GATE CE 2024 Set 1 — Question 5
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General Aptitude → Analytical Aptitude → Numerical Relations & Reasoning
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Question
On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time 12:05:00 hours to 12:55:00 hours?
Correct answer
(C) 50
Solution
The angular speed of the second-hand is .
The angular speed of the minute-hand is .
The relative angular speed is .
The time interval between successive crossings is .Let at 12:00:00. Crossings occur at seconds.
We are interested in the interval from 12:05:00 ( s) to 12:55:00 ( s).The integer values for are .
The total number of crossings is .
The angular speed of the minute-hand is .
The relative angular speed is .
The time interval between successive crossings is .Let at 12:00:00. Crossings occur at seconds.
We are interested in the interval from 12:05:00 ( s) to 12:55:00 ( s).The integer values for are .
The total number of crossings is .
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