PYQs Based test 25: Engineering Mathematics

Consider a non-singular 2×2 square matrix A. If trace (A) = 4 and trace(A²) = 5, the determinant of the matrix A is _________ (up to 1 decimal place).

Which one of the following functions is analytic in the region |z| ≤ 1?

The value of the directional derivative of the function θ (x, y, z) = xy² + yz² + zx² at the point (2, -1, 1) in the direction of the vector p = i + 2j + 2k is

Let A be a 10 × 10 matrix such that A⁵ is a null matrix, and let I be the 10 × 10 identity matrix. The determinant of A + I is ______.

Let (-1 - j), (3 - j), (3 + j) and (-1 + j) be the vertices of a rectangle C in the complex plane. Assuming that C is traversed in counter-clockwise direction, the value of the countour integral ${\oint }_C\frac{dz}{z^2(z-4)}$ is