Number of times $29^{th}$ day of the month occurs in $400$ consecutive years is

$A$ man who went out between $3$ and $4$ and returned between $8$ and $9$ found that the hands of the watch had exactly changed places. He returned at

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

If a clock started at noon,then the angle turned by the hour hand at $3:45\, PM$ is (in $^{\circ}$)

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?