MH SET 2020 Paper 2 Mathematical Science Question Paper (27-Dec-2020)

Question 1

Let $(X_{n})$ be a sequence of real numbers and $x\in\mathbf{R}$. Then which of the following is true ?

Accepted Answer

If $\lim\limits_{n\to\infty} x_{n}\lt x$, then $x_{n}\lt x$ for infinitely many numbers $n$

Answer

If $\lim\limits_{n\to\infty} x_{n}\leq x$, then $x_{n}\leq x$ for all $n$

Answer

If $\lim\limits_{n\to\infty} x_{n}\neq x$, then there exist $m$ and $n$ such that $x_{m}\lt x\lt x_{n}$

Answer

If $\lim\limits_{n\to\infty} x_{n}$ does not exist, then $(x_{n})$ has no subsequence converging to $x$

Question 2

Define a function $f:[0, 1]\to\mathbf{R}$ as $f(x)=x^{2}+e^{x}-2$. Then :

Accepted Answer

$f$ is increasing

Answer

$f(x)=0$ has no solution in $[0, 1]$

Answer

$f'(x)=0$ has a solution in $[0, 1]$

Answer

$f$ is not one-one

Question 3

Let $z, w$ be two complex numbers such that $z\,w\in\mathbf{R}$ and $z+w\in\mathbf{R}$. Then :

Accepted Answer

$z=\bar{w}$ or $z, w\in\mathbf{R}$

Answer

$z=w$

Answer

$z=\bar{w}$

Answer

$z, w\in\mathbf{R}$

Question 4

Define $f:\mathbf{C}-\{0\}\to\mathbf{C}$ by $f(z)=\dfrac{1}{z}$. Then the power series expansion of $f(z)$ about $z=1$ in the disc $\{z: |z-1|\lt 1\}$ is :

Accepted Answer

$1-(z-1)+(z-1)^{2}-(z-1)^{3}+\ldots\ldots$

Answer

$1+(z-1)+(z-1)^{2}+(z-1)^{3}+\ldots\ldots$

Answer

$1-z+z^{2}-z^{3}+\ldots\ldots$

Answer

$1+z+z^{2}+z^{3}+\ldots\ldots$

Question 5

If $\mathrm{T}:\mathbf{R}^{n}\to\mathbf{R}^{m}$ is a linear map, then it is represented by a matrix of order :

Accepted Answer

$m\times n$

Answer

$m\times m$

Answer

$n\times n$

Answer

$n\times m$

MH SET 2020 Paper 2 Mathematical Science Question Paper (27-Dec-2020)

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