The number of solutions in $\left[0, \dfrac{\pi}{2}\right)$ of the equation $\cos 3x \cdot \tan 5x = \sin 7x$ is

The area of the triangle formed by the co-ordinate axes and a line $px + qy = r$ (where p, q and r are positive real numbers) is $\dfrac{1}{54}$ sq.units, then ....

The joint equation of the pair of lines through the origin and making an angle of $\dfrac{\pi}{4}$ with the line $3x + y - 6 = 0$ is

If a circle with center $(-1, 1)$ touches the line $x + 2y + 4 = 0$, then the co-ordinates of the point of contact are