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 :

The sum of the co-efficients of all odd degree terms in the expansion of

$${\left( {x + \sqrt {{x^3} - 1} } \right)^5} + {\left( {x - \sqrt {{x^3} - 1} } \right)^5}$$, $$\left( {x > 1} \right)$$ is