Which value among 4 7 ,\, 3 11 and 12 1257 is the largest?

Answer: Option A

Given,
$$\text{root}4\text{of}7,\text{root}3\text{of}11$$   and $$\text{root}12\text{of}1257$$
Take LCM of 4, 3 and 12 = 12
$${\left(7\right)}^{\frac{1}{4}},{\left(11\right)}^{\frac{1}{3}},{\left(1257\right)}^{\frac{1}{12}}$$
Multiplying the power by 12 = 7³, 11⁴, 1257
i.e., 343, 14641, 1257
Therefore, from above greater one is $$\text{root}3\text{of}11$$