JEE Main 2025 · 2 April · evening · Single correct · +4 / −1
In the digital circuit shown in the figure, for the given inputs the P and Q values are :
- (a) P=0, Q=1
- (b) P=1, Q=0
- (c) P=0, Q=0
- (d) P=1, Q=1
Answer and solution
Answer (c) P=0, Q=0
Solution
Physics sir · 4 steps
Name the two middle wires, find each one, then feed them into the last two gates.
- Top wire X. Both inputs go into the NAND gate. 1 · 1 = 1, and the bubble flips it, so X = 0.
- Bottom wire Y. Each input passes through a NOT gate, giving 0 and 0. These go into the OR gate, so Y = 0 + 0 = 0.
Gate Inputs Output AND X = 0, Y = 0 P = 0 · 0 = 0 NOT on X X = 0 X̅ = 1 NOR X̅ = 1, Y = 0 Q = 1 + 0̅ = 0 - Q for any input. By De Morgan, Y = A̅ + B̅ = A̅B̅ = X. The NOR then gets X̅ and X, one of which is always 1, so Q = 0 for any inputs.
- So. P = 0 and Q = 0, which is option (c).
The idea to keep. In a multi-gate circuit, label every intermediate wire and work left to right. Also watch for De Morgan: A̅ + B̅ is the same as NAND.
Answer from the NTA final answer key. Solution by PrepWiser.