List of top Engineering Mathematics Questions on Mathematics

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)
The sum of eigenvalues of the matrix \( \begin{bmatrix} 4 & 3 & 2 \\ 0 & -1 & 2 \\ 0 & 0 & -3 \end{bmatrix} \) is ................... (in integer).
Order (O) and degree (D) of the differential equation \( \left(\frac{dy}{dx}\right)^3 = \sqrt{\frac{d^2y}{dx^2} + 10} \) are
The probability of setting an easy exam paper by three setters are \( \frac{1}{2}, \frac{1}{3}, \) and \( \frac{1}{4} \). If all three are setting one paper each, then the probability that at least one of the papers will be easy is ................... (round off to 2 decimal places).
Two eigenvalues of the following matrix are 3 and 6. The third eigenvalue is \[ \begin{bmatrix} -2 & -4 & 2 \\ -2 & 1 & 2 \\ 4 & 2 & 5 \end{bmatrix} \]
The value of \( x \) for which the inverse of the following matrix does not exist is \[ \begin{bmatrix} 1 & 3 & 0 \\ 2 & x & 4 \\ -1 & 0 & 2 \end{bmatrix} \]
Two vertical poles of height 6 m and 18 m are 10 m apart on a flat ground. A string needs to be connected from the top of one pole to a peg on the ground and then on to the top of the other pole. The minimum length (m) of the string is
The value of \( y \) for which the following limit exists is \[ \lim_{x \to 1} \frac{2x^2 - yx - x + 3}{3x^2 - 5x + 2} \]
The probability of the standard normal variable taking values between 0 and 1 is 0.3413, between 0 and 2 is 0.4772, and between 0 and 3 is 0.4987. The average of marks in an examination is 68 and the standard deviation is 10. The percentage of examinees getting less than 48 marks is:
The coefficient of \( x^4 \) in the polynomial \( (x - 1)^3 (x - 2)^3 \) is equal to .................