The number of solutions of $2{\cos }^2\left(\frac{x}{2}\right){\sin }^{2}x=x^2+\frac{1}{x^2},0\le x\le \frac{\pi }{2}$ is:

Let $P=(\theta :\sin \theta -\cos \theta =\sqrt{2}\cos \theta \}$ and $Q=\{\theta :\sin \theta +\cos \theta =\sqrt{2}\sin \theta \}$ be two sets. Then,

The angles of a quadrilateral are in A.P. and the greatest angle is ${120}^o$ , the angles in radians are

The circular wire of radius $7\mathrm{cm}$ is cut and bend again into an arc of a circle of radius $12\mathrm{cm}.$ The angle subtended by the arc at the centre of the circle is

The minute hand of a clock is $10 cm$ long. How far does the tip of the hand move in $20$ minutes?