English Medium इयत्ता १० - CBSE Question Bank Solutions for Mathematics

If the points  A(4,3)  and B( x,5) lie on the circle with center  O(2,3 ) find the value of x .

Find the centroid of ΔABC  whose vertices are A(2,2) , B (-4,-4) and C (5,-8).

In what ratio does the point C (4,5) divides the join of A (2,3)  and B (7,8) ?

 If the points  A (2,3),  B (4,k ) and C (6,-3) are collinear, find the value of k.

Find the coordinates of the points of trisection of the line segment joining the points (3, –2) and (–3, –4) ?

If the quadratic equation (c² – ab) x² – 2 (a² – bc) x + b² – ac = 0 in x, has equal roots, then show that either a = 0 or a³ + b³ + c³ = 3abc ?

Solve for x:

4x² + 4bx − (a² − b²) = 0

Find the ratio in which the point (−3, k) divides the line-segment joining the points (−5, −4) and (−2, 3). Also find the value of k ?

Solve the given quadratic equation for x : 9x² – 9(a + b)x + (2a² + 5ab + 2b²) = 0 ?

A cylindrical tub, whose diameter  is 12 cm and height 15 cm is full of ice-cream. The whole ice-cream is to be divided into 10 children in equal ice-cream cones, with conical base surmounted by hemispherical top. If the height of conical portion is twice the diameter of base, find the diameter of conical part of ice-cream cone ?

A metallic cylinder has radius 3 cm and height 5 cm. To reduce its weight, a conical hole is drilled in the cylinder. The conical hole has a radius of `3/2` cm and its depth is `8/9 `cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape.

In Figure 4, from a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside the region. Find the area of the shaded region.\[[Use\pi = 3 . 14]\]

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`