The sum `underset(i=0)overset(3m)(sum)((20),(3m-i))`, where `((p),(q))=0` if `p lt q` is maximum then m is_______.

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

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

Let x_(i) (1 le I le 10) be ten observation of a random variable X. If underset(i=l)overset(10)sum(x_(i) - p) = 3 and underset(i=l)overset(10)sum(x_(i) - p)^(2) = 9 where 0 ne p in R ,then the standard deviation of these observations is :

If underset(i=1)overset(n)sum cos^(-1) alpha_(i)=0," then "underset(i=1)overset(n)sum alpha_(i)=

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

If ((p)/(q))=0 for p