JEE MAIN - Mathematics (2021 - 27th August Evening Shift - No. 9)
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 2p, then the value of p is :
$$A = \{ (x,y) \in Z \times Z:{(x - 2)^2} + {y^2} \le 4\} $$
$$B = \{ (x,y) \in Z \times Z:{x^2} + {y^2} \le 4\} $$
$$C = \{ (x,y) \in Z \times Z:{(x - 2)^2} + {(y - 2)^2} \le 4\} $$
If the total number of relation from A $$\cap$$ B to A $$\cap$$ C is 2p, then the value of p is :
16
25
49
9
Explanation
_27th_August_Evening_Shift_en_9_2.png)
(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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