Solution:

7 + 8 = 15 and 15 - 9 = 6
6 + 9 = 15 and 15 - 4 = 11

Therefore, (89)^2 will be:
8 + 9 = 17 and 17 - 2 = 15

Solution:

60

Explanation:
1 + 5 = 12
But it can be true only if we multiply both digits with 2 and then add:
1*2 + 5*2 = 12

2 + 10 = 24
But it can be true only if we multiply both digits with 2 and then add:
2*2 + 10*2 = 24

3 + 15 = 36
But it can be true only if we multiply both digits with 2 and then add:
3*2 + 15*2 = 36

Similarly,
5 + 25 can be true only if we multiply both digits with 2 and then add:
=> 5*2 + 25*2 = 60

Therefore, the missing number is 60.

Solution:

The missing tile will be 3.

Explanation:
0 + 0 = 0
1 + 2 = 3
0 + 2 + 2
1 + 4 = 5
3 + 1 = 4
6 + 1 = 7
3 + 3 = 6
6 + 3 = 9

If you see the patter, with each pair the total sum is increasing by three and then decreasing by 1. Therefore the missing tile will be 3.

Solution:

Q

Explanation:
First Square:
6 + 4 + 4 = 14
N is the 14th letter.

Second Square:
4 + 1 + 7 = 12
L is the 12th letter.

Third Square:
5 + 6 + 10 = 21
U is the 21st letter.

Fourth Square:
14 + 2 + 1 = 17
Q is the 17th letter.

Solution:

100

Series of number that do not contain albhabet 'T'

Solution:

The last missing throw will have 3 as the result. This is because, with each pair of the throws you can find that the total sum is increasing by three and then decreasing by one. Therefore the missing throw be 3.

Solution:

180

2 + 2 = 4 {2 * 2 * 1}
3 + 3 = 18 {3 * 3 * 2}
4 + 4 = 48 {4 * 4 * 3}
6 + 6 = 180 {6 * 6 * 5}

Solution:

17/19

series is 2/1 3/4 5/7 7/10 11/13 13/16
Numerator is prime number series 2-3-5-7-11-13-17
and Denominator is +3 series 1-4-7-10-13-16-19

Solution:

Stephen is your grandson.

Let us explain how:
Your Uncle's sister can be your mother or can be your aunt. But in the question, you have mentioned that we have to look for the closet relation thus, it will definitely be your mother.
Now, your mother's granddaughter can either be your daughter or your niece. Again, daughter is the closer relation.
Advancing forward, your daughter's son is without a doubt your grandson.

Solution:

29

Explanation:
If you look closely, you will find that the center number can be obtained by multiplying the largest numbers on the corners and subtracting the smallest number from it.

26 = 7 * 5 – 3^2

In the same manner, every other figure follows. Thus the missing number:
9 * 5 – 4^2
= 45 – 16
= 29