Number Of Solutions Of Pair x, y of The Equation Sin x sin y = Min { –1, α2 – 4α + 5}, α Ïµ R 

The value of the determinant   

is zero if

 then roots of f (x) = 0 are

The arithmetic mean of the roots of the equation 

In the interval (0, 315) is equal to

The values of x between 0 and 2π which satisfy the equation  are in A.P. The common difference of the A.P. is

The equation (cos p – 1)x² + (cos p)x + sin p = 0 where x is a variable, has real roots if p lies in the interval

The solution of 

The smallest positive number p for which the equation

          has a solution 

The number of solutions of the equation tan²x – sec¹⁰x + 1 = 0 in (0, 10) is