JEE Main 2024MathematicsLimitsMediumNumerical

JEE Main 2024 — Limits Question with Solution

JEE Main 2024 (29 Jan Shift 2)

Question

Let the slope of the line 45x+5y+3=0 be 27r1+9r22 for some r1,  r2∈R. Then limx→3∫3x8t23r2x2-r2x2-r1x3-3xdt is equal to ______.

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Show full solutionCorrect answer: 12
Correct answer
12

Step-by-step explanation

We know that,

The slope of line 45x+5y+3=0 will be -9

Now, given 27r1+9r22=-9

Now, solving

L=limx→3∫3x8t2dt3r2x2-r2x2-r1x3-3x

Applying Newton Leibnitz Theorem and L'Hospital Rule we get,

⇒L=limx→38x23r22-2r2x-3r1x2-3

⇒L=723r22-6r2-27r1-3

⇒L=72-9r22-27r1-3

Now, using 27r1+9r22=-9 we get,

⇒L=729-3=12

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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.