JEE Main 2021MathematicsHeights and DistancesMediumMCQ

JEE Main 2021 — Heights and Distances Question with Solution

JEE Main 2021 (27 Aug Shift 2)

Question

Two poles AB of length a metres and CD of length a+b(b≠a) metres are erected at the same horizontal level with bases at B and D. If BD=x and tan∠ACB=12, then:

Choose an option

Show full solutionCorrect option: C
Correct answer
Cx2-2ax+b(a+b)=0

Step-by-step explanation

Let ∠ABC=∠BCD=α, ∠ACB=θ 

BD=AE=x

AB=DE=a

From Diagram

tan(θ+α)=xb

tanα=xa+b

tanθ=12

tan(θ+α)=tanθ+tanα1-tanθtanα
12+xa+b1−12⋅xa+b=xb

a+b+2x2(a+b)−x=xb

ab+b2+2bx=2ax+2bx−x2

x2−2ax+ab+b2=0

x2-2ax+b(a+b)=0

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About this question

This is a previous-year question from JEE Main 2021, covering the Heights and Distances 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.