Maths Chapter 4 – Determinants MCQ Question and Answers – MCQs for Practice

1.  If the equations 2x + 3y + z = 0, 3x + y – 2z = 0 and ax + 2y – bz = 0 has non-trivial solution, then

2. Find the area of the triangle whose vertices are (-2, 6), (3, -6) and (1, 5).

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

4. Given that A is a square matrix of order 3 and |A| = -4, then |adj A| is equal to

5. Question

6. Question

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

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

9. Question

10. Question

11. For a given system of equations if |A|=0 and (adj A)B≠O(zero matrix), then which of the following is correct regarding the solutions of the given equations?

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

13. If A is an invertible matrix of order 2, then det (A–1) is equal to

14. Question

15. If A is a square matrix of order 3 and |A| = 5, then the value of |2A′| is

16. Question

17. 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 =

18. Question

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

20. Which of the following conditions holds true for a system of equations to be consistent?

21. Inverse of a matrix A exists, if​

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

23. If 4x + 3y + 6z = 25, x + 5y + 7z = 13, 2x + 9y + z = 1, then z = …………….

24. 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

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

26. Question

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

28. Which of the following is correct?

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

30. Question

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

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

33. Question

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

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

36. If the points (3, -2), (x, 2), (8, 8) are collinear, then find the value of x.

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

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

39. If the system of equations x + ky – z = 0, 3x – ky – z = 0 & x – 3y + z = 0 has non-zero solution, then k is equal to

40. If A is any square matrix of order 3 x 3 such that |a| = 3, then the value of |adj. A| is?

41. If the area of the triangle is 35 sq. units with vertices (2, -6), (5, 4) and (k, 4). Then k is