The term independent of x in the expansion of ( 9 x − 3 x 1 ) 18 , x > 0 , is a times the corresponding binomial coefficient. Then a is

T r + 1 = 18 C r ( 9 x ) 18 − r ( − 3 x 1 ) r = ( − r ) r 18 C r 9 18 − 2 3 r x 18 − 2 3 r is independent of x provided r = 12 and then a = 1 .

Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremGeneralMedium2 minPYQ_2011

MathematicsMediumsingle choice

The term independent of $x$ in the expansion of $(9 x - \frac{1}{3 x})^{18}, x > 0$ , is a times the corresponding binomial coefficient. Then a is

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Solution:

$T_{r + 1} =^{18} C_{r} (9 x)^{18 - r} (- \frac{1}{3 x})^{r} = (- r)^{r}^{18} C_{r} 9^{18 - \frac{3 r}{2}} x^{18 - \frac{3 r}{2}}$ is independent of $x$ provided $r = 12$ and then $a = 1$ .

Stream:BITSATSubject:MathematicsTopic:Binomial TheoremSubtopic:General

⏱ 2mℹ️ Source: PYQ_2011

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