JEE Main 2024MathematicsLimitsEasyMCQ

JEE Main 2024 — Limits Question with Solution

JEE Main 2024 (30 Jan Shift 1)

Question

Let f:-π2,π2→R be a differentiable function such that f0=12, If limx→0x∫0xf(t)dtex2-1=α, then 8α2 is equal to :

Choose an option

Show full solutionCorrect option: B
Correct answer
B2

Step-by-step explanation

Let, y=limx→0x∫0xf(t)dtex2-1

⇒y=limx→0x∫0xf(t)dtex2-1x2×x2

We know that, limx→0ex2-1x2=1

⇒y=limx→0∫0xf(t)dtx  

Applying L-hospital's rule and Newton Leibnitz Theorem we get,

⇒y=limx→0f(x)1

⇒y=f0

It is given that, f(0)=12

⇒y=12

⇒α=12

⇒8α2=2

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About this question

This is a previous-year question from JEE Main 2024, covering the Limits 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.