GATE 2024 IN Q.14: solution and answer

Official answer: ASource: Official answer key, GATE 2024 IN (IISc Bengaluru)

1. Optical pyrometer (P): a non-contact temperature instrument that compares the brightness or colour (wavelength) of the radiation from a hot body with that of a calibrated reference filament. So (P) matches (III), wavelength of radiated energy.

2. Thermocouple (Q): the Seebeck effect. Two dissimilar metals joined at a junction generate an electromotive force that depends on the temperature difference between the measuring junction and the reference junction. So (Q) matches (IV).

3. Strain gauge (R): a strain $\epsilon$ changes the resistance of the gauge wire, with gauge factor $G=\frac{\Delta R/R}{\epsilon }$. So (R) matches (II), change in resistance.

4. Linear variable differential transformer (S): the core position changes the mutual inductance between the primary and the two secondary windings, so the differential output voltage is proportional to the core displacement. So (S) matches (I).

5. The pairing is (P)-(III), (Q)-(IV), (R)-(II), (S)-(I), which is option (A). Option (B) puts (P) with (IV) and (Q) with (III). Option (C) puts (Q) with (I) and (R) with (IV). Option (D) puts (P) with (II), (R) with (I) and (S) with (III). Each of these breaks at least one pairing above, so all three are wrong.