English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

Solve the following quadratic equation for x:

x² − 4ax − b² + 4a² = 0

Solve the following quadratic equation by factorisation.

m² - 11 = 0

If `P(a/2,4)`is the mid-point of the line-segment joining the points A (−6, 5) and B(−2, 3), then the value of a is

Two cubes each of volume 27 cm³ are joined end to end to form a solid. Find the surface area of the resulting cuboid. 

Point P(x, 4) lies on the line segment joining the points A(−5, 8) and B(4, −10). Find the ratio in which point P divides the line segment AB. Also find the value of x.

Find the area of the quadrilateral ABCD, whose vertices are A(−3, −1), B (−2, −4), C(4, − 1) and D (3, 4).

Solve the following quadratic equations by factorization:

\[16x - \frac{10}{x} = 27\]

Solve the following quadratic equations by factorization:\[\frac{1}{x - 3} + \frac{2}{x - 2} = \frac{8}{x}; x \neq 0, 2, 3\]

Solve the following quadratic equations by factorization:

\[9 x^2 - 6 b^2 x - \left( a^4 - b^4 \right) = 0\]

Solve the following quadratic equations by factorization: \[2 x^2 + ax - a^2 = 0\]

Solve the following quadratic equations by factorization: \[\frac{16}{x} - 1 = \frac{15}{x + 1}; x \neq 0, - 1\]

Solve the following quadratic equations by factorization:

\[\frac{4}{x} - 3 = \frac{5}{2x + 3}, x \neq 0, - \frac{3}{2}\]

Solve the following quadratic equations by factorization: \[\frac{x - 4}{x - 5} + \frac{x - 6}{x - 7} = \frac{10}{3}; x \neq 5, 7\]

Solve the following quadratic equations by factorization:

\[\frac{x - 2}{x - 3} + \frac{x - 4}{x - 5} = \frac{10}{3}; x \neq 3, 5\]

Solve the following quadratic equations by factorization: \[\frac{5 + x}{5 - x} - \frac{5 - x}{5 + x} = 3\frac{3}{4}; x \neq 5, - 5\]

Solve the following quadratic equations by factorization: \[\frac{3}{x + 1} - \frac{1}{2} = \frac{2}{3x - 1}, x \neq - 1, \frac{1}{3}\]

Solve the following quadratic equations by factorization: \[\frac{3}{x + 1} + \frac{4}{x - 1} = \frac{29}{4x - 1}; x \neq 1, - 1, \frac{1}{4}\]

Solve the following quadratic equations by factorization: \[\frac{2}{x + 1} + \frac{3}{2(x - 2)} = \frac{23}{5x}; x \neq 0, - 1, 2\]

Solve the following quadratic equations by factorization: \[\sqrt{3} x^2 - 2\sqrt{2}x - 2\sqrt{3} = 0\]

Find the roots of the quadratic equation \[\sqrt{2} x^2 + 7x + 5\sqrt{2} = 0\].