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The least value of a in RR for which 4a...

The least value of `a in RR` for which `4ax^2+1/x >= 1`, for all `x > 0`, is

A

`(1)/(64)`

B

`(1)/(32)`

C

`(1)/(27)`

D

`(1)/(25)`

Text Solution

Verified by Experts

The correct Answer is:
C
Using A.M.`ge` G.M.
`(4ax^2+(1)/(2x)+(1)/(2x))/(3)ge 3sqrt(4ax^2.(1)/(4x^2))`
`rArr 4ax^2+(1)/(x)ge3 3sqrt(alpha)`
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Knowledge Check

  • The least value of a in RR " for which " 4ax^(2)+(1)/(x)ge1 " for all" xgt0 , is

    A
    `(1)/(64)`
    B
    `(1)/(32)`
    C
    `(1)/(27)`
    D
    `(1)/(25)`

  • The set of values of 'a' for which x^2-ax+sin^-1(sin4)gt0 forallx in R is

    A
    R
    B
    (-2,2)
    C
    `phi`
    D
    none of these

  • The value of 'a' for which ax^2 + sin^-1 (x^2 - 2x + 2) + cos^-1 (x^2 - 2x + 2) = 0 has a real solution is

    A
    `-2/pi`
    B
    `2/pi`
    C
    `-pi/2`
    D
    `pi/2`

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