If `f(m) = sum_(i=0)^m ((30),(30-i)) ((20),(m-i))` where `((p),(q)) = pCq,` then (A) maximum value of f(m) is 50C 25 (B) `f(0)+f(1) +...+f(50) =2^50` (C) f(m) is always divisible by 50 (`1<=m<=49`) (D)`sum_(m=0)^(50) (f(m))^2=100C50`

If f(m) = sum_(i=0)^m ({:(30),(30-i):})({:(20),(m-i):}) where ({:(p),(q):})= ""^(p)C_(q) , then

If f(m) = sum_(i=0)^m ({:(30),(30-i):})({:(20),(m-i):}) where ({:(p),(q):})= ""^(p)C_(q) , then

If f(m)=sum_(i=0)^m(30(^) 30-i)(20(^)m-i)w h e r e(p q)=^p C_q ,t h e n (a) maximum value of f(m)i s^(50)C_(25) (b) f(0)+f(1)+...f(50)=2^(50) (c) f(m) is always divisible by 50(1lt=mlt=49) (d)The value of sum_(m=0)^(50)(f(m))^2=^(100)C_(50)

If f(m) = sum_(i=0)_(m) ({:(30),(30-i):})({:(20),(m-i):}) where ({:(p),(q):})= ""^(p)C_(q) , then

The sum sum_(i=0)^(m)((10),(i))((20),(m-i)) (where ((p)/(q))=0 , if pltq ) is maximum, when m is:

The sum sum_(i=0)^m ((10),(i))((20),(m-1)) , where ((p),(q))=0 if p lt q , is maximum when m is equal to (A) 5 (B) 10 (C) 15 (D) 20

The sum sum_(i=0)^m ((10)c,(i))((20),(m-1)) , where ((p),(q))=0 if p lt q , is maximum when m is equal to (A) 5 (B) 10 (C) 15 (D) 20

The sum sum_(m)^(i=0) ({:(10),(i):})({:(20),(m-i):}) , (where ({:(p),(q):})= 0 , if p lt q ) is maximum when 'm' is