1. 

At 15 min. past 5, the minute hand is at 3 and hour and slightly ahead of 5.
Now, angle through which hour hand shifts in 15 min. = 15(1/2)^{o} = 7(1/2)^{o}
So, Angle at 15 min. past 5 = 60 + 7(1/2)^{o} = 67(1/2)^{o}.
2. 

From 8 am of a particular day to 1 pm of the following day = 29 h.
Now, the clock gains 10 min in 24 h, it means that 24 h 10 min of this clock is equal to 24 h of the correct clock.
145/6 hour of this clock = 24 h of the correct clock.
29 h of this clock = (24/145) x 6 x 29 = 28 h. 48 min. of correct clock.
29 h of this clock = 28 h. 48 min. of the correct clock.
It means that the clock in question is 12 min. faster than the correct clock. Therefore, when clock indicates 1pm the correct time will be 48 min. past 12.
3. 

26 January 1950 means 1949 year and 26 days.
1600 year have 0 odd day,
300 year have 1 odd day,
49 year have (12 leap year and 37 ordinary years)
So, [(12 x 366) + (37 x 365)] days
[4392 + 13505] days = 17897 day
17897 days = 2556 weeks + 5 days
So, 49 years have 5 odd days.
Total number of odd days = 0 + 1 + 5 + 5 = 11 days.
Hence, the days on 26th Jan, 1950 was Thursday.
4. 

Today – Friday. So, the yesterday day before – Wednesday.
5. 

Angle = (360 x 2.5)/12 = 75^{o}
6. 

Anuj reached the place of meeting at 8:15 h, he reached 30 min earlier than the man who was 40 min late. He reached 10 min. Hence, the scheduled time of the meeting was 8:05 h.
7. 

Number of buzzes in a day = [12(12+1)/2]x2 = 156
8. 

In, 12 h, they are at right angles, 22 times.
So, in 24 h, they are at right angles, 44 times.
9. 

Form the properties of the clock, we know that hands of a clock coincide once in every hour but between 11 o’clock and 1 o’clock. They coincide only once. Therefore, the hands of a clock coincide 11 times in every 12 h.
Hence, they will coincide (11 x 2) = 22 times in 24 h
10. 

The hands of a clock point each other 11 times in every 12 h (Because between 5 and 7, they point towards each other only once at 6 o’clock).
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