Relation between Radian and Degree

Q. At what time between $6\text{a.m.}$ and $7\text{a.m.}$ will the minute hand and hour hand of a clock make an angle ${59}^{\circ }$ ?

1. $6:21\text{a.m.}$
2. $6:22\text{a.m.}$
3. $6:23\text{a.m.}$
4. $6:24\text{a.m.}$

Q. The angle between the minute hand and the hour hand of a clock when the time is $7:20\text{a.m.}$ is

1. ${120}^{\circ }$
2. ${75}^{\circ }$
3. ${90}^{\circ }$
4. ${100}^{\circ }$

Q. Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is:

1. $25$
2. $12.5$
3. $30$
4. $10$

Q. A cow is tied to a post by a rope. If the cow moves along a circular path, always keeping the rope tight, and describes $88\text{m}$ when it traced out ${72}^{\circ }$ at the centre, then the length of the rope is
$(\pi =\frac{22}{7})$

1. $74\text{m}$
2. $35\text{m}$
3. $70\text{m}$
4. $72\text{m}$

Q. The radian measure of $-{37}^{\circ }{30}^{\prime }$ is

1. $-\frac{5\pi }{24}$
2. $-\frac{\pi }{8}$
3. $-\frac{3\pi }{8}$
4. $-\frac{7\pi }{24}$