In the expansion of `(x^2+1+1/(x^2))^n ,n in N ,` number of terms is`2n+1`

The number n for which number of dissimilar terms in the expansion of (1+x+x^(2)+x^(3))^(n) is equal to number of terms in the expansion of (x+y+z)^(n) is (n in N) ________ .

The number of terms in the expansion of (x^2+1+1/x^2)^n, n in N , is:

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.

The total number of terms which are dependent on the value of x in the expansion of (x^2-2+1/(x^2))^n is equal to 2n+1 b. 2n c. n d. n+1

If the constant term in the binomial expansion of (x^2-1/x)^n ,n in N is 15, then find the value of n .

If the constant term in the binomial expansion of (x^2-1/x)^n ,n in N is 15, then find the value of n .

If the expansion of (x - (1)/(x^(2)))^(2n) contains a term independent of x, then n is a multiple of 2.

If the expansion of (x - (1)/(x^(2)))^(2n) contains a term independent of x, then n is a multiple of 2.

Statement-1: The number of distict term in the expansion of (1+px)^(20)+(1-px)^(20) is 42. Statement-2: Number of term in the expansion of (1+x)^(n) is (n+1).

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) !])