Between $1$ hour and $12$ hours,how many times will the hour hand and minute hand be together? (in times)

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

$A$ 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?

My watch gains $5$ seconds in $3$ minutes. It was set right at $7$ am. In the afternoon of the same day,when the watch indicates quarter past $4$ o'clock,what is the true time?

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 $\text{seconds}$)

How much does a watch gain or lose per day,if its hands coincide every $64$ minutes?