If A = $\begin{bmatrix} 10 & 2k + 5 \\\ 3k - 3 & k + 5 \end{bmatrix} $ is a symmetric matrix, the value of k is _______.

The value of the integral

$\rm \oint \left( \frac{6z}{2z^4 - 3z^3 + 7 z^2 - 3z + 5} \right) dz$

evaluated over a counter-clockwise circular contour in the complex plane enclosing only the pole z = i, where 𝑖 is the imaginary unit, is

The system of linear equations in real (x, y) given by

$\rm \begin{pmatrix} \rm x & \rm y \end{pmatrix} \begin{bmatrix} 2 & 5- 2 α \\\ α & 1 \end{bmatrix} = \rm \begin{pmatrix} \rm 0 & \rm 0 \end{pmatrix} $

involves a real parameter α and has infinitely many non-trivial solutions for special value(s) of α. Which one or more among the following options is/are non-trivial solution(s) of (x, y) for such special value(s) of α ?

Let a random variable X follow Poisson distribution such that

Prob(X = 1) = Prob(X = 2).

The value of Prob(X = 3) is __________ (round off to 2 decimal places).