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If in the Expansion of ( X 4 − 1 X 3 ) 15 , X − 17 Occurs in Rth Term, Then (A) R = 10 (B) R = 11 (C) R = 12 (D) R = 13 - Mathematics

MCQ

If in the expansion of \[\left( x^4 - \frac{1}{x^3} \right)^{15}\] ,  \[x^{- 17}\]  occurs in rth term, then

 

Options

  •  r = 10

  •  r = 11

  •  r = 12

  • r = 13

     
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Solution

r = 12

Here,

\[T_r =^{15}{}{C}_{r - 1} ( x^4 )^{15 - r + 1} \left( \frac{- 1}{x^3} \right)^{r - 1} \]

\[ = ( - 1 )^r \times^{15}{}{C}_{r - 1} x^{64 - 4r - 3r + 3} \]

\[\text{ For this term to contain } x^{- 17} , \text{ we must have:}  \]

\[67 - 7r = - 17\]

\[ \Rightarrow r = 12\]

  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 11 | Page 47
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