English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

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`

Solve the equation:`14/(x+3)-1=5/(x+1); xne-3,-1` , for x

Solve  (i) x²  + 3x – 18 = 0

(ii) (x – 4) (5x + 2) = 0

(iii) 2x² + ax – a2 = 0; where ‘a’ is a real number

Solve the following quadratic equations

(i) x²  + 5x = 0         (ii) x²  = 3x          (iii) x² = 4

Solve the following quadratic equations

(i) 7x² = 8 – 10x

(ii) 3(x² – 4) = 5x

(iii) x(x + 1) + (x + 2) (x + 3) = 42

Solve for x : 12abx² – (9a² – 8b² ) x – 6ab = 0

Find the roots of the following quadratic equation by factorisation:

x² – 3x – 10 = 0

Find the roots of the following quadratic equation by factorisation: 

2x² + x – 6 = 0

Find the roots of the following quadratic equation by factorisation:

`sqrt2 x^2 +7x+ 5sqrt2 = 0`