nth term in binomial expansion

If the constant term, in binomial expansion of (2x^(r) + (1)/(x^(2)))^(10) is 180, then r is equal to ___________ .

If the ratio of coefficients of the three consecutives terms in binomial expansion of (1+x)^(n) is 2:5:70. Then the average of these coeficients is

Let t_(n) denote the n^(th) term in a binomial expansion. If (t_(6))/(t_(5)) in the expansion of (a+b)^(n+4) and (t_(5))/(t_(4)) in the expansion of (a+b)^(n) are equal, then n is

What is General and middle term in a binomial expansion

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

If (r+1)^(th) term is (3.5...(2r-1))/(r!) (1/5)^(r) , then this is the term of binomial expansion-

The fourth term in the binomial expansion of (x^2 - (1)/(x^3) )^n is independent of x , when n is equal to