MP Board · Class 11 · Mathematics · Relations and FunctionsLet $A = \{1, 2, 3, ..., 14\}$. Define a relation $R$ from $A$ to $A$ by $R = \{(x, y) : 3x - y = 0$, where $x, y \in A\}$. The range of $R$ is:
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Total Attempts: 3
Accuracy Rate: 33.3%
Step-by-Step Solution
Given $3x - y = 0 \implies y = 3x$. For $x \in A$, we substitute values: if $x=1, y=3$; if $x=2, y=6$; if $x=3, y=9$; if $x=4, y=12$. For $x=5, y=15$ which is not in $A$. Thus $R = {(1,3), (2,6), (3,9), (4,12)}$. The range is the set of all second elements: ${3, 6, 9, 12}$. Option B is correct.
Detailed Options Breakdown
Option : {1, 2, 3, 4}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Relations and Functions.
Option 1: {3, 6, 9, 12} (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: {3, 6, 9, 12, 15}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Relations and Functions.
Option 3: {1, 2, 3, ..., 14}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Relations and Functions.
💡 Study Guide: This question tests core syllabus concepts from Relations and Functions. For formulas, key summaries, and mock exam reference guides, read the full Relations and Functions Revision Notes.