Question : Which of the following is TRUE?
I. $\sqrt[3]{11} > \sqrt{7} > \sqrt[4]{45}$
II. $\sqrt{7} > \sqrt[3]{11} > \sqrt[4]{45}$
III. $\sqrt{7} > \sqrt[4]{45} > \sqrt[3]{11}$
IV. $\sqrt[4]{45} > \sqrt{7} > \sqrt[3]{11}$
Option 1: Only I
Option 2: Only II
Option 3: Only III
Option 4: Only IV

Question

Question : Which of the following is TRUE?
I. $\frac{1}{\sqrt[3]{12}} > \frac{1}{\sqrt[4]{29}} > \frac{1}{\sqrt{5}}$
II. $\frac{1}{\sqrt[4]{29}} > \frac{1}{\sqrt[3]{12}} > \frac{1}{\sqrt{5}}$
III. $\frac{1}{\sqrt{5}} > \frac{1}{\sqrt[3]{12}} > \frac{1}{\sqrt[4]{29}}$
IV. $\frac{1}{\sqrt{5}} > \frac{1}{\sqrt[4]{29}} > \frac{1}{\sqrt[3]{12}}$
Option 1: Only I
Option 2: Only II
Option 3: Only III
Option 4: Only IV

17 Views

Answer 1

Correct Answer: Only III

Solution : LCM of 3, 2, and 4 is 12.
After taking the 12 ^th power,
$\sqrt[3]{11}$ → $11^{4} = 14641$
$\sqrt{7} \to 7^{6} \to 49^{3} = 117649$
$\sqrt[4]{45} \to 45^{3} = 91125$
Comparing the above three terms, we can conclude that
$\sqrt{7} > \sqrt[4]{45} > \sqrt[3]{11}$
Hence, the correct answer is 'Only III'.

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Question : Which of the following is TRUE? I. 113>7>454 II. 7>113>454 III. 7>454>113 IV. 454>7>113Option 1: Only IOption 2: Only IIOption 3: Only IIIOption 4: Only IV

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Question : Which of the following is TRUE?
I. $\sqrt[3]{11} > \sqrt{7} > \sqrt[4]{45}$
II. $\sqrt{7} > \sqrt[3]{11} > \sqrt[4]{45}$
III. $\sqrt{7} > \sqrt[4]{45} > \sqrt[3]{11}$
IV. $\sqrt[4]{45} > \sqrt{7} > \sqrt[3]{11}$
Option 1: Only I
Option 2: Only II
Option 3: Only III
Option 4: Only IV