Xavier Aptitude Test 2011 Paper

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Question : 55 of 101

Marks: +1, -0

The domain of the function f(x) =

log_7

{

log_3

(log_5

(20x – x

^{2}

–91))} is:

(7, 13)
(8, 12)
(7, 12)
(12, 13)
None of the above

Solution:

(b)

f(x)=\log _{7} \log _{3} \log _{5}\ (20 x-x^{2}-91\ )

The above equation would be true if

f(x)

is defined and for that it has to be greater than zero.

\⇒ \log _{3} \log _{5} (20 x-x^{2}-91 )>0

\⇒ \log _{5}\ (20 x-x^{2}-91\ )>1

\⇒(20 x-x^{2}-91\ )>5

\⇒ x^{2}-20 x+96<0

$\⇒(x-8)(x-12)<0 \⇒ 8

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