Find the angle between the two hands of a clock at $30$ $minutes$ past $4$ $O$'clock. (in $^{\circ}$)

Two clocks are set right at $10 \text{ am}$. One gains $20 \text{ seconds}$ and the other loses $40 \text{ seconds}$ in $24 \text{ hours}$. What will be the true time when the first clock indicates $4 \text{ pm}$ on the following day?

At what time between $3$ and $4$ o'clock are the hands of a clock together?

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

In the year $1996$,the Republic day was celebrated on Friday. On which day was the Independence day celebrated in the year $2000$?

On what date of $August, 1988$ did Friday fall?