If the acute angle between the tangents drwn from (0,1) to the grafh of f(x) =x^3-3x^2+3x is tan^-1 (m\n) where m,n are relatively prime 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

If the equation 3x^2 + 4ax + b = 0 has at least one root in (0,1) such that La + Mb + N = 0 , where L, M, N are co-prime numbers, then the value of L + M + N + LMN is

If f(x)=2x^3+mx^2-13x+n and 2 and 3 are 2 roots of the equations f(x)=0, then values of m and n are

If f(x)=2x^3+mx^2-13x+n and 2 and 3 are 2 roots of the equations f(x)=0, then values of m and n are

If x,yinR^+ and log_10(2x)+log_10y=2 , log_10x^2-log_10(2y)=4 and x+y=m/n ,Where m and n are relative prime , the value of m-3n^(6) is

Given that sum_(k=1)^35 sin5k^@ = tan(m/n)^@ , where m and n are relatively prime positive integers that satisfy (m/n)^@<90^@ , then m + n is equal to

If the area enclosed by the curve y^(2)=4x and 16y^(2)=5(x-1)^(3) can be expressed in the form (L sqrt(M))/(N) where L and N are relatively prime and M is a prime, find the value of (L+M+N) .

Let 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=

If in the expansion of (1 +x)^(m) (1 - x)^(n) , the coefficients of x and x^(2) are 3 and - 6 respectively, the value of m and n are

When the polynomial 5x^3+M x+N is divided by x^2+x+1, the remainder is 0. Then find the value of M+Ndot