List of top Mathematics Questions asked in Indian Institute Of Technology Joint Admission Test for MSc

The correct option for \( x \) which satisfies the following equation is \[ \begin{vmatrix} x & 2 & 3 \\ 4 & x & 6 \\ x & 8 & 9 \end{vmatrix} = \begin{vmatrix} 102 & 18 & 36 \\ 1 & 3 & 4 \\ 17 & 3 & 6 \end{vmatrix} \]

Consider 10 balls each having different colors including a blue ball. If 6 balls are selected randomly, the probability of the blue ball being selected is

Maximum value of the function \( f(r) = r^2 e^{-r} \), when \( 0<r<\infty \) is

For $\alpha>0$, the value of the integral $\displaystyle \int_{-\infty}^{+\infty} x e^{-\alpha x^2} \, dx$ is

The function \( x^4 e^{-2x^2/3} \) (for \( x > 0 \)) has a maximum at a value of \( x \) equal to ...........
(Round off to two decimal places)

The function \( f(x) = x e^{-x^2} \) has a minimum at