If the fifth term of the expansion $(a^{2 / 3} + a^{- 1})$ does not contain 'a'. Then n is equal to

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None of these

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Solution

The correct option is C
10

$T_{5} = T_{4 + 1}$

$=^{n} C_{4} {(a \frac{2}{3})}^{n - 4} (a^{- 1})^{4} =^{n} C_{4} a^{(\frac{2 n - 8}{3} - 4)}$

For this term to be independent of a , we must have:

$\frac{2 n - 8}{3} - 4 = 0$

$\Rightarrow 2 n - 20 = 0$

$\Rightarrow n = 10$

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If the fifth term of the expansion (a2/3+a−1) does not contain 'a'. Then n is equal to

The correct option is C 10 T5=T4+1 =nC4(a23)n−4(a−1)4=nC4a(2n−83−4) For this term to be independent of a , we must have: 2n−83−4=0 ⇒2n−20=0 ⇒n=10

If the fifth term of the expansion $(a^{2 / 3} + a^{- 1})$ does not contain 'a'. Then n is equal to

The correct option is C
10

$T_{5} = T_{4 + 1}$

$=^{n} C_{4} {(a \frac{2}{3})}^{n - 4} (a^{- 1})^{4} =^{n} C_{4} a^{(\frac{2 n - 8}{3} - 4)}$

For this term to be independent of a , we must have:

$\frac{2 n - 8}{3} - 4 = 0$

$\Rightarrow 2 n - 20 = 0$

$\Rightarrow n = 10$