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JEE Mains · Maths · STD 11 - 10.1 circle and system of circle

અહી \(Z\) એ બધાજ પૃણાંક નો ગણ છે . \(\mathrm{A}=\left\{(\mathrm{x}, \mathrm{y}) \in \mathbb{Z} \times \mathbb{Z}:(\mathrm{x}-2)^{2}+\mathrm{y}^{2} \leq 4\right\}\) \(\mathrm{B}=\left\{(\mathrm{x}, \mathrm{y}) \in \mathbb{Z} \times \mathbb{Z}: \mathrm{x}^{2}+\mathrm{y}^{2} \leq 4\right\} \) અને \(\mathrm{C}=\left\{(\mathrm{x}, \mathrm{y}) \in \mathbb{Z} \times \mathbb{Z}:(\mathrm{x}-2)^{2}+(\mathrm{y}-2)^{2} \leq 4\right\}\) જો  \(\mathrm{A} \cap \mathrm{B}\) થી  \(\mathrm{A} \cap \mathrm{C}\) કુલ સંબંધની સંખ્યા  \(2^{\mathrm{p}}\) હોય તો \(\mathrm{p}\) ની કિમંત મેળવો.

  1. A \(16\)
  2. B \(25\)
  3. C \(49\)
  4. D \(9\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(25\)

Step-by-step Solution

Detailed explanation

\((x-2)^{2}+y^{2} \leq 4\) \(x^{2}+y^{2} \leq 4\) No. of points common in \(\mathrm{C}_{1} \,\&\, \mathrm{C}_{2}\) is \(5 .\) \((0,0),(1,0),(2,0),(1,1),(1,-1)\) Similarly in \(\mathrm{C}_{2} \& \mathrm{C}_{3}\) is \(5\) No. of relations \(=2^{5 \times 5}=2^{25}\).
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