# NCERT Solutions for class 10 Maths Chapter 1 Exercise 1.1

NCERT Solutions for class 10 Maths Chapter 1 Exercise 1.1 Real Numbers (वास्तविक संख्याएँ) in PDF format updated for new academic session 2020-21.

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Class: | 10 |

Subject: | Maths – गणित |

Chapter 1: | Exercise 1.1 |

### 10 Maths Chapter 1 Exercise 1.1 Solutions

NCERT Solutions for class 10 Maths Chapter 1 Exercise 1.1 of Real numbers in English & Hindi medium to use it online or download in PDF form. All the solutions are updated for new academic session 2020-21. Download Offline Apps for offline use.

### Class 10 Maths Exercise 1.1 Solutions

#### Important Terms related to Real Numbers

1. Euclid’s division Lemma: For given positive integers ‘a’ and ‘b’ there exist unique whole numbers ‘q’ and ‘r’ satisfying the relation a = bq + r, o ≤ r < b.
2. Euclid’s division algorithm: HCF of any two positive integers a and b with a > b is obtained as follows:

Step 1 : Apply Euclid’s division lemma to a and b to find q and r such that a = bq + r, 0 ≤ r < b.
Step 2 : If r = 0 then HCF (a, b) = b ; if r ≥ 0 then again apply Euclid’s lemma to b and r.
Repeat the steps till we get r = 0
3. 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.

##### Important Questions for Practice on 10th Maths Chapter 1

1. Write the general form of an even integer. [Answer: 2m]

2. Find the largest integer which divides 245 and 1029 leaving remainder 5 in each case. [Answer: 16]

3. Write the form in which every odd integer can be written taking t as variable. [Answer: 2t +1]

4. If the HCF of 408 and 1032 is expressible in the form 1032y – 408×5, then find y. [Answer: 2]

5. What would be the value of n for n²–1 divisible by 8. [Answer: An odd integer]

6. Two tankers contain 650 litres and 1170 litres of petrol respectively. Find the maximum capacity of a tanker which can measure the petrol of either tanker in exact number of times. [Answer: 130 litres]

7. State whether 7 × 11 × 13 + 7 is a composite number or a prime number. [Answer: Composite]

8. A bookseller purchased 117 books out of which 45 books are of mathematics and the remaining 72 books are of Physics. Each book has the same size. Mathematics and Physics books are to be packed in separate bundles and each bundle must contain the same number of books. Find the least number of bundles which can be made for these 117 books. [Answer: 13]

9. Is 5.131131113… a rational number or irrational number? [Answer: Irrational]

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