(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

Describe the locus of a runner, running around a circular track and always keeping a distance of 1.5 m from the inner edge. 

Describe the locus of the door handle, as the door opens.

Describe the locus of points inside a circle and equidistant from two fixed points on the circumference of the circle. 

Describe the locus of the centres of all circles passing through two fixed points. 

Describe the locus of a point in rhombus ABCD, so that it is equidistant from

1. AB and BC;
2. B and D.

The speed of sound is 332 metres per second. A gun is fired. Describe the locus of all the people on the earth’s surface, who hear the sound exactly one second later.

Describe the locus of points at distances less than 3 cm from a given point.

Describe the locus of points at distances greater than 4 cm from a given point. 

Describe the locus of points at distances less than or equal to 2.5 cm from a given point. 

Describe the locus of points at distances greater than or equal to 35 mm from a given point. 

Sketch and describe the locus of the vertices of all triangles with a given base and a given altitude. 

In the given figure, obtain all the points equidistant from lines m and n; and 2.5 cm from O. 

By actual drawing obtain the points equidistant from lines m and n; and 6 cm from a point P, where P is 2 cm above m, m is parallel to n and m is 6 cm above n. 

A straight line AB is 8 cm long. Draw and describe the locus of a point which is:

1. always 4 cm from the line AB.
2. equidistant from A and B.
   Mark the two points X and Y, which are 4 cm from AB and equidistant from A and B. Describe the figure AXBY.

Draw a triangle ABC in which AB = 6 cm, BC = 4.5 cm and AC = 5 cm. Draw and label:

1. the locus of the centres of all circles which touch AB and AC,
2. the locus of the centres of all the circles of radius 2 cm which touch AB.
   Hence, construct the circle of radius 2 cm which touches AB and AC . 

The surface area of a sphere is 2464 cm², find its volume. 

The volume of a sphere is 38808 cm³; find its diameter and the surface area.

A spherical ball of lead has been melted and made into identical smaller balls with radius equal to half the radius of the original one. How many such balls can be made?

How many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 cm?

Eight metallic spheres; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere.