If the r th term in the expansion of x -3-2- x 210 contains X 4- there r is equal toA- 4B- 3C- 2D- None of these

The correct option is B 3T_r=T_(r 1)+1=^10C_r 1(x/3 )^10 (r 1)( 2/x^2 )^r 1 =^10C_r 1(1/3 )^11 4 ( 2)^r 1x^13 3r Let T_r+1contains x^4. ∴ 13 3r=4 i.e., r=3 ...

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Standard XII

Mathematics

Progression

If the r th t...

Question

If the $r^{t h}$ term in the expansion of ${(\frac{x}{3} - \frac{2}{x^{2}})}^{10}$ contains $x^{4}$ , there r is equal to

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None of these

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Solution

The correct option is B 3
$T_{r} = T_{(r - 1) + 1} =^{10} C_{r - 1} {(\frac{x}{3})}^{10 - (r - 1)} {(- \frac{2}{x^{2}})}^{r - 1} =^{10} C_{r - 1} {(\frac{1}{3})}^{11 - 4} (- 2)^{r - 1} x^{13 - 3 r} L e t T_{r + 1} c o n t a i n s x^{4} . ∴ 13 - 3 r = 4 i . e ., r = 3$

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If the rth term in the expansion of (x3−2x2)10 contains x4, there r is equal to

The correct option is B 3Tr=T(r−1)+1=10Cr−1(x3)10−(r−1)(−2x2)r−1=10Cr−1(13)11−4(−2)r−1x13−3rLet Tr+1contains x4.∴ 13−3r=4 i.e., r=3

If the $r^{t h}$ term in the expansion of ${(\frac{x}{3} - \frac{2}{x^{2}})}^{10}$ contains $x^{4}$ , there r is equal to

The correct option is B 3
$T_{r} = T_{(r - 1) + 1} =^{10} C_{r - 1} {(\frac{x}{3})}^{10 - (r - 1)} {(- \frac{2}{x^{2}})}^{r - 1} =^{10} C_{r - 1} {(\frac{1}{3})}^{11 - 4} (- 2)^{r - 1} x^{13 - 3 r} L e t T_{r + 1} c o n t a i n s x^{4} . ∴ 13 - 3 r = 4 i . e ., r = 3$