If x varies as y, then which of the following is/are correct?<br>1. x^{2}+y^{2} varies as x^{2}-y^{2}<br>2. \frac{x}{y^{2}} varies inversely as y<br>3. \sqrt[n]{x^{2}y} varies as \sqrt[2n]{x^{4}y^{2}}<br>Select the correct answer using the code given below:

Explanation

Given x = ky. Stmt 1: x^2+y^2 = y^2(k^2+1) and x^2-y^2 = y^2(k^2-1), since their ratio is constant, they vary directly (True). Stmt 2: \frac{x}{y^2} = \frac{ky}{y^2} = \frac{k}{y}, which is inverse variation with y (True). Stmt 3: \sqrt[2n]{x^4y^2} = \sqrt[n]{x^2y}, so it varies as itself, making it trivially proportional (True).

Related questions on Arithmetic

• What is the remainder when (17^{25} + 19^{25}) is divided by 18?
• A bottle contains spirit and water in the ratio 1:4 and another identical bottle contains spirit and water in the ratio 4:1. In what rat...
• Let P = 5^5 \times 15^{15} \times 25^{25} \times 35^{35} and Q = 10^{10} \times 20^{20} \times 30^{30} \times 40^{40}. What is the numbe...
• Two students X and Y appeared in a test. The score of X is 20 more than that of Y. If the score of X is 75% of the sum of the scores of X an...
• Question: The product of a natural number N and the number M written by the same digits of N in the reverse order is 252. What is the number...