Home
Class 12
MATHS
If A.M. = 24.5, G.M. = 24.375 then H.M. ...

If A.M. = 24.5, G.M. = 24.375 then H.M. =

A

24

B

24.125

C

24.5

D

24.25

Text Solution

AI Generated Solution

The correct Answer is:
To find the Harmonic Mean (H.M.) given the Arithmetic Mean (A.M.) and Geometric Mean (G.M.), we can use the relationship between these means. The formula for H.M. in terms of A.M. and G.M. is: \[ H.M. = \frac{G.M.^2}{A.M.} \] ### Step-by-Step Solution: 1. **Identify the given values**: - A.M. = 24.5 - G.M. = 24.375 2. **Calculate G.M. squared**: \[ G.M.^2 = (24.375)^2 \] \[ G.M.^2 = 24.375 \times 24.375 = 594.140625 \] 3. **Use the formula to calculate H.M.**: \[ H.M. = \frac{G.M.^2}{A.M.} = \frac{594.140625}{24.5} \] 4. **Perform the division**: \[ H.M. = \frac{594.140625}{24.5} \approx 24.25 \] 5. **Conclusion**: The Harmonic Mean (H.M.) is approximately 24.25. ### Final Answer: H.M. = 24.25 ---
Promotional Banner

Similar Questions

Explore conceptually related problems

If H.M. of two number is 4 , then A.M. 'A' and G.M. 'G' satisfy the relation 2A + G^(2) = 27 , then modulus of difference of these two numbers is

If A.M., G.M., and H.M. of the first and last terms of the series of 100 , 101 , 102 ,...(n-1),n are the terms of the series itself, then the value of n is (100ltnlt500)

If 3 arithmetic means, 3 geometric means and 3 harmonic means are inserted between 1 and 5, then the cubic equation whose roots are first A.M., second G.M. and third H.M. between 1 and 5, is

If A.M., G.M., and H.M. of the first and last terms of the series of 100 , 101 , 102 ,...n-1,n are the terms of the series itself, then the value of ni s(100

If the A.M. between two numbers exceeds their G.M. by 2 and the GM. Exceeds their H.M. by 8/5, find the numbers.

Length of a minute hand of a clock is 4.5 cm. Find the average velocity of the tip of minute's hand between 6 A.M. to 6.30 A.M. & 6 A.M. to 6.30 P.M.

A body covers 4.9m, 14.7 m, 24.5 m and 34.3m in the successive seconds of motion. The acceleration of the body is

If x,y,z be three numbers in G.P. such that 4 is the A.M. between x and y and 9 is the H.M. between y and z , then y is

If A, G & H are respectively the A.M., G.M. & H.M. of three positive numbers a, b, & c, then equation whose roots are a, b, & c is given by

If A, G & H are respectively the A.M., G.M. & H.M. of three positive numbers a, b, & c, then equation whose roots are a, b, & c is given by