Chapter Exam

Chapter 4: Determinants — Online MCQ Test

Q: The determinant is defined only for which type of matrix?

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.

Q: For the matrix A = [[2, 3], [1, 4]], what is |A|?

Answer: A. 5 — For a 2×2 matrix [[a, b], [c, d]], |A| = ad - bc. Here, |A| = (2)(4) - (3)(1) = 8 - 3 = 5.

Q: What is the area of a triangle with vertices (0, 0), (1, 0), and (0, 1)?

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.

Q: When |A| = 0 and (adj A)B ≠ O, the system AX = B is:

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.

MATHS · CLASS 12 SECOND PUC · Karnataka State Board

Practice Chapter 4: Determinants with a free chapter-wise online MCQ test for Karnataka State Board CLASS 12 SECOND PUC MATHS. 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.... AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter 4: Determinants — Important Questions & Answers (FAQ)

Frequently asked questions from Karnataka State Board CLASS 12 SECOND PUC MATHS — Chapter 4: Determinants, with answers and explanations. These are sample questions; the exam has its own separate question set.

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.

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.

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.

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.

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.