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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

     
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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
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