In a month of 31 days, third Thursday falls on 16th. What will be the last day of the month?

Angle traced by hour hand in 12 h = 360°
Angle traced by hour hand in 25/4 h = (360/12) x (25/4)° = 187.5°
Angle traced by minute hand in 60 min = 360°
Angle traced by it in 15 min = (360/60) x 15° = 90°
? Required angle = (187.5° - 90°) = 97.5°

Clock will make right angle at (5n + 15) x 12/11 min past n.
Given that, n = 3
? Clock will make right angle at ( 5 x 3 + 15 ) x 12/11 min past 3 . =30 x 12 / 11 min past 3.
= 32⁸/₁₁ min
So required time = 3 H 32⁸/₁₁ min

This being a leap year none of the next 3 year is a leap year. So, the day of the week will be 3 days beyond Monday i.e., it will be Thursday.

1600 years of 0 odd days and 30 years have 1 odd day. 49 years contain 12 leap years and 37 ordinary years and therefore (24 + 37) odd days i.e., 5 odd days i.e., 1949 years contain (0 + 1 + 5) = 6 odd days. 26 day of January contain 5 days.Total odd days = (6 + 5) = 11 or 4 days. So, the days was Thursday

1992 being a leap year, it has 2 odd days. So, the first day of the year 1993 will be two days beyond Wednesday i.e., it will be Friday.

Angle of 360° is covered by hour hand in 12 h .
So, angle of 135° is covered by hour hand in 12/360° x 135° = 4.5 h
Thus, required time = (3 + 4.5)h = 7.5 h = 7 : 30

There are 11 intervals when the clock strikes 12.
Time taken for 11 intervals = 48 s
? Time taken for 1 interval = (48/11)s
In order to strike 3, there are 2 intervals, for which the time taken = (48/11) x 2) = 8⁸/₁₁ s

Since, in a clock hour hand completes an angle of 360° in 12 h and there is a gap of 6 h between 8 am and 2 pm, so in 6 h, hour hand completes an angles of 180°.

Three days earlier than Friday means Tuesday.
So, 7th day of month will be Tuesday.
14th day of month will be Tuesday.
19th day of month will be Sunday.

1st day of month is Monday.
6th day of month is Saturday.
13th day of month is second Saturday.
17th day is the fourth day after second Saturday.