How often between $11$ $O$'clock and $12$ $O$'clock are the hands of a clock in integral number of $minutes$ apart (in $\times$)?

At what time between $7$ o'clock and $8$ o'clock will the hands of a clock be in the same straight line but,not together?

The time shown by a clock was $2$ o'clock. After a certain time, the mirror image shown by the clock was $15$ minutes past $7$. What is the time lag between the two times?

$A$ 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?

At what time between $5$ and $6$ o'clock are the hands of a clock $3$ minutes apart?

$A$ thief runs at a speed of $5 \, m/s$. $A$ policeman runs behind him $2 \, seconds$ after the thief started at a speed of $10 \, m/s$. After how much time will the policeman catch the thief? (in $seconds$)