Number Of Solutions Of Pair x, y of The Equation Sin x sin y = Min{–1, α2 – 4α + 5}, α ∈ R (where 0 < x < π, – π < Y < 0) Is

If times the sum of first n natural numbers is equal to sum of the squares of first n natural numbers. 

If k­₁ = sin x cos³ x and k₂ = cos x sin³ x then

 then ordered pair (x, y) is equal to

Number of solution of the equation tan x + sec x = 2 cos x. lying in the interval [0, 2π] is 

The arithmetic mean of the roots of the equation 4 cos³ x – 4 cos² x – cos (π + x) – 1 = 0 in the interval (0, 315) is equal to

 then cos 2x is equal to

The value of x between 0 and 2π which satisfy the equation  are in A.P. The common different 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 smallest positive number p for which the equation cos(p sinx) = sin(pcos x) has a solution x ∈ [0, 2π]

  then sin x lies in