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

Concept:Laws of exponents: When multiplying powers with the same base, add the exponents.Explanation:Verify each option using an example. Let $x = 2$, $a = 1$, $b = 2$.Option A: $x^a \times x^b = x^{ab}$? $2^1 \times 2^2 = 2^{1 \times 2} = 2^2 = 4$, but actual product is $2 \times 4 = 8$. False.Option B: $x^a \times x^b = x^{a+b}$? $2^1 \times 2^2 = 2^{1+2} = 2^3 = 8$. Matches. True.Option C: $x^a \times y^b = (xy)^{ab}$? Bases differ, rule does not apply. Example: $2^1 \times 3^2 = 2 \times 9 = 18$, while $(6)^{1 \times 2} = 6^2 = 36$. False.Option D: $x^a \div x^b = x^{a/b}$? $2^1 \div 2^2 = 2 \div 4 = 0.5$, but $2^{1/2} \approx 1.414$. False.Hence only option B is correct.Answer:Option B: $x^a \times x^b = x^{a+b}$