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If a, b, c,d positive distinct number ...

If a, b, c,d positive distinct number are in H.P., them :

A

`ab gt cd`

B

`ac gt bd`

C

`ad gt bc`

D

None of these

Text Solution

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The correct Answer is:
3
a,b,c are in H.P
`(a,b,c gt0)`
`rArr` G.M of a and `cgt H.M` of a and c
`rArrsqrt(ac) gt b`
`rArr ac gt a^(2)" "(i)`
Also b,c,d are in H.P . `(b,c,d gt0)`
G.M. of b,d gt H.M. of b,d
`sqrt(bd) gtc`
`bd gt c^(2)" "......(2)`
multiply(1) and (2)
`abcd gt b^(2) c^(3)`
`rArr ad gt bc`
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