English Medium Class 10 - CBSE Question Bank Solutions

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`

A toy is in the form of a cone of base radius 3.5 cm mounted on a hemisphere of base diameter 7 cm. If the total height of the toy is 15.5 cm, find the total surface area of the top (Use π = 22/7)

Solve the following quadratic equation for x : 4x² − 4a²x + (a⁴ − b⁴) =0.

The number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm, is:

In Fig. 4, from the top of a solid cone of height 12 cm and base radius 6 cm, a cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid. (Use `pi=22/7` and `sqrt5=2.236`)

A solid wooden toy is in the form of a hemisphere surrounded by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 166 `5/6`  cm³. Find the height of the toy. Also, find the cost of painting the hemispherical part of the toy at the rate of Rs 10 per cm^{2 .}[Use`pi=22/7`]

Solve the equation `4/x-3=5/(2x+3); xne0,-3/2` for x .

In Fig. 5, from a cuboidal solid metallic block, of dimensions 15cm ✕ 10cm ✕ 5cm, a cylindrical hole of diameter 7 cm is drilled out. Find the surface area of the remaining block [Use

`pi=22/7`]

The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and original fraction is `29/20`. Find the original fraction.

Solve for x :

`2/(x+1)+3/(2(x-2))=23/(5x), x!=0,-1,2`

From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid [take π=22/7]

Solve the equation `3/(x+1)-1/2=2/(3x-1);xne-1,xne1/3,`

Solve for x :

`3/(x+1)+4/(x-1)=29/(4x-1);x!=1,-1,1/4`