CBSE 2024-25 Competency-Based Questions With Answers: The Central Board of Secondary Education (CBSE) has increased the weightage of competency-based questions to 50%. Thus, students must prepare to understand and answer such questions.
To help students of Class 10th and 12th, the CBSE board has released the question bank of competency-based questions for different subjects. The questions have been released in the volumes that carry multiple-choice questions and descriptive ones.
Here, the competency-based questions for Class 12 Chapter 2 Maths are given. These questions will help the students prepare inverse trigonometric functions. Check and download the question PDFs.
CBSE Class 12 Maths Chapter 2 Competency-Based Questions
Q: 1 What is the domain of the function y = sec⁻¹ x + sin⁻¹x?
1) -1 and 1
2) -1≤x≤1
3) (-∞,-1] ∪ [1,∞)
4) Φ
Q: 2 Given: tan⁻¹√1+tan2 θ x sin(π-θ))=1-a2/(1+a)2
where a ∈ R and a ≠ -1
Which of the following gives the value of θ in terms of a?
Expression 1(a-1/1+a)
Expression 2 (1+a/1-a)
Expression 3 (1 + a2)/(1+a)2
Expression 4 (a-1/1+a)
1) Expression 1
2) Expression 2
3) Expression 3
4) Expression 4
Q: 3 Which of the following is the domain of the function given below?
y = cos⁻¹(x/2)
1) [-1,1]
2) [2,4]
3) (-∞, 2]∪[4,∞)
4) (-∞, -1]∪[1,∞)
Q: 4 The domain of f (x) = sin⁻¹x - cos⁻¹x is [-1, 1] while its range is [-3π/2, π/2].
If g (x) is the inverse of f (x), which of the following is true about the domain of the function g (x)?
1) It is (-1, 1).
2) It is [-3π/2, π/2].
3) It is independent of the domain and range of f (x).
4) (cannot be said without knowing g(x))
Q: 5 If sec⁻¹ (-x) = π/8, which of the following could be the value of sec⁻¹(x)?
1) (-π/8)
2) 7π/8
3) 9π/8
4) (cannot be determined without knowing the value of x)
Q: 6 Akash says that, since the domain of the sine function is (-∞,∞), sin⁻¹ x is well defined in the domain (-∞,∞).
Is Akash right or wrong? Justify your answer.
Q: 7 Simplify: cos(π/2+sin-11/√3)
Show your work.
Q: 8 cosec = π/6 = cosec 5π/6 = 2, but π/6 ≠ 5π/6.
Since the cosecant function is not one-one, how can it be made invertible? Give a reason for your answer.
Q: 9 While solving an inverse trigonometry problem on the blackboard, Satish wrote the following as part of his solution:
His teacher stopped him and said that he must have made a mistake in the solution.
How did the teacher recognise that Satish had made a mistake? Justify your answer.
Q: 10 What would be the value of cos-1(24/25)+tan-1(24/7)?
Q: 11 Prove that:
Q: 12 Chirag asked his students to find the value of:
tan-1(-x)-tan-1(1/x)
Rahul said that the value of the above expression can be found ONLY if x is known.
Is Rahul correct? Justify your answer.
Q: 13 Considering the principal value branch, prove that the property below is true ONLY for xy>(-1). tan-1x-tan-1y=tan-1(x-y/1+xy)
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There are two volumes of CBSE Class 12 Maths Chapter 2 Inverse Trignometric Functions competency-focused practice questions for the 2024-25 session. The FREE PDFs are attached here. Click on the download PDF link to get the PDF.
| CBSE Class 12 Maths Chapter 2 Inverse Trigonometric Functions Competency Focused Questions 2024-25 With Answers Volume 1 | |
| CBSE Class 12 Maths Chapter 2 Inverse Trigonometric Functions Competency Focused Questions 2024-25 With Answers Volume 2 |
Why CBSE Competency-Based Questions Are Important?
CBSE competency-based questions are important because they help students think more deeply and understand topics better. Instead of just memorising facts, these questions focus on real-life situations. This helps students apply what they have learned to solve problems. For example, instead of just knowing a math formula, students are asked to use it in daily life situations, like calculating money or time. These questions improve critical thinking and creativity, making students smarter and more prepared for future exams and jobs. Also, the CBSE has increased the CBQ questions weightage to 50%. Thus, students must prepare for such questions to get a good score.
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