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

Question 1

The set given by$\{1 + (-1)^n \mid n \in \mathbb{N}\}$is :

Accepted Answer

$\{0, 2\}$

Answer

$\{1, -1\}$

Answer

$\mathbb{N}$

Answer

$\{0, 1\}$

Question 2

The number of non-empty subsets of $X = \{1, 2, 3, 4, 5, 6, 7\}$ containing only even integers is :

Accepted Answer

$7$

Answer

$8$

Answer

$1$

Answer

$3$

Question 3

Let $K \subseteq \mathbb{R}^n$ be with the property that any real valued continuous function on $K$ is bounded. Then $K$ is :

Accepted Answer

Compact

Answer

Bounded

Answer

Dense

Answer

Connected

Question 4

Suppose a bounded function $f : [0, 1] \to \mathbb{R}$ is Riemann integrable. Then which of the following is not true ?

Accepted Answer

$f$ is not Lebesgue integrable whenever $f$ is discontinuous

Answer

$f$ is Lebesgue integrable

Answer

Riemann integral of $f$ is same as Lebesgue integral of $f$

Answer

$|f|$ is Lebesgue integrable

Question 5

Let $f : \mathbb{R} \to \mathbb{R}$ be a function. Then which of the following is not true ?

Accepted Answer

If $f$ is differentiable then so is $|f|$

Answer

If $f$ is continuous then so is $|f|$

Answer

If $f$ is integrable then so is $|f|$

Answer

If $f$ is bounded then so is $|f|$