Select the set in which the numbers are related in the same way as are the numbers of the given sets.
(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding /subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is NOT allowed)
(16, 400, 4)
(10, 256, 6)

Correct option is B

To solve this problem, we need to identify the relationship between the numbers in the given sets and then find the set among the options that follows the same relationship.
Let's analyze the given sets:
1. Set 1: (16, 400, 4)
2. Set 2: (10, 256, 6)
Let's identify a common relationship:
1. For Set 1: (16, 400, 4) - Operation: $$(16 + 4)^2$$​ = $$20^2$$​ = 400
2. For Set 2: (10, 256, 6)- Operation: $$(10 + 6)^2$$​ = $$16^2$$​ = 256
Logic: $$(First number + Third Number)^2$$​ = Second number
By applying the logic in each option, we get,
Option (a) (a) (15, 422, 9) - Operation: $$(15 + 9)^2$$​ = $$24^2$$​ = 576 ≠ 422
Option (b) (12, 441, 9) - Operation: $$(12 + 9)^2 = 21^2$$​ = 441
Option (c) (11, 388, 6) - Operation: $$(11 + 6)^2 = 17^2$$​ = 289 ≠ 388
Option (d) (13, 497, 4) - Operation: $$(13 + 4)^2 = 17^2$$​ = 289 ≠ 497
Correct answer is (b) (12, 441, 9).