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.Which of the following statement is correct:
   • A.A point $Q$ moving in a plane about a fixed line as on are with same centre.
   • B.A moving point $Q$ in a plane about another point in such a way that its distance is constant.
   • C.A point equidistant from two fixed non-parallel $AB$ and $CD$ in the same plane.
   • D.A point $Q$ moving in a plane about another point in such a way that its distance from a fixed line $AB$ is constant.
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.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.O is a fixed point. Point P moves along a fixed line AB. Q is a point on OP produced such that OP = PQ. What is the locus of point Q?
   • A.A line parallel to AB and twice as far from O as AB is
   • B.A circle centered at O with radius equal to the distance from O to AB
   • C.A line perpendicular to AB passing through O
   • D.A line identical to AB but shifted closer to O