64 m kj izns'k jktf"kZ V.Mu eqDr fo'ofo|ky;] bykgkckn

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10 527 m kj izns’k jktf"kZ V.Mu eqDr fo’ofo|ky;] bykgkckn vf/kU;kl (Assignment) 2012-2013 Lukrd foKku dk;Z e …ch-,l-lh-‰ Bachelor of Science Programme (B.Sc.) fo"k; % HkkSfrd foKku fo"k; dksM % ;w-th-ih-,p-,l- Subject : Physics Subject Code : UGPHS dkslZ ’kh"kZd % dkslZ dksM % ;w-th-ih-,p-,l--09 Subject Title: Mathematical Methods Course Code : UGPHS-09 in Physics I vf/kdre vad % 30 Maximum Marks : 30 Section - A [k.M & v vf/kdre vad % 18 Maximum Marks : 18 uksV % nhkZ m kjh; iz’uA vius iz’uksa ds m kj 800 ls 1000 ’kCnksa esa fy[ksaA lHkh iz’u vfuok;Z gSaA Note : Long Answer Question. Answer should be given in 800 to 1000 words. Answer all questions. All questions are compulsory. 1. What is normal distribution. Discuss its properties and gives at least one application of this distribution with examples. 6 lk/kkj.k forj.k D;k gksrk gSA blds xq.kksa dh foospuk dhft, rFkk de ls de ,d mnkgj.k lfgr bl forj.k dh mi;ksfxrk nhft,A 2. What are solenaidal and Irrotational vectors Find the value of n for which the vector r A = r n r Ù becomes (i) solenoidal and (ii) Lamellar 6 ifjukfydh; ,oa v/kw.kZdh; lkns’k D;k gksrs gSaA lfn’k r A = r n r Ù , fdl h ds eku ds fy, (i) ifjukfydh; rFkk (ii) v/kw.kZuh; gks tkrk gSA 3. What are cartesion, spherical and cylinderical polar co-ordinate system with the help of one example show how the cartesian co-ordinate are changed to sphered and cylinderical polar co-ordinates. 6 dkrhZ; xksyh; rFkk csyuh /kzqoh; funsZ’kkad fudk; D;k gS\ ,d mnkgj.k dh lgk;rk ls Li"V dhft, fd fdl izdkj dkrhZ; funsZ’kkadksa dks xksyh; ,d csyuh /kzqoh; funsZ’kkadksa esa ifjofrZr djrs gSaA Section - B [k.M & c vf/kdre vad % 12 Maximum Marks : 12 uksV % ykq m kjh; iz’uA vius iz’uksa ds m kj 200 ls 300 ’kCnksa esa fy[ksaA lHkh iz’u vfuok;Z gSaA Note : Short Answer Question. Answer should be given in 200 to 300 words. Answer all questions. All questions are compulsory. 4. State Gauss theorem in vector and using it define divergence of a vector. 3 lfn’k ds fy, xkSl izkes; mYysf[kr dhft, rFkk blds iz;ksx ls MkbojtsUl dh ifjHkk"kk fyf[k,A - r Ã r 2 5. Define the gradient of a sealar and show that r Ñ ( 1 ) = -r Ù r r 2 3 ,d vkns’k ds xzsfM; C dh ifjHkk"kk fyf[k, rFkk fl) dhft, % r Ñ ( 1 ) = -r Ù r r 2 6. State Poissons distribution and show that its can be deduced from Bionomial distribution. 3 ikblu forj.k dk mYys[k dhft, rFkk n’kkZb;s fd bldks f}in forj.k ls izkIr fd;k tk ldrk gSA 7. Explain r r rthe rdifference r r between r r rpolar and Axial Vectors. show that ¾ 3 a.(b ´ c) = b. (c ´ a = c. (a ´ b) iksyj r r rFkk r ,fDlsey r r rlfn’kksa r resa vUrj r Li"V dhft,A fl) dhft, a.(b ´ c) = b. (c ´ a = c. (a ´ b) ¾¾¾¾¾
11 528 m kj izns’k jktf"kZ V.Mu eqDr fo’ofo|ky;] bykgkckn vf/kU;kl (Assignment) 2012-2013 Lukrd foKku dk;Z e …ch-,l-lh-‰ Bachelor of Science Programme (B.Sc.) fo"k; % HkkSfrd foKku fo"k; dksM % ;w-th-ih-,p-,l- Subject : Physics Subject Code : UGPHS dkslZ ’kh"kZd % dkslZ dksM % ;w-th-ih-,p-,l--10 Subject Title: Mathematical Methods Course Code : UGPHS-10 in Physics II vf/kdre vad % 30 Maximum Marks : 30 Section - A [k.M & v vf/kdre vad % 18 Maximum Marks : 18 uksV % nhkZ m kjh; iz’uA vius iz’uksa ds m kj 800 ls 1000 ’kCnksa esa fy[ksaA lHkh iz’u vfuok;Z gSaA Note : Long Answer Question. Answer should be given in 800 to 1000 words. Answer all questions. All questions are compulsory. differential 1. What is the differential equation Solve the ordinary equation d 2 y dx 2 + y = e x around the point x = o. 6 vodky lehdj.k D;k gksrk gS\ fcUnq x = o ij lk/kkj.k lehdj.k d 2 y dx 2 + y = e x dks gy dhft,A vodyu 2. What is Legendre's differential equation Obtain the series solution of it. 6 yhtsUMj vody lehdj.k D;k gksrk gS\ bldk Js.kh gy izkIr dhft,A 3. What is Laplace differential equation State and prove the Orthagonality condition of spherical harmonies. 6 ykIykl dk vody lehdj.k D;k gksrk gS\ xksyh; vkorZ ds vkFkksZxksuyVh n’kk fyf[k, rFkk fl) dhft,A [k.M - c Section - B vf/kdre vad % 12 Maximum Marks : 12 uksV % ykq m kjh; iz’uA vius iz’uksa ds m kj 200 ls 300 ’kCnksa esa fy[ksaA lHkh iz’u vfuok;Z gSaA Note : Short Answer Question. Answer should be given in 200 to 300 words. Answer all questions. All questions are compulsory. 4. State Fourier Series and deduce the expression for Fourier constants. 4 Qwfj;j Js.kh ifjHkkf"kr dhft, rFkk Qwfj;j fu;rkadksa ds fy, O;atd izkIr dhft,A 5. Solve the differential equation dy dx = exy ( e x - e y ) 4 vody lehdj.k dy dx = exy ( e x - e y ) dks gy dhft,A 6. Solve the differential equation for angular motions. I d 2 Q dt 2 + gQ = O 4 dks.kh; xfr ds fy, vody lehdj.k I d 2 Q dt 2 + gQ = O dks gy dhft,A izkjfEHkd n’kk gS dq t = o, q = q 0 rFkk = O dt ¾¾¾¾¾
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74 8- lgh fodYi dks fVd djsaA ¼d½
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81 efJe
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87 6. efJeÅeeLeea meneÙelee mesJe
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89 117 Gòej ØeosMe jepeef
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153 OTHER INFORMATION : Volume 2 :
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64 m kj izns'k jktf"kZ V.Mu eqDr fo'ofo|ky;] bykgkckn

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