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)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

The value of sum_(r=1)^(49)(2r^(2) - 48r +1)/((50-r).""^(50)C_(r)) is "_____" .

The domain of f(x)i s(0,1)dot Then the domain of (f(e^x)+f(1n|x|) is (a)(-1, e) (b). (1, e) (c).(-e ,-1) (d) (-e ,1)

Let P = sum_(r=1)^(50) (""^(50+r)C_(r)(2r-1))/(""^(50)C_(r)(50+r)), Q = sum_(r=0)^(50)(""^(50)C_(r))^(2), R = sum_(r=0)^(100)(-1)^(r) (""^(100)C_(r))^(2) The value of Q + R is equal to

Let P =sum_(r=1)^(50)(""^(50+r)C_(r)(2r-1))/(""^(50)C_(r)(50+r)), Q = sum_(r=0)^(50)(""^(50)C_(r))^(2), R = sum_(r=0)^(100)(-1)^(r) (""^(100)C_(r))^(2) The value of P - R is equal to

Let P = sum_(r=1)^(50) (""^(50+r)C_(r)(2r-1))/(""^(50)C_(r)(50+r)), Q = sum__(r=1)^(50) (""^(50)C_(r))^(2), R = sum_(r=0)^(100) (-1)^(r) (""^(100)C_(r))^(2) The value of P - Q is equal to

If m, n, r, in N then .^(m)C_(0).^(n)C_(r) + .^(m)C_(1).^(n)C_(r-1)+"…….."+.^(m)C_(r).^(n)C_(0) = coefficient of x^(r) in (1+x)^(m)(1+x)^(n) = coefficient of x^(f) in (1+x)^(m+n) The value of r for which S = .^(20)C_(r.).^(10)C_(0)+.^(20)C_(r-1).^(10)C_(1)+"........".^(20)C_(0).^(10)C_(r) is maximum can not be

f(1)=1 and f(n)=2sum_(r=1)^(n-1) f (r) . Then sum_(n=1)^mf(n) is equal to (A) 3^m-1 (B) 3^m (C) 3^(m-1) (D)none of these