Which of the following statement(s) is/are true? I. (65)^{\frac{1}{6}} > (17)^{\frac{1}{4}} > (12)^{\frac{1}{3}} II. (17)^{\frac{1}{4}} > (65)^{\frac{1}{6}} > (12)^{\frac{1}{3}} III. (12)^{\frac{1}{3}} > (17)^{\frac{1}{4}} > (65)^{\frac{1}{6}}

Question 11

Which of the following statement(s) is/are true?

$$I. (65)^{\frac{1}{6}} > (17)^{\frac{1}{4}} > (12)^{\frac{1}{3}}$$
$$II. (17)^{\frac{1}{4}} > (65)^{\frac{1}{6}} > (12)^{\frac{1}{3}}$$
$$III. (12)^{\frac{1}{3}} > (17)^{\frac{1}{4}} > (65)^{\frac{1}{6}}$$

Solution

$$(65)^{\frac{1}{6}} , (17)^{\frac{1}{4}} , (12)^{\frac{1}{3}}$$
$$(12)^{\frac{1}{3}}$$=$$(144)^{\frac{1}{6}}$$
So $$(144)^{\frac{1}{6}}$$>$$(65)^{\frac{1}{6}} $$
$$(65)^{\frac{1}{6}} $$=$$(4225)^{\frac{1}{12}} $$
$$(17)^{\frac{1}{4}}$$=$$(4913)^{\frac{1}{12}} $$
Therefore $$(12)^{\frac{1}{3}}$$ > $$(17)^{\frac{1}{4}}$$ >$$(65)^{\frac{1}{6}} $$

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Which of the following statement(s) is/are true? $$I. (65)^{\frac{1}{6}} > (17)^{\frac{1}{4}} > (12)^{\frac{1}{3}}$$$$II. (17)^{\frac{1}{4}} > (65)^{\frac{1}{6}} > (12)^{\frac{1}{3}}$$$$III. (12)^{\frac{1}{3}} > (17)^{\frac{1}{4}} > (65)^{\frac{1}{6}}$$

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Which of the following statement(s) is/are true?

$$I. (65)^{\frac{1}{6}} > (17)^{\frac{1}{4}} > (12)^{\frac{1}{3}}$$
$$II. (17)^{\frac{1}{4}} > (65)^{\frac{1}{6}} > (12)^{\frac{1}{3}}$$
$$III. (12)^{\frac{1}{3}} > (17)^{\frac{1}{4}} > (65)^{\frac{1}{6}}$$