JEE Main · 2021 · 26 Aug 2021 · Shift 2 · Semiconductors

The first gate takes both inputs, giving $P=\overline{A+B}$. This output is fed to two further NOR gates whose other inputs are $A$ and $B$ respectively, so

and the last gate gives $Y=\overline{X+Q}$.
For $A=0$, $B=0$: $P=1$, so $X=0$, $Q=0$ and $Y=1$.
For $A=0$, $B=1$: $P=0$, so $X=1$, $Q=0$ and $Y=0$.
For $A=1$, $B=0$: $P=0$, so $X=0$, $Q=1$ and $Y=0$.
For $A=1$, $B=1$: $P=0$, so $X=0$, $Q=0$ and $Y=1$.
The circuit gives output $1$ when the two inputs are alike and $0$ when they differ.