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BINOMIAL THEOREM — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSBINOMIAL THEOREM1 Mark
MCQ
The coefficient of the middle term in the expansion of (2 + 3x)4 is:
  • A
    5!
  • B
    6
  • ✓
    216
  • D
    8!
✓

Answer

Correct option: C.
216
  1. 216
Solution:
If the exponent of the expression is n, then the total number of terms is n + 1.
Hence, the total number of terms is 4 + 1 = 5.
Hence, the middle term is the 3rd term.
Therefore, $\mathrm{T}_3={ }^4 \mathrm{C}_2 \times(2)^2 \times(3 \mathrm{x})^2$
$T_3=(6) \times(4) \times\left(9 x^2\right)$
$T_3=216 x^2 .$
Therefore, the coefficient of the middle term is 216.

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