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

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