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

A solid, consisting of a right circular cone standing on a hemisphere, is placed upright, in a right circular cylinder, full of water and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of the hemisphere is 2 cm and the height of the cone is 4 cm. Give your answer to the nearest cubic centimetre.

A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones used.

A conical tent is to accommodate 77 persons. Each person must have 16 m³ of air to breathe. Given the radius of the tent as 7 m, find the height of the tent and also its curved surface area. 

Find the Compound Interest on Rs. 2,000 for 3 years at 15% per annum Compounded annually.

Find the difference between the simple interest and compound interest on 2,500 for 2 years at 4% p.a., compound interest being reckoned semi-annualy.

A sum of money is lent out at compound interest for two years at 20% p.a., being reckoned yearly. If the same sum of the money was lent Gut at compound interest of the same rate of percent per annum C.I., being reckoned half yearly would have fetched Rs. 482 more by way of interest. Calculate the sum of money lent out.

A sum of money amounts to ₹ 2,240 at 4 % p.a., simple interest in 3 years. Find the interest on the same sum for 6 months at 3`(1)/(2)`% p.a.

Use the factor theorem to determine that x - 1 is a factor of x⁶ - x⁵ + x⁴ - x³ + x² - x + 1.

Use the factor theorem to factorise completely x³ + x² - 4x - 4.

Find the value of a , if (x - a) is a factor of x³ - a²x + x + 2.

If (x - 2) is a factor of the expression 2x³ + ax² + bx - 14 and when the expression is divided by (x - 3), it leaves a remainder 52, find the values of a and b.

Show that (x - 1) is a factor of x³ - 7x² + 14x - 8. Hence, completely factorise the above expression.

Given that x + 2 and x + 3 are factors of 2x³ + ax² + 7x - b. Determine the values of a and b.

In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = x³ - 3x² + 4x - 4 and g(x) = x - 2

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.