# Mathematics Solved problems

## Contents

- 1 Class 8
- 2 Class 9
- 3 Class 10
- 3.1 Chapter 2 - Sets
- 3.2 Chapter 3 - Progressions
- 3.3 Chapter 4 - Permutations and combinations
- 3.4 Chapter 6 - Statistics
- 3.5 Chapter 7 - Surds
- 3.6 Chapter 8 - Polynomials
- 3.7 Chapter 9 - Quadratic Equations
- 3.8 Chapter 11 - Pythagoras Theorem
- 3.9 Chapter 12 - Trigonometry
- 3.10 Chapter 13 - Co-ordinate Geometry
- 3.11 Chapter 15 - Circles Tangent Properties - Exercise
- 3.12 Chapter 16 - Mensuration
- 3.13 Chapter 17 - Graphs and Polyhedra
- 3.14 Problem 1

# Class 8

# Class 9

### Chapter 2-Banking

- Exercise 2.2.5

4. Prahalad invests a sum of money in a bank and gets Rs 3307.5 and Rs3472.87 in and 3rd years respectively. Find the sum he invest.[[1]]

# Class 10

Please see all chapter Formula . File:Formulas.pdf

### Chapter 2 - Sets

- Exercise 2.2 In a village, out of 120 farmers, 93 farmers have grown vegetables, 63 farmers have grown flowers, 45 have grown sugarcane, 45 farmers have grown vegetables and flowers, 24 farmers have grown flowers and sugarcane, 27 farmers have grown vegetables and sugarcane. Find how many farmers have grown vegetables, flowers and sugarcane.
**Solution**

### Chapter 3 - Progressions

#### Progressions

#### Types of Progressions

1.A company employed 400 persons in the year 2001 and each year increased by 35 persons. In which year the number of employees in the company will be 785? Solution
click here for solution

2. 2. The sum of 6 terms which form an A.P is 345. The difference between the first and last terms is 55. Find the terms.
click here for solution

3. Find two numbers whose arithmetic mean exceeds their geometric mean by 2, and whose harmonic mean is one-fifth of the larger number . Find the terms. Solution
click here for solution

4. If 'a' be the arithmetic mean between 'b' and 'c', and 'b' the geometric mean between 'a' and 'c', then prove that 'c' will be the harmonic mean between 'a' and 'b'. Solution
click here for solution

### Chapter 4 - Permutations and combinations

#### Problem 1

How many 3-digits numbers can be formed from the digits 0,1,2,3 and 4 without repetation
**Solution**

#### Problem 2

How many 4-digit numbers can be formed using the digits 1,2,3,7,8 and 9 (repetitions not allowed)

- How many of these are less than 6000?
- How many of these are even?
- How many of these end with 7?
**Solution**

#### Problem 3

How many 1) lines 2) Triangles can be drawn through 8 points on a circle?**Solution**

### Chapter 6 - Statistics

### Chapter 7 - Surds

### Chapter 8 - Polynomials

Problems of Chapter 8-Polynomials 10 STD

**Solution**

### Chapter 9 - Quadratic Equations

1.If P & q are the roots of the equation find the value of

"solution"

2.The altitude of a triangle is 6cm greter than its base. If its area is 108cmsq .Find its base.

"solution"

3.Solve By completing the square.

"solution"

### Chapter 11 - Pythagoras Theorem

### Chapter 12 - Trigonometry

### Chapter 13 - Co-ordinate Geometry

### Chapter 15 - Circles Tangent Properties - Exercise

### Chapter 16 - Mensuration

1)Craft teacher of a school taught the students to prepare cylindrical pen holders out of card board. In a class of strength 42, if each child prepared a pen holder of radius 5 cm and height 14 cm, how much cardboard was consumed?
File:Screenshot from 2014-08-15 19:15:43.png

**Solution**

2)Find the weight of a solid cone whose base is of diameter 14 cm and vertical height 51,
cm, if the material of which it is made weighs 10gm/cm^3
**Solution**

3)
A Cylindrical container of radius 6cm and height 15cm is filled with ice cream. The whole ice cream has to be distributed to 10 children in equal cones with hemispherical tops. If the height
of the conical portion is 4 times the radius of its base , find the radius of the cream cones.

**Solution**

4)Frustum of Cone (Exercise 16.3 Problem 03)

- A bucket in the shape of a frustum with the top and bottom circles of rarii 15cm and 10cm. Its depth is 12cm. Find its curved surface area and total surface area.

(Express the answer in terms of π)

**Solution**

### Chapter 17 - Graphs and Polyhedra

## Problem 1

Statement : The Königsberg bridge problem : if the seven bridges of the city of Königsberg (left figure; Kraitchik 1942), formerly in Germany but now known as Kaliningrad and part of Russia, over the river Preger can all be traversed in a single trip without doubling back, with the additional requirement that the trip ends in the same place it began.

Image Courtesy : http://mathworld.wolfram.com/KoenigsbergBridgeProblem.html

For solution click **here**