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

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 are the hands of a clock together between $6$ and $7$?

$A$ wall clock gains $2$ minutes in $12$ hours,while a table clock loses $2$ minutes every $36$ hours. Both are set right at $12$ noon on Tuesday. The correct time when both show the same time next would be

At what time between $4: 30$ and $5$ will the hands of a clock be in a straight line?

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?