If the equation $\sin 3\theta - \cos^2\theta = \dfrac{1}{4}$ and $\theta \in [0, \pi]$, then the number of solutions is...

If $A(2, -3)$ and $C(-6, 7)$ are opposite vertices of a rhombus ABCD, then the equation of diagonal BD is

The measure of the acute angle between the pair of lines $2x^2 + xy - y^2 - x + 2y - 1 = 0$ is:

The joint equation of a pair of lines passing through point $(1,4)$, one of which is parallel to X-axis and the other makes an angle of $45^\circ$ with the positive direction of X-axis, is