PYQs Based test 26: Engineering Mathematics

The matrix A = ≤ft[ {*20c 3/2&0&1/2\\ 0& - 1&0\\ 1/2&0&3/2 } ] has three distinct Eigen values and one of its Eigen vectors is ≤ft[ {*20c 1\\ 0\\ 1 } ]. Which one of the following can be another Eigen vector of A?

Let y² – 2y + 1 = x and $\sqrt{x}+y=5$. The value of $x+\sqrt{y}$ equals ________. (Give the answer up to three decimal places)

If f = 2x³ + 3y² + 4z, the value of line integral $\underset{C}{\int }\mathrm{gradf}.\mathrm{dr}$ evaluated over contour C formed by the segments (-3, -3, 2) → (2, -3, 2) → (2, 6, 2) → (2, 6, -1) is ________.

The value of the integral $\underset{C}{\oint }\frac{z+1}{z^2-4}dz$ in counter clockwise direction around a circle C of radius 1 with center at the point z = −2 is

M is a 2 × 2 matrix with eigenvalues 4 and 9. The eigenvalues of M² are