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  4. The sum of the rational terms in the expansion of (√2+31/5)10 is:

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Q. The sum of the rational terms in the expansion of $ {{(\sqrt{2}+{{3}^{1/5}})}^{10}} $ is:

KEAMKEAM 2004

Solution:

$ {{({{2}^{1/2}}+{{3}^{1/5}})}^{10}} $ $ {{=}^{10}}{{C}_{0}}{{2}^{5}}{{+}^{10}}{{C}_{1}}{{2}^{9/2}}{{.3}^{1/5}}+....+ $ $ ^{10}{{C}_{10}}{{2}^{0}}{{.3}^{2}} $ Thus, sum of rational terms of above expansion $ ={{2}^{5}}+{{3}^{2}} $ $ =32+9=41 $