The ratio of the coefficient of terms `(x^(n-r) a^r and x^r a^(n-r)` is the binomial expansion of `(x + a)^n `will be:

If the coefficients of a^(r-1),\ a^r and \ a^(r+1) in the binomial expansion of (1+a)^n are in A.P., prove that n^2-n(4r+1)+4r^2-2=0.

If A and B are coefficients of x^(r) and x^(n-r) respectively in the expansion of (1+x)^(n), then

If the coefficients of a^(r-1), a^(r ), a^(r+1) in the binomial expansion of (1 + a)^(n) are in Arithmetic Progression, prove that: n^(2) -n(4r+1) + 4r^(2) -2=0

If the coefficients of r^(th) and (r+1)^(th) term in the expansion of (1+x)^(n) are equal then n=

If n is a positive integer and r is a nonnegative integer, prove that the coefficients of x^r and x^(n-r) in the expansion of (1+x)^(n) are equal.

If A and B are coefficients of x^r and x^(n-r) respectively in the expansion of (1 + x)^n , then

Given positive integers r gt 1, n gt 2 and that the coefficient of (3rd)th and (r+2)th terms in the binomial expansion of (1+x)^(2n) are equal. Then (a) n=2r (b) n=2r+1 (c) n=3r (d) non of these