In an increasing geometric series, the sum of the second and the sixth term is $${{25} \over 2}$$ and the product of the third and fifth term is 25. Then, the sum of 4^th, 6^th and 8^th terms is equal to :

The minimum value of $$f(x) = {a^{{a^x}}} + {a^{1 - {a^x}}}$$, where a, $$x \in R$$ and a > 0, is equal to :

If $$0 < \theta ,\phi < {\pi \over 2},x = \sum\limits_{n = 0}^\infty {{{\cos }^{2n}}\theta } ,y = \sum\limits_{n = 0}^\infty {{{\sin }^{2n}}\phi } $$ and $$z = \sum\limits_{n = 0}^\infty {{{\cos }^{2n}}\theta .{{\sin }^{2n}}\phi } $$ then :

The common difference of the A.P.
b₁, b₂, … , b_m is 2 more than the common
difference of A.P. a₁, a₂, …, a_n. If
a₄₀ = –159, a₁₀₀ = –399 and b₁₀₀ = a₇₀, then b₁ is equal to :