JEE Main 2025 Jan 22 Shift 2, Physics Q13: Logic Gates

$ \text{Output of the upper AND gate}=A\overline{B} $

$ \text{Output of the lower AND gate}=\overline{A}B $

$ \therefore\text{ Inputs to gate }G\text{ are }A\overline{B}\text{ and }\overline{A}B. $

$ \text{Now, check the four given options.} $

Gate at G	Output	Truth Table (00,01,10,11)	Matches?
OR	$ A\overline{B}+\overline{A}B $	$ 0,\;1,\;1,\;0 $	No
AND	$ (A\overline{B})(\overline{A}B) $	$ 0,\;0,\;0,\;0 $	No
NAND	$ \overline{(A\overline{B})(\overline{A}B)} $	$ 1,\;1,\;1,\;1 $	No
NOR	$ \overline{A\overline{B}+\overline{A}B} $	$ 1,\;0,\;0,\;1 $	Yes

$ \text{The required truth table is }(1,\;0,\;0,\;1), $

$ \therefore\boxed{\text{The logic gate at }G\text{ is NOR Gate.}} $