MCQ for Class 10 Mathematics Chapter 1 Real Numbers
Refer to CBSE Class 10 Mathematics Real Numbers MCQs Set A provided below available for download in Pdf. The MCQ Questions for Class 10 Mathematics with answers are aligned as per the latest syllabus and exam pattern suggested by CBSE, NCERT and KVS. Chapter 1 Real Numbers Class 10 MCQ are an important part of exams for Class 10 Mathematics and if practiced properly can help you to improve your understanding and get higher marks. Refer to more Chapter-wise MCQs for CBSE Class 10 Mathematics and also download more latest study material for all subjects
नीचे दिए गए सीबीएसई कक्षा 10 गणित के वास्तविक संख्याएँ MCQ सेट A को पीडीएफ़ में डाउनलोड के लिए देखें। कक्षा 10 गणित के MCQ प्रश्न और उनके उत्तर सीबीएसई, एनसीईआरटी और केवीएस द्वारा सुझाए गए नवीनतम पाठ्यक्रम और परीक्षा पैटर्न के अनुसार तैयार किए गए हैं। अध्याय 1 वास्तविक संख्याएँ कक्षा 10 MCQ कक्षा 10 गणित की परीक्षाओं का एक महत्वपूर्ण हिस्सा हैं और अगर इनका सही तरीके से अभ्यास किया जाए तो ये आपकी समझ को बेहतर बनाने और उच्च अंक प्राप्त करने में आपकी मदद कर सकते हैं। सीबीएसई कक्षा 10 गणित के लिए और अधिक अध्याय-वार MCQ देखें और सभी विषयों के लिए नवीनतम अध्ययन सामग्री भी डाउनलोड करें।
MCQ for Class 10 Mathematics Chapter 1 Real Numbers
Class 10 Mathematics students should refer to the following multiple-choice questions with answers for Chapter 1 Real Numbers in Class 10.
✅ Chapter 1: Real Numbers – 50 MCQ Questions with Answers
| No. | Question | Options | Answer |
|---|---|---|---|
| 1 | What is the HCF of 24 and 36? | A) 6 B) 12 C) 18 D) 3 | ✅ B |
| 2 | What is the LCM of 12 and 15? | A) 60 B) 30 C) 90 D) 45 | ✅ B |
| 3 | What is the HCF of any two co-prime numbers? | A) 1 B) 0 C) Product of the numbers D) None | ✅ A |
| 4 | LCM(8, 20) = 40. Find HCF(8, 20). | A) 4 B) 2 C) 8 D) 1 | ✅ A |
| 5 | The Fundamental Theorem of Arithmetic is used in finding: | A) Prime factors B) Square roots C) LCM and HCF D) None | ✅ C |
| 6 | The prime factorization of 90 is: | A) 2×3^2×5 B) 2×5^2×3 C) 2×3×5 D) 3^2×5 | ✅ A |
| 7 | A rational number in the form ( \frac{p}{q} ), where q ≠ 0 and q has no prime factor other than 2 and/or 5, has a: | A) Terminating decimal B) Non-terminating repeating decimal C) Non-terminating non-repeating D) Irrational expansion | ✅ A |
| 8 | Decimal expansion of ( \frac{7}{8} ) is: | A) 0.875 B) 0.7777… C) 0.7 D) None | ✅ A |
| 9 | What type of decimal expansion does ( \frac{1}{3} ) have? | A) Terminating B) Repeating C) Non-repeating D) None | ✅ B |
| 10 | Which of the following is an irrational number? | A) ( \sqrt{2} ) B) ( \frac{1}{4} ) C) 3 D) 0 | ✅ A |
| 11 | Sum of a rational and an irrational number is: | A) Rational B) Irrational C) Both D) Not defined | ✅ B |
| 12 | Product of a non-zero rational and irrational number is: | A) Rational B) Irrational C) Both D) Zero | ✅ B |
| 13 | ( \frac{2}{5} ) is a: | A) Rational number B) Irrational number C) Natural number D) Integer | ✅ A |
| 14 | Which number has a non-terminating repeating decimal expansion? | A) ( \frac{4}{19} ) B) ( \frac{1}{8} ) C) ( \frac{7}{20} ) D) ( \frac{3}{25} ) | ✅ A |
| 15 | The LCM of 9 and 6 is: | A) 18 B) 9 C) 3 D) 27 | ✅ A |
| 16 | HCF(60, 72) is: | A) 6 B) 12 C) 24 D) 18 | ✅ B |
| 17 | Which of these is not a rational number? | A) ( \frac{1}{2} ) B) 0.75 C) ( \pi ) D) -5 | ✅ C |
| 18 | Every rational number is: | A) Whole B) Integer C) Real D) Irrational | ✅ C |
| 19 | Which of these is a whole number but not a natural number? | A) 1 B) 2 C) 0 D) 3 | ✅ C |
| 20 | The decimal expansion of ( \frac{1}{7} ) is: | A) 0.142857… (repeating) B) 0.25 C) 0.5 D) 0.875 | ✅ A |
| 21 | LCM × HCF = Product of two numbers. If HCF = 4, LCM = 60 and one number = 12, the other is: | A) 20 B) 24 C) 15 D) 10 | ✅ A |
| 22 | Which is not a prime number? | A) 2 B) 3 C) 4 D) 5 | ✅ C |
| 23 | The smallest prime number is: | A) 0 B) 1 C) 2 D) 3 | ✅ C |
| 24 | Which number is a perfect square? | A) 49 B) 50 C) 51 D) 52 | ✅ A |
| 25 | What is the square of √3? | A) 3 B) √3 C) 9 D) 1.73 | ✅ A |
| 26 | What is the HCF of 0 and any number a (a ≠ 0)? | A) 0 B) a C) 1 D) Undefined | ✅ B |
| 27 | The decimal representation of an irrational number is: | A) Terminating B) Repeating C) Non-terminating non-repeating D) None | ✅ C |
| 28 | If a = bq + r, what is this called? | A) Euclid’s division lemma B) Fundamental theorem of arithmetic C) Rational theorem D) HCF rule | ✅ A |
| 29 | What is the value of ( \sqrt{16} )? | A) 2 B) 4 C) ±4 D) –4 | ✅ C |
| 30 | The decimal expansion of a rational number either terminates or: | A) Repeats B) Becomes irrational C) Becomes infinite D) None | ✅ A |
| 31 | Which of the following is not a real number? | A) 0 B) –5 C) ( \sqrt{-1} ) D) 1.5 | ✅ C |
| 32 | Is √49 a rational number? | A) Yes B) No C) Can’t say D) Irrational | ✅ A |
| 33 | What is the least prime number? | A) 1 B) 2 C) 3 D) 5 | ✅ B |
| 34 | The HCF of two numbers is always a: | A) Multiple B) Factor C) Prime D) Odd number | ✅ B |
| 35 | The LCM of two co-prime numbers is equal to: | A) Their product B) Their sum C) HCF D) None | ✅ A |
| 36 | Which of the following is a composite number? | A) 7 B) 13 C) 15 D) 11 | ✅ C |
| 37 | A rational number between 0 and 1 is: | A) 3 B) 0.5 C) 2 D) 5 | ✅ B |
| 38 | The prime factorization of 60 is: | A) 2^2 × 3 × 5 B) 2 × 5 × 7 C) 2^3 × 5 D) 3^2 × 5 | ✅ A |
| 39 | Every natural number is also a: | A) Rational number B) Whole number C) Integer D) All of these | ✅ D |
| 40 | If a number is divisible by 3 and 4, it is divisible by: | A) 7 B) 6 C) 12 D) 8 | ✅ C |
| 41 | Which number is irrational? | A) ( \sqrt{11} ) B) 7 C) ( \frac{5}{3} ) D) 0 | ✅ A |
| 42 | The product of two irrational numbers is: | A) Always irrational B) Always rational C) Sometimes rational D) Zero | ✅ C |
| 43 | What is the LCM of 4 and 5? | A) 10 B) 15 C) 20 D) 25 | ✅ C |
| 44 | The value of ( \sqrt{100} ) is: | A) ±10 B) 10 C) 100 D) 5 | ✅ A |
| 45 | The HCF of 18 and 24 is: | A) 3 B) 6 C) 12 D) 9 | ✅ B |
| 46 | Which of |
80.Question : 7×11×13× 6 is: 100.Question
: If a < b < c < d < e are consecutive positive integers,
such that b + c+ d is a perfect square and a +b + c + d + e is a perfect
cube. What is the smallest possible value of c? 101.Question : If we divide a two-digit number by the sum of its digits we get 4 as quotient and 3 as remainder. 102.Question
: Four positive integers sum to 125. If the first of these numbers is
increased by 4, the second is decreased by 4, the third is multiplied by
4 and the fourth is divided by 4, we find four equal numbers, then four
original integers are: 103.Question : What is the least number which when divided by 42, 72 and 84 leaves the remainder 25, 55 and 67 respectively? 104.Question : y, z are integers, then the value of x + y - z is: 105.Question : A positive integer n has 60 divisors and 7 n has 80 divisors. What is the greatest integer k such that 7k divides n? 106.Question : What is the largest integer that is a divisor of (n +1) (n+3) (n+5) (n+7) (n+9) for all positive even integers n? 107.Question : The sum of 18 consecutive positive integers is a perfect square. The smallest possible value of this sum is… 108.Question
: When the decimal point of a certain positive decimal number is moved
two places to the right, the new number is two times the sum of the
original number and the reciprocal of the original number. The product
of 42 and the original number is: 109.Question : The sum of seven consecutive natural numbers is 1617. How many of these are prime? 110.Question
: A number when divided by 342 gives a remainder 47. When the same
number is divided by 19, what would be the remainder? 111.Question : If xyz + xy + xz + yz + x + y + z = 384where x, y, z are positive integers, then the value of x + y + z is: 112.Question
: Let x be the greatest number by which if we divide 366, 513 and 324,
then in each case the remainder is the same. The sum of digit of x is: 113.Question
: If a number m is divided by 5 leaves a remainder 2, while another
number n is divided by 5 leaves a remainder 4, then the remainder when
(m + n) is divided by 5 is: 114.Question : Among the numbers 2250 3200 4150 5100 2 ,3 ,4 and 5 the greatest is 115.Question : The sum of the digit in (104n2+8 +1)2 , , where ‘n’ is a positive integer, is………. 116.Question : The ascending order of √2 3√4, 4√6 is:
a) 2
b) 3
c) 5
d) 7
Answer: 2
48.Question: The product of three consecutive integers is divisible by
a) 6
b) 7
c) none of these
d) 5
Answer: 6
49.Question: n2 -1 is divisible by 8, if n is
a) an odd integer
b) an even integer
c) a natural number
d) an integer
Answer: an odd integer
50.Question: 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 must satisfy
a) 0 ≤ r < b
b) 0 < r < b
c) 1< r < b
d) None of these
Answer: 0 ≤ r < b
51.Question: The decimal expansion of the rational number 47/2352 will terminate after
a) three decimal places
b) one decimal place
c) two decimal places
d) more than three decimal places
Answer: three decimal places
52.Question: √7 is
a) an irrational number
b) none of these
c) an integer
d) rational number
Answer: an irrational number
53.Question: The decimal expansion of the rational number 33/225 will terminate after
a) two decimal places
b) more than three decimal places
c) one decimal place
d) three decimal places
Answer: two decimal places
54.Question: The largest number which exactly divides 70, 80, 105, 160 is
a) 5
b) none of these
c) 7
d) 10
Answer: 5
55.Question: The least number that is divisible by first five even numbers is
a) 120
b) 160
c) 80
d) 60
Answer: 120
56.Question: HCF of (x3 -3x +2) and (x2 - 4x +3) is
a) (x -1)
b) (x -1)(x -3)
c) (x -1)(x +2)
d) (x -2)3
Answer: (x -1)
57.Question: LCM of x2 - 4 and x4 -16 is
a) (x2 + 4)(x2 - 4)
b) (x2 - 4) (x +2)
c) (x -2)(x +2)
d) None of these
Answer: (x2 + 4)(x2 - 4)
58.Question: If n is an even natural number, then the largest natural number by which n(n +1)(n +2) is divisible is
a) 24
b) 6
c) 12
d) 9
Answer: 24
59.Question: The largest number which divides 318 and 739 leaving remainder 3 and 4 respectively is
a) 105
b) 110
c) 7
d) 35
Answer: 105
60.Question: When 256 is divided by 17, remainder would be
a) 1
b) 1
c) none of these
d) 16
Answer: 1
61.Question. A rational number between 3/4 and 4/5 is:
a) 7/5
b) 7/10
c) 3/10
d) 4/10
62.Question. A rational number between 1/2 and 3/4 is:
a) 2/5
b) 5/8
c) 4/3
d) 1/4
63.Question. Which one of the following is not a rational number:
a) √2
b) 0
c) √4
d) √-16
64.Question. Which one of the following is an irrational number:
a) √4
b) 3 √8
c) √100
d) √- 0.64
65.Question. 3,3/8 in decimal form is:
a) 3.35
b) 3.375
c) 33.75
d) 337.5
66.Question. 5/6 in the decimal form is: 
67.Question. Decimal representation of rational number 8/27 is: 
68.Question. 0.6666…….. in p/q form is:
a) 6/99
b) 2/3
c) 3/5
d) 1/66
69.Question. The value of (√5+√2)(√5-√2) is:
a) 10
b) 7
c) 3
d) √3
70.Question. 
a) 6/99
b) 2/3
c) 3/5
d) none of these
71.Question. Euclid’s division algorithm can be applied to :
(A) only positive integers
(B) only negative integers
(C) all integers
(D) all integers except 0
Answer: A
72.Question. If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is :
(A) 1
(B) 2
(C) 3
(D) 4
Answer: B
73.Question. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is :
(A) 10
(B) 100
(C) 504
(D) 2520
Answer: D
74.Question. 3.24636363... is :
(A) a terminating decimal number
(B) a non-terminating repeating decimal number
(C) a rational number
(D) both (B) and (C)
Answer: D
75.Question. The decimal expansion of the rational number 47/22 .52 . will terminate after :
(A) one decimal place
(B) three decimal places
(C) two decimal places
(D) more than 3 decimal places
Answer: C
76.Question.
Euclid’s division lemma states that if a and b are any two +ve
integers, then there exist unique integers q and r such that :
(A) a = bq + r, 0 < r < b
(B) a = bq + r, 0 ≤ r ≤ b
(C) a = bq + r, 0 ≤ r < b
(D) a = bq + r, 0 < b < r
(A) 30
(B) 150
(C) 100
(D) 50
Answer: C
77.Question. Which of the following numbers has terminating decimal expansion ?
(A) 37/45
(B) 21/2356
(C) 17/49
(D) 89/2232
Answer: B
78.Question. How many prime factors are there in prime factorisation of 5005 ?
(A) 2
(B) 4
(C) 6
(D) 7
Answer: B
79.Question. If a, b are coprime, then a2, b2 are :
(A) Coprime
(B) Not coprime
(C) Odd numbers
(D) Even numbers
Answer: A
a) a prime number
b) a composite number
c) an even number
d) None
Answer : B
b) 4
c) -2
d) 1
Answer : D
a) 675
b) 576
c) 475
d) 384
Answer : A
Now
if we divide that two digit number by the product of its digits, we get
3 as quotient and 5 as remainder. The two digit number is:
a) Even
b) Odd prime
c) Odd composite
d) Odd
Answer : B
a) 16, 24, 5, 80
b) 8, 22, 38, 57
c) 7, 19, 46, 53
d) 12, 28, 40, 45
Answer : A
a) 521
b) 512
c) 504
d) 487
Answer : D
a) 6
b) 8
c) 7
d) -2
Answer : C
a) 0
b) 1
c) 2
d) 3
Answer : D
a) 3
b) 5
c) 11
d) 15
Answer : B
a) 169
b) 225
c) 289
d) 361
Answer : B
a) 3
b) 6
c) 7
d) 14
Answer : C
a) 4
b) 5
c) 2
d) 7
Answer : A
(A 9
b) 8
c) 18
d) 11
Answer : C
a) 23
b) 18
c) 20
d) 35
Answer : A
a) 3
b) 4
c) 5
d) 7
Answer : B
a) 1
b) 2
c) 3
d) 4
Answer : B
a) 2 250
b) 3 200
c) 4 150
d) 5 100
Answer : A
a) 4
b) 4n
c) 2+2n
d) 4n2
Answer : C
a) √2, 3√4, 4√6
b) √2, 4√6, 3√4
c) 3√4 √2, 4√6
d) 4√6, 3√4, √2
Answer : B