The sum of the rational terms in the expansion of (√2+5√3)10 is
A
32
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B
9
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C
41
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D
None of these
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Solution
The correct option is C 41 tr+1=10Cr.210−r2.3−r5.Thisisrationalifr5and5−r2areintegers.Also,0≤r≤10.Now,rmustbeamultiplef10(LCMof2and5)So,r=0,10∴Therationaltermsare10C0.25.30,10C10.20.32∴Sumofrationalterms=32+9=41