Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremGeneralEasy2 minPYQ_2025

MathematicsEasysingle choice

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

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Solution:

$S = (2 + 3)^{8}$ For sum of rational terms $=^{8} C_{0} (2)^{8} +^{8} C_{2} (2)^{6} \cdot (3)^{2} +^{8} C_{4} (2)^{4} (3)^{4} +^{8} C_{6} (2)^{2} (3)^{6} +^{8} C_{8} (3)^{8} = 2^{8} + 28 \times 2^{6} \cdot 3 + 70. 2^{4} \cdot 9 + 28. 2^{2} .27 + 81 = 256 + 5376 + 10080 + 3024 + 81 = 18817$

Stream:JEESubject:MathematicsTopic:Binomial TheoremSubtopic:General

⏱ 2mℹ️ Source: PYQ_2025

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