Correct AnswerC. If the equation x (t) = x (t + T) is satisfied for no values of T
Quick Explanation
A continuous-time signal is periodic only if there exists at least one finite positive T such that x(t+T)=x(t) for all t. If no positive finite T satisfies that condition, the signal is non-periodic (aperiodic).
Detailed Explanation
Concept & Reasoning
The period condition must hold for every time t, but only one positive fundamental period needs to exist; integer multiples of it are also periods. Therefore the phrase 'no values of T' should be interpreted as no non-zero finite positive period.
How to Solve It in the Exam
Existence of one positive period is enough.
Important Exam PointDo not mistake 'for all t' (time variable) with 'for all T' (candidate period).
Related Revision Path
This question sits in the revision path Signals and Systems → Signal Classification → Periodic and Aperiodic Signals .
