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

Concept:For any two numbers, their HCF must exactly divide their LCM. Also, the product of the numbers equals HCF × LCM. If these conditions fail, the pair is impossible.Explanation:Check each option using the rule that HCF must divide LCM.Option A: 28 divides 84 → true. Numbers can be 28 and 84.Option B: 1 divides 105 → true. Numbers can be 1 and 105.Option C: 150 divides 900 → true. Numbers can be 150 and 900.Option D: 16 does not divide 196 (since $196 \div 16 = 12.25$). Also actual HCF of 16 and 196 is 4, and their LCM is 784, not 196. So this pair is false.Answer:Option D – HCF and LCM of two numbers x and y can be respectively 16 and 196 is not true.