For the exact differential equation,

$\frac{du}{dx}=\frac{-xu^2}{2+x^2u}$

which one of the following is the solution?

A is a 3 × 5 real matrix of rank 2. For the set of homogeneous equations Ax = 0, where 0 is a zero vector and x is a vector of unknown variables, which of the following is/are true?

If the sum and product of eigenvalues of a 2 × 2 real matrix $\begin{bmatrix}3&p\\\ p&q\end{bmatrix} $ are 4 and -1 respectively, then |p| is _______ (in integer).

Given z = x +iy, i = √-1 C is a circle of radius 2 with the centre at the origin. If the contour C is traversed anticlockwise, then the value of the integral $\frac{1}{2\pi}\int_c\frac{1}{(z-i)(z+4i)}dZ$ is ________ (round off to one decimal place.)