Model Paper 2 — Applied Maths STD 11 Science — Question
CBSE BoardEnglish MediumSTD 11 ScienceApplied MathsModel Paper 22 Marks
Question
At what time between 5:00 and 6:00 will the hands of clock be at right angles?
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Answer
At 5 O'clock, the hour hand is at 5 and the minute hand is at 12 . It means the angle between the two hands of the clock is $150^{\circ}$. The hands of the clock will be at right angles twice between 5:00 and 6:00 For the first time: The minute hand had to cover a relative distance of $60^{\circ}$. So the time required $=\frac{60}{5.5}$ minutes $=\frac{60 \times 2}{11}$ minutes $=10 \frac{10}{11}$ minutes $=10 \mathrm{~min} 55 \mathrm{sec}$ Hence, the hands of the clock are at right angles at 5:10:55 For the second time: The minute hand had to cover a relative distance of $240^{\circ}$. So the time required $=\frac{240}{5.5}$ minutes $=\frac{240 \times 2}{11}$ minutes $=43 \frac{7}{11}$ minutes $=43 \mathrm{~min} 38 \mathrm{sec}$ Hence, the hands of the clock are at right angles at 5:43:38.
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