Q101 / 155 · WBJEE 2023 · Mathematics

Let \(\rho\) be a relation defined on set of natural numbers \(\mathbb{N}\), as \(\rho=\{(x, y) \in \mathbb{N} \times \mathbb{N}: 2 x+y=41\}\). Then domain \(A\) and range B are

  • Correct answer
    A
    \(\mathrm{A} \subset\{\mathrm{x} \in \mathbb{N}: 1 \leq \mathrm{x} \leq 20\}\) and \(B \subset\{\mathrm{y} \in \mathbb{N}: 1 \leq \mathrm{y} \leq 39\}\)
  • B
    \(A=\{x \in \mathbb{N}: 1 \leq x \leq 15\}\) and \(B=\{y \in \mathbb{N}: 2 \leq \mathrm{y} \leq 30\}\)
  • C
    \(\mathrm{A} \equiv \mathbb{N}, \mathrm{B} \equiv \mathbb{Q}\)
  • D
    \(A \equiv \mathbb{Q}, B \equiv \mathbb{Q}\)

Solution

\(\begin{aligned} \text {Hint: } & 2 x +y=41 \\ & y=41-2 x \\ \therefore & x=\{1,2,3,4, \ldots .20\} \\ & y=\{1,3,5, \ldots .39\} \end{aligned}\)

Hence, the correct answer is option: 'A'.

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