### Very Short Answers Maths Class 10 Chapter 1 Real Numbers

### Fill in the blanks

**Question.1.** H.C.F. of 6, 72 and 120 is ________.

**Question.2.** 156 as a product of its prime factors __________.

**Question.3.** If a=bq+r, least value of r is ________.

**Question.4.** If every positive even integer is of the form 2q, then every positive odd integer is of the form __________, where q is some integer.

**Question.5.** The exponent of 2 in the prime factorisation of 144, is _________.

**Ans.1.** 6**Ans.2.** 2^{2}\times 3 \times 13**Ans.3.** Zero**Ans.4.** 2q+1**Ans.5.** 4

**Question.6.** \sqrt{2}, \sqrt{3}, \sqrt{7}, etc. are _______ numbers.

**Question.7.** 7\sqrt{5} is a/an ________ number.

**Question.8.** An algorithm which is used to find HCF of two positive numbers is __________.

**Question.9.** 6+\sqrt{2} is a/an __________ number.

**Question.10.** Every point on the number line corresponds to a _________ number.

**Ans.6.** Irrational**Ans.7.** irrational**Ans.8.** Euclid’s division algorithm**Ans.9.** irrational**Ans.10.** Real

**Question.11.** A _________ is a proven statement used for proving another statement.

**Question.12.** The product of three numbers is _________ to the product of their HCF and LCM.

**Question.13.** L.C.M. of 96 and 404 is __________.

**Question.14.** If p is a prime number and it divides a^{2} then it also divides _________, where a is a positive integer.

**Question.15.** \frac{35}{50} is a ________ decimal expansion.

**Ans.11.** lemma**Ans.12.** Not equal**Ans.13.** 9696**Ans.14.** a**Ans.15.** terminating

**Question.16.** An ________ is a series of well defined steps which gives a procedure for solving a type of problem.

**Question.17.** Every real number is either a _______ number or an __________ number.

**Question.18.** \frac{1}{\sqrt{2}} is a/an __________ number.

**Question.19.** Numbers having non-terminating, non-repeating decimal expansion are known as ________.

**Question.20.** \sqrt{5} is a/an _________ number.

**Ans.16.** algorithm**Ans.17.** Rational, irrational**Ans.18.** irrational**Ans.19.** Irrational numbers**Ans.20.** irrational

### True / False

**Question.1.** Given positive integers a and b, there exist whole numbers q and r satisfying a=bq+r, 0≤r<b .

**Question.2.** HCF of two numbers is always a factor of their LCM.

**Question.3.** 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.

**Question.4.** Sum of two prime numbers is always a prime number.

**Question.5.** The number zero is irrational.

**Ans.1.** True**Ans.2.** True**Ans.3.** True**Ans.4.** False**Ans.5.** False

**Question.6.** \sqrt{2} and \sqrt{3} are irrationals numbers.

**Question.7.** π is an irrational number.

**Question.8.** Some irrational numbers are negative.

**Question.9.** If x=\frac{p}{q} be a rational number, such that the prime factorisation of q is not of the form 2^{n}5^{m}, where n, m are non-negative integers. Then x has a decimal expansion which is terminates.

**Question.10.** All real numbers are rational numbers.

**Ans.6.** True**Ans.7.** True**Ans.8.** True**Ans.9.** False**Ans.10.** False

**Question.11.** Any positive odd integer is of the form 6q+1, or 6q+3, or 6q+5, where q is some integer.

**Question.12.** Sum of two irrational numbers is an irrational number.

**Question.13.** The quotient of two integers is always a rational number.

**Question.14.** Two numbers can have 12 as their LCM and 350 as their HCF.

**Question.15.** 1/0 is not rational.

**Ans.11.** True**Ans.12.** False**Ans.13.** False**Ans.14.** False**Ans.15.** True

**Question.16.** The product of any three consecutive natural numbers is divisible by 6.

**Question.17.** If x=\frac{p}{q} be a rational number, such that the prime factorisation of q is of the form 2^{n}5^{m}, where n, m are non-negative integers. Then x has a decimal expansion which is terminates.

**Question.18.** All integers are real numbers.

**Question.19.** The number of irrational numbers between 15 and 18 is infinite.

**Question.20.** Every fraction is a rational number.

**Ans.16.** True**Ans.17.** True**Ans.18.** True**Ans.19.** True**Ans.20.** True

### Match the Columns

Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in column I have to be matched with statements (p, q, r, s) in column II.

**Question.1.**

**Ans.1.** (A)-r, (B)-s, (C)-p, (D)-q

**Question.2.**

**Ans.2.** (A)-r, (B)-p, (C)-q

**Question.3.**

**Ans.3.** (A)-(t, s), (B)-(p, s), (C)-(q, u), (D)-(r, s)

**Question.4.**

**Ans.4.** (A)-q, (B)-p, (C)-r, (D)-t, (E)-s