PUNE MCA Exam 2014 Question Paper with answers for online practice

Concept:The minute hand passes the hour hand at regular intervals. Starting at 00:01, we find the exact time of the 8th crossing and extract the seconds reading.Explanation:At 00:01, the hour hand is at $0.5^\circ$ and the minute hand at $6^\circ$.The relative angular speed is $5.5^\circ$ per minute.The first crossing after 00:01 occurs when the minute hand gains $360^\circ$ relative to the hour hand: time $t_1 = \frac{360 - 5.5}{5.5} = \frac{709}{11}$ minutes.Subsequent crossings occur every $\frac{720}{11}$ minutes.The 8th crossing time from 00:01: $t_8 = \frac{709}{11} + 7 \times \frac{720}{11} = \frac{5749}{11}$ minutes.Convert to seconds: $t_8 = \frac{5749}{11} \times 60 = \frac{344940}{11} \approx 31358.1818$ seconds.The second hand reading is this time modulo 60: $31358.1818 \bmod 60 = 38.1818$ seconds.This value is not an integer and does not match any option (16, 28, 26).Answer:none of these