What is the maximum value of sin 2x ⋅ cos 2x?

Consider the following statements in respect of the points (p, p - 3), (q + 3, q) and (6, 3):

1. The points lie on a straight line.

2. The points always lie in the first quadrant only for any value of p and q.

Which of the above statements is/are correct?

What is the acute angle between the lines x - 2 = 0 and √3x - y - 2 = 0?

The point of intersection of diagonals of a square ABCD is at the origin and one of its vertices is at A(4, 2). What is the equation of the diagonal BD?