JEE Main20253 Apr 2025Morning ShiftMathematicsBinomial TheoremActual

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

Options

A16923
B3763
C33845
D18817

Correct answer

D. 18817

Step-by-step solution

S=(2+ 3 )^8 For sum of rational terms aligned & = ^8 C ₀(2)^8+ ^8 C ₂(2)^6 ( 3 )^2+ ^8 C ₄(2)^4( 3 )^4 & + ^8 C ₆(2)^2( 3 )^6+ ^8 C ₈( 3 )^8 & =2^8+28 2^6 3+70.2^4 9+28.2^2 .27+81 & =256+5376+10080+3024+81 & =18817 aligned

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