Consider a $$2 \times 2$$ square matrix $$A = \left[ {\matrix{ \sigma & x \cr \omega & \sigma \cr } } \right]$$
Where $$x$$ is unknown. If the eigenvalues of the matrix $$A$$ are $$\left( {\sigma + j\omega } \right)$$ and $$\left( {\sigma - j\omega } \right)$$, then $$x$$ is equal to

A triangle in the $$xy-$$plane is bounded by the straight lines $$2x=3y, y=0$$ and $$x=3.$$ The volume above the triangle and under the plane $$x+y+z=6Z$$ is ________.

The integral $$\int\limits_0^1 {{{dx} \over {\sqrt {\left( {1 - x} \right)} }}} $$ is equal ________.

The probability of getting a ''head'' in a single toss of a biased coin is $$0.3.$$ The coin is tossed repeatedly till a ''head'' is obtained. If the tosses are independent, then the probability of getting ''head'' for the first time in the fifth toss is ________.