PYQs Based test 26: Engineering Mathematics

For real numbers, x and y with y = 3x² + 3x + 1, the maximum and minimum value of y for x ∈ [-2, 0] are respectively, ______

The Eigen values of the matrix below are

≤ft[ {*20c 0&1&0\\ 0&0&1\\ 0& - 3& - 4 } ]

Consider the differential equation $\left(t^2-81\right)\frac{dy}{dt}+5ty=\sin \left(t\right)$ with y(1) = 2π. There exists a unique solution for this differential equation when t belongs to the interval

If C is a circle |z| = 4 and $f\left(z\right)=\frac{z^2}{{\left(z^2-3z+2\right)}^2}$, then $\oint f\left(z\right)dz$ is

If A = 2xi + 3yj + 4zk and u = x² + y² + z², then div(uA) at (1, 1, 1) is _________.