Solution:

The next three digits will be 138, 150 and 180.

If you analyze, you will find that all the numbers are increasing in order and are surrounded by two prime numbers.

For example, 4 is surrounded by 3 and 5; both are prime numbers.
6 is surrounded by 5 and 7; both are prime numbers.

Solution:

The required digit is 0.
If you add up all the digits in any diagonal, you will find the sum to be 25.

Solution:

Here, the alphabets can be re-written to their corresponding numbers:
A = 1, B = 2, C = 3... and so on

SHOP = 19 + 8 + 15 + 16 = 58
FEAR = 6 + 5 + 1 + 18 = 30
BALL = 2 + 1 + 12 + 12 = 27
DEAD = 4 + 5 + 1 + 4 = 14

Now, clearly 58 > 30 > 27 > 14

Thus, the order.

Solution:

The number missing on the left is 8 and the one on right is 7.

Explanation:
The pattern:
The number in the center of triangle is the square root of the sum of the numbers sitting outside on the corners.

Thus,
10 + 22 + 4 = 36
Square Root of 36 = 6

In the same manner:

10 + 42 + 12 = 64
Square Root of 64 = 8

12 + 22 + 15 = 49
Square Root of 49 = 7

Solution:

(210 + 6)

Explanation:
If you add the numbers, you will find that they add up to be 8, 27, 64 and 125.
8 = 2^3
27 = 3^3
64 = 4^3
125 = 5^3

Thus the next sum should be 6^3 = 216.

Since 6 has been added in each set, the first number will be (216 - 6) = 210.

Hence, the missing set will be (210 + 6).

Solution:

The correct choice will be the option 'd'.

In each succeeding row, the previous column is reversed and the lowest digits are omitted.

Solution:

276

Explanation:
6 = 1^1 + 2^1 + 3^1
14 = 1^2 + 2^2 + 3^2
36 = 1^3 + 2^3 + 3^3
98 = 1^4 + 2^4 + 3^4

Thus the next number will be
1^5 + 2^5 + 3^5 = 276

Solution:

4

Explanation:
5 = Five (four letters) => 4
7 = Seven (five letters) => 5
10 = Ten (three letters) => 3
3 = Three (five letters) => 5

Therefore, 9 = Nine (four letters) => 4.

Therefore the missing number is 4.

Solution:

3

Explanation:
Number in the series = (Top Left Number * Bottom Left Number)/(Top Right Number * Bottom Right Number)
= (30 * 2) / (4*5)
= 3

Solution:

If you look closely, you will find a sequence in every alternating number.
192, 222 and 252 form one series where 30 is added each time.
021, 324 and 627 form one series where 303 is added each time.

Thus the next two numbers will be 282 and 930.