List of top Mathematics Questions on Volume of Cube, Cuboid and Cylinder asked in CBSE CLASS XII

Find \( A^{-1} \), if \[ A = \begin{pmatrix} 1 & 2 & 1 \\ 2 & 3 & -1 \\ 1 & 0 & 1 \end{pmatrix} \] Hence, solve the following system of equations: \[ x + 2y + z = 5 \\ 2x + 3y = 1 \\ x - y + z = 8 \]

Check whether the relation \( S \) in the set of real numbers \( \mathbb{R} \), defined by \( S = \{(a, b) : a - b + \sqrt{2} \text{ is an irrational number} \} \), is reflexive, symmetric, or transitive.

A biased die is twice as likely to show an even number as an odd number. If such a die is thrown twice, find the probability distribution of the number of sixes. Also, find the mean of the distribution.