Observe that, at any instant, the minute and hour hands of a clock make two angles between them whose sum is $360^{\circ}$. At $6: 15$ the difference between these two angles is $....^{\circ}$
$165$
$170$
$175$
$180$
If $\sin \theta + \cos \theta = 1$, then $\sin \theta \cos \theta = $
Which of the following relations is correct
Find, $\sin \frac{x}{2}, \cos \frac{x}{2}$ and $\tan \frac{x}{2}$ for $\cos x=-\frac{1}{3}, x$ in quadrant $III.$
In a right angled triangle the hypotenuse is $2 \sqrt 2$ times the perpendicular drawn from the opposite vertex. Then the other acute angles of the triangle are
Find the radius of the circle in which a central angle of $60^{\circ}$ intercepts an arc of length $37.4 \,cm$ ( use $\pi=\frac{22}{7}$ ).