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

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

overset(10)underset(i=3)sum5

The sum sum_(k=1)^(10)underset(i ne j ne k)underset(j=1)(sum^(10))sum_(i=1)^(10)1 is equal to

The sum sum_(r=0)^(m) ""^(10)C_(r) xx""^(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)

If x = underset(n-0)overset(oo)sum a^(n), y= underset(n =0)overset(oo)sum b^(n), z = underset(n =0)overset(oo)sum C^(n) where a,b,c are in A.P. and |a| lt 1, |b| lt 1, |c| lt 1 , then x,y,z are in

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 =

Let x_(1) lt x_(2) lt x_(3) lt x_(4) lt x_(5) and y_(1) lt y_(2) lt y_(3) lt y_(4) lt y_(5) are in AP such that underset(I = 1)overset(5)(sum) x_(i) = underset(I = 1)overset(5)(sum) y_(i) = 25 and underset(I =1)overset(5)(II) x_(i) = underset(I = 1)overset(5)(II) y_(i) = 0 then |y_(5) - x_(5)| A. 5//2 B. 5 C. 10 D. 15

The sum sum_(0 leq i)sum_(leq j leq 10) (10C_j)(jC_i) is equal to