The harmonic mean of a-1-a b and a-1-a b is -MP PET 1996- Pb- CET 2001-A- aB- a-1-a2 b2C- a-1-a2 b2D- 1-1-a2 b2

The correct option is A aH.M. = 2(a^2/1 a^2b^2 )/a/1 ab+a/1+ab = 2a^2/2a = a. ...

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Standard XI

Mathematics

Harmonic Mean

The harmonic ...

Question

The harmonic mean of $\frac{a}{1 - a b}$ and $\frac{a}{1 + a b}$ is
[MP PET 1996; Pb. CET 2001]

\frac{a}{\sqrt{1 - a^{2} b^{2}}}

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\frac{a}{1 - a^{2} b^{2}}

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\frac{1}{1 - a^{2} b^{2}}

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Solution

The correct option is C a
$H . M . = \frac{2 (\frac{a^{2}}{1 - a^{2} b^{2}})}{\frac{a}{1 - a b} + \frac{a}{1 + a b}} = \frac{2 a^{2}}{2 a} = a .$

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Q. The harmonic mean of

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The harmonic mean of a1−ab and a1+ab is [MP PET 1996; Pb. CET 2001]

The correct option is C aH.M.=2(a21−a2b2)a1−ab+a1+ab=2a22a=a.

The harmonic mean of $\frac{a}{1 - a b}$ and $\frac{a}{1 + a b}$ is
[MP PET 1996; Pb. CET 2001]

The correct option is C a
$H . M . = \frac{2 (\frac{a^{2}}{1 - a^{2} b^{2}})}{\frac{a}{1 - a b} + \frac{a}{1 + a b}} = \frac{2 a^{2}}{2 a} = a .$