Find the 7th term of 3x2-1-310-

The correct option is D 70/3x^8 Writing the general term, we get #160; T_r+1=( 1)^r ^10C_r3^10 2r.x^20 2r For 7th term r is equal to 6.Hence #160; ...

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Standard XII

Mathematics

Substitution Method to Remove Indeterminate Form

Find the 7t...

Question

Find the $7^{t h}$ term of ${(3 x^{2} - \frac{1}{3})}^{10}$ .

\frac{66}{3} x^{7}

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\frac{70}{3} x^{7}

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\frac{66}{3} x^{8}

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\frac{70}{3} x^{8}

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Solution

The correct option is D $\frac{70}{3} x^{8}$
Writing the general term, we get
$T_{r + 1} = (- 1)^{r}^{10} C_{r} 3^{10 - 2 r} . x^{20 - 2 r}$
For 7th term r is equal to 6.
Hence
$T_{7} = (- 1)^{6}^{10} C_{6} 3^{10 - 12} . x^{20 - 12}$

$= \frac{210. x^{8}}{9}$

$= \frac{70 x^{8}}{3}$ .

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Find the 7th term of (3x2−13)10.

The correct option is D 703x8Writing the general term, we get Tr+1=(−1)r10Cr310−2r.x20−2rFor 7th term r is equal to 6.Hence T7=(−1)610C6310−12.x20−12=210.x89=70x83.

Find the $7^{t h}$ term of ${(3 x^{2} - \frac{1}{3})}^{10}$ .

The correct option is D $\frac{70}{3} x^{8}$
Writing the general term, we get
$T_{r + 1} = (- 1)^{r}^{10} C_{r} 3^{10 - 2 r} . x^{20 - 2 r}$
For 7th term r is equal to 6.
Hence
$T_{7} = (- 1)^{6}^{10} C_{6} 3^{10 - 12} . x^{20 - 12}$

$= \frac{210. x^{8}}{9}$

$= \frac{70 x^{8}}{3}$ .