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Chapter 6 Triangles - NCERT Solutions for Class 10 Mathematics CBSE - TopperLearning

The study material contains an exhaustive explanation to all the questions. These answers are written clearly and step by step to maximise retention. While going through these solutions, students will find themselves understanding the concept better. Practising regularly is a prerequisite if students want to score well in mathematics. You can consult the guide to brush up your memory or help you if you get stuck. There are 4 Exercises present in this chapter.

Students will learn about real numbers and irrational numbers in the 1st chapter of Class 10 Maths. Exercise 1. There are a total of 4 Exercises including an optional Exercise in the 2nd chapter of class 10 Maths. The first Exercise is about to find zeros of polynomials p x. In the second Exercise, the students need class 10 maths ch 6 pdf 80 find a quadratic polynomial. The third Exercise has questions on division of polynomials.

The last Exercise covers questions from all the concepts of Class 10 Maths Chapter 2. Exercise 2. The third chapter of class 10 maths is about the linear equations in two variables. It describes what Class 8 Maths Chapter 13 Question Answer Pdf a linear equation in two variables is and how to solve the problems on linear equations in two variables.

In the first Exercise Ex 3. The second Exercise, i. The next four Exercises, Ex 3. The methods explained here are algebraic method, cross-multiplication method, elimination method and substitution method. Exercise 3. It contains questions from all the Exercises. This chapter explains what a quadratic equation is and the methods of solving quadratic equations. It also explains the factorization method of solving quadratic equations and the square method.

The chapter gives the details of relationships between discriminant and nature of roots. Also, the problems of real life have been solved as examples in this chapter. Exercise 4. This chapter introduces a new topic to the students - Arithmetic Progression, commonly called as AP. Students will learn what is AP, derivation of nth term, finding the sum of first n terms of the AP and solving the real life problems using AP in this chapter.

The first Exercise of the chapter teaches how to represent a problem or situation in the class 10 maths ch 6 pdf 80 of AP, how to find the first term and difference of the AP, and to find whether the given series is Ap or not. The next Exercise, Ex 5. The third Exercise describes how to find the sum of first n terms of AP and contains questions related to the topic.

The last and fourth Exercise have questions related to the topics taught in the chapter. Exercise 5. The chapter 6 of class 10 gives details about the triangles. The chapter gives details about the figures with the same shape but different sizes. It explains the similarity of the triangles, theorems associated with the similarity of triangles and the concept of congruent triangles.

Further, theorems related to areas of triangles, the Pythagoras theorem and the converse of pythagoras theorem is explained. Exercise 6. Class 10 Maths Chapter 7 explains coordinate geometry, the maths of locating a given point with the help of an ordered pair of numbers. The coordinate or cartesian geometry helps to find the distance between two points whose coordinates are given.

The concept of finding the area of a triangle formed by three given points. Also, the ways of finding the coordinates of the point which divides a line segment joining two given points in a given ratio is explained in the chapter. Exercise 7. Trigonometry is the study of the ratio of right triangles with respect to the acute angles, which are known as trigonometric ratios of the angles.

Students will also learn to calculate trigonometric ratios for the given angles and also a few trigonometric identities. Exercise 8. Chapter 9 is the continuation of chapter 8 where the students will learn about the application of trigonometry which they learnt in the previous chapter.

This chapter helps to understand how trigonometry is applied to our everyday life to find out the height and distance of various objects. They will also learn how trigonometry is applied and used in navigation, construction and determining the position of any piece of land based on their latitude and longitudes.

Exercise 9. In this chapter, students will be introduced to the concept of tangents and number of tangents from class 10 maths ch 6 pdf 80 point on a circle. Exercise Chapter 11 is one of the interesting chapters. This chapter is all about constructing various geometric figures. The students will learn to divide class 10 maths ch 6 pdf 80 line segment, and how to draw tangents to a circle.

The methods of construction are well explained in the chapter to clear the concepts. As the name suggests, the chapter is about the perimeter and area of a circle.

The concepts of finding the area of a sector and segment of a circle is clarified. This chapter further explains how to find the area of the figures that contains a circle or part of a circle.

In the five Exercises of this chapter, finding the surface area of any object which is made up of two or more different solid shapes. The solid shapes include cuboid, cone, sphere, hemisphere and cylinder.

Then, there are questions on finding the volume of the objects that are again made up of two different solid shapes. Also, there are questions which ask about the conversion from one shape to. This chapter further explains class 10 maths ch 6 pdf 80 to find the volume, curved surface area and total surface area of a frustum of a cone.

This is another interesting chapter where the students learn about the numerical representation of data, grouped or ungrouped. They further learn about finding the mean, median and mode of the given data. In the next Exercise, they will learn about the cumulative frequency distribution and drawing cumulative frequency curves.

It elaborates and explains the difference between experimental probability and theoretical probability. The chapter is full of examples to clear the concept of probability to the learners.

Students can download the PDF easily and start going class 10 maths ch 6 pdf 80 the chapters. You will find clear categorisation and step by step solutions of all the questions with a clear conclusion. This will help you to understand how you can write answers in your exams to help you score. The exam is of marks where 80 marks is for theory whereas 20 marks is given for internal assessment.

To understand the marking class 10 maths ch 6 pdf 80 in a better way, you should understand the exam pattern clearly. To score good in the class 10 maths ch 6 pdf 80, you should know how much mark is awarded for each question and each step of the question. Every year, just before the board exams, the board releases sample papers class 10 maths ch 6 pdf 80 marking schemes so that all the doubts of the students are cleared.

The number of questions are increased and the marks per question are reduced. This marking scheme will be helpful to the students as the maximum number of questions will become objective or very short answer type as the marks per question has reduced. CBSE focuses on all-round development of Class 10 students to prepare them for their further education. To perform well in Class 10 then becomes fairly important.

CBSE marking scheme is stepwise so you have scored accordingly. Therefore students should write each step clearly and give a proper conclusion at the end of the answer.

The unit wise marks weightage of the mathematics paper is as follows:. The paper has four sections. There are a total of 30 questions for 80 marks. Number System. Coordinate geometry. Statistics and probability. The question paper design will be:. Sl No.

Type of Questions. Total Marks. Memory: Terms, answers, basic concepts and recalling of facts. Understanding: Compare, organize, interpret, translate, describe and stating main ideas.

Apply: Solving problems by applying the knowledge, facts, theorems and rules in different ways. Analyse: Analyse the information provided and making inferences. Evaluate: Opine about the validity of quality of work and validity of ideas.

Create: Creating alternative solutions of the given problem and grouping the elements.

Main points:

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In which year was the Vernacular Press Act enacted to silence those who were critical to the Government? In which year did Mahatma Gandhi arrive in India from South Africa after having led the Indians in non-violent marches against racist restrictions? From the outline map of India, name the place B, in Gujarat where the peasants organised non- violent campaigns against the high land revenue demand of the British. Among the different goals of the Non-Cooperation Movement, which one of these can be considered as the main and important goal?

Attainment of Swaraj through peaceful and legitimate means. Protest against the Jalianwala Bagh massacre. Identify this great personality marked A, who fought against injustice, who believed in ahimsa and satyagraha and worked tirelessly for the freedom of India. In the image given below, he along with other Indians established the Natal Congress in Durban, South Africa in to fight against racial indiscrimination.

State True or False: A person who welcomes new ideas or opinions is called a Moderate. The Jallianwala Bagh massacre took place in How is it formulated for solutions of non-volatile solutes? Why do gases nearly always tend to be less soluble in liquids as the temperature is raised?

All India Answer: This is because the dissolution of gas in liquid is an exothermic process. The solubility should decrease with increase in temperature. At what temperature will this solution boil?

An aqueous solution of sodium chloride freezes below K. Explain the lowering in freezing points of water with the help of a suitable diagram.

Delhi Answer: An aqueous solution of sodium chloride freezes below K because vapour pressure g of the solution is g less than that of the pure solvent. Define an ideal solution and write one of its characteristics. An ideal solution is a solution in which no volume change and no enthalpy change takes place on mixing the solute and the solvent in any proportion. What is the effect of temperature on the solubility of a gas in a liquid?

How is the vapour pressure of a solvent affected when a non-volatile solute is dissolved in it? Delhi Answer: The vapour pressure of a solvent decreases when a non-volatile solute is dissolved in it because some solvent molecules are replaced by the molecules of solute.

How can we change molality value of a solution into molarity value? Delhi Answer: The distinction between molarity and molality. Give an example. For example, Water and Ethanol. Define azeotropes. Given an example. Delhi Answer: Azeotropes : Liquid mixture which distills without change in compositions are called azeotropic mixtures or Azeotropes.

What change in temperature would you observe after mixing liquids X and Y? There will be rise in temperature. Define osmotic pressure of a solution. How is the osmotic pressure related to the concentration of a solute in a solution? Delhi Answer: Osmotic pressure : It is the external pressure which is applied on the side solution which is sufficient to prevent the entry of the solvent through semi-permeable membrane. Define the following terms : i Mole fraction x ii Molality of a solution m Comptt.

All India Answer: i Mole fraction : Mole fraction of a constituent is the fraction obtained by dividing number of moles of that constituent by the total number of moles of all the constituents present in the solution. What is osmotic pressure? Why it is a colligative property? Comptt Delhi Answer: The excess pressure applied on solution side to stop the process of osmosis.

Because it depends upon the number of solute particles but not on their nature. Define osmotic pressure. How is osmotic pressure related to the concentration of a solute in a solution? All India Answer: Osmotic pressure is the measure of excess pressure applied on solution side to stop the process of osmosis.

Define the following terms: Delhi i Colligative properties ii Molality m Answer: i Colligative properties. All those properties which depend on the number of solute particles irrespective of the nature of solute are called as colligative properties.

Number of moles of solute dissolved per kg of the solvent. If the molar mass calculated by using any of colligative properties tends to be different than theoretically expected molar mass, it is called abnormal molar mass. Extent of dissociation or association or ratio of the observed colligative property to calculated colligative property.

Explain why on addition of 1 mol of glucose to 1 litre of water, the boiling point of water increases. Delhi Answer: a Glucose is a non-volatile solute, therefore, addition of glucose to water lowers the vapour pressure of water as a result of which boiling point of water increases. If this solution has an osmotic pressure of Calculate the freezing point depression expected for 0. If this solution actually freezes at � 0.

Ky for water is 1. A solution prepared by dissolving 1. Determine the molar mass of this compound. This solution has a boiling point of What mass of glycerol was dissolved to make this solution?

The freezing point depression constant, K f , for water is 1. The resulting solution freezes at What is the molar mass of the substance? What mass of NaCl must be dissolved in The freezing point depression constant K f for water is 1. Calculate the amount of KCl which must beadded to 1 kg of water so that the freezing point is depressed by 2K.

A solution of glycerol C 3 H 8 O 3 in water was prepared by dissolving some glycerol in g of water. What mass of glycerol was dissolved to make the solution?

The resulting solution was found to freeze at What is the molar mass of this material? A solution containing 30 g of non-volatile solute exactly in 90 g of water has a vapour pressure of 2.

Further 18 g of water is added to this solution. The new vapour pressure becomes 2. Calculate i the molecular mass of solute and ii vapour pressure of water at K. If N 2 gas is bubbled through water at K, how many millimoles of N 2 gas would dissolve in 1 litre of water?

Assume that N 2 exerts a partial pressure of 0. The partial pressure of ethane over a saturated solution containing 6. If the solution contains 5. Determine the osmotic pressure of a solution prepared by dissolving 2.

If the solution were to contain 5. If the freezing point of a water-glycol solution is A solution is prepared by dissolving 10 g of non-volatile solute in g of water. It has a vapour pressure of Calculate the molar mass of the solute. A 5 percent solution by mass of cane-sugar M. Find the molecular weight of X. Delhi Answer:. An aqueous solution of 2 percent non-volatile solute exerts a pressure of 1.

What is the molecular mass of the solute? The vapour pressure of pure liquids A and B at K are and mmHg respectively.

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