Answer: Option B

Explanation:
Day before yesterday was Thursday
=>Yesterday was a Friday
=> Today is a Saturday
=> Tomorrow is a Sunday

Answer: Option D

Explanation:
We cannot find out the answer because the number of days of the current month is not given.

Answer: Option C

Explanation:
Given that January 1, 2004 was Thursday.
Odd days in 2004 = 2 (because 2004 is a leap year)
(Also note that we have taken the complete year 2004 because we need to find out the odd days from 01-Jan-2004 to 31-Dec-2004, that is the whole year 2004)
Hence January 1, 2005 = (Thursday + 2 odd days) = Saturday

Answer: Option B

Explanation:
Given that first day of a normal year was Friday 
Odd days of the mentioned year = 1 (Since it is an ordinary year)
Hence First day of the next year = (Friday + 1 Odd day) = Saturday
Therefore, last day of the mentioned year = Friday

Answer: Option A

Explanation:
Clearly it can be understood from the question that 9 days ago was a Thursday
Number of odd days in 9 days = 2 (As 9-7 = 2, reduced perfect multiple of 7 from total days)
Hence today = (Thursday + 2 odd days) = Saturday

Answer: Option C

Explanation:
Given that 1.12.91 is the first Sunday
Hence we can assume that 3.12.91 is the first Tuesday 
If we add 7 days to 3.12.91, we will get second Tuesday 
If we add 14 days to 3.12.91, we will get third Tuesday 
If we add 21 days to 3.12.91, we will get fourth Tuesday 
=> fourth Tuesday = (3.12.91 + 21 days) = 24.12.91

Answer: Option B

Explanation:
For a year to have the same calendar with 1990 ,total odd days from 1990 should be 0. 

Take the year 1992 from the given choices.
Total odd days in the period 1990-1991= 2 normal years 
≡ 2 x 1 = 2 odd days 

Take the year 1995 from the given choices.
Number of odd days in the period 1990-1994 = 4 normal years + 1 leap year 
≡ 4 x 1 + 1 x 2 = 6 odd days 

Take the year 1996 from the given choices.
Number of odd days in the period 1990-1995= 5 normal years + 1 leap year
≡ 5 x 1 + 1 x 2 = 7 odd days ≡ 0 odd days 
(As we can reduce multiples of 7 from odd days which will not change anything)

Though number of odd days in the period 1990-1995 is 0, there is a catch here. 
1990 is not a leap year whereas 1996 is a leap year.
Hence calendar for 1990 and 1996 will never be the same.

Take the year 2001 from the given choices.
Number of odd days in the period 1990-2000= 8 normal years + 3 leap years 
≡ 8 x 1 + 3 x 2 = 14 odd days ≡ 0 odd days 
Also, both 1990 and 2001 are normal years.
Hence 1990 will have the same calendar as that of 2001

Answer: Option A

Explanation:
22 Apr 2222 = (2221 years + period from 1-Jan-2222 to 22-Apr-2222)
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 2001-2200
= Number of odd days in 200 years
= 5 x 2 = 10 = 3
(As we can reduce perfect multiples of 7 from odd days without affecting anything)
Number of odd days in the period 2201-2221
= 16 normal years + 5 leap years 
= 16 x 1 + 5 x 2 = 16 + 10 = 26 = 5 odd days 
Number of days from 1-Jan-2222 to 22 Apr 2222
= 31 (Jan) + 28 (Feb) + 31 (Mar) + 22(Apr) = 112 
112 days = 0 odd day
Total number of odd days = (0 + 3 + 5 + 0) = 8 = 1 odd day
1 odd days = Monday
Hence 22 Apr 2222 is Monday.

Answer: Option B

Explanation:
59 days = 8 weeks 3 days = 3 odd days
Hence if today is Thursday, After 59 days, it will be = (Thursday + 3 odd days)
= Sunday