MH SET 2025 Paper 2 Physical Science Question Paper (15-Jun-2025)

Question 1

The value of the line integral $I = \int \vec{A}\cdot d\vec{r}$, where $\vec{r} = x\hat{i} + y\hat{j}$ and $\vec{A} = (x+y)\hat{i} + (y-x)\hat{j}$, along the path $y^{2} = x$ from the point $(1, 1)$ to the point $(4, 2)$ is:

Accepted Answer

11.33

Answer

10.33

Answer

12.33

Answer

13.33

Question 2

It is given that the residue of the complex function $\dfrac{e^{1/z}}{z^{n}}$ at an isolated singular point $z = 0$ is $\dfrac{1}{9!}$. The value of $n$ must be equal to:

Accepted Answer

$n = -8$

Answer

$n = 1$

Answer

$n = -9$

Answer

$n = -1$

Question 3

A set $V$ of complex numbers forms a two-dimensional real vector space under the usual addition of complex numbers and multiplication by real numbers. Let $T : V \to V$ be a linear transformation defined as $T(z) = \bar{z}$. Eigenvalues of $T$ are:

Accepted Answer

$1, -1$

Answer

$1, 1$

Answer

$0, 0$

Answer

$2, -2$

Question 4

The function $f(x) = \exp(2x)\sin(2x)$ can be expanded as the Taylor series:

Accepted Answer

$\displaystyle\sum_{n=0}^{\infty} 2^{3n/2}\,\sin\!\left(\dfrac{n\pi}{4}\right)\dfrac{x^{n}}{n!}$

Answer

$\displaystyle\sum_{n=0}^{\infty} 2^{2n}\,\sin\!\left(\dfrac{n\pi}{4}\right)\dfrac{x^{n}}{n!}$

Answer

$\displaystyle\sum_{n=0}^{\infty} 2^{3n}\,\sin\!\left(\dfrac{n\pi}{4}\right)\dfrac{x^{n}}{n!}$

Answer

$\displaystyle\sum_{n=0}^{\infty} 2^{n}\,\sin\!\left(\dfrac{n\pi}{4}\right)\dfrac{x^{n}}{n!}$

Question 5

The Cauchy principal value of the integral $\displaystyle\int_{-\infty}^{\infty} \dfrac{e^{2ix}\sin x}{x}\,dx$ is:

Accepted Answer

$0$

Answer

$2\pi i$

Answer

$i\pi$

Answer

$1$

MH SET 2025 Paper 2 Physical Science Question Paper (15-Jun-2025)

MAHA TAIT Mock Test Series (New)

MH-SET (Assistant Professor) Mock Tests Series (New)