JEE Main 2021MathematicsDefinite IntegrationProperties Of Definite IntegrationmediumMCQ

JEE Main 2021Definite Integration Question with Solution

From: JEE Main 2021 (Online) 24th February Evening Shift

Question

Let f(x) be a differentiable function defined on [0, 2] such that f'(x) = f'(2 x) for all x (0, 2), f(0) = 1 and f(2) = e2. Then the value of is :

Choose an option

Show full solutionCorrect option: A
Correct answer
A1 + e2

Step-by-step explanation

f'(x) = f'(2 x)

On integrating both side f(x) = f(2 x) + c

put x = 0

f(0) + f(2) = c c = 1 + e2

f(x) + f(2 x) = 1 + e2 ..... (i)

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About this question

This is a previous-year question from JEE Main 2021, covering the Definite Integration chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.