Binomial Theorem

Find the value of r if the coefficients of (2r + 4)th and (r - 2)th terms in the expansion of (1 + x)18 are equal

In the binomial expansion of (x + 1)n, the coefficients of the fifth, sixth and seventh terms are in arithmetic progression. Find all the values of n for which this can happen,

Find a if the coefficients of x2 and x3 in the expansion of (3 + ax)9 are equal.

For what value of m the coefficients of the (2m + l)th and (Am + 5)th terms, in the expansion of (1 +x)10, are equal ?

Let n be a positive integer if the coefficients of 2nd, 3rd, 4th terms in the expansion of (1+x)n are in A. P., find the value of n.

The coefficients of (r - 1)th, rth and (r + 1)th terms in the expansion of (1 + x)n are in the ratio of 1:3:5 Find n and r.