At what time between 2 and 3 the hands of a clock will consider each other and point in the opposite direction respectively?

Answer: Option D

Explanation:

At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand.

To be coincident, it must gain 15 min. spaces.

55 min. are gained in 60 min.

15 min. are gained in		60	x 15	min	=	16	4	min.
55	11

The hands are coincident at 16	4	min. past 3.
11

Answer: Option C

Explanation:

The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock).

AM

12:00 1:05 2:11 3:16 4:22 5:27 6:33 7:38 8:44 9:49 10:55

PM

12:00 1:05 2:11 3:16 4:22 5:27 6:33 7:38 8:44 9:49 10:55

The hands overlap about every 65 minutes, not every 60 minutes.

Answer: Option D

Explanation:

When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.

At 7 o'clock, they are 25 min. spaces apart.

55 min. spaces are gained in 60 min.

5 min. spaces are gained in		60	x 5	min	= 5	5	min.
55	11

Required time = 5	5	min. past 7.
11

Answer: Option B

Explanation:

At 5 o'clock, the hands are 25 min. spaces apart.

To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces.

55 min. spaces are gained in 60 min.

40 min. spaces are gained in		60	x 40	min	=	43	7	min.
55	11

Required time = 43	7	min. past 5.
11

Answer: Option B

Explanation:

Angle traced by hour hand in	17	hrs =		360	x	17		°	= 255°.
2	12	2

Angle traced by min. hand in 30 min. =		360	x 30		°	= 180°.
60