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The first day of a century cannot be
- a)Monday
- b)Tuesday
- c)Wednesday
- d)Thursday
Correct answer is option 'C'. Can you explain this answer?
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The first day of a century cannot bea) ...
Explanation:
To answer this question, we need to understand the concept of the day of the week on a particular date.
- The day of the week on a particular date is determined by the Gregorian calendar, which is a solar calendar.
- The Gregorian calendar has a cycle of 400 years, and each cycle has 146,097 days.
- The cycle starts from 1st January 1601 AD, and the days are numbered consecutively from that day.
- The day of the week on a particular date can be calculated by using a mathematical formula called the Zeller's congruence formula.
Now, let's see why the first day of a century cannot be Wednesday.
- The first day of a century can be calculated by using the following formula:
- First day of a century = (n-1)*100 + 1
- Where n is the century number. For example, the first day of the 21st century is calculated as follows:
- n = 21
- First day of the 21st century = (21-1)*100 + 1 = 2001
- Now, let's apply the Zeller's congruence formula to find the day of the week on the first day of the 21st century.
- Zeller's congruence formula:
- h = (q + (13*(m+1))/5 + K + K/4 + J/4 + 5*J) % 7
- Where
- h = day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, and so on)
- q = day of the month
- m = month (3 = March, 4 = April, ..., 14 = February)
- K = year of the century (year % 100)
- J = zero-based century (year / 100)
- For the first day of the 21st century, we have:
- q = 1
- m = 13 (January is counted as the 13th month of the previous year)
- K = 1 (2001 % 100 = 1)
- J = 20 (2001 / 100 = 20)
- Plugging these values into the formula, we get:
- h = (1 + (13*(13+1))/5 + 1 + 1/4 + 20/4 + 5*20) % 7
- h = (1 + 91 + 1 + 0 + 5 + 100) % 7
- h = 198 % 7
- h = 6
- Therefore, the first day of the 21st century was a Saturday.
- From the Zeller's congruence formula, we can see that the day of the week on a particular date depends on the values of q, m, K, and J.
- Since the values of K and J are fixed for a century, the day of the week on the first day of a century depends only on the values of q and m.
- If the first day of a century is a Wednesday, then the values of q and m must satisfy the following
To answer this question, we need to understand the concept of the day of the week on a particular date.
- The day of the week on a particular date is determined by the Gregorian calendar, which is a solar calendar.
- The Gregorian calendar has a cycle of 400 years, and each cycle has 146,097 days.
- The cycle starts from 1st January 1601 AD, and the days are numbered consecutively from that day.
- The day of the week on a particular date can be calculated by using a mathematical formula called the Zeller's congruence formula.
Now, let's see why the first day of a century cannot be Wednesday.
- The first day of a century can be calculated by using the following formula:
- First day of a century = (n-1)*100 + 1
- Where n is the century number. For example, the first day of the 21st century is calculated as follows:
- n = 21
- First day of the 21st century = (21-1)*100 + 1 = 2001
- Now, let's apply the Zeller's congruence formula to find the day of the week on the first day of the 21st century.
- Zeller's congruence formula:
- h = (q + (13*(m+1))/5 + K + K/4 + J/4 + 5*J) % 7
- Where
- h = day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, and so on)
- q = day of the month
- m = month (3 = March, 4 = April, ..., 14 = February)
- K = year of the century (year % 100)
- J = zero-based century (year / 100)
- For the first day of the 21st century, we have:
- q = 1
- m = 13 (January is counted as the 13th month of the previous year)
- K = 1 (2001 % 100 = 1)
- J = 20 (2001 / 100 = 20)
- Plugging these values into the formula, we get:
- h = (1 + (13*(13+1))/5 + 1 + 1/4 + 20/4 + 5*20) % 7
- h = (1 + 91 + 1 + 0 + 5 + 100) % 7
- h = 198 % 7
- h = 6
- Therefore, the first day of the 21st century was a Saturday.
- From the Zeller's congruence formula, we can see that the day of the week on a particular date depends on the values of q, m, K, and J.
- Since the values of K and J are fixed for a century, the day of the week on the first day of a century depends only on the values of q and m.
- If the first day of a century is a Wednesday, then the values of q and m must satisfy the following
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The first day of a century cannot bea) Monday b) Tuesday c) Wednesday d) Thursday Correct answer is option 'C'. Can you explain this answer?
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