A possible value of 'x', for which the ninth term in the expansion of … in the increasing powers of … is equal to 180, is :

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Binomial Theorem

JEE Main 2021 · 27 Jul, Evening shift · Q2932

MathematicsMedium64×since 2002Q2932

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

{\left\{ {{3^{{{\log }_3}\sqrt {{{25}^{x - 1}} + 7} }} + {3^{\left( { - {1 \over 8}} \right){{\log }_3}({5^{x - 1}} + 1)}}} \right\}^{10}}

in the increasing powers of

{3^{\left( { - {1 \over 8}} \right){{\log }_3}({5^{x - 1}} + 1)}}

is equal to 180, is :

JEE Main 2021 · 27 Jul, Evening shift · Q2932

MathematicsMedium64×since 2002Q2932

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

{\left\{ {{3^{{{\log }_3}\sqrt {{{25}^{x - 1}} + 7} }} + {3^{\left( { - {1 \over 8}} \right){{\log }_3}({5^{x - 1}} + 1)}}} \right\}^{10}}

in the increasing powers of

{3^{\left( { - {1 \over 8}} \right){{\log }_3}({5^{x - 1}} + 1)}}

is equal to 180, is :