Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(2, 3, 13)
(7, 8, 113) ​​​

Given: 

(2, 3, 13)
(7, 8, 113)

Logic: (1st number)²+ (2nd number)²= 3rd number

For, (2, 3, 13)

2²+ 3²= 4 + 9 = 13

For, (7, 8, 113)

7²+ 8²= 49 + 64 = 113

Now, we check each options.

Option (a): (11, 4, 155) (Not Follow)

11²+ 4²= 121 + 16 $$\neq$$​ 155​

Option (b): (8, 5, 75) (Not Follow)​

8²+ 5²= 64 + 25 $$\neq$$ 75

Option (c): (3, 5, 37) (Not Follow)​

3²+ 5²= 9 + 25 $$\neq$$ 37

Option (d): (5, 9, 106) (Follow)​

5²+ 9²= 25 + 81 = 106

Thus, correct option is (d).