Determinants Class 12 MCQs Questions with Answers

1. The area of a triangle with vertices (-3, 0), (3, 0) and (0, k) is 9 sq. units. The value of k will be

2. Using determinants, find the equation of the line joining the points (1, 2) and (3, 6).

3. A non-trivial solution of the system of equations x + λy + 2z = 0, 2x + λz = 0, 2λx – 2y + 3z = 0 is given by x : y : z =

4. Solve the following system of equations x – y + z = 4, x – 2y + 2z = 9 and 2x + y + 3z = 1.

5. Find the area of the triangle with vertices P(4, 5), Q(4, -2) and R(-6, 2).

6. If the points (2, -3), (k, -1) and (0, 4) are collinear, then find the value of 4k.

7. If the system of equations 2x + 3y + 5 = 0, x + ky + 5 = 0, kx – 12y – 14 = 0 has non-trivial solution, then the value of k is

8. If A and B are invertible matrices, then which of the following is not correct?

9. The minor Mij of an element aij of a determinant is defined as the value of the determinant obtained after deleting the​

10.  A system of linear equations AX = B is said to be inconsistent, if the system of equations has​

11. In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has value

12.  If A B be two square matrices such that AB = O, then

13. If A is a square matrix of order 3 and |A| = 7 then |AT| =​

14. If A is a symmetric matrix, then At =

15. System of equations AX = B is inconsistent if​

16.  

The following system of equations has

x + 3y + 3z = 2

x + 4y + 3z = 1

x + 3y + 4z = 2​

17. If A is a square matrix of order 3 and |A| = 5 then |3A| = ?​

18. Inverse of a matrix A exists, if​

19. We can add two matrices having real numbers A and B if their

20. In matrices (AB)t equals to