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JEE Main 2025 Apr 4 Shift 1, Physics Q15: Logic Gates

JEE Main2025Apr 4, Shift 1Physics
Q.

The Boolean expression can be realised with which of the following gate configurations.

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

C. 3-input OR gate, 3 NOT gates and one 2-input AND gate

Choose the correct answer from the options given below

  1. A

    B, C Only

  2. B

    A, B Only

  3. C

    A, B, C Only

  4. D

    A, C Only

Solution

Configuration A: is the AND of , (one NOT) and - uses a 3-input AND with one NOT on . uses two more NOTs and a 2-input AND. The two product terms are then combined by a 2-input OR. Total: one 3-input AND, three NOTs, one 2-input AND, one 2-input OR. Matches A exactly. ✓

Configuration B: Apply De Morgan's law: , which is just a 2-input NOR on and . needs one NOT (on ) and a 3-input AND. Combine with a 2-input OR. Total: one 3-input AND, one NOT, one 2-input NOR, one 2-input OR. Matches B exactly. ✓

Configuration C: A 3-input OR with 3 NOTs and a single 2-input AND cannot reproduce the given two-product-term sum. Does not match. ✗

A and B only.

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