WBJEE 2023 Math Solved Paper

Question : 75 of 75

Marks: +1, -0

Which of the following statements are true?

If f(x) be continuous and periodic with periodicity T, then I=
a+T
∫
a
f(x)‌dx depend on 'a'.
If f(x) be continuous and periodic with periodicity T, then I=
a+T
∫
a
f(x)‌dx does not depend on 'a'.
Let f(x)={
1 ‌ if x is rational ‌
0 ‌ if ‌x‌ is irrational ‌
, then f is periodic of the periodicity T only if T is rational.
f defined in (C) is periodic for all T.

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1	‌ if x is rational ‌
0	‌ if ‌x‌ is irrational ‌