English Medium इयत्ता १० - CBSE Question Bank Solutions for Mathematics

Solve the following quadratic equation for x: x² – 2ax – (4b² – a²) = 0

Due to sudden floods, some welfare associations jointly requested the government to get 100 tents fixed immediately and offered to contribute 50% of the cost. If the lower part of each tent is of the form of a cylinder of diameter 4.2 m and height 4 m with the conical upper part of same diameter but of height 2.8 m, and the canvas to be used costs Rs. 100 per sq. m, find the amount, the associations will have to pay. What values are shown by these associations? [Use π=22/7]

A hemispherical bowl of internal diameter 36 cm contains liquid. This liquid is filled into 72 cylindrical bottles of diameter 6 cm. Find the height of each bottle, if 10% liquid is wasted in this transfer.

A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of Rs. 5 per 100 sq. cm. [Use π = 3.14]

504 cones, each of diameter 3.5 cm and height 3 cm, are melted and recast into a metallic sphere. Find the diameter of the sphere and hence find its surface area.
[Use π=22/7]

If the total surface area of a solid hemisphere is 462 cm2 , find its volume.[Take π=22/7]

The largest possible sphere is carved out of a wooden solid cube of side 7 em. Find the volume of the wood left. (Use\[\pi = \frac{22}{7}\]).

Water in a canal, 6 m wide and 1.5 m deep, is flowing at a speed of 4 km/h. How much area will it irrigate in 10 minutes, if 8 cm of standing water is needed for irrigation?

In Figure 2, ABCD is a trapezium of area 24.5 sq. cm. In it, AD|| BC, ∠ DAB = 900, AD = 10 cm and BC = 4 cm. If ABE is a quadrant of a circle, find the area of the shaded region. [Take π=22/7]

150 spherical marbles, each of diameter 1.4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in  water. Find the rise in the level of water in the vessel.

Solve for x: `(x-3)/(x-4)+(x-5)/(x-6)=10/3; x!=4,6`

Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right-angled isosceles triangle.

Solve for x

:`1/((x-1)(x-2))+1/((x-2)(x-3))=2/3` , x ≠ 1,2,3

In Fig. 5, is a decorative block, made up two solids – a cube and a hemisphere. The base of the block is a cube of side 6 cm and the hemisphere fixed on the top has diameter of 3.5 cm. Find the total surface area of the bock `(Use pi=22/7)`

Solve for x

`(2x)/(x-3)+1/(2x+3)+(3x+9)/((x-3)(2x+3)) = 0, x!=3,`

The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder. `("use " pi=22/7)`

Find x in terms of a, b and c: `a/(x-a)+b/(x-b)=(2c)/(x-c)`

Solve for x : `(x+1)/(x-1)+(x-1)/(x+2)=4-(2x+3)/(x-2);x!=1,-2,2`

A right circular cone of radius 3 cm, has a curved surface area of 47.1 cm². Find the volume of the cone. (use π 3.14).

Solve the following quadratic equation for x:

`x^2+(a/(a+b)+(a+b)/a)x+1=0`