Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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The coefficient of x4 in ( x 2 − 3 x 2 ) 10 is - Mathematics

MCQ

The coefficient of x4 in \[\left( \frac{x}{2} - \frac{3}{x^2} \right)^{10}\] is

 

Options

  •  \[\frac{405}{256}\]

  •  \[\frac{504}{259}\]

  •  \[\frac{450}{263}\]

  • none of these

     
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Solution

 \[\frac{405}{256}\] 

\[\text{ Suppose } x^4 \text{ occurs at the (r + 1)th term in the given expansion }  . \]

\[\text{ Then, we have } \]

\[ T_{r + 1} = ^{10}{}{C}_r (\frac{x}{2} )^{10 - r} \left( \frac{- 3}{2 x^2} \right)^r \]

`= ( - 1 )^r " ^10C _r \frac{3^r}{2^{10 - r}} x^{10 - r - 2r} `

\[\text{ For this term to contain } x^4 , \text{ we must have: }  \]

\[10 - 3r = 4\]

\[ \Rightarrow r = 2\]

\[ \therefore \text{ Required coefficient } = ^{10}{}{C}_2 \frac{3^2}{2^8} = \frac{10 \times 9 \times 9}{2 \times 2^8} = \frac{405}{256}\]

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 18 Binomial Theorem
Q 17 | Page 47
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