In the expansion of `(1+a)^(m+n)` ,prove that coefficients of `a^(m)` and `a^(n)` are equal.

In the binomial expansion of (1+ x)^(m+n) , prove that the coefficients of x^(m) and x^(n) are equal.

In the binomial expansion of (1+a)^(m+n) , prove that the coefficient of a^m a n d\ a^n are equal.

In the expansion of (3+x/2)^(n) the coefficients of x^(7) and x^(8) are equal, then the value of n is equal to

If in the expansion of (1 +x)^(m) (1 - x)^(n) , the coefficients of x and x^(2) are 3 and - 6 respectively, the value of m and n are

Statement-I : In the expansion of (1+ x)^n ifcoefficient of 31^(st) and 32^(nd) terms are equal then n = 61 Statement -II : Middle term in the expansion of (1+x)^n has greatest coefficient.

If in the expansion of (1 + x)^n , the coefficients of pth and qth terms are equal, prove that p+q=n+ 2 , where p!=q .

If m and n are positive integers, then prove that the coefficients of x^(m) " and " x^(n) are equal in the expansion of (1+x)^(m+n)

If x^p occurs in the expansion of (x^2 + (1)/(x) )^(2n) , prove that its coefficient is ((2n)!)/( [ (1)/(3) (4n - p)!][(1)/(3) (2n + p) !])

In the expansion of (x^(2) + (1)/(x) )^(n) , the coefficient of the fourth term is equal to the coefficient of the ninth term. Find n and the sixth term of the expansion.

Prove that he coefficient of x^n in the expansion of (1+x)^(2n) is twice the coefficient of x^(n) in the expansion of (1+x)^(2n-1)