## Maths Chapter 4 – Determinants MCQ Question Answers for Various Entrance Exams

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

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

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

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

5. Question
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6. Question
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d.

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

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

9. Question
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b.
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d.

10. Question
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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?
a.
b.
c.
d.

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

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

14. Question
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b.
c.
d.

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

16. Question
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b.
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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 =
a.
b.
c.
d.

18. Question
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b.
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d.

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

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

21. Inverse of a matrix A exists, if​
a.
b.
c.
d.

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

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

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
a.
b.
c.
d.

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

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