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Determinants

ICSE · Class 12 · Mathematics

Practice quiz for Determinants — ICSE Class 12 Mathematics. MCQs and questions with answers to test your preparation.

100 questions30 flashcards5 concepts

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A visual representation defining a determinant as a scalar value associated with a square matrix, showing its notation and basic structure.
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Quick Quiz: Determinants

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1

The determinant of a 2×2 matrix [[3,5],[2,4]] is:

2

For a square matrix A of order 3, |kA| equals:

3

If two rows of a determinant are identical, then the value of the determinant is:

4

The cofactor C₁₁ of element 5 in matrix [[5,3],[2,4]] is:

100 Questions·
multiple choicetrue false

Sample Questions

1true false
1 marks

Every rectangular matrix has a determinant.

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False

Determinants are defined only for square matrices. Rectangular matrices (m×n with m≠n) do not have determinants.

2multiple choice
1 marks

For matrices A and B of the same order, |AB| equals:

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|A| × |B|

The product rule for determinants: |AB| = |A|·|B|. This is a fundamental property of determinants.

3true false
1 marks

The value of |A| = |Aᵀ| for any square matrix A.

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True

Transposing a matrix does not change its determinant: |Aᵀ| = |A|. This is because determinant expansion by rows equals expansion by columns.

4multiple choice
1 marks

For a non-singular matrix A, A⁻¹ equals:

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(adj A)/|A|

A⁻¹ = (1/|A|) × adj A = (adj A)/|A|. This requires |A| ≠ 0 (non-singular).

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What are the important topics in Determinants for ICSE Class 12 Mathematics?
Key topics in Determinants include Determinants: Complete Concept Map, Complete Mind Map of Determinants Chapter, Determinants - Concept Hierarchy and Structure. These are the concepts ICSE Class 12 examiners draw on most — study them first, then practise related questions.
How to score full marks in Determinants — ICSE Class 12 Mathematics?
Understand the core concepts first, then work through the 100 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

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Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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