Mathematics Tes...

The sum of all the solutions of the equation cos x. cos ((π/3) + x). cos ((π/3) – x) = 1/4, x ∈ [0, 6π] is

The area bounded by the curves y = –(x + 1)² ; y = |x + 1| and |y| = 1 – x is

The value of integral 

 where {x} denotes the fractional part of x, is equal to

The solution of the equation 

The angle between the two tangents from the origin to the circle (x – 7)² + (y + 1)² = 25 equals

A company has two plants to manufacture televisions. Plant I manufacture 70% of televisions and plant II manufacture 30%. At plant I, 80% of the televisions are rated as of standard quality and at plant II, 90% of the televisions are rated as of standard quality. A television is chosen at random and is found to be of standard quality. The probability that it has come from plant II is 

The coordinates of the middle point of the chord 2x – 5y + 18 = 0 cut off by the circle x² + y² – 6x + 2y – 54 = 0 are