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

If a, b, c are in continued proportion and a(b – c) = 2b, prove that: `a - c = (2(a + b))/a`.

Find the arithmetic mean of –5 and 41.

Find the arithmetic mean of 3x – 2y and 3x + 2y.

Find the arithmetic mean of (m + n)² and (m – n)².

What number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional?

What least number must be added to each of the numbers 5, 11, 19 and 37, so that they are in proportion?

What quantity must be added to each term of the ratio a + b: a - b to make it equal to (a + b)² : (a - b)² ?

Find the third proportional to:
x - y, x² - y²

Find the third proportional to:
`a/b + b/c, sqrt(a^2 + b^2)`.

Find the fourth proportional to:
2xy, x², y²

Find the fourth proportional to:
x³ - y², x⁴ + x²y² + y⁴, x - y.

Find the two numbers such that their mean proprtional is 24 and the third proportinal is 1,536.

Using the properties of proportion, solve for x, given. `(x^4 + 1)/(2x^2) = (17)/(8)`.

If b is the mean proportional between a and c, prove that `(a^2 - b^2 + c^2)/(a^-2 -b^-2 + c^-2)` = b⁴.

If ax = by = cz, prove that
`x^2/(yz) + y^2/(zx) + z^2/(xy) = (bc)/a^2 + (ca)/b^2 + (ab)/c^2`.

If a, b, c are in continued proportion, prove that a : c = (a² + b²) : (b² + c²).

If a, b, c, d are in continued proportion, prove that (b − c)² + (c − a)² + (d − b)² = (d − a)².

If q is the mean proportional between p and r, prove that
`p^2 - q^2 + r^2 = q^4[(1)/p^2 - (1)/q^2 + (1)/r^2]`.

If `a/b = c/d` Show that a + b : c + d = `sqrt(a^2 + b^2) : sqrt(c^2 + d^2)`.

If a : b = c : d, show that (a - c) b² : (b - d) cd = (a² - b² - ab) : (c² - d² - cd).