KVPY SA Exam 2013 Question Paper

Question : 63 of 80

Marks: +1, -0

Let ABCD be a square and let P be a point on segment CD such that DP : PC = 1 : 2 . Let Q be a point on segment AP such that ∠BQP = 90°. Then the ratio of the area of quadrilateral PQBC to the area of the square ABCD is

$31/60$
$37/60$
$39/60$
$41/60$

Validate

Solution:

CP =

2/3a

, PD

= a/3

Let ∠PAD = ϕ, tan ϕ =

1/3

(In ΔAPD)
Now, ∠DAP = ∠QBA = ϕ
Required ratio

=\text" area of PQBC"/a^2

={a^2-\text" (area of ΔADP+area of ΔAQB)"}/a^2

⇒1-(1/6+3/20)=41/60

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