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NCERT Books for Class 10 Maths Chapter 1 Real Numbers PDF Download

Show that any positive odd integer is of the formororwhere q is some integer. Hence, these expressions of numbers are odd numbers. Solutioms army contingent of members is to march behind an army band of 32 110th 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? Where k 1k 2and k 3 are some positive integers. Therefore, 6 n cannot end with the digit 0 for any natural number n. Numbers are of two types - prime and composite.

Prime numbers can be divided by 1 and only itself, whereas composite numbers have factors other than 1 fishing vessel price in india university. Therefore, the given expression has 5 and as its factors. Hence, it is a composite number. 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.

Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes dolutions they meet again at the starting point? It can be observed that Ravi takes lesser time than Sonia for completing 1 round of the circular path.

As they are going in the same direction, they will meet again numbets the same time when Ravi will have completed 1 round of that circular path with respect to Sonia. And the total time taken for completing this 1 round of circular path will be the LCM of time taken by Sonia and Ravi for completing 1 round of circular path respectively i. Prove that is irrational. Let is a rational number. Let a and b have a common factor other than 1.

Then we can divide them by the common factor, and assume that a and b are co-prime. Therefore, a 2 is divisible by 5 and it can be said that a is divisible by 5. This means that b 2 is divisible by 5 and hence, b is divisible by 5. Hence, cannot be expressed as or it can be said that is irrational. Let is rational. Since a and b are integers, will also be rational and therefore, is rational. This contradicts the fact that is irrational. Hence, our assumption that is rational is false.

Therefore, is irrational. Therefore, is rational which contradicts to the fact that is irrational. Hence, our assumption is false and is irrational.

Therefore, should be rational. Therefore, our assumption that is rational is false. Hence, is irrational. Let be rational. Since a and b are integers, is also rational and hence, should be rational. Therefore, our assumption is false and hence, is irrational. Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:.

Hence, the decimal expansion of is terminating. Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions. The following real numbers have decimal expansions as given. Numhers each case, decide whether they are rational or not.

If they are rational, and of the formwhat can you say about the prime factor of q? Since this number has a terminating decimal expansion, it is a rational number of the form and q is of the form. The soluitons expansion is neither terminating fishing vessel price in india university recurring. Therefore, the given number is an irrational number.

Since the decimal expansion is non-terminating recurring, the given number is a rational number of solutiond form and q is not of fishing vessel price in india university form i.

The first section starts with the introduction of real numbers and the two important properties of real numbers namely: 1. Euclid's division algorithmas the name suggests, it is related to the divisibility of integers. It states that a positive integer ' a ' can be divided by another positive integer ' b' in such a way that it leaves a remainder 'r' that is smaller than 'b'.

The fundamental theorem of arithmetic : It deals with the multiplication of positive integers. Since the divisor at this stage is 45, Therefore, fishing vessel price in india university HCF fishing vessel price in india university and is Since the divisor at this stage isTherefore, HCF of and is Since the divisor at this stage is 51, Therefore, Fishing vessel price in india university of and is Video Solution for real numbers Page: 7Q.

Question 2: Show that any positive odd integer is of the formororwhere q is some integer. Question 3: An army contingent of members is to march behind an army band of Real Numbers Class 10th Ncert Solutions Kit 32 real numbers class 10th ncert solutions uni in a parade. Answer: HCF32 will give the maximum number of columns in which they can march.

Therefore, they can march in 8 columns. There are three cases. Question 1: Express each number as product of its prime factors:. Answer: Video Solution for real numbers Page: 11Q. Question 5: Check whether 6 n can end with the digit 0 for any natural number n.

Hence, for any value of n6 n will not be divisible by 5. Video Solution for real numbers Page: 11Q. Answer: Numbers are of two types ui prime and nimbers. Therefore, it is a composite number.

Question 7: There is a circular path around a sports field. Answer: Real numbers class 10th ncert solutions uni can be observed that Ravi takes lesser time than Sonia for completing 1 round of the circular path. Question 1: Prove that is irrational. Answer: Let Ncert Solutions Class 10th Real Numbers Resource is a rational number.

This implies that a and b have 5 as a common factor. And this is a contradiction to the fact that a and b are co-prime. Video Solution for real numbers Page: 14Q. Question 2: Prove that is irrational. Answer: Let is rational.

Question 3: Prove clads the following are irrationals:. Question 1: Without actually performing the long division, state whether the following rational numbers will have rfal terminating decimal expansion or a non-terminating repeating decimal expansion:.

Answer: i The denominator is of the form 5 real numbers class 10th ncert solutions uni. Video Solution for real numbers Page: 17Q. Question 2: Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.

Answer: viii Video Solution for real numbers Page: 18Q. Question 3: The following real numbers have decimal expansions as given. Answer: i Video Solution for real numbers Page: 18Q.

The divisor at this stage will be HCF a, b. A lemma is a statement that is proven and acts as a stepping stone to prove other statements. The two groups are to march in the same number of columns. So 5 is not a prime factor of 6 n. Here, we will try a few of them to compute the HCF of two positive integers. Therefore, it is a composite number. In this Real Numbers Class 10th Ncert Solutions Qml post, we will see Class 10 Maths Ncert Solutions For Chapter 1 Real Number which will help you in solving all your doubts and queries in this chapter.

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