Let $$\,\,f:\left[ { - 1, - } \right] \to R,\,\,$$ where $$\,f\left( x \right) = 2{x^3} - {x^4} - 10.$$ The minimum value of $$f(x)$$ is _______.

The vector that is NOT perpendicular to the vectors $$\,\,\left( {i + j + k} \right)\,\,$$ and $$\,\left( {i + 2j + 3k} \right)\,\,$$ is _________.

An urn contains $$5$$ red and $$7$$ green balls. A ball is drawn at random and its colour is noted. The ball is placed back into the urn along with another ball of the same colour. The probability of getting a red ball in the next draw is

The value of the integral $${1 \over {2\pi j}}\int\limits_c {{{{z^2} + 1} \over {{z^2} - 1}}} dz$$
where $$z$$ is a complex number and $$C$$ is a unit circle with center at $$1+0j$$ in the complex plane is ____.