If the third term in the binomial expansion
of $${\left( {1 + {x^{{{\log }_2}x}}} \right)^5}$$ equals 2560, then a possible value of x is -

The coefficient of t⁴ in the expansion of $${\left( {{{1 - {t^6}} \over {1 - t}}} \right)^3}$$ is :

If the fractional part of the number $$\left\{ {{{{2^{403}}} \over {15}}} \right\} is \, {k \over {15}}$$, then k is equal to :

The coefficient of x² in the expansion of the product
(2$$-$$x²) .((1 + 2x + 3x²)⁶ + (1 $$-$$ 4x²)⁶) is :