If in the expansion of x 4-1- x 315- x -17 occurs in rth term- thenA- r -10B- r -11C- r -13D- r -12

The correct option is D r=12 r=12 Here, T_r =^15C_r 1 (x^4)^15 r+1 ( 1/x^3 )^r 1 =( 1)^r × ^15C_r 1 x^64 4r 3r+3 For this term to contain x^ 17, we must have: ...

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Byju's Answer

Standard XII

Mathematics

Index of (r+1)th Term from End When Counted from Beginning

If in the exp...

Question

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

r=10

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r=11

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r=12

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r=13

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Solution

The correct option is C
r=12

r=12

Here,

$T_{r} =^{15} C_{r - 1} (x^{4})^{15 - r + 1} {(\frac{- 1}{x^{3}})}^{r - 1}$

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

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

67-7r=-17

$\Rightarrow r = 12$

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If in the expansion of (x4−1x3)15,x−17 occurs in rth term, then

The correct option is C r=12 r=12 Here, Tr=15Cr−1(x4)15−r+1(−1x3)r−1 =(−1)r×15Cr−1x64−4r−3r+3 For this term to contain x−17, we must have: 67-7r=-17 ⇒r=12

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

The correct option is C
r=12

r=12

Here,

$T_{r} =^{15} C_{r - 1} (x^{4})^{15 - r + 1} {(\frac{- 1}{x^{3}})}^{r - 1}$

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

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

67-7r=-17

$\Rightarrow r = 12$