Q 12-14-177JEE MainJEE Main 2019 (10 Jan, Shift 1)Medium
In a logic circuit, input $x$ passes through a NOT gate, and its output and input $y$ are fed to an OR gate whose output is $P$. Input $x$ and the output of a NOT gate fed by $y$ are the inputs of a NAND gate whose output is $Q$. $P$ and $Q$ are the inputs of a NOR gate whose output is $R$.
To get output 1 at $R$, the input values must be:
Answer: (D) $x = 1,\ y = 0$
$P = \bar x + y$ and $Q = \overline{x\cdot\bar y}$. A NOR gate gives 1 only when both inputs are 0.
$P = 0$ needs $\bar x = 0$ and $y = 0$, i.e. $x = 1,\ y = 0$.
Check $Q$: $x\cdot\bar y = 1\cdot1 = 1$, so $Q = 0$. Both inputs are 0, so $R = 1$ for $x = 1,\ y = 0$.
Solution by Sreeraj P, M.Sc Physics