Mathematics Solved problems

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ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ

Class 8

Class 9

Chapter 2-Banking

  1. 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

  1. 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)

  1. How many of these are less than 6000?
  2. How many of these are even?
  3. 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

Surds_Problems_solution

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 2a^2-4a+1=0 find the value of p^3+q^3
"solution"
2.The altitude of a triangle is 6cm greter than its base. If its area is 108cmsq .Find its base.
"solution"
3.Solve x^2-4x-8=0 By completing the square.
"solution"

Chapter 11 - Pythagoras Theorem

Chapter 12 - Trigonometry

Chapter 13 - Co-ordinate Geometry

Chapter 15 - Circles Tangent Properties - Exercise

[Click here]

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.
Combinations of solids.png
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)
Frustum of cone.png
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.


koning4.jpg


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

For solution click here