If for `1lemlen,f(m,n)=C_(0)-C_(1)+C_(2)-....+(-1)^(m-1)*C_(m-1)`, then `f(7,8)` is

^(n)C_(m)+^(n-1)C_(m)+^(n-2)C_(m)+............+^(m)C_(m)

If quad (1+x)^(n)=C_(0)+C_(1)x+C2x2++C_(n)x^(n),n in N,thenC_(0)-C_(1)+C_(2)-+(-1)^(n-1)C_(m-) is equal to (m

f(n)=sum_(r=1)^(n)[r^(2)(*^(n)C_(r)-^(n)C_(r-1))+(2r+1)^(n)C_(r)] then f(30) is

If .^(m)C_(1)=.^(n)C_(2) prove that m=(1)/(2)n(n-1) .

If for some m,n,^(6)C_(m)+2(""^(6)C_(m+1))+^(6)C_(m+2)>^(8)C_(3) and ^(n-1)P_(3):^(n)P_(4)=1:8 ,then ""^(n)P_(m+1)+""^(n+1)C_(m) 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

If ^(m)C_(1)=^(n)C_(2) then 2m=nb2m=n(n+1) c.2m=(n-1)d2n=m(m-1)

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(0 le r le 30) for which S = .^(20)C_(r).^(10)C_(0) + .^(20)C_(r-1).^(10)C_(1) + ........ + .^(20)C_(0).^(10)C_(r) is minimum can not be