Question:
If the AM and HM of two numbers are 27 and 12 respectively, then what is their GM equal to?
यदि दो संख्याओं के समांतर माध्य (AM) और हरात्मक माध्य (HM) क्रमशः 27 और 12 हैं, तो उनका गुणोत्तर माध्य (GM) किसके बराबर है?
Options:
- 12
- 18
- 24
- 27
- 12
- 18
- 24
- 27
Correct Answer: b)
Explanation:
For any two positive numbers, the relationship between arithmetic mean (AM), geometric mean (GM), and harmonic mean (HM) is:
\[GM^2 = AM \times HM\]
Given \(AM = 27\) and \(HM = 12\):
\[GM^2 = 27 \times 12 = 324 \implies GM = \sqrt{324} = 18\]
Hence, the correct option is (b).
किन्हीं दो संख्याओं के लिए माध्यों में संबंध:
\[GM^2 = AM \times HM\]
\(AM = 27\) तथा \(HM = 12\) रखने पर:
\[GM = \sqrt{27 \times 12} = \sqrt{324} = 18\]
अतः सही विकल्प (b) है।