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Question: Answered & Verified by Expert
Let the relation $R$ is defined in $N$ by $a R b$, if $3 a+2 b=27$ then $R$ is
MathematicsSets and RelationsJEE Main
Options:
  • A $\{(1,12)(3,9)(5,6)(7,3)\}$
  • B $\left\{\left(0, \frac{27}{2}\right)(1,12)(3,9)(5,6)(7,3)\right\}$
  • C $\{(1,12)(3,9)(5,6)(7,3)(9,0)\}$
  • D $\{(2,1)(9,3)(6,5)(3,7)\}$
Solution:
2320 Upvotes Verified Answer
The correct answer is: $\{(1,12)(3,9)(5,6)(7,3)\}$
Given relation is $3 a+2 b=27$, where $a, b \in N$
$$
\begin{aligned}
& 3 a+2 b=27 \\
& \Rightarrow \quad b=\frac{27-3 a}{2} \\
& a=1 \Rightarrow b=\frac{27-3}{2}=\frac{24}{2}=12 \\
& a=3 \Rightarrow b=\frac{27-9}{2}=\frac{18}{2}=9 \\
& a=5 \Rightarrow b=\frac{27-15}{2}=\frac{12}{2}=6 \\
& a=7 \Rightarrow b=\frac{27-21}{2}=\frac{6}{2}=3
\end{aligned}
$$
Hence, we can see that all the elements of option (a) satisfies the given relation. Hence, option (a) is correct.

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