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.Construct a rhombus PQRS with diagonals PR = 8 cm and QS = 6 cm. By construction, locate point X equidistant from sides PQ and PS, and also equidistant from vertices R and S. What is the length of XR?
   • A.2.5 cm
   • B.3.2 cm
   • C.4.0 cm
   • D.5.0 cm
2. 2.A point $Q$ is always at the distance of 4 units from (3, 2). Equation of locus of a point $Q$, will be
   • A.$x^{2} + y^{2} + 6x + 4y - 3 = 0$
   • B.$x^{2} + y^{2} + 6x - 4y - 3 = 0$
   • C.$x^{2} + y^{2} - 6x - 4y - 3 = 0$
   • D.$x^{2} + y^{2} - 6x - 4y + 3 = 0$
3. 3.Construct an isosceles triangle ABC with AB = 6 cm and BC = AC = 4 cm. Bisect ∠C internally and mark a point P on this bisector such that CP = 5 cm. Points Q and R are 5 cm from P and also 5 cm from the line AB. Where are Q and R located?
   • A.On the angle bisector of ∠C, 5 cm from P.
   • B.On a circle centered at P with radius 5 cm.
   • C.On a line parallel to AB, 5 cm away from AB, and 5 cm from P.
   • D.On the perpendicular bisector of AB, 5 cm from P.
4. 4.Two straight lines PQ and PK cross each other at P at an angle of 75°. S is a stone on the road PQ, 800 m from P towards Q. Using a scale of 1 cm = 100 m, where is the flag staff X located if it is equidistant from P and S and also equidistant from the roads PQ and PK?
   • A.At the intersection of PS and PK
   • B.At the intersection of the perpendicular bisector of PS and the angle bisector of ∠KPS
   • C.At the midpoint of PS
   • D.At the intersection of PQ and the angle bisector of ∠KPS
5. 5.The locus of a point $P$ in space which is always at a distance of $5\mathrm{cm}$ from a fixed point will be the:
   • A.Sphere
   • B.Centre of circle
   • C.Centre of sphere
   • D.None of the above