The GATE Grind

GATE 2022 IN – Question 14

Signals and Systems · Signals and linear time-invariant systems · 1 mark · Multiple choice

The output is related to the input by $y(t)=x(t)\sin(2\pi t)$. This system is ______.

  1. Linear and time-variant
  2. Nonlinear and time-invariant
  3. Linear and time-invariant
  4. Nonlinear and time-variant

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Correct answer: (A) Linear and time-variant

Explanation

Multiplication distributes over weighted sums, satisfying linearity. But delaying the input does not delay the multiplying sin2πt, so the shifted-output test fails.

Thus **linear and time-variant, A**.