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

The coefficient of x^53 in sum_(r = 0)^(100) ""^100C_r (x - 3)^(100 - r) .2^r is

The coefficient of x^(50) in the expansion sum_(k=0)^(100)""^(100)C_(k)( x-2)^(100-k)3^(k) is also equal to :

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

Find the sum of the series sum_(r=0)^(50)(""^(100-r)C_(25))/(100-r)

The HCF of 100 and 101 is (a)10100 (b) 1001 (c) 10101 (d) None of these

Find the number of terms in the expansion of (a+b+c+d+e)^100

If G and L are the greatest and least values of the expression (2x^(2)-3x+2)/(2x^(2)+3x+2), x epsilonR respectively. The least value of G^(100)+L^(100) is (a) 2^(100) (b) 3^(100) (c) 7^(100) (d) none of these

The HCF of first 100 natural numbers is (a) 2 (b) 100 (c) 1 (d) None of these

Prove the following identieties using the theory of permutation where C_(0),C_(1),C_(2),……C_(n) are the combinatorial coefficents in the expansion of (1+x)^n,n in N: ""^(100)C_(10)+5.""^(100)C_(11)+10 .""^(100)C_(12)+ 10.""^(100)C_(13)+ 10.""^(100)C_(14)+ 10.""^(100)C_(15)=""^(105)C_(90)

Prove that ^100 C_0^(100)C_2+^(100)C_2^(100)C_4+^(100)C_4^(100)C_6++^(100)C_(98)^(100)C_(100)=1/2[^(200)C_(98)-^(100)C_(49)]dot