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JEE Advanced
Exam
JEE Advanced
Subject
Mathematics
Chapter
Sets and Relations

JEE Advanced · Mathematics · Sets and Relations

The number of elements in the set \ (a, b): a ^ 2 + b ^ 2 = 50; a,...

The number of elements in the set {(a,b):a2+b2=50;a,b∈Z}\left\{\left(a, b\right): {a}^{2} + {b}^{2} = 50; a, b \in Z\right\}, where ZZ is the set of all integers, is

Correct answer

12

Step-by-step solution

a2+b2=50{a}^{2} + {b}^{2} = 50
a=1⇒b2=49a = 1 ⇒ {b}^{2} = 49
⇒b=±7⇒ b = \pm 7
a=2,3,4,6a = 2, 3, 4, 6 do not give integer value of bb .
a=5⇒b2=25⇒b=±5a = 5 ⇒ {b}^{2} = 25 ⇒ b = \pm 5
a=7⇒b2=1a = 7 ⇒ {b}^{2} = 1
⇒b=±1⇒ b = \pm 1
Similarly,
a=−1⇒b=±7a = - 1 ⇒ b = \pm 7
a=−5⇒b=±5a = - 5 ⇒ b = \pm 5
a=−7→b=±1a = - 7 \to b = \pm 1
⇒⇒ The required number of elements (a,b)=12( a, b ) = 12
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