Inserting The Missing Character Questions

The numbers in the first row form a series 1², 2², 3².
So, missing number in the first row = 4² = 16.
The number in the second row from the series, 1, 2, 3, 4.
The number in the third row from the series 2, 4, 6.
So, missing number in the third row = 6 + 2 = 8.

Here in 2nd column if you add the individual digits

 we get  3 + 7 + 0 =10 , 2 + 2 + 4 = 8 , 7 + 3 + 0 = 10

7   10   3  --> 7+3 =10

6   8     2  --> 6+2 =8

x   10   1  --> x+1 =10

Here we can observe that by adding 1st and 3rd column elements we get 2nd column elements

 --> x = 9

Here 14×1521= 10 and 32×1428 = 16

In the same way  24×2624= 26.

In the first row, (42 - 38) x 11 = 44.
In the second row, (28 - 23) x 11 = 55.
.'. In the third row, missing number = (39 - 37) x 11 = 2 x 11 = 22.

The letters in the second and third rows are five steps ahead of those in the first and second trespectively.
So, the missing letter will be five steps ahead of F, which is K.

In the first column, 3 x 100 + 5 x 9 = 345.
In the second column, 4 x 100 + 6 x 10 = 460.
.'. In the third column, missing number = 5 x 100 + 7 x 11 = 577.

 Clearly, (3rd column)² + (2nd column)² = (1st column)²
In the first row, 5² + 12² = 13².
In the second row, 8² + 15² = 17².
Let the missing number in the third row be y.
Then y² + 24² = 25² or y² + 576 = 625 or y² = 49 or y = 7.