A Clock is started at Noon, by 10 minutes past 7, the hour hand has turn through:
Answer: A
In a clock, 12 hours form 360° degree. So one hour forms 30°. Therefore 7 hours form 210° (30° X 7) degree. In a minute, hour hand moves 0.5° degree, so in 10 minutes it moves 0.5° X 10 = 5°
Thus, by 10 Minutes past 7, hour hand has turn through 210° + 5° = 215°
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At what time between 7.02 and 8.02 will the hands of a watch be in the straight line but no together?
Answer: B
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.
Minute hand must gain only 5 min. space
55 min. spaces are gained in 60 min.
5 min. spaces are gained in (60/55 × 5) min = 5 (5/11) min.
Required time = 5 (5/11) min. past 7.
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What is the reflex angle between the hands of a clock at 4:30 ?
Answer: B
Correct answer: 315°
First find the ordinary angle between the hands.
\[\text{Hour hand} = 4 \times 30 + 30 \times 0.5 = 120 + 15 = 135°\]
\[\text{Minute hand} = 30 \times 6 = 180°\]
The hands are \(180 - 135 = 45°\) apart, so the reflex angle is
\[360 - 45 = 315°\]
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At what time between 1 and 2 o’clock will the hands of a clock point in opposite directions ?
Answer: A
Correct answer: 38 (2/11) min past 1
At 1 o’clock the hour hand is \(30°\) ahead. To be opposite, the minute hand must pass it and then lead by \(180°\), a total relative gain of \(30 + 180 = 210°\).
\[t = \frac{210}{5.5} = \frac{420}{11} = 38\tfrac{2}{11}\ \text{minutes}\]
So the hands are opposite at \(38\tfrac{2}{11}\) minutes past 1.
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At what time, in moment, between 3 o'clock and 4 o'clock, both are unnecessary will match one another?
Answer: D
At 3 o'clock ,the moment hand is 15 min. spaces a section
Structure the hour hand. To be coincident,
it must pick up 15 min. spaces.
55 min. are picked up in 60 min.
15 min. are picked up in (60/55*15)min.=180/11 min.
∴ The hands are correspondent at 180/11 min. past 3.
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How many times are the hands of a clock at right angles in 24 hours?
Answer: B
In each twelve-hour period the hands are at right angles 22 times - twice in most hours, but the crossings near 3 and 9 o'clock overlap so that two are lost.
\[ 22 \times 2 = 44 \text{ times in 24 hours} \]
The count is not 48, because between 2–3 and 3–4 (and again around 9) one right angle is shared rather than occurring twice.
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The minute hand of a clock is 7 cm long. How far does its tip travel in 30 minutes ? (Take \(\pi = 22/7\))
Answer: B
Correct answer: 22 cm
In 30 minutes the minute hand sweeps half a revolution, so its tip traces a semicircle of radius 7 cm.
\[\text{Distance} = \pi r = \frac{22}{7} \times 7 = 22 \text{ cm}\]
A full hour would carry the tip the whole circumference, \(2\pi r = 44\) cm.
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A watch which pick up consistently is 2 minutes moderate at twelve on Monday What's more, is 4 min.48 sec quick at 2 p.m. on the next Monday. At the point when Is it true that it was right?
Answer: B
Time structure 12 p.m. on Monday to 2 p.m. on the accompanying
Monday =7 days 2 hours =170 hours.
∴ The watch gains(2+24/5)min.
on the other hand 34/5 min. in 170 hrs.
Now,34/5 min. are picked up in 170 hrs.
∴ 2 min. are picked up in (170(5/34*2) hrs=50 hrs.
Along these lines, the watch is right 2 days 2 hour after 12 p.m. on
Monday i.e.it will be right at 2 p.m. on Wednesday.
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At 3:40, the hour hand and the minute hand of a clock form an angle of:
Answer: C
The hour hand moves \( 0.5^{\circ} \) a minute and the minute hand \( 6^{\circ} \), so at \( H \) hours \( M \) minutes the angle between them is
\[ \theta = \left| 30H - 5.5M \right| \]
\[ \theta = \left| 30(3) - 5.5(40) \right| = \left| 90 - 220 \right| = 130^{\circ} \]
Taking \( 30H \) as the hour hand's position from 12 automatically includes its drift during the 40 minutes, which is the step most often forgotten.
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How many times do the hands of the clock coincide in a day?
Answer: A
In twelve hours the hands coincide eleven times, not twelve: between 11 and 12 they meet only at 12 o'clock itself, so that hour contributes no separate coincidence.
\[ 11 \times 2 = 22 \text{ times in 24 hours} \]
Equivalently, the minute hand laps the hour hand once every \( \tfrac{720}{11} = 65\tfrac{5}{11} \) minutes, and \( \tfrac{1440}{720/11} = 22 \).
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