JEE Main 2020MathematicsArea Under CurvesMediumMCQ

JEE Main 2020 — Area Under Curves Question with Solution

JEE Main 2020 (02 Sep Shift 2)

Question

Consider a region R=x, y∈R2:x2≤y≤2x. If a line y=α divides the area of region R into two equal parts, then which of the following is true ?

Choose an option

Show full solutionCorrect option: B
Correct answer
B3α2-8α3/2+8=0

Step-by-step explanation

 

∫04y-y2dy=2∫0αy-y2dy

2y3/23-y2204=22y3/23-y240α

⇒163-4=223α3/2-α24

⇒  43=223α3/2-α24

⇒  23=8α3/2-3α212

⇒  8α3/2-3α2=8

⇒3α2-8α3/2+8=0

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About this question

This is a previous-year question from JEE Main 2020, covering the Area Under Curves 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.