List of top Questions asked in IIT JAM MS- 2020

For real constants $a$ and $b$, let \[ f(x) = \begin{cases} \frac{a \sin x - 2x}{x}, & x < 0 \\ bx, & x \ge 0 \end{cases} \] 

If $f$ is a differentiable function, then the value of $a + b$ is 
 

If $\{x_n\}_{n \ge 1}$ is a sequence of real numbers such that $\lim_{n \to \infty} \frac{x_n}{n} = 0.001$, then
 

Let $X$ be a random variable having $U(0,10)$ distribution and $Y = X - [X]$, where $[X]$ denotes the greatest integer less than or equal to $X$. Then $P(Y > 0.25)$ equals ..............
The maximum value of the function \[ y = \frac{x^2}{x^4 + 4}, x \in \mathbb{R}, \] is ............
Let $Z_1$ and $Z_2$ be i.i.d. $N(0,1)$ random variables. If $Y = Z_1^2 + Z_2^2$, then $P(Y > 4)$ equals
A packet contains 10 distinguishable firecrackers out of which 4 are defective. If three firecrackers are drawn at random (without replacement) from the packet, then the probability that all three firecrackers are defective equals
Which one of the following series is convergent?
The mean and the standard deviation of weights of ponies in a large animal shelter are 20 kg and 3 kg, respectively. A pony is selected at random. Using Chebyshev's inequality, find the lower bound of the probability that its weight lies between 14 kg and 26 kg.
Let $E$ and $F$ be two events. Then which one of the following statements is NOT always TRUE?
Let $X$ be a random variable having Poisson(2) distribution. Then $E\left(\dfrac{1}{1+X}\right)$ equals