If the acute angle between the tangents drawn from `(0,1)` to the graph of `f(x)=x^(3)-3x^(2)+3x` is `tan^(-1)((m)/(n))` where `m, n` are relatively prime natural numbers. Then the value of `m+n` is

Greatest value of (sin^-1 x)^3+(cos^-1 x)^3 is m/n pi^3 , where m and n are relatively prime, then the value of mn is

One of the roots of the equation 2000x^6 +100x^5 +10x^3+x-2=0 is the form (sqrt(m)-n))/( r) , where m is non zero integer and n and r are relatively prime natural numbers. Find the value of m+n+r .

One of the roots of the equation 2000x^(6)+100x^(5)+10x^(3)+x-2=0 is of the form (m+sqrt(n))/(r), when m29. is non zero integer and and r are relatively prime natural numbers.Find the value of m+n+r

One of the roots of the equation 2000x^6 + 100x^5 + 10x^3 + x-2 =0 is of the form (m+sqrt(n))/ (r ) , where m is non zero integer and n and r are relatively prime natural numbers. Find the value of m + n + r .

Let lim_(x rarr oo)x ln(e(1+(1)/(x))^(1-x)) equal (m)/(n) where m and n are relatively prime positive integ Find (m+n).

lim_(x rarr2)[(x-2)/(x^(2)-4)-(1)/(x^(3)-3x^(2)+x)]=(1)/(m) where l and m are mutually prime then the value of (l+m)

S={(x,y)|x,y in R,x^(2)+y^(2)-10x+16=0} The largest value of (y)/(x) can be put in the form of (m)/(n) where m,n are relatively prime natural numbers,then m^(2)+n^(2)=