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JEE Main 202120 JulyMorning Shift

Exam: JEE Main
Year: 2021
Date: 20 July
Shift: Morning Shift
Subject: Mathematics
Chapter: Binomial Theorem

JEE Main 2021 · 20 July · Morning Shift · Mathematics · Binomial Theorem

The number of rational terms in the binomial expansion of (4(1)/(4)...

The number of rational terms in the binomial expansion of

{\left(4\dfrac{1}{4} + 5\dfrac{1}{6}\right)}^{120}

is_______.

Correct answer

0

Step-by-step solution

We have,

${\left(4\dfrac{1}{4} + 5\dfrac{1}{6}\right)}^{120}$

${T}_{r + 1} = Cr 120 {\left(4\dfrac{1}{4}\right)}^{120 - r}\left(5\right)\dfrac{r}{6}$

$⇒ {T}_{r + 1} = Cr 120 \left(2\right)\dfrac{120 - r}{2}\left(5\right)\dfrac{r}{6}$

For rational terms $r = 6\lambda, 0 \le r \le 120$ , hence

$r = 0, 6, 12, . . . , 120$

So, total number of rational terms are $21$ .

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