(A) (C) relation for the Legendre polynomial is α given by Pm. (A) σ = m. (B) σ 2 = m (C) σ + m = 0 (D) σ = m

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1 . h atrix i Only Hritian i is Only Unitary Hritian and Unitary Nithr Hritian nor Unitary. What is th product of ign valus of 6. h first proprty of th orthogonality rlation for th Lgndr polynoial is α β givn by P (x) P n(x) dx = 0 for 0 0 γ = n α β / γ α γ /β n β γ /α α β γ = n = 0 = n = d z dz. h quation x + λz = 0 is dx dx calld Lgndr's quation Bssl's quation Hrit quation Bltra's quation 5. Using Fourir sris xpansion of x in th intrval ( 5 < x < 5), th valu of n= n 8 is 4 7. For th Poisson distribution, th standard dviation σ is rlatd to th an as σ = RASPURAM σ = σ + = 0 σ = 6 4. Fourir transfor of a squar puls is cos function sin function sin c function tan function 8. h valu of k for which th function f(x) = kx, 0 x is a probability distribution function is PG RB - PHYSS AND

2 9. wo bodis of ass collid with ach othr in a stationary fra of rfrnc. h rducd ass of th syst is 4 0. A cyclic co-ordinat dos not xplicitly appar in Lagrangian only Hailtonian only Both Lagrangian and Hailtonian onjugat ontu L = η + η + η α η + η η ηη whr α is ral, thn on of th noral. h quation of otion for a bad sliding co-ordinats has frquncy ω as on a uniforly rotating wir in a forc fr spac is ω = α ω = α r = rw ω α = ω = α g l θ + = 0 6. An lctron at rst is ad to ov with rr θ + r θ = 0 vlocity. ts ass thn bcos g θ + θ = 0 l o o. h gnral displacnt of a rigid body with on point fixd is a rotation about so axis is th statnt of Brtrand s thor Eulr s thor Virial thor hasl s thor. f a particl ovs undr a cntral forc fild locatd at r = 0 dscribing a spiral θ r =, thn th forc is proportional to r r r r 4 4. wo photons X and Y ar oving in th dirctions opposit to ach with th vlocity rlativ to an obsrvr in th inrtial fra. h vlocity of photon X rlativ to th photon Y is 0 / 5. h Lagrangian for a thr particl syst is givn by ( ) ( ) RASPURAM o o 7. Elctric fild intnsity on th surfac of a chargd conductor is Zro Dirctd noral to th surfac Dirctd tangntially to th surfac Dirctd along 45 to th surfac PG RB - PHYSS AND

3 8. Existnc of quadrupol ont for a charg distribution signifis that it is sphrically sytric having only +v chargs sphrically asytric having only v chargs 9. B = 0 iplis that agntic fild is solnoidal agntic fild is non-solnoidal no currnt is flowing agntic fild is not du to currnt flow 0. Bcaus of lctroagntic potntials, th nubr of Maxwll s quation is rducd to circular incrasd to 6 6. f th dbrogli wavlngth of Hliu four ato at 00 K is 0.7 A, thn at 600 K it rducd to will b. h ratio of skin dpth in coppr at 0 khz to that at 00 MHz is h charactristic ipdanc of fr spac for propagation of plan, onochroatic lctroagntic wav is around.77 Ω 77.0 Ω 7.7 Ω 777Ω. An isotropic dilctric offrs a rfractiv indx of.5 to th propagation of a plan onochroatic lctroagntic wav through it. ts dilctric constant is h rflctanc in visibl rgion at noral incidnc is nk (n ) + k (n + ) + k (n ) k (n + ) + k n k 5. h path of th chargd particl in a rgion of crossd lctric and agntic filds is hlical hyprbolic parabolic 4.9 A 49 A 0.49 A A 7. h probability currnt dnsity for an unnoralizd wav function ψ = xp (ikx) is k k 0 k RASPURAM A particl of nrgy E incidnt on a potntial barrir of hight V o can tunnl through it iff E < V o E > V o E = V o E = 0 PG RB - PHYSS AND

4 9. A nuclus has two stats with nrgis MV and MV. f th lif ti of lowr stat is ns, thn th lif ti in highr stat will b 0 ns 0 ns 0.5 ns ns 0. h vctors of dual spac ar calld kt vctors bra vctors Dirac vctors Poisson vctor. f σ x and σ z ar th Pauli spin atrics, which of th coutation rlation is corrct? [ σ x ] = 0 [ σ x ] = σ z A can nithr xchang particls [ σ x ] = i σ z nor nrgy with B [ σ x ] = i σ z A can xchang both particls and nrgy with B. Fri s Goldn rul No. is 6. f th partition function of a Haronic P = < f H i > ρ(e) oscillator with frquncy ω at a tpratur is k/ ω, thn th fr P = < i H f > ρ(e) nrgy of N such indpndnt oscillators is Nk B P = < f H i > ρ(e) ω k B ln P = < f H i > ρ(e) k B ω Nk B ln. h bhavior of th wav function of a kb syst of two idntical Frions undr th intrchang of particls is ω Sytric Vanishing Antisytric Singular 4. Which of th following is not a Maxwll s throdynaic rlation? S V S P P P V S P = V V = P V = S S = 5. n a grand canonical nsbl a syst A of fixd volu is in contact with a larg rsrvoir B, thn A can xchang nrgy only with B A can xchang only particls with B RASPURAM Nk B ln k B P V PG RB - PHYSS AND

5 7. h quantu statistics rducs to classical statistics undr th following conditions ρλ ρλ >> ρλ << ρ = 0 8. A syst has two nrgy lvls E and E. n quilibriu, at tpratur, 0 6 8hγ hγ / k particls occupy E and anothr 0 5 particls occupy E. h valu of E E is 4. h Gibb s potntial is dfind as k B l n G = U PV + S k B l n G = U + PV + S k B G = U PV S k B G = U + PV S 4. urrnt 9. h spcific hat of an idal Fri gas and flow whn larg forward voltag V in -dinsions varis as and V ar applid to a siconductor diod. f V = V thn th agnitud of rvrs saturation currnt / is 40. h tpratur of a black-body nclosur is doubld. hn th total nubr of photons insid th nclosur incrass by a factor of h Planck s law of radiation in trs of frquncy is 8hγ 8hγ hγ / hγ / k 8hγ hγ / k + k + RASPURAM A diod that has a ngativ rsistanc charactristics is th unnl diod Schottky diod Lasr diod Hot carrir cathod PG RB - PHYSS AND

6 45. h output voltag of th circuit blow is V μ V V 0. V 46. With a 00 khz clock frquncy, ight bits can b srially ntrd into a shift rgistr in 8 μ s 80 μ s 80 s 0 μ s 47. A 4 - bit binary up/down countr is in th binary stat of zro. h nxt stat in th down od is % 0.% h rsolution of a 6-bit DA with 0 V input voltag is 5 V 0.5 V 0. V.5 V 49. n th circuit givn blow, th rlation btwn Y, A and B is 50. n an xprint with a GM countr, th counts ar dtrind with a β -sourc. f 0,000 counts ar obtaind for 0 inuts, th prcntag rror is 0%.% RASPURAM A + B A + B A + B A + B PG RB - PHYSS AND

A 1 A 2. a) Find the wavelength of the radio waves. Since c = f, then = c/f = (3x10 8 m/s) / (30x10 6 Hz) = 10m.

A 1 A 2. a) Find the wavelength of the radio waves. Since c = f, then = c/f = (3x10 8 m/s) / (30x10 6 Hz) = 10m. 1. Young s doubl-slit xprint undrlis th instrunt landing syst at ost airports and is usd to guid aircraft to saf landings whn th visibility is poor. Suppos that a pilot is trying to align hr plan with