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

Mathematics · Binomial Theorem

JEE Main 2024 — 4 April, Shift 1 — Question 10

The sum of all rational terms in the expansion of $\left(2^\frac{1}{5}+5^\frac{1}{3}\right)^{15}\\$ is equal to:

Option A:
3133
Correct
Option B:
633
Option C:
931
Option D:
6131

Answer: A

Step-by-step solution

${{T}_{r+1}}={}^{15}{{C}_{r}}{{\left( 5^{\frac{1}{3}} \right)}^{r}}{{\left( 2^{\frac{1}{5}} \right)}^{15-r}}$

$={}^{15}C_r5^\frac r3.2^\frac{15-r}5\\$$\\\Rightarrow r=0,15\\2\;rational\;terms\\\Rightarrow{}^{15}C_02^3+{}^{15}C_{15}\left(5\right)^5\\=8+3125=3133\\$

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Exam: JEE Main 2024
Paper: 4 April, Shift 1
Subject: Mathematics
Chapter: Binomial Theorem
Topic: Introduction to Binomial Theorem

Let a=1+frac ^2 C 23!+frac ^3 C 24!+frac ^4 C 25!+ldots b=1+frac ^1 C 0+ ^1 C 11!+frac ^2 C 0+ ^2 C 1+ ^2 C 22!+frac ^3 C 0+ ^3 C 1+ ^3 C…

Answer: A

Step-by-step solution

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