Mathematical Physics (GATE Physics): Questions 6 - 9 of 39

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Question number: 6

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

Appeared in Year: 2014

MCQ▾

Question

The matrix A=13[11+i1i1] is –

Choices

Choice (4) Response
a.

Symmetric

b.

Anti – symmetric

c.

Unitary

d.

Orthogonal

Question number: 7

» Mathematical Physics » Linear Differential Equations

Appeared in Year: 2015

MCQ▾

Question

A function y(z) satisfies the ordinary differential equation y+1zym2z2y=0 , where m=0,1,2,3 Consider the four statements P, Q, R, S as given below.

P: Zm and Zm are linearly independent solution for all values of m

Q: Zm and Zm are linearly independent solution for all values of m>0

R: lnZ and 1 are linearly independent solution for m=0

S: Zm and lnZ are linearly independent solution for all values of m

The correct option for the combination of valid statements is –

Choices

Choice (4) Response
a.

P, R and S

b.

Q and R

c.

P and R

d.

R and S

Question number: 8

» Mathematical Physics » Vector Calculus

Appeared in Year: 2014

Short Answer Question▾

Write in Short

If the vector potential

A=αxx^+2yy^3zz^, satisfies the Coulomb gauge, the value of the constant α is ________.

Question number: 9

» Mathematical Physics » Fourier Analysis

Appeared in Year: 2015

MCQ▾

Question

The Heaviside function is defined as,

H(t)={+1,fort>01,fort<0

And its Fourier transform is given by 2iω . The Fourier transform of, 12[H(t+12)H(t12)] is –

Choices

Choice (4) Response
a.

cos(ω2)ω2

b.

sin(ω2)

c.

sin(ω2)ω2

d.

0

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