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)

Truth table of a logic gate is given below: 
\[ \begin{array}{|c|c|c|} \hline \text{Input A} & \text{Input B} & \text{Output Y} \\ \hline 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 1 & X \\ \hline \end{array} \] 

The value of X in the above table is .............. 
 

Let \( A = \begin{pmatrix} \sin \theta & \cos \theta \\ \cos \theta & \sin \theta \end{pmatrix} \) and \( A + A^T - 2I = 0 \), where \( A^T \) is the transpose of \( A \) and \( I \) is the identity matrix. The value of \( \theta \) (in degrees) is ............