Which of the following is true?
$$\eqalign{ & {\text{I}}.\frac{1}{{\root 3 \of {12} }} > \frac{1}{{\root 4 \of {29} }} > \frac{1}{{\sqrt 5 }} \cr & {\text{II}}.\frac{1}{{\root 4 \of {29} }} > \frac{1}{{\root 3 \of {12} }} > \frac{1}{{\sqrt 5 }} \cr & {\text{III}}.\frac{1}{{\sqrt 5 }} > \frac{1}{{\root 3 \of {12} }} > \frac{1}{{\root 4 \of {29} }} \cr & {\text{IV}}.\frac{1}{{\sqrt 5 }} > \frac{1}{{\root 4 \of {29} }} > \frac{1}{{\root 3 \of {12} }} \cr} $$

Solution (By Examveda Team)

$$\eqalign{ & \frac{1}{{\root 3 \of {12} }},\,\frac{1}{{\root 4 \of {29} }},\,\frac{1}{{\sqrt 5 }} \cr & {\text{Take LCM of roots}} = 12 \cr & \frac{1}{{{{12}^{\frac{1}{3}}}}},\,\frac{1}{{{{29}^{\frac{1}{4}}}}},\,\frac{1}{{{5^{\frac{1}{2}}}}} \cr & {\text{By multiplying by 12}} \cr & \frac{1}{{{{12}^4}}},\,\frac{1}{{{{29}^3}}},\,\frac{1}{{{5^6}}} \cr & \frac{1}{{20736}},\,\frac{1}{{24389}},\,\frac{1}{{15625}} \cr & {\text{Divisible by largest number gives lowest quotient}}{\text{.}} \cr} $$