Doubts
Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents
Sign in to save progress →
Doubts
Sign in

Circle question

2021 · Shift 2 · Q32
Guest · try one question or challengeGuest · try one question or challenge
  1. PYQ Library
  2. /JEE Advanced
  3. /Mathematics
  4. /Circle
  5. /2021 · Shift 2 · Q32

Circle question

2021 · Shift 2 · Q32

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=1025513r = {{1025} \over {513}}r=5131025​. 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
  1. A
    k + 2l = 22
  2. B
    2k + l = 26
  3. C
    2k + 3l = 34
  4. D
    3k + 2l = 40
PreviousNext

More from Circle

  • Let M={(x,y)∈R×R:x2+y2≤r2}, where r > 0. Consider the geometric progression an​=2n−11​, n = 1, 2, 3, ...... . Let S0 = 0 and for n ≥ 1, let Sn denote the sum of the first n…2021 · MCQ
  • Let O be the centre of the circle x2 + y2 = r2, where r>25​​. Suppose PQ is a chord of this circle and the equation of the line passing through P and Q is 2x + 4y = 5. If the centre of the circumcircle of the triangle…2020 · Numerical
  • A line y = mx + 1 intersects the circle (x−3)2+(y+2)2= 25 at the points P and Q. If the midpoint of the line segment PQ has x-coordinate −53​, then which one of the following options is correct?2019 · MCQ
  • Let the point B be the reflection of the point A(2, 3) with respect to the line 8x−6y−23=0. Let ΓA​ and ΓB​ be circles of radii 2 and 1 with centres A and B respectively. Let T be a common tangent to the circles ΓA​…2019 · Numerical
  • Let S be the circle in the XY-plane defined the equation x2 + y2 = 4. Let E1E2 and F1F2 be the chords of S passing through the point P0 (1, 1) and parallel to the X-axis and the Y-axis, respectively. Let G1G2 be the chord of S passing…2018 · MCQ
  • Let RS be the diameter of the circle x2+y2=1, where S is the point (1, 0). Let P be a variable point (other than R and S) on the circle and tangents to the circle at S and P meet at the point Q. The normal to the circle at…2016 · Multiple correct
  • A circle S passes through the point (0, 1) and is orthogonal to the circles (x−1)2+y2=16andx2+y2=1. Then2014 · Multiple correct
  • Circle (s) touching x-axis at a distance 3 from the origin and having an intercept of length 27​ on y-axis is (are)2013 · Multiple correct