30 Essential Real Numbers MCQs for Class 10 Mathematics
by Avi Pal on January 28, 2024
Welcome to this comprehensive set of 30 multiple-choice questions (MCQs) designed specifically for Class 10 students studying Mathematics. This collection focuses on 'Real Numbers'. These questions are meticulously crafted to enhance your understanding of various concepts within the chapter, including rational and irrational numbers, prime factorization, Highest Common Factor (HCF), Least Common Multiple (LCM), and divisibility rules, among others.
Questions
The decimal expansion of the rational number 5885 is:
(a) terminating
(b) non-terminating repeating
(c) non-terminating non-repeating
(d) none of the above
Answer: (a) terminating
The HCF of 36 and 60 is:
(a) 12
(b) 18
(c) 24
(d) 6
Answer: (d) 6
Which of the following is a rational number?
(a) ππ
(b) 22
(c) 0.333...
(d) 55
Answer: (c) 0.333...
The LCM of two co-prime numbers x and y is:
(a) x
(b) y
(c) xy
(d) x + y
Answer: (c) xy
The number 0.121212... can be expressed as a fraction:
(a) 12999912
(b) 1210010012
(c) 1212999999991212
(d) 1210110112
Answer: (a) 12999912
The square root of which of the following numbers is irrational?
(a) 121
(b) 144
(c) 169
(d) 150
Answer: (d) 150
Which of the following is true for any two even numbers?
(a) Their HCF is always even
(b) Their LCM is always even
(c) Both (a) and (b)
(d) Neither (a) nor (b)
Answer: (c) Both (a) and (b)
The HCF of two numbers is 11 and their LCM is 7700. If one of the numbers is 308, the other is:
(a) 275
(b) 330
(c) 220
(d) 462
Answer: (a) 275
Which of the following is not a pair of co-prime numbers?
(a) 35 and 48
(b) 30 and 47
(c) 18 and 25
(d) 14 and 21
Answer: (d) 14 and 21
If a and b are co-prime numbers, then their LCM is:
(a) equal to their HCF
(b) equal to ab
(c) equal to the greater of a and b
(d) cannot be determined
Answer: (b) equal to ab
The decimal expansion of 7887 is:
(a) terminating
(b) non-terminating repeating
(c) non-terminating non-repeating
(d) none of the above
Answer: (a) terminating
The sum of two prime numbers is:
(a) always even
(b) always odd
(c) can be either odd or even
(d) none of the above
Answer: (c) can be either odd or even
The HCF of 81 and 27 is:
(a) 27
(b) 81
(c) 9
(d) 3
Answer: (a) 27
The product of LCM and HCF of two numbers is:
(a) equal to the product of the numbers
(b) greater than the product of the numbers
(c) less than the product of the numbers
(d) cannot be determined
Answer: (a) equal to the product of the numbers
The LCM of 15, 20, and 25 is:
(a) 150
(b) 300
(c) 600
(d) 1200
Answer: (b) 300
If a number is divisible by both 9 and 12, it must also be divisible by:
(a) 3
(b) 6
(c) 36
(d) 108
Answer: (b) 6
The number of prime factors of 36 is:
(a) 2
(b) 3
(c) 4
(d) 5
Answer: (c) 4
The greatest number of 4 digits which is divisible by 15, 25, 40 and 75 is:
(a) 9600
(b) 9800
(c) 9950
(d) 9999
Answer: (a) 9600
The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively is:
(a) 1394
(b) 2794
(c) 4194
(d) 5594
Answer: (c) 4194
The decimal representation of the rational number 3443 is:
(a) 0.75
(b) 0.333...
(c) 0.6
(d) 0.5
Answer: (a) 0.75
The HCF and LCM of two numbers are 11 and 330 respectively. If one of the numbers is 55, the other is:
(a) 60
(b) 66
(c) 30
(d) 33
Answer: (b) 66
A number is divisible by 10 if:
(a) it is even
(b) its last digit is 0
(c) it is divisible by 5
(d) it is divisible by 2 and 5
Answer: (b) its last digit is 0
The LCM of two prime numbers x and y (x > y) is:
(a) x
(b) y
(c) xy
(d) x - y
Answer: (c) xy
If a number is divisible by 3, then the sum of its digits is:
(a) even
(b) odd
(c) divisible by 3
(d) a prime number
Answer: (c) divisible by 3
The number of whole number solutions for x in the equation 10x = 100 is:
(a) 1
(b) 10
(c) 100
(d) infinite
Answer: (a) 1
A bag contains red and blue marbles only. If there are 4 red marbles for every 3 blue marbles, which of the following cannot be the total number of marbles?
(a) 35
(b) 50
(c) 70
(d) 100
Answer: (a) 35
The sum of two irrational numbers is:
(a) always rational
(b) always irrational
(c) sometimes rational
(d) sometimes irrational
Answer: (c) sometimes rational
If two numbers are in the ratio 4:9, then their LCM is:
(a) 4 times their HCF
(b) 9 times their HCF
(c) 13 times their HCF
(d) 36 times their HCF
Answer: (b) 9 times their HCF
The number of digits in the decimal representation of the rational number 2105353210 is:
(a) 3
(b) 5
(c) 7
(d) 10
Answer: (c) 7
The LCM of two numbers is 840 and their HCF is 20. If one of the numbers is 120, the other number is:
(a) 140
(b) 160
(c) 180
(d) 200
Answer: (a) 140
These questions cover a range of topics under the chapter "Real Numbers" and are formulated to test various concepts such as HCF, LCM, divisibility, and properties of rational and irrational numbers.
