Mathematical Physics (GATE Physics): Questions 16 - 20 of 39

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Question number: 16

» Mathematical Physics » Elements of Complex Analysis » Residue Theorem and Applications

Appeared in Year: 2012

MCQ▾

Question

The value of the integral Ce1zdz , using the contour C of circle with unit radius z =1 is –

Choices

Choice (4) Response
a.

Zero

b.

2πi

c.

12πi

d.

1+2πi

Question number: 17

» Mathematical Physics » Elements of Complex Analysis » Cauchy-Riemann Conditions

Appeared in Year: 2012

MCQ▾

Question

The number of independent component of the symmetric Aij with indices i,j=1, 2,3 is –

Choices

Choice (4) Response
a.

6

b.

3

c.

1

d.

9

Question number: 18

» Mathematical Physics » Elements of Complex Analysis » Residue Theorem and Applications

Appeared in Year: 2013

Short Answer Question▾

Write in Short

For the function f(z)=16z(z+3)(z1)2 , the residue at the pole z=1 is (your answer should be an integer) _ .

Question number: 19

» Mathematical Physics » Laplace Transforms

Appeared in Year: 2013

MCQ▾

Question

Which of the following pairs of the given function F(t) and its Laplace transform f(s) is NOT CORRECT?

Choices

Choice (4) Response
a.

F(t)=sinkt,f(s)=ss2+k2,(s>0)

b.

F(t)=1,f(s)=1s,(s>0)

c.

F(t)=δ(t),f(s)=1 (Singularity at + 0)

d.

F(t)=tekt,f(s)=1(sk)2,(s>k,s>0)

Question number: 20

» Mathematical Physics » Matrices

Appeared in Year: 2011

MCQ▾

Question

A 3×3 matrix has elements such that its trace is 11 and its determinant is 36 . The eigenvalues of the matrix are all known to be positive integers. The largest eigenvalue of the matrix is –

Choices

Choice (4) Response
a.

12

b.

6

c.

18

d.

9

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