The angle between the $minute$ hand and the $hour$ hand of a clock when the time is $10.30$ is (in $^{\circ}$)

The angle between the hour hand and the minute hand of a clock when the time is $4:55$ is (in $^{\circ}$)

Two clocks are set right at $10 \text{ am}$. One gains $20 \text{ seconds}$ and the other loses $40 \text{ seconds}$ in $24 \text{ hours}$. What will be the true time when the first clock indicates $4 \text{ pm}$ on the following day?

$A$ clock is set right at $5\, am.$ The clock loses $16\, minutes$ in $24\, hours.$ What will be the true time when the clock indicates $10\, pm$ on the $4^{th}$ day?

$A$ clock takes $9$ seconds to strike $4$ times. In order to strike $12$ times at the same rate,the time taken is (in $seconds$)

$A$ man who went out between $3$ and $4$ and returned between $8$ and $9$ found that the hands of the watch had exactly changed places. He returned at