# 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

•  r = 10

•  r = 11

•  r = 12

• r = 13

#### Solution

r = 12

Here,

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

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

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

$67 - 7r = - 17$

$\Rightarrow r = 12$

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#### APPEARS IN

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

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