JEE Mains · Maths · STD 11 - 8. sequence and series
For three positive integers \(p , q , r , x ^{ pq p ^2}= y ^{ qr }= z ^{ p ^2 r }\) and \(r=p q+1\) such that \(3,3 \log _y x, 3 \log _z y, 7 \log _x z\) are in A.P. with common difference \(\frac{1}{2}\). Then \(r - p - q\) is equal to
- A \(2\)
- B \(6\)
- C \(12\)
- D \(-6\)
Answer & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
\(pq ^2=\log _{ x } \lambda\) \(qr =\log _{ y } \lambda\) \(p ^2 r =\log _{ z } \lambda\) \(\log _{ y } x =\frac{ qr }{ pq ^2}=\frac{ r }{ pq } \ldots(1)\) \(\log _{ x } z =\frac{ pq ^2}{ p ^2 r }=\frac{ q ^2}{ pr } \ldots(2)\)…
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