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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-20-CT
Loci — Full Chapter Test
Chapter: Loci
Topic: Complete chapter — all topics
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • This is a full-length test covering the whole chapter — every topic is included.
  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
The locus of points at a fixed distance from a fixed point is a:
  • A.line
  • B.circle
  • C.pair of lines
  • D.parabola
2.
The locus equidistant from two fixed points is the:
  • A.circle
  • B.perpendicular bisector
  • C.angle bisector
  • D.midpoint
3.
The locus equidistant from two intersecting lines is the:
  • A.perpendicular bisector
  • B.pair of angle bisectors
  • C.circle
  • D.midpoint
4.
The fixed point is the:
  • A.radius
  • B.centre
  • C.diameter
  • D.chord
5.
This locus is a:
  • A.curve
  • B.straight line
  • C.circle
  • D.point
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Name the locus of points $3$ cm from a point $O$.
7.
Name the locus equidistant from $A$ and $B$.
8.
Name the locus equidistant from two intersecting lines.
9.
What is the centre of such a locus?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Describe the locus of a point that is always $4$ cm from a fixed point $A$.
11.
Describe the locus of a point equidistant from two points $A$ and $B$.
12.
Describe the locus of a point equidistant from two intersecting lines.
13.
Describe the locus of points $6$ cm from one of two points $6$ cm apart.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Describe the locus of a point $P$ whose distance from a fixed point $O$ is always $5$ cm, and state how many such points lie on a given line through $O$.
15.
Find the equation of the locus of a point equidistant from $A(1,2)$ and $B(5,6)$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) circle
  2. (B) perpendicular bisector
  3. (B) pair of angle bisectors
  4. (B) centre
  5. (B) straight line
Section B — Short Answer (2 marks)
  1. A circle of radius $3$ cm centred at $O$.
  2. The perpendicular bisector of $AB$.
  3. The pair of angle bisectors.
  4. The fixed point.
Section C — Short Answer (3 marks)
  1. A circle of radius $4$ cm, centre $A$.
  2. The perpendicular bisector of $AB$.
  3. The pair of bisectors of the angles between them.
  4. A circle of radius $6$ cm around that point.
Section D — Long Answer (5 marks)
  1. A circle of radius $5$ cm centred at $O$; a line through $O$ meets it at $2$ points.
  2. $x+y=7$.
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