GATE 2026 EC Q.19: solution and answer

GATE 2026 · ECQ.19 · 1 mark · MCQ

A control system is shown in the Figure.

Which option represents the correct transfer function of the system?

GATE 2026 EC question 19: Block diagram. — Figure from the GATE 2026 EC paper. It is part of the question.

(A)
$\frac{1}{( s + 4 ) ^{2}}$
(B)
$\frac{1}{( s + 4 )}$
(C)
$\frac{2}{( s + 4 )}$
(D)
$\frac{1}{( s ^{2} + 8 s + 17 )}$

Answer and solution

ANSWER

$\frac{C ( s )}{R ( s )} = \frac{1}{( s + 4 )}$ . The answer is option (B).

Official answer: BSource: Official answer key, GATE 2026 EC (IIT Guwahati)

Call the signal leaving the first summing junction $E (s)$ . The top block and the bottom block both take $E (s)$ as input, so the top block gives $C (s) = \frac{E ( s )}{s + 4}$ and the bottom block also gives $\frac{E ( s )}{s + 4}$ .
Summing junction 2 takes $+ C (s)$ and subtracts the bottom-block output, so the feedback signal is $F (s) = C (s) - \frac{E ( s )}{s + 4} = \frac{E ( s )}{s + 4} - \frac{E ( s )}{s + 4} = 0$
Summing junction 1 gives $E (s) = R (s) - F (s) = R (s)$ . The feedback path carries no signal because the two identical branches cancel exactly.
Check with the general reduction. Take $G_{1}$ as the top block and $G_{2}$ as the bottom block. Since $E = C / G_{1}$ , the feedback is $F = C - G_{2} E = C (1 - \frac{G _{2}}{G _{1}})$ , so $H_{eq} = 1 - \frac{G _{2}}{G _{1}}$ and $\frac{C}{R} = \frac{G _{1}}{1 + G _{1} H _{eq}} = \frac{G _{1}}{1 + G _{1} - G _{2}}$ With $G_{1} = G_{2} = \frac{1}{s + 4}$ the denominator is $1$ .
Therefore $\frac{C ( s )}{R ( s )} = \frac{1}{s + 4}$ which is option (B).

KEY IDEA

Work out what signal actually reaches each summing junction before you reach for a reduction formula. Summing junction 2 subtracts two copies of the same signal, $E (s) / (s + 4)$ , so the feedback is exactly zero. The loop is effectively open and $C / R$ is just the forward block $\frac{1}{s + 4}$ .

WATCH OUT FOR

Treating the two $\frac{1}{s + 4}$ blocks as a parallel pair whose outputs add, which gives $\frac{2}{s + 4}$ (option C). Only the top block feeds $C (s)$ . The other common error is using the standard $\frac{G}{1 + G H}$ with $H = \frac{1}{s + 4}$ and ignoring the $+ C$ input at summing junction 2. That misses the cancellation, and the resulting denominator is not in the options.

From the GATE 2026 EC paper. Every question of this paper · Download the full paper · All 10 Block diagrams & SFG questions, with notes

GATE 2026 EC Q.19: solution and answer

Answer and solution

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