Calendar

 The answer is option b.
Simply If today is Monday, then after 7 days it will be again Monday. 
Since after 45 days means we should separate it as multiple of 7. 
Then 42 + 3 = 5
Which means,
6×7 = 42.
And then 43rd day will be Tuesday.
And 44th day will be wednesday.
And 45th day will be Thursday.
Hence option b is correct.

Nine days after Thursday is Saturday. Because Thursday is when Sanjay goes to movie Usually.

 J is the correct answer. 
June, July, January - 3 times.
March, May - 2 times.
April, August - 2 times.
February - 1 time.

Output: Using Zeller's rule:

Output: Here, k = 2, m = 9, D = 65, C = 19

Output: F = 2 + [(13*9-1)/5] + 65 + [65/4] + [19/2]-2*19.

Output: F = 79 and then divide it by 7 and the remainder would be 2. Since 0 refers Sunday and consequently 2 refers Tuesday.

Output:

Counting odd days:

94 years = (23 leap years + 71 ordinary years)

[(23×2) + (71×1)] odd days = 117 odd days => 16 weeks + 5 days = 5 odd days.

1994 = (0 + 1 + 5) odd days => 6 odd days.

Jan(31) + Feb(28) + March(31) + April (30) + May(31) + June(30) + July(16) = 197 days = (28 weeks + 1 day) => 1 odd day.

Total number of odd days: 6+1 => 7 days which in turns 0 odd day.

Output:

Counting odd days:

46 years = (11 leap years + 35 ordinary years)

[(11×2) + (35×1)] odd days = 57 odd days => 8 weeks + 1 days = 1 odd days.

1946 = (0 + 1 + 1) odd days => 2 odd days.

Jan(31) + Feb(28) + March(31) + April (30) + May(31) + June(30) + July(31) + August(15) = 227 days = (32 weeks + 3 day) => 3 odd day.

Total number of odd days: 2+3 => 5 odd days.

Output:

Counting odd days:

99 years = (24 leap years + 75 ordinary years)

[(24×2) + (75×1)] odd days = 123 odd days => 17 weeks + 4 days = 4 odd days.

1999 = (0 + 1 + 4) odd days => 5 odd days.

Jan(31) + Feb(14) = 45 days = (6 weeks + 3 day) => 3 odd day.

Total number of odd days: 5+3 => 8 days which in turns 1 odd day.

Output:

Counting odd days:

Jan(1) = 1 odd day.

Total number of odd days: 0+1 => 1 odd day.