The calendar for the year $2000$ will be the same for which of the following years?

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?

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

The time taken by a clock between two single strikes is $2 \text{ seconds}$. What is the time taken to complete its strikes at $10$ o'clock? (in $\text{seconds}$)

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

$A$ watch which gains uniformly is $6$ minutes slow at $4$ $p.m.$ on a Sunday and $10 \frac{2}{3}$ minutes fast on the following Sunday at $8$ $p.m.$ During this period,when was the watch correct?