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

In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = 2x³ + 4x + 6 and g(x) = x + 1

In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = x³ + x² + 3x + 175 and g(x) = x + 5.

Find the value of the constant a and b, if (x – 2) and (x + 3) are both factors of expression x³ + ax² + bx - 12.

The expression 2x³ + ax² + bx - 2 leaves the remainder 7 and 0 when divided by (2x - 3) and (x + 2) respectively calculate the value of a and b. With these value of a and b factorise the expression completely.

If x – 2 is a factor of 2x³ - x² - px - 2.
Find the value of p

If x – 2 is a factor of 2x³ - x² - px - 2.
with the value of p, factorize the above expression completely.

Show that 2x + 7 is a factor of 2x³ + 5x² - 11 x - 14. Hence factorise the given expression completely, using the factor theorem.

Using factor theorem, show that (x - 3) is a factor of x³ - 7x² + 15x - 9, Hence, factorise the given expression completely.

Find the volume and surface area of a sphere of diameter 21 cm.

The volume of a sphere is 905 1/7 cm³, find its diameter.

There is surface area and volume of a sphere equal, find the radius of sphere.

There is a ratio 1: 4 between the surface area of two spheres, find the ratio between their radius.

A spherical cannon ball, 28 cm in diameter is melted and recast into a right circular conical mould, the base of which is 35 cm in diameter. Find the height of the cone, correct to one place of decimal.

The radius of two spheres are in the ratio of 1 : 3. Find the ratio between their volume.

A sphere cut out from a side of 7 cm cubes. Find the volume of this sphere?

How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter?

A vessel is in he form of an inverted cone. Its height is 11 cm., and the radius of its top which is open is 2.5 cm. It is filled with water up to the rim. When lead shots, each of which is a sphere of radius 0.25 cm., are dropped 2 into the vessel, `2/5`th of the water flows out. Find the number of lead shots dropped into the vessel.

The radius of a sphere is 10 cm. If we increase the radius 5% then how many % will increase in volume?

The cylinder of radius 12 cm have filled the 20 cm with water. One piece of iron drop in the stands of water goes up 6.75 cm. Find the radius of sphere piece.

The surface area of a solid metallic sphere is 616 cm². It is melted and recast into smaller spheres of diameter 3.5 cm. How many such spheres can be obtained?