PYQs Based Test - 11 : Engineering Mathematics

$\vec{a},\vec{b},\vec{c}$ are three orthogonal vectors. Given that $\vec{a}=\hat{i}+2\hat{j}+5\hat{k}$ and $\vec{b}=\hat{i}+2\hat{j}-\hat{k}$, the vector $\vec{c}$ is parallel to

Consider two functions f(x) = (x - 2)² and g(x) = 2x - 1, where x is real. The smallest value of x for which f(x) = g(x) is ________.

Let A be an n × n matrix with rank r(0 < r < n). Then Ax = 0 has p independent solutions, where p is

The value of $\oint \frac{1}{z^2}dz,$ where the contour is the unit circle traversed clockwise, is

The vector function $\vec{A}=\vec{\nabla }u$, where u (x, y) is a scalar function. Then $\left|\vec{\Delta }\times \vec{A}\right|$ is