KVPY SA Exam 2016 Question Paper

Question : 64 of 80

Marks: +1, -0

Let

S_1

be the sum of areas of the squares whose sides are parallel to coordinate axes. Let

S_2

be the sum of areas of the slanted squares as shown in the figure. Then

S_1 / S_2

Solution:

S_1=a^2+a^2/4+a^2/16+...∞

=a^2/{1-1/4}={4a^2}/3

S_2=a^2/2+a^2/8+a^2/32+...∞

={a^2/2}/{1-1/4}={4a^2}/6

∴S_1/S_2=2

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