JEE Determinants Quiz
Chapter-wise practice on evaluating determinants, their properties, Cramer's rule, and applications to areas and the consistency of linear systems.
Skill map
Levels in this jee determinants quiz
Every question is generated fresh by AI and calibrated to your level - clear a level and the next one gets harder. Miss one and the AI tutor explains Determinants until it sticks, then aims a follow-up at the gap. Want to grind one level? Start the quiz and type that sub-topic as your own.
Exam focus
How Determinants is asked
A chapter where using the properties rather than expanding is the difference between a thirty-second answer and a three-minute one. JEE sets determinants with a parameter or a common factor precisely to reward students who simplify by row and column operations first.
Cheat sheet
Determinants formulas worth memorising
| Quantity | Formula |
|---|---|
| 2 × 2 determinant | |A| = ad − bc |
| Row/column swap | changes the sign of the determinant |
| Identical rows | determinant = 0 |
| Scalar multiple of a matrix | |kA| = kⁿ|A| for an n × n matrix |
| Product rule | |AB| = |A| · |B| |
| Area of a triangle | ½ |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)| |
| Cramer's rule | x = Dx/D, y = Dy/D, requires D ≠ 0 |
Marks lost here
Common mistakes in Determinants
- Expanding a 3 × 3 determinant directly when row operations would collapse it. Creating a row of zeros or extracting a common factor first turns most JEE determinant questions into simple ones.
- Using |kA| = k|A|. The scalar multiplies every entry, so for an n × n matrix the determinant scales by kⁿ.
- Applying Cramer's rule when D = 0. The rule requires a non-zero determinant; when D = 0 you must instead examine Dx, Dy and Dz to distinguish no solution from infinitely many.
- Forgetting the absolute value in the area formula. A determinant can be negative, but an area cannot, and the sign only tells you the orientation of the vertices.
- Confusing a minor with a cofactor. The cofactor is the minor with the sign (−1)^(i+j) applied, and dropping that sign is a routine source of arithmetic errors in expansions.
Game rules
How a round works
- 01Spawn
Press play - the AI generates Determinants questions in seconds.
- 02Level up
Answer to earn XP and build a streak. Difficulty adapts to your accuracy and speed.
- 03Learn or lose
Every answer - right or wrong - gets an AI tutor explanation. Wrong answers respawn as follow-ups.
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Player's guide
JEE Determinants Quiz - FAQs
What is the fastest way to evaluate a determinant in an exam?
Simplify before expanding. Use row and column operations to create zeros, take out common factors, and check for identical or proportional rows, which make the determinant zero immediately. Direct expansion should be the last resort, not the first move.
How do determinants tell you whether a system is consistent?
If D ≠ 0 there is exactly one solution. If D = 0 and all of Dx, Dy and Dz are also zero, the system has infinitely many solutions; if D = 0 but at least one of them is non-zero, the system is inconsistent and has none.
Is the jee determinants quiz free?
Yes - completely free, with no sign-up required. Type a topic, press start, and the AI generates an adaptive Determinants quiz with an explanation for every answer.
Can teachers host this jee determinants quiz live for a class?
Yes - create a free teacher account, host a live room on "Determinants", and students join with a 6-character code at quff.in/join. No student accounts needed.
From the blog
Determinants guides & reading
JEE Determinants: 30 Practice Questions with Solutions
Thirty solved Determinants questions, built around the habit that saves the most time: simplify with row operations before expanding.
Exam PrepJEE Matrices: 30 Practice Questions with Full Solutions
Thirty solved Matrices questions, focused on the properties that fail - because matrix algebra is not ordinary algebra.
Exam PrepJEE Permutations and Combinations: 30 Solved Questions
Thirty solved counting questions. The formulas are trivial; modelling the situation correctly is the entire difficulty.
More exam prep quizzes
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