Rank of matrix A=[1 2 −1; 0 1 7; 0 0 0] is:
- 1
- 2
- 3
- 4
Show answer and explanation
Answer: B. 2
Two nonzero rows remain ⇒ rank=2.
FSC Mathematics: Matrices and Determinants, questions with answers
Practise 29 real Federal Board questions on Matrices and Determinants from 2023 to 2026. See the answer and explanation as soon as you answer.
29real questions
10multiple choice
5exam sessions
About Matrices and Determinants in FSC Mathematics
Matrices and Determinants is one of the 14 main chapters in our Federal Board FSC Mathematics question bank (11th class), and about 6% of its real questions come from it. Tayyari Karo has 29 real questions on this chapter from 2023 to 2026; 10 are multiple choice and marked instantly, and the rest are short and long questions with a model answer. By difficulty: 14 medium, 9 hard, 6 easy.
Work through the questions below, then open the explanation for each one. Redo the ones you missed a few days later.
Try 8 real questions
These are real past-paper questions. Think of your answer first, then open the explanation.
A consistent system MUST have at least:
- At least one solution
- Infinite solutions
- No solution
- Maximum two solutions
Show answer and explanation
Answer: A. At least one solution
Consistent means it has a solution — at least one.
If A is a 3×3 matrix, then |3A| results
- 3|A|
- 6|A|
- 9|A|
- 27|A|
Show answer and explanation
Answer: D. 27|A|
|kA|=kⁿ|A| for n×n matrix; k=3, n=3 ⇒ 27|A|.
The system x+y+z=2, x+y+z=3, x+y+z=4 is:
- Dependent
- Inconsistent
- Consistent with infinitely many solutions
- Consistent with a unique solution
Show answer and explanation
Answer: B. Inconsistent
Same LHS with different constants ⇒ no solution ⇒ inconsistent.
If A is a matrix of order 3×2, then order of the product Aᵗ A is:
- 3×2
- 3×3
- 2×2
- 2×3
Show answer and explanation
Answer: C. 2×2
Aᵗ is 2×3 and A is 3×2, so Aᵗ A has order (2×3)(3×2) = 2×2.
If det A = 5, what is the value of det(15A)? (where order of A is 2×2)
- 75
- 225
- 375
- 1125
Show answer and explanation
Answer: D. 1125
det(kA) = kⁿ det(A) for an n×n matrix. Here n = 2, so det(15A) = 15² × 5 = 225 × 5 = 1125.
Find the rank of matrix [1 2 3; 2 4 6; 1 1 1]
Show model answer
R₂→R₂−2R₁: [0 0 0]; R₃→R₃−R₁: [0 −1 −2]
Nonzero rows: [1 2 3] and [0 −1 −2]
Rank = 2
Find the value of k if the given system is consistent (has nontrivial solution): x−4y+3z=0, 2x+ky+z=0, x−2y+kz=0
Show model answer
For nontrivial solution, determinant must be zero:
|1 −4 3; 2 k 1; 1 −2 k| = (k²+2)+4(2k−1)+3(−4−k) = k²+5k−14 = 0
k = 2 or k = −7
Sessions with Matrices and Determinants questions
| Session | Questions |
|---|---|
| 2026 Annual | 6 |
| 2025 1st Annual | 6 |
| 2025 2nd Annual | 6 |
| 2024 Annual | 6 |
| 2023 Annual | 5 |
Common questions
What does the Matrices and Determinants chapter cover on this page?
29 real Federal Board (FBISE) Mathematics questions on Matrices and Determinants from 2023 to 2026, for 11th class. Each one shows the session it came from.
Are the answers official?
No. We could not find an official FBISE marking scheme for these papers, so the answers and explanations are written by Tayyari Karo for practice. Check anything important with your teacher or textbook.
Is it free?
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