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

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.

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.