JEE Main20244 Apr 2024Morning ShiftMathematicsBinomial TheoremActual

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

Options

A3133
B931
C6131
D633

Correct answer

A. 3133

Step-by-step solution

aligned & T _ r +1 = ¹⁵ C _ r (5^ 1 3 )^ r ( 1 2^5 )^ 15- r & = ¹⁵ C _ r 5^ r 3 2^ 15- r 5 & R =3 , 15 & r =0,15 aligned 2 rational terms aligned & ¹⁵ C ₀ 2^3+ ¹⁵ C ₁₅(5)^5 & =8+3125=3133 aligned

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