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GATE 2026 IN – Question 42

Signals and Systems · Signals and linear time-invariant systems · 2 marks · Multiple choice

List I gives system responses to an input, and List II gives system properties. Choose the correct matching.

List I:

(M) $x^2(t)$; (N) $x(-t)$; (O) $|x(3-t)|$; (P) $x(t-3)$.

List II:

(I) Linear and time-invariant; (II) Nonlinear and time-varying; (III) Linear and time-varying; (IV) Nonlinear and time-invariant.

  1. M–IV, N–III, O–II, P–I
  2. M–II, N–I, O–IV, P–III
  3. M–III, N–IV, O–II, P–I
  4. M–I, N–IV, O–III, P–II

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Show answer and explanation

Correct answer: (A) M–IV, N–III, O–II, P–I

Explanation

Squaring is nonlinear because $(ax)^2\ne ax^2$ in general, but it commutes with time shifts, so M matches IV. Time reversal is linear, but delaying the input produces $x(-t-t_0)$ while delaying the output gives $x(-t+t_0)$; hence N matches III.

The absolute value in O destroys linearity, and its reversed time argument destroys time invariance, so O matches II. A fixed delay preserves superposition and commutes with any further delay, so P matches I.

The correct matching is **A**.