The value of $${\left( {{{ - 1 + i\sqrt 3 } \over {1 - i}}} \right)^{30}}$$ is :

If the mean and the standard deviation of the
data 3, 5, 7, a, b are 5 and 2 respectively, then a and b are the roots of the equation :

If L = sin²$$\left( {{\pi \over {16}}} \right)$$ - sin²$$\left( {{\pi \over {8}}} \right)$$ and
M = cos²$$\left( {{\pi \over {16}}} \right)$$ - sin²$$\left( {{\pi \over {8}}} \right)$$, then :

$$\mathop {\lim }\limits_{x \to 0} {{x\left( {{e^{\left( {\sqrt {1 + {x^2} + {x^4}} - 1} \right)/x}} - 1} \right)} \over {\sqrt {1 + {x^2} + {x^4}} - 1}}$$