JEE Main 2022MathematicsHeights and DistancesHardMCQ

JEE Main 2022 — Heights and Distances Question with Solution

JEE Main 2022 (27 Jul Shift 2)

Question

The angle of elevation of the top P of a vertical tower PQ of height 10 from a point A on the horizontal ground is 45°. Let R be a point on AQ and from a point B, vertically above R, the angle of elevation of P is 60°. If ∠BAQ=30°,AB=d and the area of the trapezium PQRB is α, then the ordered pair d,α is

Choose an option

Show full solutionCorrect option: A
Correct answer
A103-1,25

Step-by-step explanation

As per the given information, the figure would be 

Here, 

RA=dcos30°=3 d2

QR=AQA-RA=10-3 d2

BR=dsin30°=d2

Now tan60°=10-BRQR=10-d210-3 d2

⇒3=20-d20-3d

⇒203-3d=20-d

⇒2d=203-1

⇒d=103-1

Now artrap PQRB=12PQ+BRQR

=1210+d210-3d2

=1210+53-510-15+53

=1253+553-5=1275-25=25

i.e. α=25

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About this question

This is a previous-year question from JEE Main 2022, 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.