A possible value of 'x', for which the ninth term in the expansion of 3^(log ₃√(25ˣ⁻¹ + 7)) + 3^((- 1/8) log ₃(5ˣ⁻¹ + 1)) \¹⁰ in the increasing powers of 3^((- 1/8) log ₃(5ˣ⁻¹ + 1)) is equal to 180, is:

Binomial Theorem and Its Simple Applications: JEE Main 2021 Mathematics question

JEE Main 2021 · 27 Jul, Evening shift · Q2932

JEE Main 202127 Jul, Evening shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

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

JEE Main 202127 Jul, Evening shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

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 :