JEE Main2003MathematicsBinomial TheoremActual

The number of integral terms in the expansion of ( 3 +8 5 )²⁵⁶ is

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Correct answer

C. 33

Step-by-step solution

T _ r +1 = ²⁵⁶ C _ r ( 3 )^ 256- r ( [8] 5 )^ r = ²⁵⁶ C _ r (3)^ 256- r 2 (5)^ r / 8 Terms will be integral if 256- r 2 & r 8 both are +ve integer. As 0 r 256 r =0,8,16,24, 256 For above values of r , ( 256- r 2 ) is also an integer.

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