QJEEM21Ma8ef7: JEE Main 2021 Mathematics - Class 11 JEEM21Ma8ef7 Solution: A possible value of 'x', for which the ninth term in the…

Question

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A possible value of 'x', for which the ninth term in the expansion of

{3^{\log_{3} \sqrt{25^{x - 1} + 7}} + 3^{(- \frac{1}{8}) \log_{3} (5^{x - 1} + 1)}}^{10}

in the increasing powers of

3^{(- \frac{1}{8}) \log_{3} (5^{x - 1} + 1)}

is equal to 180, is :

Accepted Answer

^{10} C_{8} (25^{(x - 1)} + 7) \times (5^{(x - 1)} + 1)^{- 1} = 180

\Rightarrow \frac{25^{x - 1} + 7}{5^{(x - 1)} + 1} = 4

\Rightarrow \frac{t^{2} + 7}{t + 1} = 4

;

\Rightarrow

t = 1, 3 = 5^{x $-$ 1}

\Rightarrow

x

-

1 = 0 (one of the possible value).

\Rightarrow

x = 1

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