Analogy (SSC CHSL 2019 Tier 1)

For the given set: (4)³ + 3 = 67
4 × (4 + 1) = 20
Similarly
(3, 30, 12) ⇒ (3)³ + 3 = 30
⇒ 3 × (3 + 1) = 12
However, this condition does not meet any other option.

1st digit remains constant & the other two interchange their places.

PTR : R38
⇒ P + 2 = R and T = 20, R = 18
⇒ T + R = 38 ⇒ PTR ⇒ R38
Similarly, ⇒ I → K and M = 13, K = 11
⇒ M + K = 13 + 11 = 24 ⇒ IMK ⇒ K24

The words in a given word pair are antonyms of each other.
Antonym of stringent is - flexible.
Similarly, the antonym of authoritarian is - liberal.

8² −5² →39  
Similarly... 12² −9² →63 

$(29)²-3\to 841-3\to 838$
Similarly, $²$

$132:156\to 11\times 12:12\times 13$
Similarly, 462 →  21 × 22 
Therefore,
21 × 22 : 22 × 23 → 462 : 506 

In the given set:
(13)²−(6)² → 169 − 36 → 133 
Similarly, (9)² − (4)² → 81 − 16 → 65 

The capital of India → Delhi.
Similarly, the capital of Jharkhand → Ranchi.