Question

In the expansion of (4^1/3 + 6^–1\4)²⁰, consider the following statements –

(i) the number of irrational terms = 18

(ii) the number of rational terms = 2

(iii) the middle term is irrational.

Then the correct statements are -

• A. (i) and (iii)
• B. (ii) and (iii)
• C. (i) and (ii)
• D. All three

Answer 1

Answer: (B)

(ii) and (iii)

Answer 2

$\left( 4^{\frac{1}{3}} + \frac{1}{6^{\frac{1}{4}}} \right)^{20}$ T_{r + 1} = ²⁰C_r . 4^{20 – r/3}$\left( \frac{1}{3} \right)^{\frac{r}{4}}$

The number of rational term = 2

when r = 12, 20

middle term T₁₁ = ²⁰C₁₀ (4^1/3)¹⁰$\left( \frac{1}{6} \right)^{\frac{10}{4}}$

is irrational.