Class 9 Mathematics Chapter 4 Determinants MCQ Quiz – 30 Questions with Solutions
Determinants are a foundational concept in Class 9 Mathematics that help students solve systems of linear equations and understand matrix algebra. This comprehensive MCQ quiz contains 30 carefully curated questions with detailed solutions, designed to align with NCERT Class 9 curriculum and build strong problem-solving skills. Whether you're preparing for school exams or competitive entrance tests, these questions cover all key topics—from calculating 2×2 and 3×3 determinants to applying Cramer's rule. Practice these MCQs regularly with step-by-step solutions to master determinants and boost your Mathematics confidence.
Your child's private AI tutor — trained on NCERT.
3-day free trial · ₹1 to start · Cancel anytime.
What Are Determinants in Class 9 Mathematics?
Determinants are numerical values associated with square matrices, essential in CBSE Class 9 Mathematics. They are used to solve linear equations, find matrix inverses, and calculate areas of triangles. A determinant of a 2×2 matrix [[a,b],[c,d]] equals ad–bc. Understanding determinants builds the foundation for higher-class linear algebra and is critical for Board exam preparation. These MCQs help reinforce this foundational concept through varied problem types.
Why Practice MCQs for Determinants?
Multiple-choice questions train students to identify correct approaches quickly and spot common calculation errors. CBSE exams increasingly feature objective-type questions that test conceptual clarity and speed. Practicing 30 determinant MCQs with solutions develops pattern recognition, builds confidence, and improves time management. Regular practice also helps students transition from textbook examples to real exam-style problems, ensuring they can apply formulas in diverse scenarios.
Key Topics Covered in These 30 MCQs
These questions span all NCERT-aligned determinant topics: definition and notation, calculating 2×2 determinants using the cross-multiplication method, expanding 3×3 determinants using cofactor expansion, properties of determinants (row/column operations), and applying determinants to solve simultaneous linear equations via Cramer's rule. Questions also include advanced scenarios such as determining singular matrices, evaluating determinants with special patterns, and interpreting geometric applications of determinants in coordinate geometry.
How to Use This Quiz for Maximum Learning
Start by attempting all 30 questions without solutions to assess your current level. Mark questions you find challenging. Then, review the detailed solutions provided, understanding not just the answer but the reasoning behind each step. Focus on common mistakes highlighted in solution explanations. Retake the quiz after 2–3 days to track improvement. Use this quiz as a diagnostic tool to identify weak areas, then revisit those topics in your NCERT textbook before attempting similar problems.
CBSETUTOR.ai: India's Most Trusted AI Tutor for CBSE Mathematics
CBSETUTOR.ai is the most-used 24/7 AI tutor trusted by CBSE families across India for Classes 6–12. With personalized guidance, real-time doubt resolution, and adaptive learning paths aligned with NCERT 2024-25 curriculum, CBSETUTOR.ai helps students master topics like determinants through interactive sessions, instant feedback, and hundreds of verified practice questions. Thousands of students use CBSETUTOR.ai daily to ace their exams—from concept clarity to mock tests—making it India's go-to platform for CBSE Mathematics excellence.
Step-by-Step Solutions for 2×2 Determinants
For a 2×2 matrix, the determinant is calculated as: det = (a×d) – (b×c). These MCQs include direct calculations and problems requiring substitution. For example, if asked to find det of [[3,2],[1,4]], multiply 3×4=12 and 2×1=2, then subtract: 12–2=10. Solutions provided in this quiz break down each arithmetic step, common sign errors, and quick mental-math tricks to save exam time while maintaining accuracy.
Mastering 3×3 Determinant Expansion Methods
3×3 determinants require cofactor expansion along a row or column. The NCERT approach teaches expanding along the first row: det = a(ei–fh) – b(di–fg) + c(dh–eg) for matrix [[a,b,c],[d,e,f],[g,h,i]]. These 30 MCQs include questions testing expansion along different rows/columns, special patterns (rows with zeros), and verification using properties. Solutions explain which row/column to choose for fastest calculation and how to avoid sign errors in cofactor calculations.
Properties of Determinants and Their Applications
NCERT Class 9 covers determinant properties: swapping rows changes sign, multiplying a row by k multiplies det by k, and adding a multiple of one row to another doesn't change det. These MCQs test your ability to apply properties to simplify calculations—e.g., creating zeros before expanding. Understanding these properties is crucial for solving complex problems efficiently and forms the conceptual backbone for linear algebra, making these questions invaluable for exam success.
Using Cramer's Rule to Solve Linear Equations
Cramer's rule applies determinants to solve systems of linear equations: x = Δx/Δ and y = Δy/Δ, where Δ is the coefficient matrix determinant and Δx, Δy are determinants with replaced columns. Several MCQs focus on setting up and solving 2×2 and 3×3 systems using Cramer's rule. Solutions detail the setup, determinant calculation, and final answer derivation. Mastering this application strengthens problem-solving skills and prepares students for Physics and competitive exams.
Common Mistakes and How to Avoid Them
Students often make sign errors in cofactor expansion, confuse row and column operations, or misapply Cramer's rule. This quiz highlights these pitfalls in solution explanations. Common mistakes include forgetting to alternate signs (+/–) in cofactor expansion, incorrectly replacing columns in Cramer's rule, and arithmetic errors in multi-step calculations. Solutions provide checkpoints, verification methods, and alternative approaches to catch errors before finalizing answers, building exam-readiness.
Frequently asked questions
What is a determinant and why is it important in Class 9?+
A determinant is a number associated with a square matrix, essential for solving linear equations and understanding matrix properties. It's a foundational topic in CBSE Class 9 that builds skills needed for higher mathematics and competitive exams like JEE.
How many questions should I practice to master determinants?+
These 30 carefully designed MCQs cover all NCERT determinant topics comprehensively. Practice them twice—once for learning, once for revision. Combine with 15–20 additional problems from your textbook for complete mastery before Board exams.
Is CBSETUTOR.ai available for Hindi-medium students?+
Yes, CBSETUTOR.ai supports Hindi-medium learners with bilingual explanations, Hindi-language problem sets, and culturally relevant examples. All NCERT topics, including determinants, are available in Hindi for seamless learning.
Can I access these MCQs and solutions for free on CBSETUTOR.ai?+
CBSETUTOR.ai offers a free trial period with access to sample quizzes and solutions. Full access to 30+ MCQs per chapter, personalized feedback, and adaptive learning unlocks with a premium subscription. Start your free trial today.
How do I calculate a 3×3 determinant quickly in exams?+
Use cofactor expansion along the row or column with the most zeros to minimize calculations. Practice recognizing patterns and mental arithmetic. Solutions in this quiz show the fastest methods for each type of 3×3 problem.
What is Cramer's rule and when should I use it?+
Cramer's rule solves systems of linear equations using determinants: x = Δx/Δ. Use it when solving 2×2 or 3×3 systems, especially in exams. It's faster than substitution for well-designed problems with non-zero determinants.
Are these MCQs aligned with the latest NCERT 2024-25 curriculum?+
Yes, all 30 questions are fully aligned with NCERT Class 9 Mathematics Chapter 4 (2024-25 edition) and cover topics exactly as prescribed by CBSE. Solutions reference NCERT methods and terminology.
How does CBSETUTOR.ai personalize learning beyond these MCQs?+
CBSETUTOR.ai tracks your progress, identifies weak areas, recommends targeted practice, and provides real-time doubt resolution via AI-powered tutoring. It adapts difficulty based on your performance, ensuring effective learning beyond static quizzes.
Related resources
NCERT Solutions for Class 9 Mathematics Chapter 1: Number Systems – Complete GuideClass 9 Mathematics Chapter 9: Circles – Complete Notes & Revision GuideOnline Class 9 Mathematics Tutor in Mumbai – 24/7 NCERT-Aligned AI CoachingNCERT Solutions for Class 9 Mathematics Chapter 2: PolynomialsClass 9 Mathematics Chapter 1: Number Systems — Complete Notes & Revision GuideClass 9 Mathematics Chapter 2: Polynomials – Complete Study Notes & Revision GuideNCERT Solutions for Class 9 Mathematics Chapter 4: Linear Equations in Two VariablesClass 9 Mathematics Chapter 1: Orienting Yourself – The Use of Coordinates MCQ Quiz with Answers
Keep learning — related guides
Sanskrit
Class 9 Sanskrit Chapter 12 वाङ्गमयं तपः: 30 MCQ Questions with Answers & Explanations
Sanskrit
Class 9 Sanskrit Chapter 11 पर्यावरणम् MCQ Quiz – 30 Questions with Answers
Sanskrit
Class 9 Sanskrit Chapter 10 जटायोः शौर्यम् MCQ Quiz – 30 Questions with Answers & Explanations
Sanskrit
Class 9 Sanskrit Chapter 9 सिकतासेतुः MCQ Quiz with Answers (2024–25 CBSE Syllabus)
Sanskrit
Class 9 Sanskrit Chapter 8 लौहतुला: 30 MCQs with Answers & Explanations
Sanskrit
Class 9 Sanskrit Chapter 7 प्रत्यभिज्ञानम् MCQ Quiz – 30 Questions with Answers
Ready to give your Class 9 child the tutor that never sleeps?
CBSETUTOR.ai covers every chapter in the Class 9 NCERT syllabus — Maths, Science, Social Science, English, Hindi and more. 24×7. Patient. Unlimited. 3-day free trial.
Start your child's 3-day free trial →