The sum of the co-efficients of all odd degree terms in the expansion of

$${\left( {x + \sqrt {{x^3} - 1} } \right)^5} + {\left( {x - \sqrt {{x^3} - 1} } \right)^5}$$, $$\left( {x > 1} \right)$$ is

Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series
1² + 2.2² + 3² + 2.4² + 5² + 2.6² ...........
If B - 2A = 100$$\lambda $$, then $$\lambda $$ is equal to

Let $${a_1}$$, $${a_2}$$, $${a_3}$$, ......... ,$${a_{49}}$$ be in A.P. such that

$$\sum\limits_{k = 0}^{12} {{a_{4k + 1}}} = 416$$ and $${a_9} + {a_{43}} = 66$$.

$$a_1^2 + a_2^2 + ....... + a_{17}^2 = 140m$$, then m is equal to

If the curves y² = 6x, 9x² + by² = 16 intersect each other at right angles, then the value of b is :