Number System – Fully Solved MCQs

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1. Which of the following is a natural number ?

Options: (a) 0 (b) –5 (c) 3 (d) –1
Ans: (c) 3
Explanation: Natural numbers are the counting numbers starting from 1, 2, 3, etc. Since 3 is a positive counting number, it qualifies as a natural number.

2. Whole numbers start from:

Options: (a) 1 (b) 0 (c) –1 (d) 2
Ans: (b) 0
Explanation: Whole numbers include 0 and all positive integers. Therefore, the smallest whole number and starting point of whole numbers is 0.

3. Which of the following is an integer ?

Options: (a) 2.5 (b) –7 (c) 3/4 (d) √3
Ans: (b) –7
Explanation: Integers include positive numbers, negative numbers, and zero without fractions or decimals. –7 fits this definition, whereas the other options do not.

4. Rational number means a number that can be written as:

Options: (a) 2 (b) a/b (c) π (d) 5
Ans: (b) a/b
Explanation: A rational number is any number that can be expressed as a fraction a/b, where a and b are integers and b ≠ 0.

5. Which one is an irrational number ?

Options: (a) 4/9 (b) 0.25 (c) √11 (d) –2
Ans: (c) √11
Explanation: Irrational numbers cannot be written as a/b and have non-terminating, non-repeating decimals. √11 is irrational because it cannot be expressed as a simple fraction.

6. All rational and irrational numbers together are called:

Options: (a) Integers (b) Whole numbers (c) Real numbers (d) Natural numbers
Ans: (c) Real numbers
Explanation: Real numbers include both rational numbers (fractions, integers) and irrational numbers (√2, π). Together they form the complete set of real numbers.

 

7. Which number is not a whole number?

Options: (a) 0 (b) 5 (c) 10 (d) –3
Ans: (d) –3
Explanation: Whole numbers are 0, 1, 2, 3,… and do not include negative numbers. Therefore, –3 is not a whole number.

8. The smallest natural number is:

Options: (a) 0 (b) 1 (c) 2 (d) –1
Ans: (b) 1
Explanation: Natural numbers are the set of counting numbers beginning with 1. Hence, the smallest natural number is 1.

9. The value of 16 belongs to:

Options: (a) Natural numbers (b) Integers (c) Both A and B (d) None
Ans: (c) Both A and B
Explanation: 16 is a natural number because it is positive and used for counting, and it is an integer because integers include all whole numbers.

10. Which number is rational ?

Options: (a) π (b) 7 (c) –3/8 (d) 3
Ans: (c) –3/8
Explanation: Rational numbers must be expressible as a/b. –3/8 is already a fraction, so it is rational. π is irrational; 7 and 3 are rational but fraction form fits best.

11. The set of integers includes:

Options: (a) Only positive numbers (b) Only negative numbers (c) Positive, negative and zero (d) Only whole numbers
Ans: (c) Positive, negative and zero
Explanation: Integers represent the set … −3, −2, −1, 0, 1, 2, 3 …; this includes all positive and negative whole numbers and zero.

12. The number 0.333... is:

Options: (a) Rational (b) Irrational (c) Natural (d) Not a real number
Ans: (a) Rational
Explanation: 0.333… is a repeating decimal equivalent to 1/3, which can be written as a fraction a/b. Therefore, it is a rational number.

13. Which is a real number?

Options: (a) √2 (b) –9 (c) 5.7 (d) All of these
Ans: (d) All of these
Explanation: Real numbers include rational and irrational numbers. √2 (irrational), –9 (integer), and 5.7 (decimal) all belong to the real number system.

14. Which is an irrational number ?

Options: (a) 1.2 (b) 3/5 (c) √2 (d) –1
Ans: (c) √2
Explanation: Irrational numbers cannot be written as a/b and have non-terminating, non-repeating decimals. √2 is a classic example of an irrational number.

15. Every natural number is also a:

Options: (a) Whole number (b) Integer (c) Rational number (d) All of these
Ans: (d) All of these
Explanation: Natural numbers are part of whole numbers, integers, and rational numbers. Each natural number can be written as n, an integer, and n/1, a rational number.

16. √15 is —. √15 হ’ল — .

(a) a natural number / প্ৰাকৃতিক সংখ্যা
(b) not a real number / বাস্তৱ সংখ্যা নহয়
(c) a rational number / ভগ্ন সংখ্যা
(d) an irrational number / অবিভাজ্য সংখ্যা

Ans / উত্তৰ: (d) an irrational number | অবিভাজ্য সংখ্যা

Explanation / ব্যাখ্যা: √15 cannot be written as p/q and its decimal expansion is non-terminating and non-recurring. √15 ক p/q ৰূপত লিখিব নোৱাৰি আৰু ইয়াৰ দশমিক মান অসীম আৰু পুনৰাবৃত্তিহীন।

17. The decimal expansion of √15 —. √15 ৰ দশমিক বিস্তাৰ — .

(a) is terminating / সমাপ্ত হয়
(b) is non-terminating and non-recurring / অসীম আৰু পুনৰাবৃত্তিহীন
(c) is non-terminating and recurring / অসীম আৰু পুনৰাবৃত্ত
(d) does not exist / অস্তিত্ব নাই

Ans / উত্তৰ: (b) is non-terminating and non-recurring | অসীম আৰু পুনৰাবৃত্তিহীন

Explanation / ব্যাখ্যা: √15 is an irrational number, so its decimal expansion never ends and does not repeat. √15 অবিভাজ্য সংখ্যা, সেয়েহে ইয়াৰ দশমিক মান কেতিয়াও শেষ নহয় আৰু পুনৰাবৃত্ত নহয়।

18. Which of the following is NOT a rational number ? তলৰ কোনটো ভগ্ন সংখ্যা নহয় ?

(a) √6 | (b) √9 | (c) √25 | (d) √36

Ans / উত্তৰ: (a) √6

Explanation / ব্যাখ্যা: √6 is not a perfect square, so it is an irrational number. √6 পূৰ্ণ বৰ্গ নহয়, সেয়েহে ই অবিভাজ্য সংখ্যা।

19. Which of the following is a rational number ? তলৰ কোনটো ভগ্ন সংখ্যা ?

(a) √36  (b) √14  (c) √21  (d) √12

Ans / উত্তৰ: (a) √36

Explanation / ব্যাখ্যা: √36 = 6, which is a rational number., √36 = ৬, যি এটা ভগ্ন সংখ্যা।