GATE 2017 EC (EC2) – Question 28

For the system shown in the figure, $Y(s)/X(s)=$ ________.

Show answer and explanation

Correct answer: 0.95 to 1.05

Explanation

The first summing junction forms $E=X-Y$ because the output feedback enters with a minus sign. The gain block produces $2E$.

At the second junction, the direct input X is added to that block output: $Y=2(X-Y)+X$. Collecting terms gives $3Y=3X$.

Hence **$Y/X=1$**, within the official interval 0.95–1.05.

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