Find the term independent of x in the expansion - 2x2-3-x3 25

The correct option is C 25!/10! 15!2^153^10 Writing the general term, we get #160; T_r+1=( 1)^r ^25C_rx^50 5r.2^25 r.3^r Now for the term independent ...

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Standard XI

Mathematics

Sum of product of binomial coefficients

Find the term...

Question

Find the term independent of x in the expansion : ${(2 x^{2} - \frac{3}{x^{3}})}^{25}$

\frac{25!}{10! 15!} 2^{15} 3^{- 10}

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\frac{25!}{10! 5!} 2^{10} 3^{- 15}

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\frac{25!}{10! 15!} 2^{15} 3^{10}

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\frac{25!}{10! 5!} 2^{15} 3^{10}

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Solution

The correct option is C $\frac{25!}{10! 15!} 2^{15} 3^{10}$
Writing the general term, we get
$T_{r + 1} = (- 1)^{r}^{25} C_{r} x^{50 - 5 r} {.2}^{25 - r} {.3}^{r}$
Now for the term independent of x,
$50 - 5 r = 0$
$r = 10$
$T_{11}$
$=^{25} C_{10} {.2}^{15} {.3}^{10}$

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Find the term independent of x in the expansion : (2x2−3x3)25

The correct option is C 25!10!15!215310Writing the general term, we get Tr+1=(−1)r25Crx50−5r.225−r.3rNow for the term independent of x, 50−5r=0r=10T11=25C10.215.310

Find the term independent of x in the expansion : ${(2 x^{2} - \frac{3}{x^{3}})}^{25}$

The correct option is C $\frac{25!}{10! 15!} 2^{15} 3^{10}$
Writing the general term, we get
$T_{r + 1} = (- 1)^{r}^{25} C_{r} x^{50 - 5 r} {.2}^{25 - r} {.3}^{r}$
Now for the term independent of x,
$50 - 5 r = 0$
$r = 10$
$T_{11}$
$=^{25} C_{10} {.2}^{15} {.3}^{10}$