Q172 / 270 · NDA 2023 (Phase 2) · Mathematics

Let $\mathrm{A}=\{1,2,3, \ldots 20\}$. Define a relation R from A to A by $\mathrm{R}=\{(x, y): 4 x-3 y=1\}$, where $x, y \in \mathrm{~A}$. Which of the following statements is/are correct? 1. The domain of R is {1, 4, 7, 10, 13, 16}. 2. The range of R is {1, 5, 9, 13, 17}. 3. 3. The range of R is equal to codomain of R. Select the correct answer using the code given below:

  • A
    1 only
  • Correct answer
    B
    2 only
  • C
    1 and 2
  • D
    2 and 3

Solution

$\begin{aligned} \text { } & \text { Since, } \mathrm{R}=\{(\mathrm{x}, \mathrm{y}): 4 \mathrm{x}-3 \mathrm{y}=1\} \\ & \text {Now, } 4 \mathrm{x}-3 \mathrm{y}=1 \\ \Rightarrow & \mathrm{x}=\frac{1+3 \mathrm{y}}{4} \\ & \text {So, } \mathrm{R}=\{(1,1),(4,5),(7,9),(10,13)(13,17)\} \\ \because & \text { Domain of } \mathrm{R}=\{1,4,7,10,13\} \\ & \text {Range of } \mathrm{R}=\{1,5,9,13,17\}\end{aligned}$

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

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