MH SET 2019 Paper 2 Mathematical Science Question Paper (23-Jun-2019)

Question 1

Let for $n \in \mathbb{N}$, $I_n = \left(0, \frac{1}{n}\right)$, $J_n = \left[0, \frac{1}{n}\right]$, $K_n = (n, \infty)$ and $L_n = [n, \infty)$. Which of the following sets is non-empty ?

Accepted Answer

$\bigcap_{n=1}^{\infty} J_n$

Answer

$\bigcap_{n=1}^{\infty} I_n$

Answer

$\bigcap_{n=1}^{\infty} K_n$

Answer

$\bigcap_{n=1}^{\infty} L_n$

Question 2

Let $f(x, y) = |\sin x - \sin y|$ for $x, y \in \mathbb{R}$. Then :

Accepted Answer

$f(x, y) \le |x - y|$ for all $x, y$

Answer

$f(x, y) \le |x|$ for all $x, y$

Answer

$f(x, y) \ne 0$ for $x \ne y$

Answer

$f(x, y) \ge |y|$ for all $x, y$

Question 3

Limsup of the sequence $\left\{-2, 2, -\frac{3}{2}, \frac{3}{2}, -\frac{4}{3}, \frac{4}{3} ........\right\}$ is :

Accepted Answer

1

Answer

3/2

Answer

2

Answer

0

Question 4

One of the values of $i^i$ is :

Accepted Answer

$e^{-\pi/2}$

Answer

$e^{-i\pi/2}$

Answer

$e^{\pi/2}$

Answer

$e^{i\pi/2}$

Question 5

Let V denote the vector space of $n \times n$ symmetric complex matrices, over $\mathbb{R}$. Then dim V as a vector space over $\mathbb{R}$ is :

Accepted Answer

$n^2 + n$

Answer

$n^2$

Answer

$\frac{n^2 + n}{2}$

Answer

$n^2 - n$

MH SET 2019 Paper 2 Mathematical Science Question Paper (23-Jun-2019)

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