MH SET 2024 Paper 2 Physical Science Question Paper (07-Apr-2024)

Question 1

For the differential equation$x^{2}\frac{d^{2}y}{dx^{2}}+x\frac{dy}{dx}+(x^{2}-n^{2})y=0$Which of the following statements is true ?

Accepted Answer

$x = 0$ is a regular singular point, while the point at infinity is an irregular singular point

Answer

$x = 0$ and the point at infinity are regular singular points

Answer

$x = 0$ is an ordinary point, while the point at infinity is a regular singular point.

Answer

$x = 0$ is an ordinary point, while the point at infinity is singular.

Question 2

The matrix $\begin{pmatrix}1 & 1 & 1 & 1 \ 2 & 2 & 2 & 2 \ 1 & 3 & 3 & 3 \ 4 & 4 & 4 & 4\end{pmatrix}$ has rank :

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 3

Most generic eigenvalues of a $3\times 3$ traceless matrix with zero determinant are given as ($a$ is some constant) :

Accepted Answer

$a, -a, 0$

Answer

$0, 0, 0$

Answer

$0, 0, a$

Answer

$a, -2a, a$

Question 4

Consider a differential equation$\left(\frac{d^{4}}{dx^{4}}+2\frac{d^{2}}{dx^{2}}\right)f(x)=g(x)$Let F($k$) and G($k$) be the Fourier transforms of $f(x)$ and $g(x)$ respectively. Then F($k$) is :

Accepted Answer

$F(k)=\frac{G(k)}{(k^{4}-2k^{2})}$

Answer

$F(k)=(k^{4}-2k^{2})G(k)$

Answer

$F(k)=(k^{4}+2k^{2})G(k)$

Answer

$F(k)=\frac{G(k)}{(k^{4}-2ik^{2})}$

Question 5

Laplace transform of (1 + sin (2$t$)) is :

Accepted Answer

$\frac{1}{s}+\frac{2}{s^{2}+4}$

Answer

$\frac{1}{s}+\frac{1}{s^{2}+1}$

Answer

$\frac{1}{s}+\frac{4s}{s^{2}+4}$

Answer

$1+\frac{1}{s^{2}+4}$

MH SET 2024 Paper 2 Physical Science Question Paper (07-Apr-2024)

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