CUET 2024 Maths Chapter 4 – Determinants MCQ Question and Answers – MCQs for Practice

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

2. 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?

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

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

5. Question

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

7. 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

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

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

10. Question

11. Question

12. Question

13. 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 =

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

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

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

17. Which of the following is correct?

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

19. Question

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

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

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

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

24. Question

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

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

27. Inverse of a matrix A exists, if​

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

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

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

31. Question

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

33. Question

34. 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

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

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

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

38. Question

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

40. Question

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