JEE Main 2013MathematicsHeights and DistancesMediumMCQ

JEE Main 2013 — Heights and Distances Question with Solution

JEE Main 2013 (07 Apr)

Question

ABCD is a trapezium such that AB and CD are parallel and BC⊥CD. If ∠ADB=θ, BC=p and CD=q, then AB is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
Cp2+q2sinθpcosθ+qsinθ

Step-by-step explanation

Let ∠BDC=α, then

tanα=BCCD=pq

AE=BC=p

tanα+θ=AEED

⇒ED=ptanα+θ

=p1-tanαtanθtanα+tanθ

=p1-pqtanθpq+tanθ

Now, AB=q-ED

=q-pq-ptanθpq+qtanθ

=pq+q2tanθ-pq+p2tanθp+qtanθ

=p2+q2tanθp+qtanθ

=p2+q2sinθpcosθ+qsinθ

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About this question

This is a previous-year question from JEE Main 2013, 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.