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By Karan Singh Bisht
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Updated on 11 Jun 2025, 18:12 IST
The RD Sharma Solutions for Class 12 Maths Chapter 6: Determinants are expertly crafted by Infinity Learn subject specialists to help students build a solid understanding and boost their confidence in this important topic. These solutions are available in an easy-to-download PDF format, making them accessible for students anytime, anywhere.
Aligned with the latest CBSE syllabus, RD Sharma Solutions are an excellent resource for students preparing for board exams. Designed especially for CBSE Class 12 students, these solutions provide detailed explanations to all textbook problems, helping learners grasp complex concepts more effectively.
This chapter on Determinants includes five comprehensive exercises that cover various aspects such as the definition of determinants, their properties, and application in solving problems. Consistent practice using these solutions can significantly enhance problem-solving skills and improve overall performance in Mathematics.
To excel in the final exams, students are strongly encouraged to study these RD Sharma Solutions thoroughly. Regular practice will not only help in concept retention but also in scoring higher marks in the board examinations.
RD Sharma Class 12 Maths Solutions Chapter 6 Determinants cover all the questions from the textbook, crafted by expert Mathematics teachers at Infinity Learn. Download our free PDF of Chapter 6 Determinants RD Sharma Solutions for Class 12 to boost your performance in board exams and competitive exams.
1. Evaluate
|1 2|
|3 4|
Answer: (1×4) − (2×3) = 4 − 6 = −2
2. Evaluate
|2 5 7|
|3 1 2|
|6 7 9|
Answer: 20
3. If rows are interchanged, how does determinant change?
Answer: The sign of the determinant changes.
4. Prove that
|a b|
|a b| = 0
Answer: Rows are identical. So determinant = 0
5. Find the value of k if |1 2|
|k 4| = 0
Answer: 1×4 − 2×k = 0 → 4 = 2k → k = 2
6. Expand along R1
|1 0 2|
|−1 3 4|
|2 −2 1|
Answer: 3
7. Evaluate
|3 2 −1|
|1 0 5|
|2 −1 3|
Answer: 30
8. Show that determinant of matrix with two proportional rows = 0.
Answer: Determinant is 0 if any two rows are proportional.
9. If A = |1 2|
|3 4| then det(AT) = ?
Answer: −2 (Same as det(A))
10. Find determinant of matrix where one row is all zeros.
Answer: Determinant is always 0.
11. Evaluate
|1 1 1|
|1 2 3|
|1 3 6|
Answer: 1
12. Solve using Cramer’s Rule: x + y = 4, 2x − y = 1
Answer: x = 5/3, y = 7/3
13. Evaluate |a b|
|c d|
Answer: ad − bc
14. Evaluate Vandermonde determinant
|1 a a²|
|1 b b²|
|1 c c²|
Answer: (b−a)(c−a)(c−b)
15. If determinant = 0 and matrix is square, what does it imply?
Answer: The matrix is singular (non-invertible).
16. Evaluate trigonometric determinant
|cos²θ cosθsinθ|
|cosθsinθ sin²θ|
Answer: 0
17. Show that |a b|
|−b a| = a² + b²
Answer: a² + b²
18. Find det(A): A = |0 2 −3|
|1 −1 4|
|2 3 1|
Answer: −1
19. If a matrix has two equal columns, determinant is?
Answer: Zero
20. Evaluate
|2 3 1|
|0 4 2|
|5 1 3|
Answer: 30
To download the RD Sharma Class 12 Maths Chapter 6 Determinants from Infinity Learn, visit the official website infinitylearn.com, go to the “Rd Sharma solutions” section, select “RD Sharma Class 12 Maths,” and click on Chapter 6. The solutions are available for free PDF download without any login.
Students should refer to RD Sharma Solutions for Chapter 6 because they offer stepwise, CBSE-aligned explanations that help strengthen conceptual understanding. These solutions are ideal for board exam preparation and are created by expert faculty to simplify complex inverse trigonometric problems.
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