NCERT Mathematics · Class XII · Chapter 4

Determinants

Previous Years' Objective Questions — Entrance Exam Series

50Questions

1995From

2022To

8Exams

AIEEEAIIMSAIPMTBITSATIIT-JEEJEE AdvancedJEE MainKVPY

Properties of DeterminantsArea of a TriangleMinors and CofactorsAdjoint of a MatrixInverse of a MatrixApplications of Determinants

How to Attempt

Expand along the row/column with most zeros for speed.
Use properties of determinants to simplify before expanding.
Area of triangle — remember the ½|det| shortcut.
MathJax renders all determinant notation — wait for it.
Timer starts on Q1 — 2 min average per question.
Review all answers before Submit.

Determinants pairs tightly with Matrices and is a near-guaranteed JEE topic. These 50 questions from 1995–2022 cover properties, cofactor expansion, adjoint/inverse, and applications to systems of equations.

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Frequently Asked Questions

Determinants are scalar values associated with square matrices and are used to solve linear equations, find matrix inverses, test consistency, and calculate areas.

The questions cover properties of determinants, minors and cofactors, adjoint and inverse, determinant evaluation, special matrices, Vandermonde determinants, areas, and collinearity.

Yes. The collection includes standard and repeatedly modelled determinant concepts that are useful for JEE Main revision and objective-question practice.

Yes. Several questions involve conceptual properties, determinant identities, adjoint matrices, skew-symmetric matrices, and algebraic manipulation relevant to JEE Advanced.

Yes. Although Mathematics is not tested in NEET, the questions are useful for students preparing for examinations or curricula where determinant-based mathematics is included.

Yes. Every question is followed by the correct option and a concise explanation showing the key concept or calculation.

Important properties include the effects of row and column operations, interchange of rows or columns, multiplication by a scalar, transpose, product of matrices, and determinant of an inverse.

The area of a triangle with coordinates is obtained as one-half of the absolute value of the corresponding third-order determinant.

Three points are collinear when the determinant formed using their coordinates and a final column of ones is equal to zero.

First attempt each question without assistance, check the answer, study the explanation, and then revise the underlying determinant property before attempting similar problems.

Determinants

Determinants — Learning Resources

Frequently Asked Questions

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Determinants

Determinants — Learning Resources

Frequently Asked Questions

Q 01 What are determinants in Class 12 Mathematics?

Q 02 Which topics are covered in these Determinants MCQs?

Q 03 Are these Determinants MCQs useful for JEE Main preparation?

Q 04 Are these Determinants questions useful for JEE Advanced?

Q 05 Are these Determinants MCQs useful for NEET preparation?

Q 06 Do these MCQs include answers and explanations?

Q 07 Which determinant property is most important for competitive exams?

Q 08 How are determinants used to find the area of a triangle?

Q 09 How can determinants be used to test whether three points are collinear?

Q 10 How should I use these Determinants MCQs for exam preparation?

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