WBJEE 2024 Physics & Chemistry Paper

To find the pattern and the correct expression for the output Q in the given network of AND and OR gates, let's analyze the structure and the recursive formation of the expressions.
Step-by-Step Analysis
First Layer (Base case):
Q1=X0∧X1
Second Layer:

‌Q2=(X0∧X1)∨X2
‌Q2=X0X1+X2
Third Layer:
‌Q3=((X0∧X1)∨X2)∧X3
‌Q3=(X0X1+X2)∧X3
‌Q3=X0X1X3+X2X3

Fourth Layer:
‌Q4=((X0∧X1)∨(X2∧X3))∨X4
‌Q4=(X0X1X3+X2X3)+X4
‌Q4=X0X1X3+X2X3+X4

Fifth Layer:
‌Q5=((X0∧X1∧X3)∨(X2∧X3)∨X4)∧X5
‌Q5=(X0X1X3+X2X3+X4)∧X5
‌Q5=X0X1X3X5+X2X3X5+X4X5

General Pattern
From the above steps, the output Q at each layer can be generalized as:
Thus, we can see that:
The output Q consists of products of increasing sequences of inputs, where each sequence starts from the lowest indexed unpaired input and progresses through alternating even and odd indices.
Correct Answer
Based on the general pattern and the final expression for Q :
Option D: