MCQ
The number of integral terms in$ (\sqrt{3}+\sqrt[8]{2})^{64}$ is-
- A8
- B7
- ✓9
- D6
✓
Answer
Correct option: C.
9
- 9
The general term of expansion $(x + y)^n$ is $^nC_rx^{n−r}y^r$
So the general term of $ (\sqrt{3}+\sqrt[8]{2})^{64}$ is $ {^{64}}{\text{C}}_{\text{r}}3\frac{64-\text{r}}{2}2\frac{\text{r}}{8}$
For the term to be integer, r must be divided by 8 and 64 - r must be divided by 2
The possible values of r are 0, 8, 16, 24, 32, 40, 48, 56, 64 the number of integral values is 9.
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