The number of integral terms in the expansion of -3-5256 is

The correct option is B 33 T_r+1=^256C_r ( 3^1/2 )^256 6 ( 5^1/8 )^r. It is an integer if 256 r/2 and r/8 are positive integers. ∴ 256 r≥ 0 and r is a multiple ...

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Byju's Answer

Standard XI

Mathematics

Number of Terms in Binomial Expansion

The number of...

Question

The number of integral terms in the expansion of ${(\sqrt{3} - \sqrt[8]{5})}^{256}$ is

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Solution

The correct option is A
33

$T_{r + 1} =^{256} C_{r} {(3^{\frac{1}{2}})}^{256 - 6} {(5^{\frac{1}{8}})}^{r} .$ It is an integer if $\frac{256 - r}{2} a n d \frac{r}{8}$ are positive integers.

$∴ 256 - r \geq 0$ and r is a multiple of 8 $\Rightarrow$ r can be 0, 8, 16, 24 . . . . . 8 $\times$ 32. These are 33

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The number of integral terms in the expansion of (√3−8√5)256 is

The correct option is A 33 Tr+1=256Cr(312)256−6(518)r. It is an integer if 256−r2 and r8 are positive integers. ∴ 256−r≥0 and r is a multiple of 8 ⇒ r can be 0, 8, 16, 24 . . . . . 8 × 32. These are 33

The number of integral terms in the expansion of ${(\sqrt{3} - \sqrt[8]{5})}^{256}$ is