Solution:

Actually, there are two series in the question. If you separate the alternate places, you will find that the first series is:
0, 1, 2, 3, 4
Where the digits are multiple of 1.

The second series is:
0, 2, 4, 6, __
Here, the digits are progressing with the multiples of 2.
Therefore, the next digit will be 8.

Solution:

252

Explanation:
A unique pattern has been made into use in this series.
All numbers are (n^3 + n^2) where n is 1, 2, 3 and so on.

In first number, n = 1
1^3 + 1^2 = 1 + 1 = 2

In second number, n = 2
2^3 + 2^2 = 8 + 4 = 12

In third number, n = 3
3^3 + 3^2 = 27 + 9 = 36

In fourth number, n = 4
4^3 + 4^2 = 64 + 16 = 80

In fifth number, n = 5
5^3 + 5^2 = 125 + 25 = 150

Similarly for the sixth number, n = 6
6^3 + 6^2 = 216 + 36 = 252.

Solution:

The missing number is 11.

Explanation:
The patter here is that the number on the right is half of the product of the other two numbers.

(18*4)/2 = 36
(15*6)/2 = 45

In the same manner,
(8*x)/2 = 44
=> x = 11

Solution:

The missing number is 399.

Explanation:
84 = 4^3 + 3^2 + 4
155 = 5^3 + 5^2 + 5
258 = 6^3 + 6^2 + 6
584 = 8^3 + 8^2 + 8
819 = 9^3 + 9^2 + 9

Thus,
399 = 7^3 + 7^2 + 7

Solution:

23

Explanation:
If you interchange the digits in the squares, you will see that all the resulting numbers are square of some number. Now square root all the thus formed numbers and add them together and you will have the required number in the circle.

In the third figure:
61 = 16 and square root = 4
90 = 09 and square root = 3
18 = 81 and square root = 9
94 = 49 and square root = 7

4 + 3 + 9 + 7 = 23.

Solution:

181

Explanation:
+11 =>16
+33 =>49
+55 =>104
+77 =>181

Solution:

The number will be 30.

In the first circle
(5 + 4) * 2 = 18

In the third circle
2. (12 + 8) * 3 = 60

In the fourth circle
3. (3 + 9) * 4 = 48

Similarly In the fifth circle
4. (4 + 2) * 5 = 30

Solution:

125

Explanation:
The trick that has been used here is that all the corner digits have been reversed and then added. The sum is than placed in the center.

In the first square:
13 + 32 + 11 + 34 = 90

In the second square:
21 + 19 + 27 + 16 = 83

In the third square:
33 + 33 + 22 + 26 = 125

Thus the missing number is 125

Solution:

The solution is given in the attached image.

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.