Скачать или смотреть The sum of all rational terms in the expansion of (2^(1/5)+5^(1/3) )^15 is equal to

The sum of all rational terms in the expansion of (2^(1/5)+5^(1/3) )^15 is equal to ,
[Main 4th April 1st Shift 2024]
(a) 3133 (b) 633 (c) 931 (d) 6131
Ans: a
Sol.
We have, (2^(1/5)+5^(1/3) )^15
∴T_(r+1)=(_^15)C_r^ (2^(1/5) )^(15-r) (5^(1/3) )^r
=(_^15)C_r^ 5^(r/3) 2(3-r/5)
For rational terms, r/3 and r/5 must be an integer.
∴3 and 5 divide r
⇒15 divides r⇒r=0 and r=15
Hence, (_^15)C_0^ 5^0 2^3+(_^15)C_15^ 5^5 2^0



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