CBSE Class 12 Sample Paper for 2023 Boards
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CBSE Class 12 Sample Paper for 2023 Boards
Last updated at April 16, 2024 by Teachoo
Question 19 Assertion (A): The domain of the function γπ ππγ^(β1) 2π₯ ππ (ββ,1/2]βͺ[1/2,β ) Reason (R): γπ ππγ^(β1) (β2)=βπ/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 γπ ππγ^(β1) 2π₯ ππ (ββ,1/2]βͺ[1/2,β ) We know that Domain of γπ ππγ^(β1) ΞΈ ππ (ββ,1]βͺ[1,β ) Thus, ββ<ΞΈβ€1 and 1β€ ΞΈ<β Putting ΞΈ = 2x ββ<2π₯β€1 and 1β€2π₯<β Dividing both sides by 2 ββ/2<2π₯/2β€1/2 and 1/2β€2π₯/2<β/2 ββ<πβ€π/π and π/πβ€π<β Thus, Domain of γπ ππγ^(β1) 2π₯ ππ (ββ,π/π]βͺ[π/π,β ) Thus, Assertion is true Checking Reason Reason (R): γπ ππγ^(β1) (β2)=βπ/4 Let y = secβ1 (β2) y = πβ secβ1 (2) y = π β π/3 y = ππ /π Since Range of secβ1 is [0, Ο] β {π/2} Hence, Principal Value is ππ /π Thus, Reasoning is false So, Assertion is true Reasoning is false So, the correct answer is (c)
