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

Prove that (5x - 4) is a factor of the polynomial f(x) = 5x³ - 4x² - 5x +4. Hence factorize It completely.

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?

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.

A hemispherical bowl of internal radius 9 cm is full of liquid. This liquid is to be filled into conical shaped small containers each of diameter 3 cm and height 4 cm.  How many containers are necessary to empty the bowl?

The total area of a solid metallic sphere is 1256 cm². It is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate: the number of cones recasted [π = 3.14]

The surface area of a solid metallic sphere is 2464 cm². It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate : the number of cones recast.  `("Take"  pi =22/7)`