JEE Main 2022MathematicsStraight LinesMediumMCQ

JEE Main 2022 — Straight Lines Question with Solution

JEE Main 2022 (27 Jun Shift 1)

Question

In an isosceles triangle ABC, the vertex A is 6,1 and the equation of the base BC is 2x+y=4. Let the point B lie on the line x+3y=7. If α,β is the centroid ∆ABC, then 15α+β is equal to

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Show full solutionCorrect option: A
Correct answer
A51

Step-by-step explanation

In △ABC, AB=AC

Solving 2x+y=4 & x+3y=7, we get 

B≡1,2

Let C≡h,k and as it lies on 2x+y=4

so 2h+k=4

Now, AB2=AC2

26=(h-6)2+k-12⇒26=h-62+3-2h2

⇒26=5h2-24h+45 ⇒h-15h-19=0

⇒h=195    (as h=1rejected)

so k=-185

Hence, centroid =6+1+1953,1+2-1853≡185,-15

i.e. 15α+β=15×175=51

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About this question

This is a previous-year question from JEE Main 2022, covering the Straight Lines 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.