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17/01/2022 2:53 pm
Topic starter
Let Z be the set of all integers,
A = {(x, y) ∈ Z × Z : (x – 2)2 + y2 ≤ 4},
B = {(x, y) ∈ Z × Z : x2 + y2 ≤ 4} and
C = {(x, y) ∈ Z × Z : (x – 2)2 + (y – 2)2 ≤ 4}
If the total number of relation from A ∩ B to A ∩ C is 2p, then the value of p is :
(1) 16
(2) 25
(3) 49
(4) 9
1 Answer
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17/01/2022 2:58 pm
Correct answer: (2) 25
Explanation:
(x – 2)2 + y2 ≤ 4
x2 + y2 ≤ 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 = 25x5 = 225