which of the following statement(s) is/are true? i. (65) 1/6 (17)

| which of the following statement(s) is/are true?
i. (65)^1/6>(17)^1/4>(12)^1/3
ii. (17)^1/4>(65)^1/6>(12)^1/3
iii. (12)^1/3>(17)^1/4>(65)^1/6

A. only i

B. only iii

C. only ii

D. None of these

Please scroll down to see the correct answer and solution guide.

Right Answer is: B

SOLUTION

LCM of (3,4,6) = 12
Taking 12th power of each, we get
(65)^12/6, (17)^12/4,(12)^12/3
(65)²,(17)³,(12)⁴ 4225, 4913, 20736
Hence
(12)^1/3>(17)^1/4>(65)^1/6