The constant term in the expansion of ( 54 + 54 x + 108 x 3 ) ( 2 3 x 2 − 3 x 1 ) 9 is

General term of ( 2 3 x 2 − 3 x 1 ) 9 is 9 C r ( 2 3 ) 9 − r ( 3 − 1 ) r x 18 − 3 r Constant term = 54 × 9 C 6 ( 2 3 ) 3 ( 3 − 1 ) 6 + 0 + 108 × 9 C 7 ( 2 3 ) 2 ( 3 − 1 ) 7 = 21 − 4 = 17

Start Free Mock LoginAlready registered? Login here

Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremSpecific TermsMedium2 minQB

MathematicsMediummultiple choice

The constant term in the expansion of $(54 + 54 x + 108 x^{3}) (\frac{3 x ^{2}}{2} - \frac{1}{3 x})^{9}$ is

Options:(select one or more)

Answer:

A, D

Solution:

General term of $(\frac{3 x ^{2}}{2} - \frac{1}{3 x})^{9}$ is $^{9} C_{r} (\frac{3}{2})^{9 - r} (\frac{- 1}{3})^{r} x^{18 - 3 r}$ Constant term $= 54 \times^{9} C_{6} (\frac{3}{2})^{3} (\frac{- 1}{3})^{6} + 0 + 108 \times^{9} C_{7} (\frac{3}{2})^{2} (\frac{- 1}{3})^{7} = 21 - 4 = 17$

Stream:JEESubject:MathematicsTopic:Binomial TheoremSubtopic:Specific Terms

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...