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

A determinant of the second order is made with the elements 0 and 1. If (m)/(n) be the probability that the determinant made is non negative, where m and n are relative primes, then the value of n-m is

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

Given lim_(n->oo)((.^(3n)C_n)/(.^(2n)C_n))^(1/n) =a/b where a and b are relatively prime, find the value of (a + b) .

Using the identity sin^(4) x=3/8-1/2 cos 2x+1/8 cos 4x or otherwise, if the value of sin^(4)(pi/7)+sin^(4)((3pi)/(7))+sin^(4)((5pi)/(7))=a/b , where a and b are coprime, find the value of (a-b) .

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 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) .

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

Let lim _( x to oo) n ^((1)/(2 )(1+(1 )/(n))). (1 ^(1) . 2 ^(2) . 3 ^(3)....n ^(n ))^((1)/(n ^(2)))=e^((-p)/(q)) where p and q are relative prime positive integers. Find the value of |p+q|.

If the value of the definite integral int_0^1(sin^(-1)sqrt(x))/(x^2-x+1)dx is (pi^2)/(sqrt(n)) (where n in N), then the value of n/(27) is