JEE Mains · Maths · STD 12 - 1. relation and function
Let \(A =\{2,3,4,5, \ldots ., 30\}\) and \(^{\prime} \simeq ^{\prime}\) be an equivalence relation on \(A \times A ,\) defined by \((a, b) \simeq (c, d),\) if and only if \(a d=b c .\) Then the number of ordered pairs which satisfy this equivalence relation with ordered pair \((4,3)\) is equal to :
- A \(5\)
- B \(6\)
- C \(8\)
- D \(7\)
Answer & Solution
Correct Answer
(D) \(7\)
Step-by-step Solution
Detailed explanation
\(A =\{2,3,4,5, \ldots ., 30\}\) \((a, b)=(c, d) \quad \Rightarrow \quad a d=b c\) \((4,3)=( c , d ) \quad \Rightarrow \quad 4 d =3 c\) \(\Rightarrow \frac{4}{3}=\frac{c}{d}\) \(\frac{c}{d}=\frac{4}{3}\) and \(c,d\, \in \, \{2,3, \ldots \ldots, 30\}\)…
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