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 :

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

If the sum of the second, third and fourth terms of a positive term G.P. is 3 and the sum of its sixth, seventh and eighth terms is 243, then the sum of the first 50 terms of this G.P. is :