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

If \[ P = \begin{pmatrix} \cos\alpha & \sin\alpha \\ -\sin\alpha & \cos\alpha \end{pmatrix} \] and \(P + P^T = I\), the value of \(\alpha \; (0 \leq \alpha \leq \pi/2)\) is

The length of the edge of a variable cube is increasing at the rate of 25 cm s\(^{-1}\). If the initial length of the edge of the cube is 10 cm, the rate of increase of the surface area of the cube is .............. cm\(^2\) s\(^{-1}\). (answer in integer)

The area bounded by the curve \( y = \sin x \) and the x-axis between \( x = 0 \) and \( x = \frac{3\pi}{2} \) is ............. sq. units. (answer in integer)