The value of [C(7, 0) + C(7, 1)] + [C(7, 1) + C(7, 2)] + ..... + [C(7, 6) + C(7, 7)] is

The expansions of (x $$-$$ y)ⁿ, n $$\ge$$ 5 is done in the descending powers of x. If the sum of the fifth and sixth terms is zero, then $${x \over y}$$ is equal to

What is the coefficient of the middle term in the binomial expansion of (2 + 3x)⁴ ?

Let the coefficient of the middle term of the binomial expansion of (1 + x)²ⁿ be $$\alpha$$ and those of two middle terms of the binomial expansion of (1 + x)^{2n $$-$$ 1} be $$\beta$$ and $$\gamma$$. Which one of the following relations is correct?