Solution:

20741616380

Explanation:
5 * 5 - 5 =>20
20 * 20 - 20 => 380
380 * 380 -380 =>144020
144020 * 144020 - 144020 => 20741616380

Solution:

The next number is 392.

The first number = (Square of 1 + Cube of 1)
The second number = (Square of 2 + Cube of 2)
The third number = (Square of 3 + Cube of 3)
The fourth number = (Square of 4 + Cube of 4)
The fifth number = (Square of 5 + Cube of 5)
The sixth number = (Square of 6 + Cube of 6)
Therefore, the seventh number will be
Square of 7 + Cube of 7 = 392.

Solution:

89 (ASCII CODE OF Y)

Q W E R T Y
81 87 69 82 84 ?

Solution:

The series are prime numbers with one added to it.
The original prime numbers are as follows.
101, 103, 107, 109, 113, 127

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.