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The Class 10 Maths NCERT Solution PDFs cover all the Exercises from Chapters 1 - 15 present in the NCERT books. These Class 10 Maths solutions are written in accordance with the CBSE exam guidelines to increase the students understanding of the subject and help to score myboat360 boatplans NCERT solutions for class 10 Mathematics PDFs will not only prepare the students for final exams but will also help to understand the concept better. Science and Maths are two important subjects of class 10 and if you are looking for reliable and accurate NCERT Solutions for Class 10 Science you will find that on Vedan. Free NCERT Solutions for Class 6 Maths. All Maths NCERT Books chapter-wise solutions (Text & Videos) are accurate, easy-to-understand and most helpful in Homework & Exam Preparations.� Class NCERT Solutions for Class NCERT Solutions for Class 10 Math. NCERT Solutions for Class 10 Science. NCERT Solutions for Class 10 English. Notes and NCERT Solutions for Class 10 Maths. Welcome to our class 10 Maths page. In this page you can find class 10 Maths Ncert solutions, notes, assignments, worksheets,Practice questions etc. You can share the link to free Class 10 NCERT Maths solutions with your classmates as all study material is free of cost. How to use this page to learn Maths. First read and understand the notes.

Basic definition of even and odd numbers and the fact that addition and, multiplication of integers is always an integer are applicable here. Question 3: An army contingent of members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march? Therefore, the maximum number of columns in which an army contingent of members can march behind an army band of 32 members in a parade is 8.

Alternatively: Let n be the number of columns such that the value of n be maximum and it must divide both the numbers and Alternatively: Let a be a positive integer, q be the quotient and r be the remainder. Hence, proved. Let a be a positive integer, q be the quotient and r be the remainder. Question 1: Express each number as a product of its prime factors: i ii iii iv v Solution:.

Question 5: Check whether 6 n can end with the digit 0 for any natural number n. So, there is no natural number VT for which 6 n ends with the digit zero.

Solution: Method 1: Both N 1 and N 2 are expressed as a product of primes. Therefore, both are composite numbers. Question 7: There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point? Solution: Method By taking LCM of time taken in minutes by Sonia and Ravi, we can get the actual number of minutes after which they meet again at the starting point after both start at same point and of the same time, and go in the same direction.

Question 1. Solution: Let us assume that is rational. But Ncert Solutions Class 10th Maths Chapter 4 Model this contradicts the fact that a and b are co-primes. Thus, 5 is a common factor of both p and q. Question 2.

But, it is a contradiction. Question 3. Prove that the following are irrational. Hence proved. Question 1: Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or non-terminating repeating decimal expansion: Solution: Alternatively: Alternatively: Alternatively: Alternatively: Alternatively: Alternatively: vii Alternatively: Viii Alternatively: ix Alternatively: x Alternatively:.

Write down the decimal expansions of those rational numbers in the question 1, which have terminating decimal expansions. Question 3: The following real numbers have decimal expansions as given below.

In each case, decide whether they are rational or not. Alternatively: i Hence, the number is a rational number, specifically a terminating decimal. We have studied the following points: 1. The divisor at this stage will be HCF a, b. The Fundamental Theorem of Arithmetic: Every composite number can be expressed factorized as a product of primes and this factorization is unique, apart from the order in which the prime factors occur.

If p is a prime and p divides a 2 , then p divides a also, where a is a positive integer. The divisor at this stage will be the required HCF. Every composite number can be expressed factorised as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur. The prime factorisation of a natural number is unique, except for the order of its factors.

If we combine the same primes, we will get powers of primes. Number which is not a rational number or whose decimal expansion is non-terminating and non-repeating Note: i The sum or difference of a rational and an irrational number is irrational, e. Thus we conclude that the decimal expansion of every rational number is either terminating or non-terminating repeating. Real Numbers Class 10 Ex 1.

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Thus:

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