This Class 12 Mathematics worksheet on Determinants, along with its detailed solutions, is prepared mainly for CBSE board exam practice and concept-based revision. The worksheet contains 75 multiple-choice questions, all framed strictly from NCERT. It covers properties of determinants, minors and cofactors, adjoint of a matrix, inverse of a matrix, singular and non-singular matrices, determinant identities, system of linear equations, consistency of solutions, and application-based questions like area of a triangle and collinearity of points. The provided solutions explain each answer step by step, making the worksheet suitable for both practice and clarity building Determinants WS 1 (1).
I am writing about this worksheet because Determinants is a chapter where students often feel confident but still lose easy marks in MCQs. Most mistakes happen due to careless use of properties, confusion between adjoint and inverse, or incorrect interpretation of system of equations. A solution-based worksheet like this helps bridge that gap. By carefully analysing these questions, students can clearly understand how NCERT theory is converted into one-mark logic-based questions and where examiners usually set traps.
Structure of the Determinants Worksheet
The worksheet consists of 75 MCQs, each carrying one mark, followed by detailed explanations. The questions range from direct determinant evaluation to concept-heavy reasoning involving adjoint, inverse, and system of equations. Many questions are calculation-light but logic-intensive.
The overall difficulty level ranges from moderate to high, making this worksheet ideal for revision after completing the chapter.
Properties of Determinants
A large number of questions are based on standard properties of determinants, including:
- Effect of row and column operations
- Determinant of triangular and diagonal matrices
- Determinant of identity and zero matrices
- Conditions when determinant becomes zero
These questions test whether students can apply properties instead of expanding determinants every time.
Minors, Cofactors and Adjoint Matrix
Several MCQs focus on the relationship between determinants and adjoint matrices. Topics include:
- Finding minors and cofactors
- Cofactor matrix and adjoint matrix
- Identities like A(adj A) = |A|I
- Value of adj(adj A)
These questions require conceptual clarity rather than lengthy calculations.
Singular and Non-Singular Matrices
The worksheet strongly emphasises identifying singular and non-singular matrices. Students are tested on:
- Conditions for existence of inverse
- Determinant equal to zero or non-zero
- Effect of determinant on solvability of equations
These MCQs are direct scoring areas if definitions are clear.
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Inverse of a Matrix Using Determinants
Many questions test understanding of inverse matrices using determinants. These include:
- Formula A⁻¹ = (1/|A|) adj A
- Conditions for inverse to exist
- Properties of inverse matrices
- Relationship between determinant and inverse
Such questions combine matrix algebra with determinant logic.
System of Linear Equations
A major portion of the worksheet deals with system of linear equations. Students are tested on:
- Unique solution, no solution, or infinitely many solutions
- Consistency and inconsistency of systems
- Determinant-based conditions for solutions
These MCQs are frequently asked in board exams.
Area of Triangle and Collinearity
Application-based questions include:
- Finding area of triangle using determinants
- Checking collinearity of three points
- Interpreting determinant value geometrically
These are easy-scoring questions if formulas are remembered.
Determinant Identities and Logic-Based Questions
Many questions test determinant identities, such as:
- |AB| = |A||B|
- |kA| and its effect on determinant
- |Aᵀ| = |A|
- Determinant of skew-symmetric matrices
These MCQs require careful reading and logical reasoning.
