`(x-2)^(100)=sum_(r=0)^100 a_r x^r`, then `a_1+2a_2+......+100a_100=`

If (1+2x+x^2)^n=sum_(r=0)^(2n)a_r x^r ,then a_r is a. (.^nC_2)^2 b. .^n C_r .^n C_(r+1) c. .^(2n) C_r d. .^(2n) C_(r+1)

If (2+x)(2+x^2)(2+x^3)………..(2+x^100)=sum_(r=0)^n k_rx^r, then n= (A) 2550 (B) 5050 (C) 2^8 (D) none of these

If (2+x)(2+x^2)(2+x^3)………..(2+x^100)=sum_(r=0)^n k_rx^r, then n= (A) 2550 (B) 5050 (C) 2^8 (D) none of these

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

sum_(r=0)^(300)a_rx^r=(1+x+x^2+x^3)^(100) . If a=sum_(r=0)^(300)a_r , then sum_(r=0)^(300)ra_r is equal to

Let (1 + x + x^(2))^(100)=sum_(r=0)^(200)a_(r)x^(r) and a=sum_(r=0)^(200)a_(r) , then value of sum_(r=1)^(200)(ra_(r))/(25a) is

Let t_(100)=sum_(r=0)^(100)(1)/(("^(100)C_(r ))^(5)) and S_(100)=sum_(r=0)^(100)(r )/(("^(100)C_(r ))^(5)) , then the value of (100t_(100))/(S_(100)) is (a) 1 (b) 2 (c) 3 (d) 4

Let t_(100)=sum_(r=0)^(100)(1)/(("^(100)C_(r ))^(5)) and S_(100)=sum_(r=0)^(100)(r )/(("^(100)C_(r ))^(5)) , then the value of (100t_(100))/(S_(100)) is (a) 1 (b) 2 (c) 3 (d) 4