The sum of the series

2.²⁰C₀ + 5.²⁰C₁ + 8.²⁰C₂ + 11.²⁰C₃ + ... +62.²⁰C₂₀ is equal to :

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 :