On a 12-hour digital clock, what is the smallest interval between two times that are palindromic (can be read forwards and backwards as the same number)?

I think it must be the palindrome times 9:59 and 10:01 for which there is the least time gap which is 2 minutes. All other palindrome times within 12 hr format are atleast 10-11 minutes apart.

Answer: 2 minutes (duration between 9:59 and 10:01)

On a regular 12-hour digital clock how many times would the same three digits in a row be displayed (e.g. 1:11,11:12,12:22) in one day?

Time 12:21 is a palindrome as it reads the same forwards or backwards. What is the shortest interval between two palindromic times? Example => 11:11 and 12:21 has interval of 1 hr 10 minutes.

I noticed that in my big wall clock, there is a time when the minute and hour clock are exactly between one and two. Also I notice both hands lie on top of each other.

What is the time I am talking about ?

A clock is so placed that at 12 noon its minute hand points towards North-East. In which direction does its hour hand point at 1.30 p.m.?