In the following number pairs, the second number is obtained by applying certain mathematical operations to the first number. Select the set in which the numbers are related in the same way as 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 /deleting /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.)
(12, 145)
(9, 82)

Logic: Add 1 to the square of the first number of the given set to get the second number.

(12, 145) = $$(12)^2 + 1 = 144 + 1 = 145$$​​

(9, 82) = $$(9)^2 + 1 = 81 + 1 = 82$$

Explanation:​

(a) (16, 256) = $$(16)^2 + 1 = 256 + 1 = 257\not=256$$​​

(b) (14, 197) = $$(14)^2 + 1 = 196 + 1 = 197$$​​

(c) (22, 483) = $$(22)^2 + 1 = 484 + 1 = 485\not= 483$$​​

(d) (8, 69) = $$(8)^2 + 1 = 64 + 1 = 65\not=69$$​​

So, only option (b) follows the same logic.

Thus, the correct option is (b).