Solution:

1726

A) 1345 sum of digits(13, prime)
B) 1754 sum of digits(17, prime)
C) 1726 sum of digits(16, not prime)
D) 1235 sum of digits(11, prime)

Solution:

99 matches.

The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 99 matches were played.

Solution:

457730 * 4 = 1830920
(DOLLAR * 4 = QUARTER)

Solution:

TIF56

Explanation:
The password is formed as:
T (5th letter of Shruti)
I (5th letter of Arshika)
F(1st letter of Friday)
5(5th day of week)
6(Length of Friday)

Similarly, we will pick the 1st letter for Monday and 3rd letter for Wednesday.

Solution:

The bridge won't break.

When the car has travelled half of the bridge, that is 15km, the car must have used more than 300 grams of fuel. Therefore, the impact of bird's added weight will be zero literally.

Solution:

Daughter.

Solution:

Q = 1
U = 9
I = 6
C = 8
K = 3.

Explanation:
Replace values in( Q + U + I + C + K)^3 = QUICK
(1+9+8+6+3)^3 = 19863
27^3 = 19863
19863 = 19863

Solution:

3 1 2 2 1 1
1 3 1 1 2 2 2 1

Read Line as one 1 => 1
Read Line 2 as two one => 2 1
Read Line 3 as one two and one one => 1 2 1 1
and so on.

Solution:

Since each one of them gave one answer wrong, this means that each one of them gave two answers right.

Let us assume that Student A gave a wrong answer to the first question. This will mean that Student B also gave a wrong answer for the first. This will conclude that the rest of the two answers given by them are correct. However, the answers are different and thus it is not possible.

Thus both Student A and Student B must be right with the first question and the answer to the first is two.

If you keep applying the same logic, you will come to a conclusion that following are the correct answers:
Q1. Two
Q2. Three
Q3. Two

Solution:

Birbal drew another line that was larger than the pre-drawn line. Now the pre drawn line was smaller.

Solution:

This is more of a philosophical question than being a riddle or a puzzle. The action of Brian directly led to the result which is the death of Chris. Thus he murdered Chris. In a sense, Chris died due to the lack of water. It is the circumstances that ultimately led to his death.