In the expansion of `(1 + x)^(n) (1 + y)^(n) (1 + z)^(n)` , the sum of the co-efficients of the terms of degree 'r' is

If the sum of the coefficients in the expansion of (1 -3x + 10x^2)^(n) is a and the sum of the coefficients in the expansion of (1 - x^(2))^(n) is b , then

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

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

Show that the coefficient of the middle term in the expansion of (1+x)^2n is equal to the sum of the coefficients of two middle terms in the expansion of (1 + x)^2n-1

Find the sum of the coefficients in the expansion of (1+2x+3x^2+ n x^n)^2dot

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

If the sum of n terms of an A.P is cn (n-1)where c ne 0 then the sum of the squares of these terms is

Show that the middle term in the expansion of (1 + x)^(2n) is (1.3.5.........(2n - 1))/(n!)2^(n)x^(n) , where n is a positive integer.