QJEEM20Ma9f94: JEE Main 2020 Mathematics - Class 11 JEEM20Ma9f94 Solution: If the term independent of x in the expansion of is k, then 18…

Question

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If the term independent of x in the expansion of

{\left( {{3 \over 2}{x^2} - {1 \over {3x}}} \right)^9}

is k, then 18 k is equal to :

Accepted Answer

General term,

{T_{r + 1}} = {}^9{C_r}{\left[ {{3 \over 2}{x^2}} \right]^{9 - r}}{\left( { - {1 \over {3x}}} \right)^r}

{T_{r + 1}} = {}^9{C_r}{\left[ {{3 \over 2}} \right]^{9 - r}}{\left( { - {1 \over 3}} \right)^r}{x^{18 - 3r}}

For independent of x

18

-

3r = 0

\Rightarrow

r = 6

\therefore

{T_7} = {}^9{C_6}{\left( {{3 \over 2}} \right)^3}{\left( { - {1 \over 3}} \right)^6} = {{21} \over {54}} = k

\therefore

18k = {{21} \over {54}} \times 18 = 7

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