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JEE Main 20253 AprilMorning Shift
Exam
JEE Main
Year
2025
Date
3 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Binomial Theorem

JEE Main 2025 · 3 April · Morning Shift · Mathematics · Binomial Theorem

The sum of all rational terms in the expansion of (2+ 3 )^8 is

The sum of all rational terms in the expansion of (2+3)8(2+\sqrt{3})^8 is

Options

  1. A1692316923
  2. B37633763
  3. C3384533845
  4. D1881718817

Correct answer

D. 1881718817

Step-by-step solution

S=(2+3)8S=(2+\sqrt{3})^8 For sum of rational terms =8C0(2)8+8C2(2)6⋅(3)2+8C4(2)4(3)4+8C6(2)2(3)6+8C8(3)8=28+28×26⋅3+70.24⋅9+28.22.27+81=256+5376+10080+3024+81=18817\begin{aligned} & ={ }^8 \mathrm{C}_0(2)^8+{ }^8 \mathrm{C}_2(2)^6 \cdot(\sqrt{3})^2+{ }^8 \mathrm{C}_4(2)^4(\sqrt{3})^4 \\ & \quad+\quad{ }^8 \mathrm{C}_6(2)^2(\sqrt{3})^6+{ }^8 \mathrm{C}_8(\sqrt{3})^8 \\ & =2^8+28 \times 2^6 \cdot 3+70.2^4 \cdot 9+28.2^2 .27+81 \\ & =256+5376+10080+3024+81 \\ & =18817\end{aligned}
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