CUET · MATHS · PYQ PAPER 2023
If \(R=\left\{(x, y) \mid x, y \in Z , x^2+y^2 \leq 4\right\}\) is a relation in \(Z\), then domain of \(R\) is :
- A \(\{0,1,2\}\)
- B \(\{0,-1,-2\}\)
- C \(\{-2,-1,0,1,2\}\)
- D \(\{-1,0,2\}\)
Answer & Solution
Correct Answer
(C) \(\{-2,-1,0,1,2\}\)
Step-by-step Solution
Detailed explanation
\(x, y \in Z, x^2+y^2 \leq 4\) \(x^2 \leq 4 - y^2\) Since \(y^2 \geq 0\), \(x^2 \leq 4\) \(-2 \leq x \leq 2\) As \(x \in Z\), \(x \in \{-2, -1, 0, 1, 2\}\) For each \(x\), there exists \(y=0 \in Z\) such that \(x^2+0^2 \leq 4\) is satisfied since \(x^2 \leq 4\). Domain of…
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