Jamia Millia Islamia MCA Clock Previous Year Questions (PYQs)
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A watch ticks 90 times in 95 seconds and another watch ticks 315 times in 323 seconds.
If both watches are started together, how many times will they tick together in the first hour?
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Solution
Time for one tick of first watch = 95/90 sec = 19/18 sec
Time for one tick of second watch = 323/315 sec = 323/315 sec
Their tick intervals = 19/18 and 323/315.
LCM of time intervals = (19/18, 323/315) → LCM = (GCD of numerators/LCM of denominators)
Simplify ratio-based → They tick together every 19 × 323 / LCM(18, 315) seconds
≈ every 19.2 seconds (approx).
So, in one hour (3600 seconds): 3600 / 35.6 ≈ 101 times.
A clock is so placed that at 12 noon its minute hand points towards north-east.
In which direction does its hour hand point at 1:30 p.m.?
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Solution
At 12 noon → both hands overlap, pointing north-east.
At 1:30 p.m.:
The minute hand is at 6, i.e., pointing south-west (opposite to north-east).
The hour hand at 1:30 lies halfway between 1 and 2 → i.e., $45° + 15° = 52.5°$ clockwise from 12.
So, relative to the minute hand’s original north-east direction,
the hour hand is now $52.5°$ clockwise → this points roughly toward south.
A clock is placed so that at 12 noon its minute hand points towards north-east. In which direction does its hour hand point at 1:30 p.m.?
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Solution
At 1:30, hour hand is 45° clockwise from 12 o’clock. From NE, 45° clockwise = East.
How many times are the hands of a clock at right angles in a day?
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Solution
In 12 hours, hands are at right angles 22 times ⇒ in 24 hours = 44.
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