First slide

Introduction to sets

Question

The number of elements in the set $\{(a, b) : 2 a^{2} + 3 b^{2} = 35, a, b \in Z\},$ where Z is the set of all integers, is

Easy

A

2
B

4
C

8
D

12

Solution

Given set is $\{(a, b) : 2 a^{2} + 3 b^{2} = 35, a, b \in Z\}$
We can see that, $2 {(\pm 2)}^{2} + 3 {(\pm 3)}^{2} = 35$
and $2 {(\pm 4)}^{2} + 3 {(\pm 1)}^{2} = 35$
$∴ (2, 3), (2, - 3), (- 2, - 3), (- 2, 3), (4, 1), (4, - 1),$
$(- 4, - 1), (- 4, 1)$ are 8 elements of the set, $∴ n = 8 .$

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