CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard

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Question 19 - CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at Dec. 13, 2024 by

Question 19

Statement A (Assertion): HCF of any two consecutive even natural numbers is always 2.

Statement R (Reason) : Even natural numbers are divisible by 2.

(a) Both assertion (A) and reason (R) are true and reason (R) is the correct

explanation of assertion (A)

(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

(c) Assertion (A) is true but reason (R) is false.

(d) Assertion (A) is false but reason (R) is true.

 

 

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Transcript

Question 19 Statement A (Assertion): HCF of any two consecutive even natural numbers is always 2. Statement R (Reason): Even natural numbers are divisible by 2. (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true.Checking Assertion HCF of any two consecutive even natural numbers is always 2. Two consecutive even natural numbers is 2, 4 OR 6, 8 OR 18, 20 Finding HCF of 6 & 8 6 = 2 × 3 8 = 2 × 2 × 2 ∴ H.C.F = 13 Finding HCF of 18 & 20 18 = 2 × 3 × 3 20 = 2 × 2 × 5 ∴ H.C.F = 2 Since HCF is 2 in both cases Hence, the Assertion is true Checking Reason Even natural numbers are divisible by 2. Since even numbers are always divisble by 2 Thus, Reason is true. Is Reason correct explanation for Assertion? It is true that HCF of two consecutive even natural numbers is 2. But, it is not just because they are divisible by 2. Like, HCF of two even natural numbers is not always 2 (like HCF of 10 & 20 is 10). But for consecutive even natural numbers it is 2. Therefore, Reasoning is NOT a correct explanation for Assertion So, Assertion is true Reasoning is true But, Reasoning is NOT a correct explanation for Assertion So, the correct answer is (b)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo