The number of integral terms in the expansion of ( 5 2 1 + 7 8 1 ) 1016 is

T r = 1016 C r ( 5 ) 2 1016 − r 7 8 r ⇒ r = 0 , 8 , 16 , 24 , … . , 1016 1016 = 0 + ( n − 1 ) 8 ⇒ n − 1 = 8 1016 = 127 So, n = 128 .

Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremIntegral and Fractional Part of a NumberEasy2 minPYQ_2025

MathematicsEasysingle choice

The number of integral terms in the expansion of $(5^{\frac{1}{2}} + 7^{\frac{1}{8}})^{1016}$ is

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Solution:

$T_{r} =^{1016} C_{r} (5)^{\frac{1016 - r}{2}} 7^{\frac{r}{8}} \Rightarrow r = 0, 8, 16, 24, \dots ., 1016 1016 = 0 + (n - 1) 8 \Rightarrow n - 1 = \frac{1016}{8} = 127$ So, $n = 128$ .

Stream:JEESubject:MathematicsTopic:Binomial TheoremSubtopic:Integral and Fractional Part of a Number

⏱ 2mℹ️ Source: PYQ_2025

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