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Find the Coefficient Of: (I) X10 in the Expansion of ( 2 X 2 − 1 X ) 20 - Mathematics

Find the coefficient of: 

(i) x10 in the expansion of  \[\left( 2 x^2 - \frac{1}{x} \right)^{20}\]

 
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Solution

(i) Suppose x10 occurs in the (+ 1)th term in the given expression.

Then, we have: \[T_{r + 1} =^{n}{}{C}_r x^{n - r} a^r\]

Here,

\[T_{r + 1} = ^{20}{}{C}_r (2 x^2 )^{20 - r} \left( \frac{- 1}{x} \right)^r \]
`=(-1)^r "^20C_r (2^(20-r) ) ( x^(40-2r-r) )`
\[\text{ For this term to contain } x^{10} , \text{ we must have:}  \]
\[40 - 3r = 10\]
\[ \Rightarrow 3r = 30\]
\[ \Rightarrow r = 10\]

` therefore "Coefficient of"  x^10 = (-1)^10  ^20 C_10 (2^(20-10))="^20C_10 (2^10)`

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 18 Binomial Theorem
Exercise 18.2 | Q 9.1 | Page 37
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