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 May 29, 2023 by Teachoo

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.

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

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)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Hi, it looks like you're using AdBlock :(

Displaying ads are our only source of revenue. To help Teachoo create more content, and view the ad-free version of Teachooo... please purchase Teachoo Black subscription.

Please login to view more pages. It's free :)

Teachoo gives you a better experience when you're logged in. Please login :)

Solve all your doubts with Teachoo Black!

Teachoo answers all your questions if you are a Black user!