Binomial Theorem
Rational and Irrational Terms
JEE Main 2022
Grade 11

Question:

The number of rational terms in the expansion of $(2^{1/2} + 3^{1/5})^{10}$ is:
(1) $1$
(2) $2$
(3) $3$
(4) $0$

Step-by-Step Solution

Key Concept: Write the general term $T_{r+1} = \binom{10}{r} 2^{(10-r)/2} 3^{r/5}$, and determine for how many integer values of $r$ between 0 and 10 both $\frac{10 - r}{2}$ and $\frac{r}{5}$ are integers.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)

Master Binomial Theorem with Mathbee

Practice this topic under real exam conditions with strict timers, or ask our AI Mentor to explain the concepts step-by-step.

Start Practicing for Free