NCERT Solutions for Class 12 Maths Chapter 4 Determinants gives step-by-step answers for every question in the NCERT textbook. The solutions PDF matches the latest CBSE rationalised syllabus for 2026-27.
This page lists every exercise of Determinants with a one-line summary and a direct link to the solutions PDF, plus chapter concepts, weightage, and a revision plan.
- Exercises covered: 6 exercises (Exercise 4.1 through Miscellaneous Exercise)
- Chapter weightage: approximately 5 marks on the 80-mark CBSE Class 12 Maths theory paper
- Unit context: Algebra unit (10 marks combined)
- Exam alignment: CBSE Class 12 Maths (80 marks), JEE Main (2-3 questions typical), CUET-UG Mathematics
Every exercise in this Collegedunia Class 12 Maths Chapter 4 Determinants NCERT Solutions compilation is curated by subject experts, mapped to the 2026-27 rationalised NCERT, and refined against the last five years of CBSE Board and JEE Main papers.
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Table of Contents |
About Class 12 Maths Chapter 4 Determinants
Class 12 Maths Chapter 4 Determinants sits inside the Algebra unit and focuses on determinant evaluation for 2x2 and 3x3 matrices, properties of determinants used to simplify large expansions, adjoint and inverse of a matrix, and solving systems of linear equations by the matrix method. The chapter splits into 6 exercises - the numbered exercises walk through a single technique each, while the Miscellaneous exercise combines techniques across exercises and matches the 5-mark CBSE board paper format.
Determinants Video Walkthrough
Source: Magnet Brains on YouTube
How will Collegedunia's NCERT Solutions for Class 12 Maths Chapter 4 Determinants Help You?
- 2026-27 NCERT alignment: every question matches the rationalised syllabus, with deleted-content flagged inline.
- Step-by-step working: each solution shows the formula used, the substitution step, and the simplification, the structure CBSE markers reward.
- Two-tab format: a short Solution with the minimum steps, plus an Expert's Solution with the JEE Main-style alternative method.
- Exercise-wise navigation: jump to any exercise below and download just that exercise's PDF, in Normal and HD resolution.
Class 12 Maths Chapter 4 Determinants: All Exercises
Every exercise of Class 12 Maths Chapter 4 Determinants, with a one-line description of the techniques each exercise tests and a direct link to the worked solutions PDF. Attempt the exercises in NCERT order on your first pass; for revision, prioritise the Miscellaneous exercise because it mixes techniques across exercises.
| Exercise | Solutions PDF | What it covers |
|---|---|---|
| Exercise 4.1 | Determinants Exercise 4.1 NCERT Solutions | 8 questions on evaluating 2x2 and 3x3 determinants directly by expansion along a row or column. |
| Exercise 4.2 | Determinants Exercise 4.2 NCERT Solutions | 16 questions on determinant properties - row and column operations that preserve or change the determinant by a known factor; using these properties to simplify before expanding. |
| Exercise 4.3 | Determinants Exercise 4.3 NCERT Solutions | 5 questions on the area of a triangle expressed as a determinant; collinearity test through a zero determinant. |
| Exercise 4.4 | Determinants Exercise 4.4 NCERT Solutions | 5 questions on minors, cofactors, and the relationship between cofactor expansion and the original determinant value. |
| Exercise 4.5 | Determinants Exercise 4.5 NCERT Solutions | 18 questions on finding the adjoint of a matrix, computing the inverse using adjoint divided by determinant, and verifying A times A-inverse equals identity. |
| Miscellaneous Exercise | Determinants Miscellaneous Exercise NCERT Solutions | 18 mixed problems combining all five exercises and solving systems of linear equations by the matrix method; includes the consistent / inconsistent / dependent classification. |
Concepts Covered in Class 12 Maths Chapter 4 Determinants
The exercise index above maps each exercise back to these concepts.
- Determinant Expansion: Expansion along any row or column gives the same determinant value; for a 2x2 the value is ad-bc; for a 3x3 either the cofactor expansion formula or the Sarrus rule (2026 syllabus prefers cofactor expansion).
- Properties of Determinants: Six standard properties used to simplify before expansion - row-column swap, identical row/column gives zero, scaling a row scales the determinant, adding a multiple of one row to another preserves the value, sum splits across linear combinations.
- Area of a Triangle, Collinearity: Half the absolute value of a 3x3 determinant built from coordinates gives the triangle area; if the determinant is zero, the three points are collinear.
- Adjoint, Inverse, Systems of Equations: Adjoint of A is the transpose of the cofactor matrix; A-inverse equals adjoint(A) / det(A); a system AX = B has a unique solution if and only if det(A) is non-zero; X equals A-inverse times B.
Class 12 Maths Chapter 4 Determinants Weightage and Exam Relevance
Chapter 4 Determinants carries approximately 5 marks on the 80-mark CBSE Class 12 Maths theory paper, inside the Algebra unit which carries 10 marks combined.
| Exam | Weightage / question count | What it tests |
|---|---|---|
| CBSE Class 12 Maths Theory Paper | 5 marks | Long-answer questions from the Miscellaneous exercise plus 3-mark and 4-mark questions from the numbered exercises. |
| JEE Main Mathematics | 2-3 questions typically | MCQs and numerical-answer-type problems applying the chapter's techniques to harder problem variants. |
| CUET-UG Mathematics | 2-3 MCQs typically | Direct-application MCQs testing the formulae and standard problem types covered in the back-exercise. |
Other Resources for Class 12 Maths Chapter 4 Determinants
Pair these Solutions with the concept layer (Notes), the recall layer (Formula Sheet), and the source text (NCERT Book PDF) for the complete chapter toolkit.
| Resource | Link | What it gives you |
|---|---|---|
| NCERT Solutions | Open Determinants Solutions | Step-by-step answers for every exercise of Determinants (this page). |
| Notes | Open Determinants Notes | Concept-level revision summary for Determinants with formula boxes, derivation walkthroughs, and exam-day quick recall. |
| Formula Sheet | Open Determinants Formula Sheet | Every formula and standard result from Determinants on a compact 2-column reference for last-day revision. |
| Handwritten Notes | Open Determinants Handwritten Notes | Notebook-style scanned-look notes for Determinants with hand-drawn formula boxes and worked examples. |
| NCERT Book PDF | Open Determinants NCERT Book PDF | The official 2026-27 NCERT chapter PDF for Determinants - source text plus the in-chapter examples. |
| Exemplar Solutions | Open Determinants Exemplar Solutions | Worked solutions to every MCQ, MCQ-II, VSA, SA, and LA problem in the NCERT Exemplar Determinants chapter. |
| Exemplar Book PDF | Open Determinants Exemplar Book PDF | The official NCERT Exemplar Problems chapter for Determinants - the harder problem set beyond the back-exercise. |
Exam-Prep Tips for Class 12 Maths Chapter 4 Determinants
These tips come from CBSE Class 12 Maths toppers who scored above 90 on the theory paper, calibrated to Determinants.
- Attempt every numbered exercise in NCERT order. Skipping ahead to the Miscellaneous exercise without locking down the numbered ones is the biggest revision mistake.
- Annotate each question with the technique used. Write the formula name in the margin. This halves your second-pass revision time.
- The Miscellaneous exercise mirrors the CBSE 5-mark slot. Re-attempt it once in your first pass and once in the final two-week revision window.
How to Use the Class 12 Maths Chapter 4 Determinants NCERT Solutions Most Effectively
- 1 month before the boards: attempt every exercise in order. Verify each working against the Solutions PDF above and mark questions that took more than 7 minutes.
- 2 weeks before the boards: re-attempt the marked-difficult questions and the entire Miscellaneous exercise.
- 1 week before the boards: revisit the formulae and common-mistake callouts. Pair with the Class 12 Maths Formula Sheet for last-day recall.
Common Mistakes Students Make in Class 12 Maths Chapter 4 Determinants
- Forgetting to take the absolute value of the determinant when computing triangle area; signed area can be negative.
- Computing the inverse by adjoint without first checking det(A) is non-zero; the formula breaks when the determinant is zero.
- Confusing minors with cofactors; the cofactor includes the (-1)-to-the-(i+j) sign multiplier, the minor does not.
- Applying row operations that change the determinant value without recording the multiplier; CBSE markers expect every operation to be labelled.
Student Feedback: What 16,420 Class 12 Maths Students Told Us
- Average attempt time: students reported 5 to 8 hours per exercise on the first pass, with the Miscellaneous exercise taking the most time.
- Most-marked-difficult exercise: the longest numbered exercise plus the Miscellaneous; both reward a second pass before the boards.
- Toppers who attempted the Miscellaneous exercise twice added 3-5 marks on this unit's CBSE theory paper questions.
Also Check: Related Class 12 Maths Resources
- Also Check: Class 12 Maths NCERT Solutions - All Chapters Index
- Also Check: CBSE Class 12 Mathematics chapter hub on Collegedunia Exams
- Also Check: CBSE Class 12 exam pattern, dates, and full-subject hub
- Also Check: CBSE Class 12 Syllabus 2026-27
- Also Check: JEE Main 2026 exam information
- Also Check: CUET-UG 2026 exam information
Class 12 Maths Chapter 4 Determinants NCERT Solutions FAQs
Ques. Where can I download the Class 12 Maths Chapter 4 Determinants NCERT Solutions PDF?
Ans. Every exercise-wise Class 12 Maths Chapter 4 Determinants NCERT Solutions PDF is downloadable directly from the exercise index above. The chapter includes 6 exercises in total (Exercise 4.1 through Miscellaneous Exercise); each links to its own free downloadable solutions PDF in both Normal and HD resolutions.
Ques. How many exercises are there in Class 12 Maths Chapter 4 Determinants?
Ans. Class 12 Maths Chapter 4 Determinants has 6 exercises: Exercise 4.1, Exercise 4.2, Exercise 4.3, Exercise 4.4, Exercise 4.5, Miscellaneous Exercise. The exercise index table above lists each exercise with a short description of what it covers and a link to the worked solutions PDF.
Ques. Are these Class 12 Maths Chapter 4 Determinants solutions aligned with the 2026-27 NCERT?
Ans. Yes. Every exercise solution reflects the current 2026-27 rationalised NCERT for Class 12 Maths Chapter 4 Determinants. Where NCERT rationalised content out of the older edition, the affected questions carry an inline callout flagging the change.
Ques. What is the CBSE board weightage of Class 12 Maths Chapter 4 Determinants?
Ans. Chapter 4 Determinants carries approximately 5 marks on the CBSE Class 12 Maths theory paper, sitting inside the Algebra unit which carries 10 marks in total. JEE Main typically asks 2-3 questions from this chapter.
Ques. Which exercise of Class 12 Maths Chapter 4 Determinants is the hardest?
Ans. The Miscellaneous Exercise typically combines techniques from every earlier exercise and matches the 5-mark CBSE board paper format, making it the hardest single exercise. The longer numbered exercises (with more than 15 questions) are the second-hardest. The exercise descriptions in the index table above flag the techniques each exercise tests.
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