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 INTER II YEAR · Andhra State Board

Practice Chapter 4: Determinants with a free chapter-wise online MCQ test for Andhra State Board CLASS 12 INTER II YEAR 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.

Questions

20m

Time Limit

Attempts Left

10 random questions from this chapter (mixed difficulty)
Questions you've seen before won't repeat until the pool resets
You have 20 minutes — exam auto-submits when time is up
Maximum 3 attempts per chapter
Results and explanations shown immediately after submission

New here? Register free — includes 3 free chapter exams.

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

Frequently asked questions from Andhra State Board CLASS 12 INTER II YEAR 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.