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?

$A$ 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?

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

January $7, 1992$ was a Tuesday. Find the day of the week on the same date after $5$ years,i.e.,on January $7, 1997$?

The watch which gains uniformly is $2$ minutes slow at noon on Sunday and is $4$ minutes $48$ seconds fast at $2$ $pm$ on the following Sunday. When was the watch correct?