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GATE EC 2026 Set 1 — Question 43

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MCQ+2 / -0.67EasyEnergy & Power SignalsContinuous-Time SignalsSignals & SystemsShifting, Convolution & Modulation

Signals & Systems → Continuous-Time Signals → Energy & Power Signals

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Question

Consider a real signal x(t)x(t), −∞<t<∞-\infty < t < \infty, such that x(t)=0x(t) = 0 for t<0t < 0, x(t)=2x(t) = 2 for 0≤t<10 \leq t < 1 and x(t)=0x(t) = 0 for t≥1t \geq 1.
Let E[x(t)]=∫−∞∞[x(t)]2dtE[x(t)] = \int_{-\infty}^{\infty} [x(t)]^2 dt.
Which of the following options correctly represents the ratio,
E[x(t)]/E[3x(−3t+5)]E[x(t)] / E[3 x(-3t + 5)]?
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