How many times do the hands of a clock point towards each other in a day?

$A$ 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

$A$ watch which gains uniformly is $2$ minutes slow at noon on Monday and is $4$ minutes $48$ seconds fast at $2$ p.m. on the following Monday. When was it correct?

The time taken by a clock between two single strikes is $2 \text{ seconds}$. What is the time taken to complete its strikes at $10$ o'clock? (in $\text{seconds}$)

An accurate clock shows $8$ o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows $2$ o'clock in the afternoon (in $^{\circ}$)?

If the day after tomorrow is Sunday,what day was tomorrow's day before yesterday?