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