HOT PRACTICE TEST
Chapter 4 – Determinants
Class XII Mathematics • 25 Marks • 60 Minutes
Geometrical Meaning of Determinant
Section A – 6 × 1 = 6
1. Find the determinant of [[2,3],[4,5]].
2. When is the determinant of a square matrix zero?
3. What happens to a determinant if two rows are interchanged?
4. State the determinant of the identity matrix.
5. If two rows are proportional, what is the determinant?
6. Can a determinant be used to test whether a system has a unique solution?
Section B – 3 × 2 = 6
1. Evaluate |2 3; 4 5| and interpret the sign of the result.
2. Using determinant properties, simplify a determinant having identical rows.
3. Find the area of the triangle with vertices (0,0), (2,0), and (0,3).
Section C – 3 × 3 = 9
1. Use Cramer's rule to solve 2x+y=5 and x−y=1.
2. Find the value of k for which the equations x+2y=3 and 2x+ky=6 have infinitely many solutions.
3. Find the area of the triangle with vertices (1,2),(3,5),(5,2) using determinants.
Section D – 1 × 4 = 4
1. Using determinant properties, derive the condition on a,b,c for the three points (a,a²),(b,b²),(c,c²) to be collinear. Interpret the result geometrically.