MH SET 2023 Paper 2 Physical Science Question Paper (26-Mar-2023)

Question 1

Which of the following is an analytic function ?

Accepted Answer

$z^{2}$

Answer

$z+\bar{z}$

Answer

$z\bar{z}$

Answer

$z/\bar{z}$

Question 2

Which of the following statements is true ?

Accepted Answer

Trace (AB) = Trace (BA)

Answer

Trace (ABC) = Trace (BAC)

Answer

Trace (ABCD) = Trace (BACD)

Answer

Trace (AB) = Trace (A) Trace (B)

Question 3

Laplace transform F($s$) of a function $f(x)=1$, for $0\le x\le\infty$ is equal to :

Accepted Answer

$1/s$

Answer

$1/s^{2}$

Answer

$s$

Answer

$2s$

Question 4

A function $f(x)$ satisfies the differential equation $\frac{d^{2}f}{dx^{2}}-\omega^{2}f(x)=-\delta(x-a)$, where $\omega$ is positive. The Fourier transform $F(k)=\int_{-\infty}^{\infty}f(x)e^{ikx}dx$ and solution $f(x)$ of the differential equations are respectively :

Accepted Answer

$\frac{e^{ika}}{k^{2}+\omega^{2}}$ and $\frac{1}{2\omega}e^{-\omega|x-a|}$

Answer

$\frac{e^{ika}}{k^{2}-\omega^{2}}$ and $\frac{1}{2\omega}\left(e^{-i\omega|x-a|}+e^{i\omega|x-a|}\right)$

Answer

$\frac{e^{ika}}{k^{2}-\omega^{2}}$ and $\frac{1}{2i\omega}\left(e^{-i\omega|x-a|}-e^{i\omega|x-a|}\right)$

Answer

$\frac{e^{ika}}{k^{2}+\omega^{2}}$ and $\frac{1}{2\omega}\left(e^{-\omega|x-a|}+e^{\omega|x-a|}\right)$

Question 5

The integral$\frac{1}{2\pi i}\oint\frac{\exp\left[\frac{z}{2}\left(t-\frac{1}{t}\right)\right]}{t^{n+1}}\,dt$,where $n$ is an integer and the closed contour is a circle enclosing the origin, can be used to :

Accepted Answer

generate Bessel’s functions of first kind

Answer

generate Hermite polynomials

Answer

generate Legendre polynomials

Answer

generate associated Legendre polynomials

MH SET 2023 Paper 2 Physical Science Question Paper (26-Mar-2023)

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