Chapter 4: Determinants — Online MCQ Test
MATHS · CLASS 12 SECOND PUC · Karnataka State Board
Practice Chapter 4: Determinants with a free chapter-wise online MCQ test.
This chapter covers: Chapter 4 of the CBSE Class 12 Mathematics curriculum covers Determinants. It is closely tied to Chapter 3 (Matrices), and together they carry a weightage of roughly 10 marks in th....
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Chapter 4: Determinants — Important Questions & Answers
The determinant is defined only for which type of matrix?
- A. Rectangular matrices
- B. Square matrices
- C. Row matrices
- D. Column matrices
Answer: B. Square matrices
By definition, determinants can only be calculated for square matrices (n×n matrices). For non-square matrices, determinants are not defined.
By definition, determinants can only be calculated for square matrices (n×n matrices). For non-square matrices, determinants are not defined.
For the matrix A = [[2, 3], [1, 4]], what is |A|?
- A. 5
- B. -5
- C. 11
- D. 12
Answer: A. 5
For a 2×2 matrix [[a, b], [c, d]], |A| = ad - bc. Here, |A| = (2)(4) - (3)(1) = 8 - 3 = 5.
For a 2×2 matrix [[a, b], [c, d]], |A| = ad - bc. Here, |A| = (2)(4) - (3)(1) = 8 - 3 = 5.
What is the area of a triangle with vertices (0, 0), (1, 0), and (0, 1)?
- A. 1
- B. 0.5
- C. 2
- D. 1.5
Answer: B. 0.5
Area = (1/2)|det| where det = 0(0-1) - 0(0-0) + 1(0-0) = 0. Using the distance formula or basic geometry: Area = (1/2) × base × height = (1/2) × 1 × 1 = 0.5.
Area = (1/2)|det| where det = 0(0-1) - 0(0-0) + 1(0-0) = 0. Using the distance formula or basic geometry: Area = (1/2) × base × height = (1/2) × 1 × 1 = 0.5.
When |A| = 0 and (adj A)B ≠ O, the system AX = B is:
- A. Consistent with unique solution
- B. Consistent with infinite solutions
- C. Inconsistent (no solution)
- D. Undefined
Answer: C. Inconsistent (no solution)
When |A| = 0 (matrix is singular) and (adj A)B is non-zero, the system is inconsistent and has no solution.
When |A| = 0 (matrix is singular) and (adj A)B is non-zero, the system is inconsistent and has no solution.
Which statement about the system AX = B is NOT correct?
- A. If |A| ≠ 0, the system has a unique solution
- B. If |A| = 0 and (adj A)B = O, the system may have infinitely many solutions
- C. If |A| = 0 and (adj A)B ≠ O, the system has infinitely many solutions
- D. X = A⁻¹B is the solution when |A| ≠ 0
Answer: C. If |A| = 0 and (adj A)B ≠ O, the system has infinitely many solutions
When |A| = 0 and (adj A)B ≠ O, the system is inconsistent with NO solution, not infinitely many solutions.
When |A| = 0 and (adj A)B ≠ O, the system is inconsistent with NO solution, not infinitely many solutions.