In this article, we are providing you NCERT Exemplar Solutions for all the questions of Class 12 Mathematics Chapter 4 – Determinants. Questions from NCERT Exemplar are frequently asked in CBSE Class 12 Board examination and various engineering entrance examinations like JEE Main, JEE Advanced, WBJEEE, AIPMT etc.
Important Topics of Chapter – Determinants
- Determinant of a square matrix (up to 3 × 3 matrices)
- Properties of determinants
- Adjoint and inverse of a square matrix
- Consistency, inconsistency and number of solutions of system of linear equations
- Solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.
About NCERT Exemplar Solutions Class 12 Maths:
Students must go through the basic concepts before checking the solutions given here. All the solutions of the chapter Determinants are solved by subject experts of Mathematics. Students can easily understand all the solutions as all the steps are included while solving questions.
Few problems along with their solutions from this chapter are given follows:
Question:
If the area of a triangle with vertices (- 3, 0), (3, 0) and (0, k) is 9 sq units. Then, the value of k will be
(a) 9
(b) 3
(c) -9
(d) 6
Solution: (b)
Question:
If A is a matrix of order 3 × 3, then (A2)-1 is equal to ........ .
Solution:
We know that, (An)-1 = (A-1)n, where n ∈ N.
Substituting n = 2 on both sides, we get
(A2)-1 = (A-1)2
Question:
If A is a matrix of order 3 × 3, then the number of minors in determinant of A are ........ .
Solution:
Since, the order of the matrix A is 3 × 3. It means there are 9 elements in the matrix A.
Hence, the number of minors in determinant of A is 9.
Question:
The sum of products of elements of any row with the cofactors of corresponding elements is equal to ........ .
Solution:
= Sum of products of elements of R1 with their corresponding cofactors.
Hence, the sum of products of elements of any row with the cofactors of corresponding elements is equal to value of the determinant.
Students can download the complete solutions in PDF form using the links given below:
| Types |
Number of questions |
Link to download PDF |
| Short answer type questions |
17 |
|
| Long answer type questions |
6 |
|
| Objective type questions |
14 |
|
| Fillers type questions |
10 |
|
| True/False type questions |
11 |
|
| Total |
58 |
|
About NCERT Exemplar Book Class 12 Maths:
Students must practice the questions given in these books as the level of these questions matches the difficulty level of the questions generally asked in engineering entrance exams. Each chapter of NCERT Exemplar Class 12 Maths book starts with a brief overview of the chapter followed by solved examples and unsolved exercises.
In this chapter of the book, students will get the following things.
| Brief summary of the complete chapter |
| Objective type questions or MCQs |
| Short answer type questions |
| Long answer types questions |
| Fill in the blanks |
| True and False |
Students can download the complete NCERT Exemplar book from the link given below:
