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

In  Δ ABC, the perpendicular bisector of AB and AC meet at 0. Prove that O is equidistant from the three vertices. Also, prove that if M is the mid-point of BC then OM meets BC at right angles. 

In a quadrilateral PQRS, if the bisectors of ∠ SPQ and ∠ PQR meet at O, prove that O is equidistant from PS and QR. 

In a quadrilateral ABCD, if the perpendicular bisectors of AB and AD meet at P, then prove that BP = DP. 

The radius of a sphere is 9 cm. It is melted and drawn into a wire of diameter 2 mm. Find the length of the wire in metre. 

Find the length of the wire of diameter 4 m that can be drawn from a solid sphere of radius 9 m. 

Find the radius of a sphere whose surface area is equal to the area of the circle of diameter 2.8 cm 

Find the radius of the sphere whose surface area is equal to its volume .

How many lead balls of radii 1 cm each can be made from a sphere of 8 cm radius?

A sphere has the same curved surface area as the curved surface area of a cone of height 36 cm and base radius 15 cm . Find the radius of the sphere . 

A solid metallic cylinder has a radius of 2 cm and is 45 cm tall. Find the number of metallic spheres of diameter 6 cm that can be made by recasting this cylinder . 

Find the volume of the hollow sphere whose inner diameter is 8 cm and the thickness of the material of which it is made is 1 cm . 

The sum of first 14 terms of an A.P. is 1050 and its 14^th term is 140. Find the 20^th term.

Find the sum of first 10 terms of the A.P.

4 + 6 + 8 + .............

Find the sum of first 20 terms of an A.P. whose first term is 3 and the last term is 57.

How many terms of the series 18 + 15 + 12 + ........ when added together will give 45?

Find the 5^th term of the G.P. `5/2, 1, .........`

The first two terms of a G.P. are 125 and 25 respectively. Find the 5^th and the 6^th terms of the G.P.

Find the sum of the sequence `-1/3, 1, -3, 9, ..........` upto 8 terms.

Find a G.P. for which the sum of first two terms is – 4 and the fifth term is 4 times the third term.

The internal and external diameters of a hollow hemi-spherical vessel are 21 cm and 28 cm respectively. Find volume of material of the vessel.