NDA Mathematics Question (2025) — Solution

Step-by-step solution

The given curve is y = |x - 3| and the line is y = 3. To find the points of intersection, we equate the two equations: |x - 3| = 3 x - 3 = 3 or x - 3 = -3 x = 6 or x = 0 The points of intersection are (0, 3) and (6, 3). The vertex of the curve y = |x - 3| is at (3, 0). The area bounded by the curve and the line forms a triangle with vertices (0, 3), (6, 3), and (3, 0). The length of the base of this triangle (along the line y = 3) is 6 - 0 = 6 units. The height of the triangle (perpendicular distance from the vertex to the base) is 3 - 0 = 3 units. The required area is given by: Area = 1 2 base height Area = 1 2 6 3 = 9 square units. Answer: 9 square units