QJEEM21Ma6711: JEE Main 2021 Mathematics - Class 11 JEEM21Ma6711 Solution: Let Z be the set of all integers, If the total number of…

Question

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Let Z be the set of all integers,

A = \{ (x,y) \in Z \times Z:{(x - 2)^2} + {y^2} \le 4\}

B = \{ (x,y) \in Z \times Z:{x^2} + {y^2} \le 4\}

C = \{ (x,y) \in Z \times Z:{(x - 2)^2} + {(y - 2)^2} \le 4\}

If the total number of relation from A

\cap

B to A

\cap

C is 2^p, then the value of p is :

Accepted Answer

(x

-

2)² + y²

\le

4

x² + y²

\le

4

No. of points common in C₁ & C₂ is 5.

(0, 0), (1, 0), (2, 0), (1, 1), (1,

-

1)

Similarly in C₂ & C₃ is 5.

No. of relations = 2^{$5 \times 5$} = 2²⁵.

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