Question

Assertion :If the arithmatic mean of two numbers is 5/2, geometric mean of the numbers is 2, then the harmonic mean will be 8/5 Reason: For a group of positive numbers $(G.M.{)}^2=(A.M.)\times (H.M.)$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

For two positive numbers $(GM{)}^2=(AM)\times (HM)$.

$H,M=\frac{G.M^2}{A.M}$

$H.M=\frac{2^2}{5/2}$

$H.M=\frac{8}{5}$