यदि \(A=\{1,2,3,4,5,6\}\) और \(B=\{1,2,3,4,5,6\}\) हैं, तो \(A\times B\) में कितने युग्म ((a,b)) ऐसे हैं जिनमें (\gcd(a,b)=2) है?
If \(A=\{1,2,3,4,5,6\}\) and \(B=\{1,2,3,4,5,6\}\), how many pairs ((a,b)) in \(A\times B\) satisfy (\gcd(a,b)=2)?
Explanation opens after your attempt
Correct Answer
C. (7)
Concept
Both numbers must be multiples of (2), and after division the reduced pair must be coprime, giving (7) pairs. Factor out the common divisor in \(\gcd\) questions.
Why this answer is correct
The correct answer is C. (7). Both numbers must be multiples of (2), and after division the reduced pair must be coprime, giving (7) pairs. Factor out the common divisor in \(\gcd\) questions.
Exam Tip
दोनों संख्याएँ (2) से गुणित हों और भाग देने पर परस्पर अभाज्य रहें, ऐसे (7) युग्म हैं। \(\gcd\) प्रश्न में सामान्य गुणनखंड निकालें।
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