QJEEM19Ma5b31: JEE Main 2019 Mathematics - Class 11 JEEM19Ma5b31 Solution: A ratio of the 5th term from the beginning to the 5th term from …

Question

Verified Solution • 2025–26 Session moderate

A ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of

{\left( {{2^{1/3}} + {1 \over {2{{\left( 3 \right)}^{1/3}}}}} \right)^{10}}

is :

Accepted Answer

{{{T_5}} \over {T_5^1}} = {{{}^{10}{C_4}{{\left( {{2^{1/3}}} \right)}^{10 - 4}}{{\left( {{1 \over {2{{\left( 3 \right)}^{1/3}}}}} \right)}^4}} \over {{}^{10}{C_4}{{\left( {{1 \over {2\left( {{3^{1/3}}} \right)}}} \right)}^{10 - 4}}{{\left( {{2^{1/3}}} \right)}^4}}} = 4.{\left( {36} \right)^{1/3}}

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