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Roll No……..
B010703T
M.Sc. (First Semester)
(NEP) EXAMINATION, 2023-24
PHYSICS
(Electromagnetic Theory)
Time : 2 Hours ] [ Maximum Marks 75
Note : attempt questions from all sections as directed.
Instruction : The candidates are required to answer only in serial order if there are many parts of equation answer them in continuation.
Section – A
(Short Answer Type Questions)
Note : All questions are compulsory each questions carries 5 marks
1 (A) Check whether 1/z analytic or not where z is a complex variable.
(B) Determine the pole and residue at the pole of a function f (z) = z/z-1
(C) Write down Rodrigues formula for legendre’s polynomial and plot Po(x) and P1(x)
(D) Prove :
(E) What is Cayley-Hamilton theorem ? Verify it for the matrix :
(F) Prove that the matrix :
Is unitary.
(G) Ai and Bj are Contravariant vector. Show that AiBj is a Contravariant vector of rank two.
(H) Show that Kronecker delta § is a second order mixed tensor .
(I) From a bucket containing two apples and three mangoes, two fruits are selected find probability distribution of a number apples into fruits drown.
Section – B
(Long Answer Type Questions)
Note: Attempt anyone questions. Questions carries 15 marks.
2. By contour integration evaluate :
3. Find Laurent series expression of :
4. Express the polynomial :
f(x) = 4x³ – 2x² – 3x + 8
in term of legendre polynomials.
5. Prove the following :
Section – C
(Long Answer Type Questions)
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Note: Attempt anyone questions. Questions carries 15 marks.
6. Determine the eigen values and eigen vectors of the matrix :
and check whether the vectors are orthogonal or not.
7. Find the inverse of the following Matrix by elementary row transformation :
8. Joint probability density function of two random variables X and Y is :
Find the probability density function of Z = X – Y
9. Find metric tensor gij in spherical polar coordinates also prove for an arbitrary vector A,
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MSc 1st Semester Classical Mechanics Question Paper 2024 : Click Here
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