English Medium कक्षा १० - CBSE Question Bank Solutions

The sum of the squares of two consecutive multiples of 7 is 637. Find the multiples ?

Solve the following quadratic equation for x:

`4sqrt3x^3+5x-2sqrt3=0`

A vessel is in the form of hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the total surface area of the vessel. `[\text{Use}pi=22/7]`

Show that the points (−2, 3), (8, 3) and (6, 7) are the vertices of a right triangle ?

If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:

In Fig. 6, OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region. `[\text\ User=22/7]`

From a solid cylinder of height 7 cm and base diameter 12 cm, a conical cavity of same height and same base diameter is hollowed out. Find the total surface area of the remaining solid. [User `pi22/7`]

Solve for x: `3x^2-2sqrt3x+2=0`

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:

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