ISI MS(QMBA) 2023 Question Paper with Solutions: 47 Questions, Answer Key & Section-wise Analysis

Let $C$ be the circle in the $xy$-plane which passes through the origin and touches the line $y=-2$. If the centre of $C$ lies on the straight line $x+y=1$, then the radius of $C$ is

Twelve points are located on the circumference of a circle. Lines are drawn to connect all possible pairs of points. How many lines are drawn?

Find the length of the arc of the parabola $x^2=4y$ from the vertex to the point $x=2$, where $x\in R$ and $y\in R$.

Find the length of the arc of the parabola $x^2=4y$ from the vertex to the point $x=2$, where $x\in R$ and $y\in R$.

The set of positive real numbers $x$ for which the series

$$\sum _{n=1}^{\infty }\frac{1}{x^n+x^{-n}}$$

diverges

What is the interval on which the function $f(x)=\frac{\log (x)}{x}$, $x\in (0,\infty )$ is increasing?

Let $X$ be a non-empty set and let $\mathcal{P}(X)$ be its power set. Define two operations ‘+’ and ‘$\ast$’ on $\mathcal{P}(X)$ as follows. For $A,B\in \mathcal{P}(X)$, let

$$A+B=A\cup B,A\ast B=A\cap B.$$

If $G_1=(\mathcal{P}(X),+)$ and $G_2=(\mathcal{P}(X),\ast )$, then,