2021 · Q105
If 'a' varies as 'b', then which of the following statements is/are correct?
- 1nth root of a2b varies as (2n)th root of a4b2.
- 2a/(b2) varies inversely as b.
Select the correct answer using the code given below:
General Mental Ability, Quantitative Aptitude and StatisticsAlgebra and data interpretation
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
If a varies as b, then a = kb for some constant k. Statement 1: the nth root of a²b is (a²b)^{1/n} = a^{2/n}b^{1/n}, and the (2n)th root of a⁴b² is (a⁴b²)^{1/2n} = a^{2/n}b^{1/n} — the two are equal, hence vary directly with each other. Statement 2: a/b² = kb/b² = k/b, which varies inversely as b. Hence both statements are correct, option (C).