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JEE Main 20202 SeptemberMorning Shift
Exam
JEE Main
Year
2020
Date
2 September
Shift
Morning Shift
Subject
Mathematics
Chapter
Sets and Relations

JEE Main 2020 · 2 September · Morning Shift · Mathematics · Sets and Relations

If R = \ (x, y): x, y ∈ Z, x ^ 2 + 3 y ^ 2 ≤ 8\ is a relation on...

If R={(x,y):x,y∈Z,x2+3y2≤8}R = \left\{\left(x, y\right): x, y \in Z, {x}^{2} + 3{y}^{2} \le 8\right\} is a relation on the set of integers ZZ, then the domain of R−1{R}^{- 1} isIf R = \ (x, y): x, y ∈ Z, x ^ 2 + 3 y ^ 2 ≤ 8\ is a relation on the set of integers Z , then the domain of R ^ - 1 is

Options

  1. A{−2,−1,1,2}\left\{- 2, - 1, 1, 2\right\}
  2. B{0,1}\left\{0, 1\right\}
  3. C{−2,−1,0,1,2}\left\{- 2, - 1, 0, 1, 2\right\}
  4. D{−1,0,1}\left\{- 1, 0, 1\right\}

Correct answer

D. {−1,0,1}\left\{- 1, 0, 1\right\}

Step-by-step solution

Given x28+y283≤1;x,y∈Z\dfrac{{x}^{2}}{8} + \dfrac{{y}^{2}}{\dfrac{8}{3}} \le 1; x, y \in Z

If R = \ (x, y): x, y ∈ Z, x ^ 2 + 3 y ^ 2 ≤ 8\ is a relation on the set of integers Z , then the domain of R ^ - 1 is

Domain of R−1={R}^{- 1} = Range of RR is possible integral y−y -coordinates

={−1,0,1}= \left\{- 1, 0, 1\right\}

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