if ${1 \over {10}}:{1 \over a} = {1 \over a}:{1 \over 1},$ ,110:1a=1a:11,then value of a is

if ${1 \over {10}}:{1 \over a} = {1 \over a}:{1 \over 1},$ $\frac{1}{10} : \frac{1}{a} = \frac{1}{a} : \frac{1}{1},$ then value of a is

A $\sqrt 5$

B $\sqrt {10}$

C $2\sqrt 3$

D 5

E 10

Solution

Correct Answer: Option B

Given that,

$\eqalign{ & {{{1 \over {10}}} \over {{1 \over a}}} = {{{1 \over a}} \over 1} \cr & \Rightarrow {a \over {10}} = {1 \over a} \cr & \Rightarrow {a^2} = 10 \cr & \Rightarrow a = \sqrt {10} \cr}$

Solution

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