The sum of the co-efficients of all even degree terms in x in the expansion of
$${\left( {x + \sqrt {{x^3} - 1} } \right)^6}$$ + $${\left( {x - \sqrt {{x^3} - 1} } \right)^6}$$, (x > 1) is equal to:

The total number of irrational terms in the binomial expansion of (7^1/5 – 3^1/10)⁶⁰ is :

A ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of $${\left( {{2^{1/3}} + {1 \over {2{{\left( 3 \right)}^{1/3}}}}} \right)^{10}}$$ is :

Let (x + 10)⁵⁰ + (x $$-$$ 10)⁵⁰ = a₀ + a₁x + a₂x² + . . . . + a₅₀x⁵⁰, for all x $$ \in $$ R; then $${{{a_2}} \over {{a_0}}}$$ is equal to