CBSE BoardEnglish MediumSTD 11 ScienceMathsBinomial Theorem1 Mark
Question
Middle term in the expansion of $(a^3 + b^a)^{28}$ is _________.
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Answer
Middle term in the expansion of $(a^3 + b^a)^{28}$ is $=\ ^{28}\text{C}_{14}\text{a}^{56}\text{b}^{14}$.
Given expression is $(a^3 + ba)^{28}.$
Since index is $n = 28 ($even$)$
So$,$ there is only one middle term which is $\Big(\frac{28}{2}+1\Big)^\text{th}$ term or $15^{th}$ term.
$\therefore$ Middle term, $\text{T}_{15}=\text{T}_{14+1}=\ ^{28}\text{C}_{14}(\text{a}^3)^{28-14}(\text{ba})^{14}$
$=\ ^{28}\text{C}_{14}\text{a}^{42}\text{b}^{14}\text{a}^{14}=\ ^{28}\text{C}_{14}\text{a}^{56}\text{b}^{14}$
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