Answer: Option C

Explanation:
28th May 2006 = (2005 years + period from 1-Jan-2006 to 28-May-2006)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)
Number of odd days in the period 2001-2005
= 4 normal years + 1 leap year 
= 4 x 1 + 1 x 2 = 6
Days from 1-Jan-2006 to 28-May-2006 = 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 28(may) = 148
148 days = 21 weeks + 1 day = 1 odd day
Total number of odd days = (0 + 6 + 1) = 7 odd days = 0 odd day
0 odd day = Sunday
Hence May 28 2006 is Sunday.

Answer: Option C

Explanation:
61 days = 8 weeks 5 days = 5 odd days
Hence if today is Monday, After 61 days, it will be = (Monday + 5 odd days)
= Saturday

Answer: Option D

Explanation:
15th Aug 2010 = (2009 years + period from 1-Jan-2010 to 15-Aug-2010)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)
Number of odd days in the period 2001-2009
= 7 normal years + 2 leap year 
= 7 x 1 + 2 x 2 = 11 = (11 - 7x1) odd day = 4 odd day
Days from 1-Jan-2010 to 15-Aug-2010 
= 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 31(may) + 30(Jun) + 31(Jul) + 15(Aug)
= 227
227 days = 32 weeks + 3 day = 3 odd day
Total number of odd days = (0 + 4 + 3) = 7 odd days = 0 odd day
0 odd day = Sunday
Hence 15th August, 2010 is Sunday.

Answer: Option B

Explanation:
x weeks x days = (7 × x) + x = 7x + x = 8x days

Answer: Option B

Explanation:
We need to find out the day of 01-Apr-2001
01-Apr-2001 = (2000 years + period from 1-Jan-2001 to 01-Apr-2001)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)
Days from 1-Jan-2001 to 01-Apr-2001 = 31 (Jan) + 28 (Feb) + 31 (Mar) + 1(Apr) = 91
91 days = 13 weeks = 0 odd day
Total number of odd days = (0 + 0) = 0 odd days
0 odd day = Sunday. Hence 01-Apr-2001 is Sunday.
Hence first Wednesday of Apr 2011 comes in 04th and successive Wednesdays come in 11th, 18th and 25th

Answer: Option A

Explanation:
Given that 8th Feb, 2005 was Tuesday
Number of days from 8th Feb, 2004 to 7th Feb, 2005 = 366 (Since Feb 2004 has 29 days as it is a leap year)
366 days = 2 odd days
Hence 8th Feb, 2004 = (Tuesday - 2 odd days) = Sunday

Answer: Option B

Explanation:
For a year to have the same calendar with 2007 ,the total odd days from 2007 should be 0.

Take the year 2014 given in the choice.

Total odd days in the period 2007-2013 = 5 normal years + 2 leap year 
= 5 x 1 + 2 x 2 = 9 odd days 
= 2 odd day (As we can reduce multiples of 7 from odd days which will not change anything)

Take the year 2016 given in the choice.

Number of odd days in the period 2007-2015 = 7 normal years + 2 leap year 
= 7 x 1 + 2 x 2 = 11 odd days 
= 4 odd days 
(Even if the odd days were 0, calendar of 2007 will not be same as the calendar of 2016 because 2007 is not a leap year whereas 2016 is a leap year. In fact, you can straight away ignore this choice due to this fact without even bothering to check the odd days) 

Take the year 2017 given in the choice.

Number of odd days in the period 2007-2016 = 7 normal years + 3 leap year 
= 7 x 1 + 3 x 2 = 13 odd days 
= 6 odd days 

Take the year 2018 given in the choice.

Number of odd days in the period 2007-2017 = 8 normal years + 3 leap year 
= 8 x 1 + 3 x 2 = 14 odd days 
= 0 odd day (As we can reduce multiples of 7 from odd days which will not change anything)

Also, both 2007 and 2018 are not leap years. 
Since total odd days in the period 2007-2017 = 0 and both 2007 and 2018 are of same type, 2018 will have the same calendar as that of 2007

Answer: Option C

Explanation:
Given that January 1, 2007 was Monday.
Odd days in 2007 = 1 (we have taken the complete year 2007 because
we need to find out the odd days from 01-Jan-2007 to 31-Dec-2007, that is the whole year 2007)
Hence January 1, 2008 = (Monday + 1 Odd day) = Tuesday

Answer: Option C

Explanation:
Remember the leap year rule (Given in the formulas)
1. Every year divisible by 4 is a leap year, if it is not a century.
2. Every 4th century is a leap year, but no other century is a leap year.
800,1200 and 2000 comes in the category of 4th century (such as 400,800,1200,1600,2000 etc). 
Hence 800,1200 and 2000 are leap years
700 is not a 4th century, but it is a century. Hence it is not a leap year

Answer: Option C

Explanation:
We know that number of odd days in 100 years = 5
Hence last day of the first century is Friday
Number of odd days in 200 years = 5 x 2 = 10 = 3 (As we can reduce multiples of 7 from odd days which will not change anything)
Hence last day of the 2nd century is Wednesday
Number of odd days in 300 years = 5 x 3 = 15 = 1
Hence last day of the 3rd century is Monday
We know that umber of odd days in 400 years = 0. (∵ 5 x 4 + 1 = 21 = 0)
Hence last day of the 4th century is Sunday
Now this cycle will be repeated. Hence last day of a century will not be Tuesday or Thursday or Saturday.
its better to learn this by heart which will be helpful to save time in objective type exams