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Question:

Select the option that is related to the fifth term in the same way as the second term is related to the first term and fourth term related to third term.
27 : 196 :: 19 : 100 :: 17 : ?

Explanation:

27 : 196 :: 19 : 100 :: 17 : ?

Logic:
(2^nd number) = ((1^st number + 1)/2)²

196 = ((27 + 1)/2)²
100 = ((19 + 1)/2)²​​​​​​​

∴ 6^th number = ((17 + 1)/2)²​​​​​​​ = 81.

Hence, option (b).