथक क लय प रस म तब ध य ह ग (I) च बक य क ल ववत अवक लन प र समतल पर श य (II) व य त क टय य अ श श य नह ह ग (III) च बक य क ल ववत अवकलन प र समतल पर श य नह ह ग (IV) व य त क य य अ श श य ह ग I and IV I और IV I and II II और II II and III II और III II and IV II और IV nswer Key Q17 When a particular mode is excited in a a wave guide there appears a magnetic field in the direction of propagation also. The resulting mode is जब एक तर ग पथक क वष श वध म उ त जत कय ज त ह त च बक य उसक ग त क दश म ह त ह त इस क न स वध कह ग Transverse electric mode TE वध

32 Transverse Magnetic mode TM वध TEM mode TEM वध avity resonator क वट र ज न टर nswer Key Q18 The in-homogenous electromagnetic wave equations using Lorentz gauge given by एक असम ग व य त च बक य त रग क न न स द श त कर सकत ह य द ल र ज ग ज दय गय ह nswer Key Q19 Using oulomb gauge क ल व ग ज, which is the e.m. wave equations are true? क य ग करत ह ए न न म क न स स य ह

33 nswer Key Q20 Given a wave with dispersion relation I. Group velocity is greater than phase velocity II. Group velocity is less than the phase velocity III. Group and phase velocity are same IV. Group velocity is finite but phase velocity is zero k > 0 और m > 0 क लय एक तर ग क प र पण स वध I. सम ह व ग कल व ग स य द ह II. सम ह व ग कल व ग स कम III. सम ह और कल व ग द न सम न IV सम ह व ग स मत तथ कल व ग श य = ck + m for k > 0 and m > 0, which statement is true? = ck + m ह त क न स कथन स य ह I and II I और II only II क वल II only IV क वल IV Only I and III I और II nswer Key Q21 The energy in the ground state of the hydrogen atom can be calculated as ह इ जन परम ण क न नतक अव थ क ऊज कस तर क स त कर ग Variation method व रय सन म थड WK approximation WK ए सम सन तर क oth variation and WK approximation द न व रयसन एव WK None of these क ई नह

34 nswer Key Q22 The WK approximation is used to the system where WK ए स क शन क य ग कस ण ल क लय कय ज त ह जह Potential function vary rapidly वभव फलन त ग त स बदलत Potential function vary fast वभव फलन त ज बदलत Potential function vary slowly वभव फलन ध र ध र Potential function has no relation with WK approximation वभव फलन क WK ए स म सकस क ई स ब ध नह ह nswer Key Q23 Which statement is correct? क न स कथन स य ह य न क न Scattering of neutrons by electrons gives about the structural properties of the nucleus इस न, य ल यस क स रचग मक ग ण न द त ह From a nucleus gives the idea about the magnetic properties of the nucleus य ल यस क च बक य वश षत From a nucleus gives idea electrical properties of the nucleus य ल यस क व य त य वश षत ll of these ऊपर सभ nswer Key Q24 The orn approximation will be hold good only when, ब न ए स म सन स य ह ग य द The wave function must differ with larger value from the incident wave function. तर ग फलन, आप तत तर ग फलन स क फ बड़ The wave function is not much different from the incident wave function.

35 तर ग फलन, आप तत तर ग स बह त अलग नह ह The wave function must be same with the value of the incident wave function. तर ग फलन और आप तत तर ग फलन एक ज स ह Wave function has no relation with this. तर ग फलन क इसस क ई स ब ध नह ह nswer Key Q25 The dipole moment amplitude p 0 in terms of charge (q) and acceleration व आध ण आय म p 0 आव श (q) और तवरण क पद म of accelerated charge is nswer Key Q26

36 -II,-III,-IV,-I ए-II,ब -III,स -IV,ड -I -I,-IV,-III,-II ए-I,ब -IV,स -III,ड -II -III,-IV,-I,-II ए-III,ब -IV,स -I,ड -II -I,-III,-IV,-II ए-I,ब -III,स -IV,ड -II nswer Key Q27 Scattering cross section is given by क ण प र क न न स दय ज य ग थर म न nswer Key

37 Q28 ssertion () If Reason (R) Mark your answer as नश चय मक कथन ए य द are irac matrices then डर क म क ह त ह त आर oth () and (R) are true and (R) is the correct explanation of () (ए) और (आर) द न स य तथ (आर), (ए) क य य करत ह oth () and (R) are true and (R) is not the correct explanation of () (ए) और (आर) स य पर त (आर), (ए) क य य नह करत () is true but (R) is false (ए) सह ल कन (आर) गलत () is false but (R) is true (ए) गलत ल कन (आर) सह nswer Key Q29 ssertion () Klein - Gordan equation is valid for electron Reason (R) The Klein - Gordan equation is valid only for spin less particles orbiting about nucleus Mark your answer as न चय मक कथन ए ल न ग ड न सम करण एक इन न क लय सह ह ह त आर ल न ग ड न सम करण क वल पन वह न कण क लय ज य स मस क च र और घ म रह ह oth () and (R) are true and (R) is the correct explanation of () (ए) और (आर) द न स य तथ (आर), (ए) क य य करत ह oth () and (R) are true and (R) is not the correct explanation of () (ए) और (आर) स य पर त (आर), (ए) क य य नह करत () is true but (R) is false (ए) सह ल कन (आर) गलत () is false but (R) is true (ए) गलत ल कन (आर) सह

38 nswer Key Q30 ssertion () The charge and current densities defines by and satisfy the continuity equation Reason (R) For free particle, the orbital angular momentum is not a constant of motion. Mark your answer as न चयत मक कथन ए आव ष और ध र घन व, ज ह और स दष य गय, स त य सम करण क स त ट करत ह ह त आर कस म तमकण क लय क य क ण य स ब ग थर नह ह ग oth () and (R) are true and (R) is the correct explanation of () (ए) और (आर) द न स य तथ (आर), (ए) क य य करत ह oth () and (R) are true and (R) is not the correct explanation of () (ए) और (आर) स य पर त (आर), (ए) क य य नह करत () is true but (R) is false (ए) सह ल कन (आर) गलत () is false but (R) is true (ए) गलत ल कन (आर) सह nswer Key Q31 Increase in entropy, when one gram of water at 0 o is raised to 1 gm of water at 100 o य द एक म प न 0 o क त पम न क 100 o व ल एक म प न गम कय ज य त ए प कतन बढ़ ग al/k al/k al/k al/k al/k al/k al/k al/k nswer Key Q32 Wein's displacement law states that the monochromatic emissive power varies directly as the वय न व थ पक नयन स एक र ग य उ स ज त श त कस क आन प तक बदलत ह Square of the absolute temperature.

39 नरप त पम न क वग ube of absolute temperature. नरप त पम न क घन Fourth power of absolute temperature. नरप त पम न क चत थ प वर Fifth power of absolute temperature. नरप त पम न क प चव प वर nswer Key Q33 Which statement is correct? क न स कथन स य ह The wave function is symmetric under interchange of two bosons. तर ग फलन सम मत ह त ह य द द ब स स व नयम कर The wave function is symmetric under interchange of two fermions. य द द फर मय स व नमय कर त तर ग फलन सम मत ह त ह The wave function is asymmetric under interchange of two bosons. तर ग फलन असम तत ह ग य द द ब स न व नयम कर ll are true. सभ स य nswer Key Q34 Match the following न न क मल न कर

40 -I,-III,-IV,-II ए-I,ब -III,स -IV,ड -II -IV,-II,-I,-III ए-IV,ब -II,स -I,ड -III -III,-II,-I,-IV ए-III,ब -II,स -I,ड -IV -III,-IV,-II,-I ए-III,ब -IV,स -II,ड -I nswer Key Q35 What will be the mean free path, if molecular diameter is and molecular density is n per unit volume य द आण वक य स ह और आण वक घन व n त घन ह त औसत म तम प थ त कर

41 nswer Key Q36 The root mean square speed < v 2 > 1/2 for Maxwellian distribution of velocities of gas molecules will be कस ग स क म सव लयन वतरण क वग म यम ल ग त< v 2 > 1/2 य ह ग nswer Key Q37 The Ising model investigates the behavior of substances whose molecules poses कस पद थ क वभ व क Ising model स ज च कर जसक अण Electric dipole moment. व य त व व आप ण Magnetic flux. च बक य ल स Magnetic moment. च बक य घ ण न Electric flux. व य त ल स nswer Key Q38 In a pressure transducer, we use एक दवव सडय सर म क न स य ग ह त ह Strain gauge.

42 न ग ज Hall effect transducer. ह ल भ व सडय सर Photo emissive cell. क श उ स ज त स ल Photo transistor. क श ज टर nswer Key Q39 Gauge factor of a transducer is defined as ग ज ग ण क कस सडय सर क क स प रम त कर ग nswer Key

43 Q40 test is क ई वग पर ण ह nswer Key Q41 - I, -II, -IV,- III ए -I,ब - II,स - IV,ड III -III,- I,-II,-IV ए -III,ब -I,स - II,ड IV -II,- I,-III,-IV ए- II,ब - I,स - III,ड IV

44 - I,- III,- II,-IV ए- I,ब - III,स -II,ड - IV nswer Key Q42 ssertion () Strain gauge is a semi conducting material Reason (R) Resistance changes when pressure is applied Mark your answer as नशचय मक कथन ए न ग ज एक अध च बक पद थ ह ह त आर दव ब क स थ तर ध बदलत ह न च दय त न श न क न न न स र उ तर द oth () and (R) are true and (R) is the correct explanation of () (ए) और (आर) द न सह और (आर), (ए)क सह य य करत ह oth () and (R) are true and (R) is not the correct explanation of () द न (ए) और (आर) सह पर त (आर), (ए) क सह य य नह करत स () is true but (R) is false (ए) सह ल कन (आर) गलत () is false but (R) is true (ए) गलत ल कन (आर) सह nswer Key Q43 ssertion () Transducer converts physical quality to electrical quantity Reason (R) Piezoelectric effect tells about conversion of voltage when current is applied Mark your answer as नशचय मक कथन ए सडय सर एक भ तक प रम ण स व य त प रम ण म बदलत ह ह त आर प ज इल क पद थ जव ध र व ह करत ह त वभव उ प न करत ह oth () and (R) are true and (R) is the correct explanation of () (ए) और (आर) द न सह और (आर), (ए)क सह य य करत ह oth () and (R) are true and (R) is not the correct explanation of () द न (ए) और (आर) सह पर त (आर), (ए) क सह य य नह करत () is true but (R) is false (ए) सह ल कन (आर) गलत () is false but (R) is true

45 (ए) गलत ल कन (आर) सह nswer Key Q44 ssertion If the maximum peak to peak voltage of M wave is 16 mv and the minimum peak to peak voltage is 4 mv, then modulation factor is 0.6. Reason R Modulation factor Mark your answer as नशचय मक कथन ए य द एक M तर ग क च ट स च ट क वभव 16 mv ह और च ट स च ट य मतम वभव 4 mv ह त उसक म ड ल सन ग णक 0.6 ह ह त आर म ड ल सन ग णक oth () and (R) are true and (R) is the correct explanation of () (ए) और (आर) द न सह और (आर),(ए) क सह य य करत ह oth () and (R) are true and (R) is not the correct explanation of () (ए) और (आर) सह पर त (आर),(ए) क सह य य नह करत () is true but (R) is false (ए) सह ल कन (आर) गलत () is false but (R) is true (ए) गलत ल कन (आर) सह nswer Key Q45 The inverse Fourier Transform of the function sin t sin t cos t cos t sin(t) sin(t) cosec(t) cosec(t) फलन क तल म फ रयर प तरण य ह ग

46 nswer Key Q46 The frequency dependence of noise power and noise voltage is श र श त और श र व टत क आव त कस पर आ त ह Noise Power ष र श त and Noise Voltage और ष र oth varies as श र व टत oth Noise Power and Voltage vary as द न श र श त तथ व टत Noise Power श र श त and Noise Voltage और श र व टत nswer Key Q47 For digital modulation of the signals, MOEM uses MOEM म क न स अ क य म ड ल सन य ग ह त ह SK and PSK SK और PSK FSK and SK FSK और SK PSK and FSK PSK और FSK SK, FSK and PSK SK, FSK और PSK nswer Key

47 Q48 Probability of error in FSK is FSK म टय क य कत य ह nswer Key Q49 Which statement is correct? क न स कथन स य ह ll unit cells are primitive cells. स र एकक स ल अभ य स ल ह ll the primitive cells need not to be unit cells. स र अभ य स ल एकक स ल ह, ज र नह The unit cell is not related with primitive cells. एकक स ल क अभ य स ल स क ई स ब ध नह ll of these are correct. सभ स य ह nswer Key

48 Q50 simple intercepts at a, b/2, 3c in a simple cubic unit cell. The Miller indices of the plane are एक समतल एक घन स ल क a, b/2, 3c पर ख ड करत ह त उसक मलर ईड ई सस य ह ग (1 3 2) (1 3 2) (2 6 1) (2 6 1) (3 6 1) (3 6 1) (1 2 3) (1 2 3) nswer Key Q51 Which is / are the correct statements? I) ebye theory of specific heat is based on that all atoms are vibrating with same frequency. II) ebye theory of specific heat is based on all atoms are vibrating with different frequency. III) ll atoms are vibrating with same energy. क न स कथन स य ह I. व श ट ऊ म क डब ई स द त इस ब त पर आध रत ह क स र परम ण एक ह आव त पर क पन करत ह II. व श ट ऊ म क डव ई स द त म सभ परम ण अलग-अलग आव तय पर क पन करत ह III. स र परम ण एक ह सम न ऊज पर क पन करत ह Only I and III क वल I और III Only III क वल III Only II क वल II I and II क वल I और II nswer Key

49 Q52 phonon of wave vector k interacts with other particles and fields as if its momentum were एक फ न न क तर ग स दष k अ य उण और प र प रक कय करत ह य द उसक स व ग nswer Key Q53 If H c is critical mag. field for a Superconductor and T c is transition temperature, then एक अ त च लक क तक च बक य H c और स मण त प T c ह त nswer Key Q54 Width of the depletion layer in a p - n junction diode is given by p - n ज व सक ड य ड क व स तर च ड़ ई य ह ग

50 nswer Key Q55 For an intrinsic semiconductor m e * and m h * are the effective,asses of electrons and holes near the corresponding band edges. t a finite temperature the position if the fermilateral. एक न ज अध च लक म m e * और m h * इल क और ह ल क भ व वयम न उसक प क र क स गत ह एक प रम त त पम न पर फम तल क थ त बत य depends on m e * but not on m h * m e * पर आध रत ह ल कन m h * पर नह depends on m h * but not on m e * m h * पर आध रत ह ल कन m e * पर नह depends on both m e * and m h * द न m e * और m h * पर आध रत Neither on m e * nor on m h * m e * और m h * पर आध रत नह nswer Key

51 Q56 The unit Hall coefficient R H is ह ल थर क R H क इक ई य ह nswer Key Q57 The normalized wave function for a particle in a rectangular box of dimension a,b,c is एक कण क स म य क त तर ग फलन नक ल य द एक आयत य व स जसक वभ य a,b,c ह

52 None of these are correct क ई भ नह nswer Key Q58 If E F is the Fermi energy of a metal at 0 K and E f is the fermi energy at T K then य द कस ध त क फम ऊज 0 K पर E F ह तथ T K पर E f ह त nswer Key Q59 For a given dielectric as the temperature increases, the ionic polarizability एक पर व य त क लय य द त पम न बढ़ य त इसक आय नत वणत क य ह ग Increases. बढ़त ह ecreases.

53 घटत ह Remains unchanged. क ई प रवत न नह Varies sinusoidally. स इन स इ डयल तर क स बदल ग nswer Key Q60 In a Frenkel defect, एक कल द ष म Positive ion goes at substitutional site and keeps charge neutrality. घन मक आयन त थ पत जगह पर ज त ह और आव श उद स नत रखत ह Positive ion goes at interstitial site maintaing charge neutrality. घन मक आयन अ तर ल जगह पर ज त ह और आव श उद स नत रखत ह Positive charge goes at interstitial and negative goes at substitution site. घन मक आयन अ तर ल जगह पर ज त ह और ऋण मक आयन तसथ पत जगह पर Negative ion goes at the surface and positive ion at interstitial disturbing charge neutrality. ऋण मक आयन प ठ पर ज त और घन मक आयन अ तर ल जगह पर ज त ह और आव श उद स नत बदल ज त nswer Key Q61 n atom of mass M can be exited to a state of mass (M + photon which can cause this transition is एक M म क परम ण उ त जत ह कर (M + ज त ह फ ट न क आव त ज इस स मण क ल त ह ) by phonon capture. The frequency of a ) क म म बदलत ह और फ न न व र हण कर लय

54 nswer Key Q62 ngular momentum quantisation is directly established by I) Photo electric effect and avison Germar experminet II) Stern - Gerlach experment and Frank - Hertz experiment III) Stern - Gerlach experiment IV) Frank - Hertz experiment क ण य स ब ग क व ट इज सन स ध त र पर न न व र तप दत कय गय ह I. फ ट इल क भ व और ड व सन जम र य ग II. टन ग रल क य ग तथ क तथ हड क य ग III. टन ग रल क य ग IV. क और हड क य ग I and II I और II Only III क वल III Only IV क वल IV Only II क वल II nswer Key

55 Q63 Optical spectrum is the characteristics of the क शय प म कसक व र मलत ह ll electrons in the atom. सभ इल न व अण ओ स ll protons on the nucleus. सभ ट न स Valence electrons. स य जक इल न स Nucleons only. य लय न स nswer Key Q64 oublet - doublet transition will be due to वध व य- वध व य क स मण कसक क रण ह 2 5/2 2 5/2 2 P 3/2 2 P 3/2 2 5/2 2 5/2 2 S 3/2 2 S 3/2 2 P 3/2 2 P 3/2 2 S 1/2 2 S 1/2 2 P 3/2 2 P 3/2 2 S 3/2 2 S 3/2 nswer Key Q65

56 - I, - III, - II, - IV ए-I, ब -III, स - II, ड -IV - II, - III, - IV, - I ए-II, ब -III, स -IV, ड - I -II, -I, -III, - IV ए -II, ब - I, स -III, ड - IV -II, -III, - IV, - I ए -II, ब -III, स - IV, ड - I nswer Key Q66 What will be the frequency at which electron orbital magnetic moment processes in a magnetic field? एक इल न क य च बक य आघ ण स च बक य म प र सरण कर रह ह त उसक आव त य ह ग

57 nswer Key Q67 In a Kerr effect experiment the plane of polarization by Where K is Kerr constant, then voltage necessary for rotating /2 is known as एक क र भ व य ग म ह जह K फ र थर क ह त वण क समतल क /2 म घ म न क लय उपय त व ट ज क य कहत ह Kerr voltage. क र ब ट ज Quarter wave voltage. वट र तर ग ब ट ज Half wave voltage. अध तर ग व ट ज Polarization voltage. वण व ट ज nswer Key Q68 The difference in a stimulated emission and spontaneous emission is उ पत उ सज न और वत उ सज ज म य अ तर ह The incident wave determines the direction and phase in stimulated while no definite phase in spontaneous emission. उ पत उ सज न म आप तत तर ग दष और कल नध रत ह जब क वत उ सज न म क ई न चत कल नध रत नह ह The incident wave determines the direction in stimulated but same phase in spontaneous emission. आप तत तर ग उ पत उ सज न म दष ल कन वत उ सज न म एक ह कल क नध रत करत ह oth direction and phase are not determined by incident wave in stimulated while direction and phase both are maintained in spontaneous emission. द न दष और कल द न उ पत उ सज न स नध रण नह ह त ह तथ दष और कल वत उ सज न स नध रत ह त ह There in no phase and directions are changed in both emissions.

58 द न उ सज न म क ई कल और दष नह बदलत nswer Key Q69 The minimum photon energy required for e - e + pair production is 2mc 2, hence its corresponding wavelength is e - e + य गम उ प दक क लय न नतम फ ट न ऊज 2mc 2, क बर बर ज रत ह त ह त इसक स गत तर ग ल ब ई य ह ग X m X m X m X m 1.02 X 10-8 m 1.02 X 10-8 m X m X m nswer Key Q70 Find the threshold energy for the pion production in the reaction N + N N + N +. You may require M N c 2 =940 MeV and m c 2 = 140 MeV. एक N + N + M N 2 =940 MeV और m 300 MeV 300 MeV MeV MeV MeV MeV MeV MeV nswer Key, प यन उ प दक क अ म कय म द हल आव त बत ऐ य द 2 = 140 MeV. Q71-1 What is the parity of an - particle एक - कण क प रट य ह ग

59 nswer Key Q72 Find the energy release, if two 1 H 2 nuclei can fuse together to form 2 He 4 nucleus. The binding energy per nucleon of 1 H 2 and 2 He 4 is 1.1 MeV and 7.0 MeV respectively. य द द, 1 H 2 य लयस स ग लत ह कर 2 He 4 य लयस बन त ह त कतन ऊज उ स ज त ह ग य द 1 H 2 और 2 He 4 क त य लय ई क ब धन ऊज 1.1 MeV और 7.0 MeV द गय ह 23.6 ev ev MeV MeV MeV MeV ev ev. nswer Key Q7 3 न न क मल न कर उ तर द

60 nswer Key Q74 Match the following. मल न कर उ त र द

61 nswer Key Q75 The decay process य म violates इनम स कसक प लन नह करत ह aryon Number ब रयन स य Lepton number ल ट न स य Isospin आइस पन

62 Strangeness जन स nswer Key

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