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

The coefficien of x¹⁰ in the expansion of (1 + x)²(1 + x²)³(1 + x³)⁴ is equal to :

If n is the degree of the polynomial,

$${\left[ {{2 \over {\sqrt {5{x^3} + 1} - \sqrt {5{x^3} - 1} }}} \right]^8} + $$ $${\left[ {{2 \over {\sqrt {5{x^3} + 1} + \sqrt {5{x^3} - 1} }}} \right]^8}$$

and m is the coefficient of xⁿ in it, then the ordered pair (n, m) is equal to :