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Question 19 [Assertion Reasoning] - CBSE Class 12 Sample Paper for 2023 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by

Assertion (A): The domain of the function sec -1 2x is (-∞,1/2]∪[1/2,∞ )

Reason (R ): sec -1 (-2)=-π/4

 

In the following questions, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices.

(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.

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Transcript

Question 19 Assertion (A): The domain of the function 〖𝑠𝑒𝑐〗^(−1) 2𝑥 𝑖𝑠 (−∞,1/2]∪[1/2,∞ ) Reason (R): 〖𝑠𝑒𝑐〗^(−1) (−2)=−𝜋/4 In the following questions, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices. (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 domain of function 〖𝑠𝑒𝑐〗^(−1) 2𝑥 𝑖𝑠 (−∞,1/2]∪[1/2,∞ ) We know that Domain of 〖𝑠𝑒𝑐〗^(−1) θ 𝑖𝑠 (−∞,1]∪[1,∞ ) Thus, −∞<θ≤1 and 1≤ θ<∞ Putting θ = 2x −∞<2𝑥≤1 and 1≤2𝑥<∞ Dividing both sides by 2 −∞/2<2𝑥/2≤1/2 and 1/2≤2𝑥/2<∞/2 −∞<𝒙≤𝟏/𝟐 and 𝟏/𝟐≤𝒙<∞ Thus, Domain of 〖𝑠𝑒𝑐〗^(−1) 2𝑥 𝑖𝑠 (−∞,𝟏/𝟐]∪[𝟏/𝟐,∞ ) Thus, Assertion is true Checking Reason Reason (R): 〖𝑠𝑒𝑐〗^(−1) (−2)=−𝜋/4 Let y = sec−1 (−2) y = 𝜋− sec−1 (2) y = 𝜋 − 𝜋/3 y = 𝟐𝝅/𝟑 Since Range of sec−1 is [0, π] – {𝜋/2} Hence, Principal Value is 𝟐𝝅/𝟑 Thus, Reasoning is false So, Assertion is true Reasoning is false So, the correct answer is (c)

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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, Social Science, Physics, Chemistry, Computer Science at Teachoo.