With every square matrix A of a certain order, we associate a number called the determinant of A and it is denoted by|A| or det A. If a matrix is not square, we can not associate a determinant with it.

Properties: (1)   The value of the determinant remains unaltered if the rows and columns are interchanged.

(2) If two adjacent rows (or columns) of a determinant are interchanged, the numerical value remains same but the sign of the determinant is changed.

(3) If two rows (or columns) of a determinant are identical, the value of the determinant is zero.

(4) If all the elements of any row (or column) are multiplied by the same constant, then the original determinant is multiplied by that constant.

(5) If the elements of any row (or column) of a determinant are multiplied in order by the cofactors of the corresponding elements of any other row (or column), then the sum of the products thus obtained is zero.

(6) If each element of any row (or column) is the sum of two numbers, then the determinant can be expressed as the sum of the determinants whose other rows (or columns) are not altered.

 

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ISC              Class 12                   Mathematics Previous Years Board Questions Solutions of Previous years Board Questions Inverse Trigonometric Functions (2000 to Sem 1-2021) Inverse Trigonometric Functions (2000 to Sem 1-2021) Matrices (2000 to Sem 1 – 2021) Matrices (2000 to Sem 1-2021) Determinants (2000 to Sem1-2021) Determinants (2000 to Sem1-2021) Differentiation (2000 to Sem 1- 2021) Differentiation (2000 to Sem 1- 2021) L’ Hospital’s Rule (2001 to Sem1-2021) L’ Hospital’s Rule (2001 to Sem1-2021) Rolle’s Theorem and Lagrange’s Mean Value Theorem (1998 to 2020) Rolle’s Theorem and Lagrange’s Mean Value Theorems (1998 to 2020) Maxima and Minima (2000 to Sem 1-2021) Maxima and Minima (2000 to Sem 1 – 2021) Integration (1990 – 2011) Integration (1990 – 2011) Integration (2012 to 2022) Integration (2012 to 2022) Differential Equations (1991 to 2005) Differential Equations (1991 to 2005) Differential Equations (2006 to 2022) Differential Equations (2006 to 2022) Probability (Addition and Multiplication Theorem-Conditional Probability) (1993 to 2022) Probability (Addition and Multiplication Theorem, Conditional Probability) (1993 to 2022) Probability (Baye’s Theorem) (2000 to Sem 2-2022) Probability (Baye’s Theorem) (2000 to Sem 2-2022) Probability (Probability distribution and Binomial distribution) (1992 to 2020) Probability (Probability distribution and Binomial distribution) (1992 to 2020) Application of Calculus in Commerce and Economics (2005 to Sem 1-2021) Application of Calculus in Commerce and Economics (2005 to Sem 1-2021) Linear Programming (2008 to Sem 2-2022) Linear Programming (2008 to 2022) Linear Regression (2005 to 2022)

MCQ              Class 12         Mathematics Relations and Functions Inverse Trigonometric Functions Matrices Determinants Continuity and Differentiability Tangents and Normals Maxima and Minima Increasing and Decreasing Functions Application of Calculus in Commerce and Economics (Set I) Application of Calculus in Commerce and Economics (Set II) Integration MCQs (Set 1)  Integration MCQs (Set 2) Specimen Paper for Semester 1 – 2021 – ISC – Class XII Mathematics Linear Regression

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CBSE    Class 12   NCERT Solutions    Mathematics

Inverse Trigonometric Functions

Determinants – Chapter 4

Determinants Chapter 4 Exercise 4.1 and 4.2

Determinants Chapter 4 Exercise 4.3 and 4.4

Determinants – Chapter 4 – Exercise 4.5

Determinants – Chapter 4 – Exercise Miscellaneous

Continuity and Differentiability – Chapter 5 – Exercise 5.2

Continuity and Differentiability – Chapter 5 – Exercise 5.3

Continuity and Differentiability – Chapter 5 – Exercise 5.4

Continuity and Differentiability – Chapter 5 – Exercise 5.5

Continuity and Differentiability – Chapter 5 – Exercise 5.6

Continuity and Differentiability – Chapter 5 – Exercise 5.7

Integrals – Chapter 7 – Exercise 7.1

Integrals – Chapter 7 – Exercise 7.2

Integrals – Chapter 7 – Exercise 7.3

Integrals – Chapter 7- Exercise 7.4

MCQ              Class 12         Mathematics Relations and Functions Inverse Trigonometric Functions Matrices Determinants Continuity and Differentiability Tangents and Normals Maxima and Minima Increasing and Decreasing Functions Application of Calculus in Commerce and Economics (Set I) Application of Calculus in Commerce and Economics (Set II) Integration MCQs (Set 1)  Integration MCQs (Set 2) Specimen Paper for Semester 1 – 2021 – ISC – Class XII Mathematics Linear Regression

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ISC- Class 12 – Mathematics – Sem 2 – 2022 – Chapterwise Questions                       Differential Equations

 

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ISC – Sem 1 – 2021 – Examination 

Question 24

Select and write the correct option for the following question:

If then the value of A is equal to:

1.     0
2.     xyz
3.     1
4.    

Answer:   ____(a)_______

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