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Class 8 Maths Notes PDF Important questions for Class 10 Maths Chapter 1, Real Numbers is prepared by experts of Vedantu with a purpose of creating important questions for the chapter is to enable the students to pivotal concepts of the chapter that has been introduced in Maths NCERT Solutions Class The important questions pdf version is prepared to give a better conceptual understanding to the students and help. Click here to get access to the best NCERT Solutions for Class 8 myboat279 boatplans through this Letter Writing for Class 8 CBSE Format, Topics Exercises, and Examples to learn English. Each and every question of English grammar exercises for class 8 CBSE with answers have been answered with easy to download solutions in PDF format. CBSE Class 8 English Letter Writing. Introduction to Letter Writing A letter is a written form of communication that is addressed to a specific person or a specific organisation. It is one of the easiest and non-expensive means of communication. The relationship between the writer and the receiver determines the way a letter is written.
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It is also known as Unique Factorization Theorem. Thus, any integer that is greater than 1 can be either a prime number or can be expressed as a product of prime factors. Note :. It is the only number that is both prime and even. A chain of factors that is demonstrated in the form of a tree, is called a factor tree. HCF is the product of the smallest power of each common prime factor present in the numbers. The product of the largest power of each prime factor present in the numbers is the LCM.

Important Note:. We use the method of contradiction in order to prove irrationality of the numbers. If a prime number p divides a 2 , then p divides a, where a is a positive integer. Let us understand how to write the decimal expansion of those rational numbers with terminating decimal expansion. The important questions for this chapter is basically a compilation of higher and more advanced techniques a student can expect in Class 10 examinations.

The questions of the chapter and the notes related to the topic provided by Vedantu will not only help you to understand the concept better but also solve the questions successfully. If you harbour any doubts then you can get answers to all your queries with our experienced teachers by registering with Vedantu and gain expertise in the subject.

On a particular day, she had newspapers out of which are in English and remaining in Hindi. Find the ratio a the number of English newspapers to the number of Hindi newspapers. The students of a school belong to different religious backgrounds. The number of Hindu students is , the number of Muslim students is , the number of Sikh students is and the number of Christian students is Find the ratio of a the number of Hindu students to the number of Christian students.

When Chinmay visited chowpati at Mumbai on a holiday, he observed that the ratio of North Indian food stalls to South Indian food stalls is 5 : 4. If the total number of food stalls is , find the number of each type of food stalls. Solution: Let the number of North Indian food stalls be 5x and the number of South Indian food stalls be 4x.

At the parking stand of Ramleela ground, Kartik counted that there are cycles, 75 scooters and 45 bikes. Find the ratio of the number of cycles to the total number of vehicles. A train takes 2 hours to travel from Ajmer to Jaipur, which are km apart.

How much time will it take to travel from Delhi to Bhopal which are km apart if the train is travelling at the uniform speed? Solution: A train covers a distance of km in 2 hours and let it covers a distance of km in x hours. According to the question, km : 2 hours : : km : x hours Thus, the required time is 12 hours.

The length and breadth of a school ground are m and 90 m respectively, while the length and breadth of a mela ground are m and m, respectively. Are these measurements in proportion? Solution: Hence, both ratios are equal.

In the given figure, the comparative areas of the continents are given : What is the ratio of the areas of a Africa to Europe b Australia to Asia c Antarctica to Combined area of North America and South America. Comparative areas of the continents Solution: Let each square is of unit length. A tea merchant blends two varieties of tea costing her Rs. If the weight of the mixture is 84 kg, then find the weight of each variety of tea.

Solution: The ratio of the costs of two varieties of tea is Rs. An alloy contains only zinc and copper and they are in the ratio of 7 : 9. If the weight of the alloy is 8 kg, then find the weight of copper in the alloy. Solution: The ratio of the weight of zinc and copper is 7 : 9. Let the weight of zinc be 7 : x kg and the weight of copper be 9x kg. Find two numbers whose sum is and whose ratio is 9 : Solution: The ratio of two numbers is 9 : Let the numbers be 9x and 16x.

In figure i and figure ii , find the ratio of the area of the shaded portion to that of the whole figure: Solution:. A typist has to type a manuscript of 40 pages. She has typed 30 pages of the manuscript. What is the ratio of the number of pages typed to the number of pages left? In a floral design made from tiles each of dimensions 40 cm by 60 cm see figure , find the ratios of: a the perimeter of shaded portion to the perimeter of the whole design.

In the given figure, what is the ratio of the areas of a shaded portion I to shaded portion II? A car can travel km in 15 litres of petrol. How much distance will it travel in 25 litres of petrol?

Bachhu Manjhi earns Rs. At this rate, a how much does he earn in one year? The yield of wheat from 8 hectares of land is quintals.

Find the number of hectares of land required for a yield of quintals? By how much degree will it rotate in 2 hours? Shivangi is suffering from anaemia as haemoglobin level in her blood is lower than the normal range.

Doctor advised her to take one iron tablet two times a day. If the cost of 10 tablets is Rs. What will be the fee for seven months?

In an electron, the votes cast for two of the candidates were in the ratio 5 : 7. If the successful candidate received votes, how many votes did his opponent receive? Solution: Let the number of votes cast for the candidates be 5x and 7. A metal pipe 3 metre long was found to weigh 7. What would be the weight of the same kind of 7.

Find the amount of sugar needed for 6 cups of the juice? Before you begin practising Class 9 Chapter 1 Maths Important Questions, you need to know the different topics and subtopics to cover in the chapter. Chapter 1 of Mathematics Class 9 covers a total of 6 exercises with a small introduction of the number system, number lines, defining real numbers, natural numbers, whole numbers, rational, and irrational numbers.

Also, students become familiar with the concepts of addition, subtraction, division, and multiplication of the real numbers. The last topic in the chapter will be covering the law of exponents in the real numbers. Below are the mentioned section-wise topics and concepts that a student to prepare through important questions.

Under exercise 1. There is also a revision on whole numbers, real number, integers, and natural numbers and definition. Further moving to in-depth study about rational and irrational numbers, there are questions on justification with true and false. Also, students become familiar with the concept of representing rational and irrational numbers on the number line. A new concept of constructing a square root spiral comes in exercise 1. Here the student will know how to represent fractions into decimal form and find if it is terminating or non-terminating.

Thus the concepts of terminating and non-terminating fractions will further help to identify it is a rational or irrational number. A new concept of representing decimal expansion on the number line is introduced through exercise 1.

Here students will learn about magnifying the number to the maximum requirement and representing it on the number line. These decimal places can be either terminating or non-terminating. Hence there are two different concepts in number line representation of decimal expansions. Now comes the basic calculations of different rational and irrational numbers. It includes addition, multiplication, subtraction, and division of the rational and irrational numbers. Questions will be based on such concepts, and thus you have to simplify the statement accordingly.

Also, students become familiar with the concept of rationalising. Here students will learn to solve questions based with a number having power in fractional form. Also, it might cover the basic addition and subtraction of powers for in-depth conceptual and extra knowledge.

Hence students can prepare questions according to the concepts discussed above.

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