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

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

Find the sum sum_(k=0)^(10).^(20)C_k .

1cm is equal to: (a) 0.1m (b) 0.01m (c) 0.10m (d) 0.001m

The sum sum_(r=0)^(m) ""^(10)C_(r) xx""^(20)C_(m -r) is maximum . When m=

If ""^(m)C_(r)=0" for "rgtm then the sum sum_(r=0)^(m)""^(18)C_(r)""^(20)C_(m-r) is maximum when m =

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)

Let P=[(1, 0, 0),(3, 1, 0),(9, 3, 1)]Q=[q_(ij)] and Q=P^5+I_3 then (q_21+q_31)/q_32 is equal to (A) 12 (B) 8 (C) 10 (D) 20

("lim")_(x->oo)sum_(x=1)^(20)cos^(2n)(x-10) is equal to (a) 0 (b) 1 (c) 19 (d) 20

sum_(p=1)^(n) sum_(m=p)^(n) (("n"),("m"))(("m"),("p")) is equal to