Question 1 In a particular year, the month of january had exactly 4 thursdays, and 4 sundays. On which day of the week did january 1st occur in the year?
If a month has 31 days, and it starts with sunday, Then Sundays, Mondays, tuesdays are 5 for that month. If this month starts with monday, then mondays, tuesdays, and wednesdays are 5 and remaining days are 4 each. so this month start with Monday.
Question 2 What is the angle between two hands when time is 5:30?
15° At 5:30 minute hand will be at position 6 and hour hand will be exactly between 5 and 6 and will cover 15°, so angle between two hands=30 -15 = 15°
Question 3 The famous church in the city of Kumbakonam has a big clock tower and is said to be over 300 years old. Every Monday 10.00 A M the clock is set by Antony, doing service in the church. The Clock loses 6 minutes every hour. What will be the actual time when the faulty clock shows 3 P.M on Friday?
Let us start from Monday 10 am to friday 3.00 pm…..total hours=4 days 5 hrs.=4*24+5=101 hrs. so total time loses=101*6 minutes=606 minutes=606/60=10 hrs 10 minutes so actual time=friday 3.00 pm +10 hrs 10 minutes=staurday 1.10 am.
Question 4 How many times do the hands of a clock coincide in 5 hours?
hour hand and minute hand coincide every 65:5 minute, so in 5 hour they will coincide 4 times The hour hand covers 2*360 degrees in 24 hours, i.e 1440 minutes. So, in one minute, it covers 1440/720 = 1/2 degree. Difference in angular distance travelled by the minute hand and the hour hand in one minute is thus 6-1/2 = 11/2 degrees. So, on a full rotation (360ᵒ), any similar event between them will be repeated every 360/(11/2) = 65 5/11 minutes.
Question 5 What is the chance that a leap year selected at random contains 53 Fridays?
ans- 2/7 in aleap year there are 366 days means 52 weeks and 2days. so already we have 52 fridays. now the rest two days can be (sun, mon), (mon,tues),(tues, wed), (wed, thrus), (thrus, fri),(fri, sat), (sat, sun) so, the probability of 53 fridays= 2/7
Question 6 Between 9 a.m and 9 p.m of a particular day for how many times are the minute and hour hands together?
11..the hands will be together for once per hour..e.g 9.45,10.50..but between 11 and 12 the coming together will be counted as 1 for both hence in 12 hrs time they will be together for 12-1=11 times
Question 7 How many palindromes are there in a clock from noon to midnight ( For Example 5.45 is a palindrome)?
57 after 12 o’clock 12:21…….=1 from 1 to 9 it is 1.01, 1.11, 1.21, 1.31, 1.41, 1.51.= 6 similarly 2.02,2.12,…………….. 6*9=54+1=55 after 10 o’clock 10:01, 11:11 Ans: 55+2=57
Question 8 One quarter of the time till now from midnight and half of the time remaining from now up to midnight adds to the present time. What is the present time?
x is present time 1/4(x)+1/2(24-x)=x solve it then x = 9:36
Question 9 A clock loses 1% time during first week and then gains 2% time during the next one week. if the clock was set right at 12noon on Sunday what will be the the time exactly that the clock will show 14days from the time it was set right?
A.1 : 30 : 48 P.M.
B.1 : 40 : 48 P.M.
C.1 : 40 : 38 P.M.
D.1 : 30 : 48 A.M.
The clock loses 1% time during the first week. In a day there are 24 hours and in a week there are 7 days. Therefore, there are 7 * 24 = 168 hours in a week. If the clock loses 1% time during the first week, then it will show a time which is 1% of 168 hours less than 12 Noon at the end of the first week = 1.68 hours less. Subsequently, the clock gains 2% during the next week. The second week has 168 hours and the clock gains 2% time = 2% of 168 hours = 3.36 hours more than the actual time. As it lost 1.68 hours during the first week and then gained 3.36 hours during the next week, the net result will be a -1.68 + 3.36 = 1.68 hour net gain in time. So the clock will show a time, which is 1.68 hours more than 12 Noon two weeks from the time it was set right. 1.68 hours = 1 hour and 40.8 minutes = 1 hour + 40 minutes + 48 seconds. i.e. 1 : 40 : 48 P.M.