JEE Physics 2025 Question with Solution

Step-by-step solution

Standard Method

Given: Boolean expression

$$Y = A\overline{B}C + \overline{AC}$$

Find: Which gate configurations can realise the expression.

From the extracted solution, configuration A and configuration B are identified as matching the Boolean expression.

The solution explicitly states:

• A. One $3$-input AND gate, $3$ NOT gates and one $2$-input OR gate, One $2$-input AND gate
• B. One $3$-input AND gate, $1$ NOT gate, One $2$-input NOR gate and one $2$-input OR gate

Therefore, the correct combination is A, B Only.

The correct option is B.

Common mistakes

• Mistake: Treating $\overline{AC}$ as $\overline{A}\,\overline{C}$ without checking the gate implementation carefully. Why wrong: the complemented product is naturally realised by a NOR/NAND-style combination depending on the circuit structure. What to do instead: identify whether the complement applies to the whole product term or to individual variables before mapping gates.

• Mistake: Ignoring that the options refer to configurations A, B, and C shown in the question, not to answer labels A, B, C, D. Why wrong: this mixes circuit names with multiple-choice option labels. What to do instead: first determine which circuit configurations are correct, then select the matching final option.

• Mistake: Assuming configuration C must also work without verifying each gate sequence. Why wrong: logic circuit realisation depends on exact inversion and combination of signals. What to do instead: trace the signal path term by term and compare it with $A\overline{B}C + \overline{AC}$.