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.Draw an angle ABC = 75°. The locus of all the points equidistant from AB and BC is:
   • A.A circle centered at B with radius equal to the length of AB
   • B.The angle bisector of ∠ABC
   • C.A line parallel to AB passing through point C
   • D.The perpendicular bisector of segment AC
2. 2.A circle with centre O and radius $r$ cm is the locus of a point which moves in a plane in such a way that its distance from the fixed point O is always equal to $r$ cm. What does the concept of locus represent in this context?
   • A.The locus is the fixed point O itself, as it remains stationary while the point moves.
   • B.The locus is the path traced by the moving point, which forms a circle since every point on it is at a constant distance $r$ cm from O.
   • C.The locus is the radius $r$ cm, as it defines the distance from O to the moving point.
   • D.The locus is the set of all possible distances from O, varying continuously as the point moves.
3. 3.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.$x = -2$
4. 4.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
5. 5.Locus of a point whose distance from origin is always equal to is:
   • A.$a^2 + b^2 = 2$
   • B.$a^2 - b^2 = 4$
   • C.$a^2 + b^2 = 4$
   • D.$a^2 - b^2 = 2$