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

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

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

$A$ 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?

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

March $5, 1999$ was a Friday. What day of the week was March $5, 2000$?