The coefficient of `x^(53)` in the expansion `sum_(m=0)^(100)^100C_m(x-3)^(100-m)2^m` is (a) `100 C_(47)` (b.) `100 C_(53)` (c.) `-100C_(53)` (d.) none of these

Find the coefficient of x^(50) in the expansion of (1+x)^(101)xx(1-x+x^2)^(100)dot

The coefficient of x^9 in the expansion of (1+x)(1+ x^2)(1+x^3)....(1+x^(100)) is

The coefficient of x in the expansion of (1 + x)(1 + 2x)(1 + 3x) ... (1 + 100x) is

The number of terms in the expansion of (x + a)^(100) + (x - a)^(100) is

Evaluate lim_(x to 1) sum_(k=1)^(100) x^(k) - 100)/(x-1).

The value of lim_(m->oo)(cos(x/m))^("m") is 1 (b) e (c) e^(-1) (d) none of these

If ""^(100)C_(r)=""^(100)C_(3r) then r is:

The value of x in the expression (x+x^((log)_(10)x))^5 if third term in the expansion is 10,00,000 is/are a. 10 b. 100 c. 10^(-5//2) d. 10^(-3//2)

sum_(m=1)^(n)(sum_(k=1)^(m)(sum_(p=k)^(m)"^(n)C_(m)*^(m)C_(p)*^(p)C_(k)))=

Let S_(1)=underset(0 le i lt j le 100)(sumsum)C_(i)C_(j) , S_(2)=underset(0 le j lt i le 100)(sumsum)C_(i)C_(j) and S_(3)=underset(0 le i = j le 100)(sumsum)C_(i)C_(j) where C_(r ) represents cofficient of x^(r ) in the binomial expansion of (1+x)^(100) If S_(1)+S_(2)+S_(3)=a^(b) where a , b in N , then the least value of (a+b) is