Question 20 - Assertion (A): The function 𝑓: 𝑅 − {(2𝑛 + 1) 𝜋2 :

Question 20 Statement A Assertion (A): The function 𝑓:𝑅−{(2𝑛+1)𝜋/2:𝑛∈𝑍}→(−∞,−1]∪[1,∞) defined by 𝑓(𝑥)=sec 𝑥 is not one-one function in its domain. Statement R Reason (R): The line 𝑦=2 meets the graph of the function at more than one point. (A) Both (A) and (R) are true and (R) is the correct explanation of (A). (B) Both (A) and ( 𝑅 ) are true but (𝑅) is not the correct explanation of (𝐴). (C) (A) is true but (R) is false. (D) (A) is false but (𝑅) is true.Checking Assertion Assertion (A): The function 𝑓:𝑅−{(2𝑛+1)𝜋/2:𝑛∈𝑍}→(−∞,−1]∪[1,∞) defined by 𝑓(𝑥)=sec 𝑥 is not one-one function in its domain. Given 𝑓(𝑥)=sec⁡𝑥 Now, sec⁡〖𝜋/3〗=2 sec⁡〖(−𝜋)/3〗=2 Also, sec⁡〖5𝜋/3〗=2 sec⁡〖(−5𝜋)/3〗=2 Since sec x = 2 is for more than one value of x ∴ 𝑓(𝑥)=sec⁡𝑥 is not a one-one function ∴ Assertion is true Checking Reason Reason (R): The line 𝑦=2 meets the graph of the function at more than one point. Since 𝑓(𝑥)=sec 𝑥 Thus, 𝑦=2 means 𝐬𝐞𝐜 𝒙=𝟐 And sec x = 2 is true for x = 𝝅/𝟑,(−𝝅)/𝟑,𝟓𝝅/𝟑,(−𝟓𝝅)/𝟑… So, line 𝑦=2 meets the graph of f(x) at more than one point ∴ Reasoning is true Is Reason a Correct explanation for Assertion? Since sec x = 2 is for more than one value of x And, it means that line 𝑦=2 meets the graph of f(x) at more than one point Therefore, Reasoning is a correct explanation for Assertion So, Assertion is true Reasoning is true And, Reasoning is a correct explanation for Assertion So, the correct answer is (a)

Question 20 [Assertion Reasoning] - CBSE Class 12 Sample Paper for 2025 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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