The sum of the series

2.²⁰C₀ + 5.²⁰C₁ + 8.²⁰C₂ + 11.²⁰C₃ + ... +62.²⁰C₂₀ 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