Thenumber of distinct terms in the expansion of `(x_1+x_2+……..+x_p)^n` is
(A) `.^(n+p)C_n`
(B) `.^n C_1`
(C) `n+1`
(D) `.^(n+p-1)C_(p-1)`

The number of terms in the expansion of (x+1/x+1)^n is (A) 2n (B) 2n+1 (C) 2n-1 (D) none of these

The middle term in the expansion of ((2x)/3-3/(2x^2))^(2n) is a. \ ^(2n)C_n b. (-1)^n\ ^(2n)C_(n\ )x^(-n) c. \ ^(2n)C_n x^(-n) d. none of these

If C_(0),C_(1), C_(2),...,C_(n) denote the cefficients in the expansion of (1 + x)^(n) , then C_(0) + 3 .C_(1) + 5 . C_(2)+ ...+ (2n + 1) C_(n) = .

If ""(n)C_(0), ""(n)C_(1), ""(n)C_(2), ...., ""(n)C_(n), denote the binomial coefficients in the expansion of (1 + x)^(n) and p + q =1 sum_(r=0)^(n) r^(2 " "^n)C_(r) p^(r) q^(n-r) = .

If C_(0), C_(1), C_(2), ..., C_(n) denote the binomial cefficients in the expansion of (1 + x )^(n) , then a C_(0) + (a + b) C_(1) + (a + 2b) C_(2) + ...+ (a + nb)C_(n) = .

If C_(0), C_(1), C_(2), ..., C_(n) denote the binomial cefficients in the expansion of (1 + x )^(n) , then a C_(0) + (a + b) C_(1) + (a + 2b) C_(2) + ...+ (a + nb)C_(n) = .

If C_(0), C_(1), C_(2),...,C_(n) denote the binomial coefficients in the expansion of (1 + x)^n) , then xC_(0)-(x -1) C_(1)+(x-2)C_(2)-(x -3)C_(3)+...+(-1)^(n) (x -n) C_(n)=

The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (a). (n !)/((n-1)!(n+1)!) (b). ((2n)!)/((n-1)!(n+1)!) (c). ((2n)!)/((2n-1)!(2n+1)!) (d). none of these

If r^[th] and (r+1)^[th] term in the expansion of (p+q)^n are equal, then [(n+1)q]/[r(p+q)] is (a) 1/2 (b) 1/4 (c) 1 (d) 0

If n is not a multiple of 3, then the coefficient of x^n in the expansion of log_e (1+x+x^2) is : (A) 1/n (B) 2/n (C) -1/n (D) -2/n