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Official PYQ · 2026

GATE EC 2026 Set 1 Q33 — Continuous-time Signals

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Consider a real signal x(t),−∞<t<∞x(t),-\infty < t < \infty, such that

x(t)=0fort<0,x(t)=2for0≤t<1andx(t)=0fort≥1x(t) = 0\quad\text{for}\quad t <0, x(t) =2 \quad\text{for} \quad0 \leq t < 1\quad \text{and}\quad x(t) = 0\quad \text{for} \quad t \geq 1.

Let E[x(t)]=∫−∞∞[x(t)]2dtE[x(t)]=\int_{-\infty}^{\infty}[x(t)]^{2} d t.

Which of the following options correctly represents the ratio, E[x(t)]/E[3x(−3t+5)]?E[x(t)] / E[3 x(-3 t+5)] ?

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Answer: C

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