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Mathematics Part - I Solutions Textbook Solutions for Class 10 Math The set of real numbers, The real number system, Natural. CBSE Class 10 Maths Important Questions Chapter 1 � Real Numbers 1 Mark Questions 1. Use Euclid�s division lemma to show that the square of any positive integer .
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Reason a missile true compartment it cools.

Question 2. Question 3. Find the largest number that will divide , and leaving remainders 7, 11, and 15 respectively. Question 5. Solution: HCF of and is Question 6. If one of the numbers is 27, find the other number. Question 7. Question 8. Question 9. Find the LCM of 96 and by using fundamental theorem of arithmetic. Question Find the largest number which divides 70 and leaving remainder 5 and 8 respectively.

Complete the following factor tree and find the composite number x. Check whether 4n can end with the digit 0 for any natural number n. Therefore, 4 n does not end with the digit zero for any natural number n. Give reasons. But this contradicts the fact that p and q have no common factor. So, our assumption is wrong, is irrational. Three bells toll at intervals of 9, 12, 15 minutes respectively. If they start tolling together, after what time will they next toll together? Two tankers contain liters and liters of petrol.

Find the maximum capacity of a container which can measure the petrol of each tanker in the exact number of times. The length, breadth, and height of a room are 8 m 50 cm, 6 m 25 cm and 4 m 75 cm respectively. An imaginary number on the other hand cannot be perceived. Square root of all negative numbers is imaginary. A real number can be represented as an infinite decimal expansion. A real number can be rational or irrational.

All rational numbers and all irrational numbers together make a group of real numbers. A rational number an be written in the form p q , both p and q being integers q 0 while an irrational number can not be impressed in such a way. The decimal expansion of a rational number say x can terminate after a finite number of digits.

On the other hand in case of an irrational number, the decimal expansion continues without repeating. Ex: 1. First, let us understand the meaning of Lemma and Algorithms. A Lemma is a minor proven statement which is used to prove other statements. An algorithm means a series of well defined steps, which provides a procedure of calculations repeatedly successfully on the results of earlier steps. With the help of defined procedure the desired result can be obtained. F Highest Common Factor of the given positive integers.

Ordinarily, if we want to find the HCF of two positive integers, we first find the factors of the two integers. For ex: For two integers 24 and 42, the common factors are 1, 2, 3 and 6.

As 6 is the highest of other numbers, 6 is the HCF of 24 and Next the smaller integer is divided by the above remainder and the process is repeated till zero is obtained. The remainder in the last but one division is the required HCF.

According to this theorem every positive integer is either a prime number or it can be expressed as the product of primes. 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.

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