MH SET 2021 Paper 2 Mathematical Science Question Paper (26-Sep-2021)

Question 1

Let $(x_{n})\, n\in\mathbf{N}$ be a convergent sequence of positive real valued numbers. Which of the following statements is true ?

Accepted Answer

The limit of every subsequence of the sequence is non-negative

Answer

Limit of the sequence is positive

Answer

Limit of the sequence may be negative

Answer

There is a subsequence of the sequence which has positive limit

Question 2

Let $f:\mathbf{R}\to \mathrm{Q}$ be a non-constant increasing function. Then :

Accepted Answer

$f$ is constant on some interval $[a, b]$

Answer

$f$ is one-one

Answer

$f$ is onto

Answer

$f$ is not constant on any interval

Question 3

Which of the following is true for a complex number $z=x+iy$ ?

Accepted Answer

$|x|+|y|\geq |z|$

Answer

$|x|+|y|=|z|$

Answer

$|x|+|y|=\sqrt{2}\,|z|$

Answer

$|x|+|y|\leq |z|$

Question 4

The function $f:\mathbf{C}\to\mathbf{C}$ defined by $f(z)=\cos z$ is :

Accepted Answer

onto

Answer

one-one

Answer

bijective

Answer

bounded

Question 5

Let $\mathrm{R}_{n}[x]$ denote the vector space of all polynomials over $\mathbf{R}$ having degree atmost $n$. Then the dimension of $\mathbf{R}_{n}[x]$ is :

Accepted Answer

$n + 1$

Answer

$n^{2}$

Answer

$n$

Answer

$\infty$

MH SET 2021 Paper 2 Mathematical Science Question Paper (26-Sep-2021)

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