ISRO CS 2025 Q.55: solution and answer

Official answer: CSource: ISRO's final answer key of 15 May 2026

1. The first gate has an OR shape with a bubble on its output, so it is a NOR gate. Its output is $P=\overline{A+B}$.

2. The second gate has an AND shape with a bubble on its output, so it is a NAND gate. Its inputs are $P$ and $C$, so $$Y=\overline{P\cdot C}=\overline{\overline{A+B}\cdot C}.$$

3. A NAND output is $0$ only when both of its inputs are $1$. So $Y=0$ needs $P=1$ and $C=1$.

4. $P=\overline{A+B}=1$ needs $A+B=0$, which happens only when $A=0$ and $B=0$.

5. So $Y=0$ only for $A=0,B=0,C=1$.

6. Check each option. (a) $A=1,B=1,C=0$: $P=\overline{1+1}=0$, so $Y=\overline{0\cdot 0}=1$. (b) $A=1,B=1,C=1$: $P=0$, so $Y=\overline{0\cdot 1}=1$. (c) $A=0,B=0,C=1$: $P=\overline{0+0}=1$, so $Y=\overline{1\cdot 1}=0$. (d) $A=0,B=0,C=0$: $P=1$, so $Y=\overline{1\cdot 0}=1$. Only option (c) gives a low output.