How many times in a day are the hands of a clock at a right angle?

If the hands of a clock coincide every $65$ minutes (true time),how many minutes will the clock gain in $24$ hours?

How many times in a day,are the hands of a clock in a straight line but opposite in direction?

India got independence on August $15, 1947$. What was the day of the week?

$A$ watch which gains uniformly is $2$ minutes slow at noon on Monday and is $4$ minutes $48$ seconds fast at $2$ p.m. on the following Monday. When was it correct?

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