Class 10 Maths Real Numbers Question Answer: Important Chapter

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Class 10 Maths Real Numbers Question Answer

Board	CBSE Board, UP Board, JAC Board, Bihar Board, HBSE Board, UBSE Board, PSEB Board, RBSE Board, JK Board
Textbook	NCERT
Class	Class 10
Subject	Maths
Chapter	Real Numbers
Post Type	Important Question in Hindi
Medium	Hindi/English

Class 10 Maths Real Numbers Important Questions

Prove that √2 is an irrational number.
(साबित करें कि √2 एक अपरिमेय संख्या है।)

Find the HCF of 56 and 72 using Euclid’s division algorithm.
(यूक्लिड की विभाजन विधि का उपयोग करके 56 और 72 का महत्तम समापवर्तक (HCF) ज्ञात करें।)

Express 135 as a product of its prime factors.
(135 को इसके अभाज्य गुणकों के रूप में व्यक्त करें।)

Find the LCM and HCF of 12 and 15 using the prime factorization method.
(12 और 15 का LCM और HCF अभाज्य गुणनखंड विधि का उपयोग करके ज्ञात करें।)

Prove that 5 + √3 is an irrational number.
(साबित करें कि 5 + √3 एक अपरिमेय संख्या है।)

Use Euclid’s division lemma to show that the square of any positive integer is of the form 3m or 3m+1.
(यूक्लिड का विभाजन लेमा का उपयोग करके दिखाएं कि किसी भी धनात्मक पूर्णांक का वर्ग 3m या 3m+1 के रूप में होता है।)

Find the HCF of 60, 72, and 120 using Euclid’s algorithm.
(यूक्लिड की विधि का उपयोग करके 60, 72, और 120 का HCF ज्ञात करें।)

Prove that 3 + √7 is an irrational number.
(साबित करें कि 3 + √7 एक अपरिमेय संख्या है।)

If the HCF of 96 and 404 is 4, find the LCM.
(यदि 96 और 404 का HCF 4 है, तो उनका LCM ज्ञात करें।)

Show that any positive integer is of the form 6q, 6q + 1, 6q + 2, 6q + 3, 6q + 4, or 6q + 5, where q is an integer.
(दिखाएं कि कोई भी धनात्मक पूर्णांक 6q, 6q + 1, 6q + 2, 6q + 3, 6q + 4, या 6q + 5 के रूप में होता है, जहाँ q एक पूर्णांक है।)

Find the largest number which divides 245 and 1029, leaving remainders 5 and 7 respectively.
(सबसे बड़ी संख्या ज्ञात करें जो 245 और 1029 को क्रमशः 5 और 7 शेषफल छोड़ते हुए विभाजित करे।)

Prove that √5 is irrational.
(साबित करें कि √5 अपरिमेय है।)

Find the smallest number that is divisible by both 48 and 60.
(सबसे छोटी संख्या ज्ञात करें जो 48 और 60 दोनों से विभाज्य हो।)

Prove that the product of a non-zero rational number and an irrational number is irrational.
(साबित करें कि किसी शून्य के अतिरिक्त परिमेय संख्या और अपरिमेय संख्या का गुणनफल अपरिमेय होता है।)

If d is the HCF of 45 and 75, find x and y such that d = 45x + 75y.
(यदि d, 45 और 75 का HCF है, तो x और y का मान ज्ञात करें ताकि d = 45x + 75y हो।)

Class 10 Maths Real Numbers One Word Question Answers

What is the smallest prime number?
Answer: 2

What is the HCF of 16 and 24?
Answer: 8

What is the LCM of 5 and 7?
Answer: 35

What is the prime factorization of 50?
Answer: 2 × 5²

What is the LCM of 15 and 20?
Answer: 60

What is the square root of 121?
Answer: 11

What is the HCF of 36 and 54?
Answer: 18

What is the smallest composite number?
Answer: 4

Is √3 rational or irrational?
Answer: Irrational

What is the LCM of 12 and 15?
Answer: 60

What is the HCF of 9 and 28?
Answer: 1

What is the prime factorization of 72?
Answer: 2³ × 3²

What is the HCF of 45 and 75?
Answer: 15

What is the LCM of 8 and 14?
Answer: 56

Is √7 rational or irrational?
Answer: Irrational

Class 10 Maths Real Numbers Fill In The Blank

The HCF of two co-prime numbers is _____.
Answer: 1

The LCM of 9 and 12 is _____.
Answer: 36

The smallest prime number is _____.
Answer: 2

Every composite number can be expressed as a product of its _____.
Answer: Prime factors

The HCF of 15 and 25 is _____.
Answer: 5

The LCM of 6 and 8 is _____.
Answer: 24

If two numbers are co-prime, then their LCM is equal to their _____.
Answer: Product

The prime factorization of 90 is _____ × 3² × 5.
Answer: 2

The decimal expansion of an irrational number is _____.
Answer: Non-terminating and non-repeating

The smallest composite number is _____.
Answer: 4

The HCF of 56 and 98 is _____.
Answer: 14

The LCM of 14 and 35 is _____.
Answer: 70

Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where r is _____.
Answer: Less than b

The number 2 is the only even _____.
Answer: Prime number

The square root of a prime number is always _____.
Answer: Irrational

Class 10 Maths Real Numbers Multiple Choice Questions

What is the HCF of 18 and 24?
(a) 2
(b) 3
(c) 6
(d) 12
Answer: (c) 6

Which of the following is a prime number?
(a) 9
(b) 11
(c) 15
(d) 21
Answer: (b) 11

The LCM of 5 and 7 is:
(a) 35
(b) 12
(c) 30
(d) 20
Answer: (a) 35

The HCF of two co-prime numbers is:
(a) 1
(b) 0
(c) 2
(d) 3
Answer: (a) 1

Which of the following is a composite number?
(a) 13
(b) 17
(c) 21
(d) 23
Answer: (c) 21

The decimal expansion of an irrational number is:
(a) Terminating
(b) Non-terminating and repeating
(c) Non-terminating and non-repeating
(d) Terminating and repeating
Answer: (c) Non-terminating and non-repeating

What is the HCF of 72 and 120?
(a) 12
(b) 24
(c) 18
(d) 36
Answer: (b) 24

The LCM of 8 and 12 is:
(a) 48
(b) 24
(c) 36
(d) 72
Answer: (b) 24

Which of the following numbers is irrational?
(a) √4
(b) 0.75
(c) 3/5
(d) √3
Answer: (d) √3

The LCM of 9 and 15 is:
(a) 30
(b) 90
(c) 45
(d) 60
Answer: (b) 45

Which of the following is the prime factorization of 60?
(a) 2² × 3 × 5
(b) 2 × 3 × 10
(c) 2³ × 5
(d) 2² × 5²
Answer: (a) 2² × 3 × 5

The smallest prime number is:
(a) 3
(b) 1
(c) 2
(d) 4
Answer: (c) 2

What is the LCM of 6, 8, and 12?
(a) 12
(b) 24
(c) 48
(d) 36
Answer: (b) 24

Which of the following numbers has a terminating decimal expansion?
(a) 7/9
(b) 2/5
(c) 4/7
(d) 1/3
Answer: (b) 2/5

Euclid’s division lemma states that for any two positive integers a and b, there exist unique integers q and r such that a = bq + r, where r is:
(a) r ≥ b
(b) r > b
(c) 0 ≤ r < b
(d) r ≤ 0
Answer: (c) 0 ≤ r < b

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