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BINOMIAL THEOREM — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSBINOMIAL THEOREM1 Mark
MCQ
If n is even in the expansion of (a + b)n, the middle term is:
  • A
    $\text{n}^\text{th }\text{term}$
  • B
    $\big(\frac{\text{n}}{2}\big)^\text{th }\text{term}$
  • C
    $\big[\big(\frac{\text{n}}{2})-1\big]^\text{th }\text{term}$
  • ✓
    $\big[\big(\frac{\text{n}}{2})+1\big]^\text{th }\text{term}$
✓

Answer

Correct option: D.
$\big[\big(\frac{\text{n}}{2})+1\big]^\text{th }\text{term}$
  1. $\big[\big(\frac{\text{n}}{2})+1\big]^\text{th }\text{term}$
Solution:
In general, if " $n$ " is the even in the expansion of $(a+b)^n$, then the number of terms will be odd. (i.e) $n+1$. Hence, the middle term of the expansion $(a+b)^n$ is $\left[\left(\frac{n}{2}\right)+1\right]^{\text {th }}$ term.

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