JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Let \(Z\) be the set of all integers, \(\mathrm{A}=\left\{(\mathrm{x}, \mathrm{y}) \in \mathbb{Z} \times \mathbb{Z}:(\mathrm{x}-2)^{2}+\mathrm{y}^{2} \leq 4\right\}\) \(\mathrm{B}=\left\{(\mathrm{x}, \mathrm{y}) \in \mathbb{Z} \times \mathbb{Z}: \mathrm{x}^{2}+\mathrm{y}^{2} \leq 4\right\} \text { and }\) \(\mathrm{C}=\left\{(\mathrm{x}, \mathrm{y}) \in \mathbb{Z} \times \mathbb{Z}:(\mathrm{x}-2)^{2}+(\mathrm{y}-2)^{2} \leq 4\right\}\) If the total number of relation from \(\mathrm{A} \cap \mathrm{B}\) to \(\mathrm{A} \cap \mathrm{C}\) is \(2^{\mathrm{p}}\), then the value of \(\mathrm{p}\) is :
- A \(16\)
- B \(25\)
- C \(49\)
- D \(9\)
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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