In the expansion of `(x^2+1+1/(x^2))^n ,n in N ,` (a)number of terms is`2n+1` (b)coefficient of constant terms is `2^(n-1)` (c)coefficient of `x^(2n-1)i sn` (d)coefficient of `x^2` in `n`

In the expansion of (x^3-1/x^2)^n, n in N if sum of the coefficients of x^5 and x^(10) is 0 then n is

The coefficient of x^(n) in expansion of (1 + x)(1 - x)^(n) is

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

If the number of terms in the expansion (1+2x-3y+4z)^(n) is 286 , then find the coefficient of term containing xyz .

Prove that the 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 .

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)]!) .

If the number of terms in the expansion of (1-2/x+4/(x^2))^n , x!=0, is 28, then the sum of the coefficients of all the terms in this expansion, is : (1) 64 (2) 2187 (3) 243 (4) 729

(i) What is the second term in the expansion of (1 + x)^(n) ? (ii) Write the 3^(rd) and 4^(th) terms in the expansion of (1 + x)^(n) . (iii) If the coefficients of 2^(nd) , 3^(rd) and 4^(th) terms in the expansion of (1 + x)^(n) are in A.P, then show that n^(2) - 9n + 14 = 0 .