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

Question 1

Let $X$ be a connected metric space. Then which of the following is true ?

Accepted Answer

$|X| \neq 10$

Answer

$X$ is finite

Answer

$X$ is infinite

Answer

$X$ is uncountable

Question 2

Let $X, Y$ be metric spaces. Suppose $f, g : X \to Y$ are continuous functions and $D = \{x \mid f(x) = g(x)\}$. Then $f \equiv g$ if $D$ is :

Accepted Answer

Dense in $X$

Answer

Unbounded

Answer

Compact

Answer

Closed

Question 3

Which of the following statements is not true in any metric space ?

Accepted Answer

There is a finite set which is not closed

Answer

Every open set is closed

Answer

Every subset is bounded

Question 4

The series :$\frac{2}{1} + \frac{3}{4} + \frac{4}{9} + \ldots + \frac{n+1}{n^2} + \ldots$

Accepted Answer

Diverges

Answer

Converges to an irrational number

Answer

Converges to a positive transcendental number

Answer

Converges to a rational number

Question 5

For any two sequences $\{x_n\}$ and $\{y_n\}$, it is known that,$\liminf x_n + \liminf y_n \le \liminf (x_n + y_n) \le \limsup (x_n + y_n) \le \limsup x_n + \limsup y_n \quad (*)$Suppose that $x_n = \begin{cases} 0 & \text{if } n \text{ is even} \ 1 & \text{if } n \text{ is odd} \end{cases}$ and $y_n = 1 - x_n$, for all $n \ge 1$.Then, which of the following statements is/are true for $\{x_n\}$ and $\{y_n\}$ ?$S_1$ : strict inequalities hold in $(*)$ above.$S_2$ : $\{x_n + y_n\}$ converges, while $\{x_n\}$ and $\{y_n\}$ do not.

Accepted Answer

Only $S_2$ is true

Answer

Neither $S_1$ nor $S_2$ is true

Answer

Both $S_1$ and $S_2$ are true

Answer

Only $S_1$ is true

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

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