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STD 11 - 4.1 complex nubers — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 4.1 complex nubers4 Marks
MCQ
If $(1 +x + x^2)^n = a_0 + a_1x + a_2x^2 +......+a_{2n}x^{2n}$, then $a_0 + a_3 + a_6 +..... =$
  • A
    $3^n$
  • ✓
    $3^{n-1}$
  • C
    $3^{n-2}$
  • D
    $3$
✓

Answer

Correct option: B.
$3^{n-1}$
b
$\left(1+\mathrm{x}+\mathrm{x}^{2}\right)^{\mathrm{n}}=\mathrm{a}_{0}+\mathrm{a}_{1} \mathrm{x}+\mathrm{a}_{2} \mathrm{x}^{2}+\ldots \ldots+\mathrm{a}_{2 \mathrm{n}} \mathrm{x}^{2 \mathrm{n}}$

Put ${\rm{x}} = 1,\omega ,{\omega ^2}$ and add, we get

$3\left(a_{0}+a_{3}+a_{6}+\ldots . .\right)=3^{n}$

$\Rightarrow a_{0}+a_{3}+a_{6}+\ldots .=3^{n-1}$

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