JEE Main2013MathematicsBinomial TheoremActual

The sum of the rational terms in the binomial expansion of (2^ 1 2 +3^ 1 5 )¹⁰ is :

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Correct answer

D. 41

Step-by-step solution

(2^ 1 / 2 +3^ 1 / 5 )¹⁰= ¹⁰ C ₀ (2^ 1 / 2 )¹⁰ + ¹⁰ C ₁ (2^ 1 / 2 )^9 (3^ 1 / 5 )+ + ¹⁰ C ₁₀ (3^ 1 / 5 )¹⁰ There are only two rational terms - first term and last term. Now sum of two rational terms =(2)^5+(3)^2=32+9=41

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