Please refer to Chapter 1 Real Numbers MCQ Class 10 Mathematics with answers below. These multiple-choice questions have been prepared based on the latest NCERT book for Class 10 Mathematics. Students should refer to MCQ Questions for Class 10 Mathematics with Answers to score more marks in Grade 10 Mathematics exams. Students should read the chapter Real Numbers and then attempt the following objective questions.

MCQ Questions Class 10 Mathematics Chapter 1 Real Numbers

The Real Numbers MCQ Class 10 Mathematics provided below covers all important topics given in this chapter. These MCQs will help you to properly prepare for exams.

Question. If HCF (a, b) = 12 and a × b = 1800 then LCM (a, b) is   
(a) 3600
(b) 900
(c) 150
(d) 90

Question . If 3 is the least prime factor of number a and 7 is the least prime factor of number b, then the least prime factor of (a + b) is     
(a) 2
(b) 3
(c) 5
(d) 10

Question . If a = 2³ × 3, b = 2 × 3 × 5, c = 3n × 5 and LCM (a, b, c) = 2³ × 3² × 5, then n is equal to     
(a) 1
(b) 2
(c) 3
(d) 4

Question . If HCF (26, 169) = 13 then LCM (26, 169) is   
(a) 26
(b) 52
(c) 338
(d) 13

Question. If mn = 32, where m and n are positive integers, then the value of (n)mn is   
(a) 9765625
(b) 9775625
(c) 9785625
(d) 9865625

Question. Given that LCM of (91, 26) = 182 then HCF (91, 26) is   
(a) 13
(b) 26
(c) 7
(d) 9

Question. The decimal expansion of number 44122×53×7 is   
(a) A terminating decimal
(b) Non-terminating but repeating
(c) Non-terminate non repeating
(d) terminating after two places of decimal

Question . The LCM of smallest two digit composite number and smallest composite number is     
(a) 12
(b) 4
(c) 20
(d) 44

Question . HCF × LCM for the numbers 150 and 10 is     
(a) 1500
(b) 150
(c) 10
(d) None of these

Question . If (–1)ⁿ + (–1)⁴ⁿ = 0, then n is       
(a) any negative integer
(b) any even natural number
(c) any positive integer
(d) any odd natural number

Question. The values of x and y is the given figure are   

(a) x + 10, y = 14
(b) x = 21, y = 84
(c) x = 21, y = 25
(d) x = 10, y = 40

Question. The decimal expansion of 178 will terminate after how many places of decimals?
(a) 1
(b) 2
(c) 3
(d) will not terminate

Question. The decimal expansion of n is   
(a) terminating
(b) non-terminating and non-recurring
(c) non-terminating and recurring
(d) does not exist.

Question. If HCF of 55 and 99 is expressible in the form 55 m – 99, then the value of m:   
(a) 4
(b) 2
(c) 1
(d) 3

Question . The total number of factors of a prime number is     
(a) 1
(b) 0
(c) 2
(d) 3

Question . The sum of exponents of prime factors in the prime factorisation of 196 is     
(a) 3
(b) 4
(c) 5
(d) 2

Question . The HCF of 135 and 225 is       
(a) 15
(b) 75
(c) 45
(d) 5

Question . The decimal form of 129/2 2⁵ 5⁷ 7⁵ is   
(a) terminating
(b) non-terminating
(c) non-terminating non-repeating
(d) none of them

Question . The decimal representation of 37/50 will     
(a) terminate after 1 decimal place
(b) terminate after 2 decimal places
(c) terminate after 3 decimal places
(d) not terminate

Question . If two positive integers a and b are written as a = xy² and b = x³y, where x, y are prime numbers, then LCM (a, b) is   
(a) x²y²
(b) xy
(c) x³y²
(d) none of these

Question . The largest number which divides 70 and 125 leaving remainders 5 and 8 respectively is       
(a) 13
(b) 65
(c) 875
(d) 1750

Question . The least number that is divisible by all the numbers from 1 to 5 is     
(a) 30
(b) 20
(c) 60
(d) 120

Question . Which of these rational number is a terminating decimal?       
(a) 18 7
(b) 21 13
(c) 200 8
(d) 225 16

Question . If the HCF of 65 and 117 is expressible in the form 65m –117, then the value of m is   
(a) 4
(b) 2
(c) 11
(d) 3

Question. For any positive integer a and b, there exist unique integers q and r such that a = 3q + r, where r must satisfy.   
(a) 0 ≤ r < 3
(b) 1 < r < 3
(c) 0 < r < 3
(d) 0 < r ≤ 3

Question . The largest number which divides 615 and 963 leaving remainder 6 in each case is     
(a) 82
(b) 95
(c) 87
(d) 93

Question . If 3 is the least prime factor of number a and 7 is the least prime factor of number b, then the least prime factor of (a + b) is     
(a) 2
(b) 3
(c) 5
(d) 10

Question . The decimal expansion of the rational number 14587/1250 will terminate after     
(a) one decimal place
(b) two decimal places
(c) three decimal places
(d) four decimal places

Question . If p and q are prime numbers than the HCF of p³q² and p²q is     
(a) p³q² 
(b) p²q
(c) p²q²
(d) pq

Question . Which of the following rational numbers will have a terminating decimal expansion?       
(a) 17/8
(b) 7/105
(c) 9/14
(d) 13/30

Question . Arnav has 40 cm long red and 84 cm long blue ribbon. He cuts each ribbon into pieces such that all pieces are of equal length. What is the length of each piece?   
(a) 4 cm as it is the HCF of 40 and 84
(b) 4 cm as it is the LCM of 40 and 84
(c) 12 cm as it is the LCM of 40 and 84
(d) 12 cm as it is the HCF of 40 and 84

Question . A teacher creates the question “Which of the following could be the sum of two rational numbers?”. She now needs to create three incorrect choices and one correct answer. Which option shows the choices that the teacher should create?     
(a) First choice: 125; Second choice: 36+42; Third choice: 81; Correct Answer: 169
(b) First choice: 227; Second choice: 25+16; Third choice: 64; Correct Answer: 5
(c) First choice: p; Second choice: 20+16; Third choice: 50 – 1; Correct Answer: 49
(d) None of them

Question . The fractions a 3 and 7 b are equivalent to decimals that terminate. Which best describes the product of a and b?     
(a) It is a prime number.
(b) It cannot be an odd number.
(c) It is of the form 21k, where k could be multiples of 7 or 9.
(d) It is of the form 21k, where k could be multiples of 2 or 5.

Question . The decimal representation of 15/400 will     
(a) terminate after 1 decimal place.
(b) terminate after 2 decimal places.
(c) terminate after 3 decimal places.
(d) terminate after 4 decimal places.

Question . The decimal representation of 11/2³×5 will     
(a) terminate after 1 decimal place
(b) terminate after 2 decimal places
(c) terminate after 3 decimal places
(d) not terminates

Question . √7 is   
(a) an integer
(b) an irrational number
(c) a rational number
(d) none of these

Question . The HCF of 8, 9 and 5 is   
(a) 8
(b) 25
(c) 9
(d) 1

Question . The decimal expansion of the rational number 47/2³5² will terminate after   
(a) one decimal place
(b) two decimal places
(c) three decimal places
(d) more than three decimal places

Question . If 6370 = 2m . 5n . 7k . 13p, then the value of m + n + k + p is       
(a) 2
(b) 3
(c) 4
(d) 5

Question . The product of two consecutive integers is divisible by     
(a) 2
(b) 3
(c) 5
(d) 7

Question. If (97)3 × (4981)2x-6 = (79)9 then value of x is   
(a) 12
(b) 9
(c) 8
(d) 6

Question . n² – 1 is divisible by 8 if n is     
(a) an integer
(b) a natural number
(c) an odd integer
(d) an even integer

Question.HCF of 96 and 404 is     
(a) 4
(b) 2
(c) 3
(d) 101

Question . The largest number which divides 70 and 125 leaving remainders 5 and 8 respectively is   
(a) 13
(b) 65
(c) 875
(d) 1750

Question . 5 is the prime factor of   
(a) 78
(b) 240
(c) 1001
(d) 1547

Question . If two positive integers a and b are written as a = x³y² and b = xy³; x, y are prime numbers, then LCM (a, b) is   
(a) xy
(b) xy²
(c) x3y³
(d) x²y²

Question . The pair of co-prime is     
(a) 32, 40
(b) 21, 28
(c) 18, 25
(d) 9, 27

Question . ⁻3.27 is     
(a) an integer
(b) a rational number
(c) a natural number
(d) an irrational number

Question . The product of two numbers is 320 and their LCM is 80. The HCF of the numbers is     
(a) 8
(b) 4
(c) 16
(d) 10

Question . If n is any natural number then 6n – 5n always end with   
(a) 1
(b) 3
(c) 5
(d) 7

Question . The LCM of two numbers is 1200. Which of the following cannot be their HCF?   
(a) 600
(b) 500
(c) 400
(d) 200

Question . Three bulbs red, green and yellow flash at intervals of 80 seconds, 90 seconds and 110 seconds. All three flash together at 8:00 am. At what time will the three bulbs flash altogether again?   
(a) 8:12 am
(b) 9:12 am
(c) 10:12 am
(d) 11:12 am

Question . The product of a non zero rational and an irrational number is   
(a) always irrational
(b) always rational
(c) rational or irrational
(d) one

We hope you liked the above Real Numbers MCQ Class 10 Mathematics. In case you have any questions please put them in the comments box below and our teachers will provide you a response.