Previous Year Question
Given the following statementsStatement 1:Convolution of an odd and an even function is an odd function.Statement 2:Convolution of two odd or two even functions is an even function.Choose the correct option for the above statements
Correct answer: D
Explanation
Convolution preserves parity according to the same even/odd combination rules: even*even is even, odd*odd is even, and odd*even is odd. Therefore both statements are true, giving option D.
Formula
E*E→E; O*O→E; E*O→O
Step-by-step solution
Correct Answer
D — Both statements 1 and 2 are true
Statement-wise Analysis
Statement 1: True
Statement 2: True
Concept and Reasoning
Convolution preserves parity according to the same even/odd combination rules: even*even is even, odd*odd is even, and odd*even is odd. Therefore both statements are true, giving option D.
Calculation / Key Relation
E*E→E
O*O→E
E*O→O
Exam Takeaway
Two same parities give even; mixed parities give odd.
Common Mistake
Do not assume odd convolved with odd remains odd.
Common mistake
Do not assume odd convolved with odd remains odd.
Exam tip
Two same parities give even; mixed parities give odd.
Quick method
Two same parities give even; mixed parities give odd.