# ML Aggarwal Rational and Irrational Number MCQs Class 9 ICSE Maths Solutions

ML Aggarwal Rational and Irrational Number MCQs Class 9 ICSE Maths Solutions. We Provide Step by Step Answer of  MCQs Questions for Rational and Irrational Number as council prescribe guideline for upcoming board exam. Visit official Website CISCE for detail information about ICSE Board Class-9.

## ML Aggarwal Rational and Irrational Number MCQs Class 9 ICSE Maths Solutions

 Board ICSE Subject Maths Class 9th Chapter-1 Rational and Irrational Topics Solution of MCQs Questions Edition 2024-2025

### Rational and Irrational Number MCQs

ML Aggarwal Class 9 ICSE Maths Solutions

Multiple Choice questions:

#### Question 1. Choose the correct statement:

(a) Reciprocal of every rational number is a rational number.

(b) The square roots of all positive integers are irrational numbers.

(c) The product of a rational and an irrational number is an irrational number

(d) The difference of a rational number and an irrational number is an irrational number.

Answer: (d) The difference of a rational number and an irrational number is an irrational number.

#### Question 2. Every rational number is

(a) A natural number

(b) An integer

(c) A real number

(d) A whole number

#### Question 3. Between two rational numbers

(a) There is no rational number

(b) There is exactly one rational number

(c) There are infinitely many rational numbers

(d) There are only rational numbers and no irrational numbers.

Answer: (c) There are infinitely many rational numbers

#### Question 4. Decimal representation of a rational number cannot be

(a) Terminating

(b) Non-terminating

(c) Non-terminating repeating

(d) Non-terminating non-repeating

#### Question 5. The product of any two irrational numbers is

(a) Always an irrational number

(b) Always a rational number

(c) Always an integer

(d) Sometimes rational, sometimes irrational

Answer: (a) Always an irrational number

#### Question 6. The division of two irrational numbers is

(a) A rational number

(b) An irrational number

(c) Either a rational number or an irrational number

(d) Neither rational number nor irrational number

Answer: (c) Either a rational number or an irrational number

(a) √4/9

(b) √12/√3

(c) √7

(d) √81

#### Question 8. Which of the following numbers has terminating decimal representation?

(a) 3/7

(b) 3/5

(c) 1/3

(d) 3/11

Answer: (b) 3/5 = 3×2/5×2 = 6/10 = 0.6

#### Question 9. Which of the following is an irrational number?

(a) 0.14

(b) 0.1416

(c) 0.1416

(d) 0.4014001400014…

### ML Aggarwal Rational and Irrational Number MCQs Class 9 ICSE Maths Solutions

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(a) 11/80

(b) 17/160

(c) 63/240

(d) 93/420

(c) 63/240

#### Question 11. A rational numbers between √2 and √3 is

(a) √2+√3/2

(b) √2×√3/2

(c) 1.5

(d) 1.8

Answer: (c) 1.5, √2 = 1.44, √5 = 1.732

#### Question 12. The decimal expansion of 2 – √3 is

(a) Terminating and non-repeating

(b) Terminating and repeating

(c) Non-terminating and non-repeating

(d) Non-terminating and repeating

#### Question 13. The decimal expansion of the rational number 33/22×5 will terminate after

(a) One decimal place

(b) Two decimal places

(c) Three decimal places

(d) Four decimal places

33/22×5 = 33×5/22×52 = 33×5/102 – 33×5/100

Since no. of zeros is 2.

#### Question 14. √10×√15 is equal to

(a) 6√5

(b) 5√6

(c) √25

(d) 10√5

Answer: option (b) 5√6 is correct

Hint: √10 × √15

= √2 × √5 × √3 × √5

= 5 × √6

= 5√6

#### Question 15.  2√3 + √3 is equal to

(a) 2√6

(b) 6

(c) 3√3

(d) 4√6

= 3√3 option (c) is correct

#### Question 16. The value of √8 + √18 is

(a) √26

(b) 2 (√2 + √3)

(c) 5√2

(d) 6√2

Hint : √8 + √18

= √2 ×√4 + √2 × √9

= √2 (2+3)

= 5√2

#### Question 17. The number (2 – √3)2 is

(a) A natural number

(b) An integer

(c) A rational number

(d) An irrational number

Answer: (d) An irrational number is correct

Hint : (2 – √3)2 = 22 – 2 × 2 ×√3 + (√3)2

= 4 – 4√3 + 3

= 7 – 4√3 is an irrational number

#### Question 18. If x a positive rational number which is not a perfect square, then -5√x is

(a) A negative integer

(b) An integer

(c) A rational number

(d) An irrational number

(d) Irrational number

#### Question 19. If x, y are both positive rational numbers, then (√x + √y) (√x – √y) is

(a) A rational number

(b) An irrational number

(c) Neither rational nor irrational number

(d) Both rational as well as irrational number

(√x + √y) (√x – √y) = (√x)2– (√y)2. x – y is a rational number option (c) is correct

#### Question 20. After rationalising the denominator of 7/3√3-2√2, we get the denominator as

(a) 13

(b) 19

(c) 5

(d) 35

7/3√3-2√2 = 7/3√3-2√2 × 3√3+2√2/3√3+2√2 = 21√3+14√2/(3√3)2-(2√2)2

= 7(3√3+2√2)/17-8 = 7(3√3+2√2)/19  option (b) is correct

#### Question 21. The number obtained on rationalising the denominator of 1/√7-2 is

(a)√7+2/3

(b) √7-2/3

(c) √7+2/5

(d) √7+2/45

1/√7-2 = 1/√7-2 ×√7+2/√7+2

= √7+2/(√7)2-22

= √7+2/7-4

= √7+2/3

option is correct (a) √7+2/3

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