CTET Paper II (Mathematics and Science) 12 Jan 2023 Solved Paper

Concept:An irrational number cannot be written as $\frac{p}{q}$ with integers $p, q$ and $q \neq 0$. The sum or product of two irrational numbers can be rational or irrational depending on the numbers.Explanation:Check each statement:Statement A is false. A number is irrational if it cannot be expressed in the form $\frac{p}{q}$.Statement B is true. For example, $\sqrt{2} + (-\sqrt{2}) = 0$ (rational), but $\sqrt{2} + \sqrt{3}$ is irrational.Statement C is false. For instance, $\sqrt{2} \times \sqrt{2} = 2$ (rational).Statement D is false. $(\sqrt{2})^2 = 2$ (rational), but $(1+\sqrt{3})^2 = 4 + 2\sqrt{3}$ (irrational).Thus, only statement B is correct.Answer:Option B: Sum of any two irrational numbers is sometimes a rational number and sometimes an irrational number.