If some three consecutive in the binomial expansion of (x + 1)ⁿ is powers of x are in the ratio 2 : 15 : 70, then the average of these three coefficient is :-

If the fourth term in the binomial expansion of $${\left( {{2 \over x} + {x^{{{\log }_8}x}}} \right)^6}$$ (x > 0) is 20 × 8⁷, then a value of x is :

If the fourth term in the binomial expansion of
$${\left( {\sqrt {{x^{\left( {{1 \over {1 + {{\log }_{10}}x}}} \right)}}} + {x^{{1 \over {12}}}}} \right)^6}$$ is equal to 200, and x > 1, then the value of x is :

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: