• The clock loses 1% time during the first week. In a day there are 24 hours and in a week there are 7 days. Therefore, there are 7 * 24 = 168 hours in a week. If the clock loses 1% time during the first week, then it will show a time which is 1% of 168 hours less than 12 Noon at the end of the first week = 1.68 hours less. Subsequently, the clock gains 2% during the next week. The second week has 168 hours and the clock gains 2% time = 2% of 168 hours = 3.36 hours more than the actual time.
• As it lost 1.68 hours during the first week and then gained 3.36 hours during the next week, the net result will be a -1.68 + 3.36 = 1.68 hour net gain in time. So the clock will show a time, which is 1.68 hours more than 12 Noon two weeks from the time it was set right. 1.68 minutes = 1 hour + 40 minutes + 48 seconds. i.e. 1 : 40 : 48 P.M.

Palindromes after 12 o’clock 12:21 = 1
From 1 to 9 , it is 1.01, 1.11, 1.21, 1.31, 1.41, 1.51 = 6, similarly 2.02, 2.12…= 6
So, total palindromes from 1 to 9 is (6 * 9) 54.
Palindromes after 10 o’clock are 10:01 and 11:11
Hence total number of palindromes from noon to midnight : 54 + 1 + 2 = 57

• At 5:30 minute hand will be at position 6 and hour hand will be exactly between 5 and 6 and will cover 15°, so angle between two hands=30 -15 = 15°.