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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At what time between 10 and 11 o’clock will the hands of a clock coincide ?
Answer: D
Correct answer: 54 (6/11) min past 10
At 10 o’clock the hour hand leads the minute hand by \(300°\), and the minute hand gains \(5.5°\) per minute.
\[t = \frac{300}{5.5} = \frac{600}{11} = 54\tfrac{6}{11}\ \text{minutes}\]
So they coincide at \(54\tfrac{6}{11}\) minutes past 10, the last coincidence before the hands meet again at 12.
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The angle between the minute hand and the hour hand of a clock when the time is 4.20 is:
Answer: B
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
\[ \theta = \left| 30H - 5.5M \right| \]
\[ \theta = \left| 30(4) - 5.5(20) \right| = \left| 120 - 110 \right| = 10^{\circ} \]
The minute hand is at the 4, and the hour hand has drifted a third of the way past it - \( 20 \times 0.5 = 10^{\circ} \) - which is exactly the gap.
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At what time between 7 and 8 will the hands of a clock be in the same straight line but, not together?
Answer: A
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 would be gained in (60/55) x 5 = 5 (5/11) min
Required time = 5 (5/11) min past 7
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If the minute hand of a clock has moved 300º, how many degrees has the hour hand moved?
Answer: A
The speed of hour hand is 0.5 dpm (Degree per Minute)
And the speed of minute hand is 6 dpm.
So, 300 degree traverse by minute hand in 300/6 = 50 Minutes.
Thus, angle moved by the hour hand in 50 minutes is 50/0.5 = 25° degrees.
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What is the angle between the hour and minute hand at 3:40?
Answer: B
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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Ramesh sets his grandfather’s clock to the right time at 2.00 am on Thursday. But he didn’t know that the clock gains 20s for every 3 hours. What will the clock indicate on Friday night 6.30 pm?
Answer: D
The clock gains 20 seconds in every 3 hours, so first count the hours.
From Thursday 2:00 am to Friday 6:30 pm is
\[ 22 + 18.5 = 40.5 \text{ hours} \]
\[ \text{gain} = 20 \times \frac{40.5}{3} = 20 \times 13.5 = 270 \text{ s} = 4 \text{ min } 30 \text{ s} \]
The clock therefore reads ahead of the true 6:30 pm:
\[ 6{:}30{:}00 + 4{:}30 = 6{:}34{:}30 \text{ pm} \]
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