Angle traced by hour hand in$ \dfrac{13}{3} $hrs =$\left(\dfrac{360}{12}\times\dfrac{13}{3}\right)^\circ$= 130$^\circ$
Angle traced by min. hand in 20 min. =$ \left(\dfrac{360}{60} \times 20\right)^\circ $= 120$^\circ$.
$\therefore$ Required angle = (130 - 120)$^\circ$ = 10$^\circ$.
Angle traced by hour hand in$ \dfrac{21}{4} $hrs =$\dfrac{360}{12}\times\dfrac{21}{4} ^\circ $=157$ \dfrac{1}{2} ^\circ $
Angle traced by min. hand in 15 min. =$ \left(\dfrac{360}{60} \times 15\right)^\circ $= 90$^\circ$.
$\therefore$ Required angle =$ \left(157\dfrac{1}{2} \right)^\circ $- 90$^\circ$ = 67$ \dfrac{1}{2} ^\circ $
In 12 hours, they are at right angles 22 times.
$\therefore$ In 24 hours, they are at right angles 44 times.
The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours.
(Because between 5 and 7 they point in opposite directions at 6 oclcok only).
So, in a day, the hands point in the opposite directions 22 times.
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 oclock)
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.
$\therefore$ The hands coincide 22 times in a day.
In 12 hours, the hands coincide or are in opposite direction 22 times.
$\therefore$ In 24 hours, the hands coincide or are in opposite direction 44 times a day.
In 12 hours, hands of a clock are at right angles 22 times.
In 24 hours, hands of a clock are at right angles 44 times.
The hands of a clock coincide 11 times in every 12 hours (Between 11 and 1, they coincide only once, at 12 oclock).
12:00 am
1:05 am
2:11 am
3:16 am
4:22 am
5:27 am
6:33 am
7:38 am
8:44 am
9:49 am
10:55 am
12:00 pm
1:05 pm
2:11 pm
3:16 pm
4:22 pm
5:27 pm
6:33 pm
7:38 pm
8:44 pm
9:49 pm
10:55 pm
Hence the hands coincide 22 times in a day.
The hands of a clock point in opposite directions (in the same straight line, making an angle 180° between them) 11 times in every 12 hours because between 5 and 7 they point in opposite directions at 6 o clock only. Hence the hands point in the opposite directions 22 times in a day.
The hands of a clock coincide(0° between them) 11 times in every 12 hours (between 11 and 1, they coincide only once, at 12 oclock). Hence the hands coincide 22 times in a day.
So In 24 hours, the hands come in opposite direction or coincide 44 times.
This is already given as a formula and its is better to learn the answer by heart as 44
which can save time in competitive exams.(However you should know the theory behind).
The hands of a clock point in opposite directions (in the same straight line, making an angle 180° between them) 11 times in every 12 hours because between 5 and 7 they point in opposite directions at 6 o clock only.
Hence the hands point in the opposite directions 22 times in a day.
This is already given as a formula and its is better to learn the answer by heart as 22 which can save time in competitive exams.(However you should know the theory behind).