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Circle question

2021 · Shift 2 · Q33
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  5. /2021 · Shift 2 · Q33

Circle question

2021 · Shift 2 · Q33

JEE AdvancedMathematicsCircleMCQ+3 / −1
Let M={(x,y)∈R×R:x2+y2≤r2}M = \{ (x,y) \in R \times R:{x^2} + {y^2} \le {r^2}\}M={(x,y)∈R×R:x2+y2≤r2}, where r > 0. Consider the geometric progression an=12n−1{a_n} = {1 \over {{2^{n - 1}}}}an​=2n−11​, n = 1, 2, 3, ...... . Let S0 = 0 and for n ≥\ge≥ 1, let Sn denote the sum of the first n terms of this progression. For n ≥\ge≥ 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.Consider M with r=(2199−1)22198r = {{({2^{199}} - 1)\sqrt 2 } \over {{2^{198}}}}r=2198(2199−1)2​​. The number of all those circles Dn that are inside M is
  1. A
    198
  2. B
    199
  3. C
    200
  4. D
    201
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