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If positive quantities a,b,c are in H.P....

If positive quantities `a,b,c` are in `H.P.`, then which of the following is not true ? a. `b gt (a+c)/(2)` b. `(1)/(a-b)-(1)/(b-c) gt 0` c. `ac gt b^(2)` d. none of these

A

`b gt (a+c)/(2)`

B

`(1)/(a-b)-(1)/(b-c) gt 0`

C

`ac gt b^(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `b` is `H.M.` of `a` and `c`
`b lt (a+c)/(2)`
and `b lt sqrt(ac)`
`impliesb^(2) lt ac`
`impliesb-a lt c-b`
`impliesa-b gt b-c`
`implies(1)/(a-b)-(1)/(b-c) lt 0`
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