Q87 / 180 · KCET 2023 · Mathematics

Let the relation $R$ be defined in $N$ by $a R b$, if $3 a+2 b=27$, then $R$ is

  • A
    $\left\{\left(0, \frac{27}{2}\right),(1,12),(3,9),(5,6),(7,3)\right\}$
  • B
    $\{(1,12),(3,9),(5,6),(7,3),(9,0)\}$
  • C
    $\{(2,1),(9,3),(6,5),(3,7)\}$
  • Correct answer
    D
    $\{(1,12),(3,9),(5,6),(7,3)\}$

Solution

Given that $3 a+2 b=27$ $\begin{array}{ll}\Rightarrow & 2 b=27-3 a \\ \Rightarrow & b=\frac{27-3 a}{2}\end{array}$ For $a=1, b=12$ $\begin{aligned} & a=3, b=9 \\ & a=5, b=6 \\ & a=7, b=3 \\ & R=\{(1,12),(3,9),(5,6),(7,3)\} \\ & \end{aligned}$

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

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