CBSE Class 12 Mathematics CBQ Questions With Answer Key 2024-25

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%. So students should prepare themselves to understand and answer such questions.

In order to help students of class 10 and 12, CBSE board has released the question bank of competency based questions for various subjects. The questions have been released in the volumes of multiple choice questions and descriptive questions.

Here are given the competency based questions for Class 12 Chapter 2 Mathematics. These questions help the students to prepare inverse trigonometric functions. View and download the question pdfs.

CBSE Class 12 Mathematics 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

Question: 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 the range is (-3π/2, π/2).

If g(x) is the inverse of f(x), which of the following statements 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)

Question 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? Explain your answer.

Question: 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 board, Satish wrote the following as part of his solution:

His teacher stopped him and said that he had probably made a mistake in the solution.

How did the teacher recognize that Satish had made a mistake? Explain your answer.

Q: 10 What is the value of cos-1(24/25)+tan-1(24/7)?

Q: 11 Prove that:

Question 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 ONLY be found if x is known.

Is Rahul right? Explain your answer.

Question 13 Prove, taking into account the principal value branch, that the following property holds ONLY for xy>(-1): tan-1x-tan-1y=tan-1(xy/1+xy)

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There are two parts of CBSE Class 12 Maths Chapter 2 Inverse Trignometric Functions competency based practice questions for the session 2024-25. The FREE PDFs are attached here. Click on the download PDF link to get the PDF.

CBSE Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Competency Based Questions 2024-25 With Answers Part 1
CBSE Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Competency Based Questions 2024-25 With Answers Part 2

Why are CBSE competency-based questions important?

CBSE competency-based questions are important because they help students think deeper and understand topics better. Instead of just memorizing 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 mathematical formula, students are asked to use it in real-life situations like calculating money or time. These questions improve critical thinking and creativity, making students smarter and better prepared for future exams and jobs. Also, CBSE has increased the weightage of CBQ questions to 50%. So, students need to prepare for such questions to score well.

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