ICSE Class 10 Locus — Mock Test (2027)

Free online mock test for Locus (ICSE Class 10 Mathematics) — 20 competency-based questions based on the latest CISCE 2027 syllabus, with instant marking. Try the samples below, then take the full test free.

Sample questions

1. 1.Given: CP is the bisector of angle C of Δ ABC. Which property explains why point P is equidistant from sides AC and BC?
   • A.P lies on the angle bisector of ∠C, so it is equidistant from AC and BC.
   • B.P is the midpoint of side AB, making it equidistant from AC and BC.
   • C.P divides CP in the ratio of the adjacent sides, so distances are equal.
   • D.P lies on the perpendicular bisector of AB, ensuring equal distances.
2. 2.Points A, B, and C represent three towers with AB = 60 m, BC = 73 m, and CA = 52 m. Using a scale of 10 m to 1 cm, draw ΔABC and find the point equidistant from A, B, and C. What is the actual distance of this point from any of the towers?
   • A.30 m
   • B.37 m
   • C.45 m
   • D.50 m
3. 3.In the given diagram , a point P moves such that it remains equidistant from a fixed point O. Which of the following best describes the path (locus) traced by point P?
   • A.A straight line passing through O
   • B.A circle with O as the centre and the constant distance as radius
   • C.A parabola with O as the focus
   • D.An ellipse with O as one of its foci
4. 4.A point $P$ moves two units above the $x$-axis at a constant distance. The locus of point $P$ is:
   • A.$x = 2$
   • B.$y = -2$
   • C.$y = 2$
   • D.$x = -2$
5. 5.Locus of a point which remaining at a distance of $6\mathrm{cm}$ from line $PQ$ is:
   • A.Two parallel lines below the line $PQ$ at a distance of $6\mathrm{cm}$.
   • B.Two parallel lines on both sides of $PQ$ at a distance $6\mathrm{cm}$.
   • C.Two parallel lines above $PQ$ at a distance of $6\mathrm{cm}$.
   • D.None of these.