If A and B are coefficients of xⁿ in the expansions of (1 + x)²ⁿ and (1 + x)^{2n $$-$$ 1} respectively, then A/B is equal to

If n > 1 is an integer and x $$\ne$$ 0, then (1 + x)ⁿ $$-$$ nx $$-$$ 1 is divisible by

If $\left(1+x-2 x^2\right)^6=1+a_1 x+a_2 x^2+\ldots+a_{12} x^{12}$, then the value of $a_2+a_4+a_6+\ldots+a_{12}$ is

If $$\left(1+x+x^2+x^3\right)^5=\sum_\limits{k=0}^{15} a_k x^k$$ then $$\sum_\limits{k=0}^7(-1)^{\mathbf{k}} \cdot a_{2 k}$$ is equal to