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JEE Advanced 2021 Paper 2

Question Stem for Question Nos. 51 and 52

Let M={(x,y)∈ℝ×ℝ:x2+y2≤r2} where r>0.
Consider the geometric progression an=‌

2n−1

,n=1,2,3,....
Let S0=0 and, for n≥1, let Sn denote the sum of the first n terms of this progression. For n≥1, let Cn denote the circle with center (Sn−1,0) and radius an, and Dn denote the circle with center (Sn −1,Sn−1 ) and radius an.

Question : 51

Total: 57

Consider M with r=‌

1025

513

. Let k be the number of all those circles Cn that are inside M. Let l be the maximum possible number of circles among these k circles such that no two circles intersect. Then

k+2l=22
2k+l=26
2k+3l=34
3k+2l=40

Validate

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