# If the Fifth Term of the Expansion ( a 2 / 3 + a − 1 ) N Does Not Contain 'A'. Then N is Equal To(A) 2 (B) 5 (C) 10 (D) None of These - Mathematics

MCQ

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

#### Options

• 2

• 5

•  10

•  none of these

#### Solution

10

$T_5 = T_{4 + 1}$

$= ^{n}{}{C}_4 ( a^{2/3} )^{n - 4} ( a^{- 1} )^4$

$= ^{n}{}{C}_4 a^\left( \frac{2n - 8}{3} - 4 \right)$

$\text{ For this term to be independent of a, we must have}$

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

$\Rightarrow 2n - 20 = 0$

$\Rightarrow n = 10$

Concept: Rth Term from End
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 18 Binomial Theorem
Q 22 | Page 48