Master Real Numbers with Our Interactive MCQ Mock Test!

Are you confident about your understanding of Real Numbers? Test your skills and boost your exam readiness with our Class 10 Maths Chapter 1 – Real Numbers MCQ Mock Test!

This test is designed to help you strengthen your grasp of key concepts such as Euclid’s Division Lemma, Fundamental Theorem of Arithmetic, HCF & LCM, irrational numbers, and decimal expansions of rational numbers. Each question challenges your logic, accuracy, and speed — just like in your final board exams!

What You’ll Get:

  • A variety of concept-based MCQs covering every important topic.
  • Instant feedback with detailed explanations for better understanding.
  • A chance to analyze your performance and identify weak areas.
  • Exam-style practice to boost your confidence and speed.

Why Attempt This Test?
Because mastering Real Numbers is the first step to mastering the entire Maths syllabus! Sharpen your problem-solving skills and make sure you start your preparation strong.

Take the test now and see how well you know your Real Numbers!

1. If A = 2n + 13, B = n + 7, where n is a natural number, then HCF of A and B is:

 
 
 
 

2. The largest number which divides 71 and 126 leaving remainder 6 and 9 respectively is

 
 
 
 

3. The total number of factors of a prime number is

 
 
 
 

4. The HCF and the LCM of 12, 21, 15 respectively are

 
 
 
 

5. The HCF of smallest prime number and the smallest composite number is

 
 
 
 

6. There are 576 boys and 448 girls in a school that are to be divided into equal sections of either boys or girls alone. The total number of sections thus formed are:

 
 
 
 

7. The HCF of k and 93 is 31, where k is a natural number. Which of these CAN be true for SOME VALUES of k?

(i)     k is a multiple of 31.

(ii)    k is a multiple of 93.

(iii)    k is an even number.

(iv)    k is an odd number.

 
 
 
 

8. 4 Bells toll together at 9.00 am. They toll after 7, 8, 11 and 12 seconds respectively. How many times will they toll together again in the next 3 hours?

 
 
 
 

9. If p and q are two co-prime numbers, then the HCF and LCM of p and q is

 
 
 
 

10. If the prime factorisation of a natural number N is 24 × 34 × 53 × 7, then number of consecutive zeroes in N are

 
 
 
 

11. If p is prime, then HCF and LCM of p and p + 1 would be

 
 
 
 

12. If two positive integers a and b are written as a = x3y2 and b = xy3, where x, y are prime numbers, then HCF(a, b) is

 
 
 
 

13. Two alarm clocks ring their alarms at regular intervals of 50 seconds and 48 seconds. If they first beep together at 12 noon, at what time will they beep again for the first time?

 
 
 
 

14. The HCF and LCM of two numbers are 33 and 264 respectively. When the first number is completely divided by 2 the quotient is 33. The other number is

 
 
 
 

15. In the following questions, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices.

Assertion (A): 2 × 3 × 5 × 7 + 7 is a composite number.
Reason (R): Every composite number can be expressed as product of primes.

 
 
 
 

16. If product of two numbers is 3691 and their LCM is 3691, then their HCF =

 
 
 
 

17. The ratio between the LCM and HCF of 5, 15, 20 is:

 
 
 
 

18. In the following questions, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices.

Assertion (A): For no value of n, where n is a natural number, the number 6n ends with the digit zero.

Reason (R): For a number to end with digit zero, its prime factors should have 2 and 5.

 
 
 
 

19. The LCM and HCF of two non-zero positive numbers are equal, then the numbers must be

 
 
 
 

20. The missing entries in the following factor tree are

 
 
 
 

21. The LCM of smallest prime and smallest odd composite natural number is

 
 
 
 

22. In the following questions, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices.

Assertion (A): If LCM of two numbers is 2475 and their product is 12375, then their HCF is 5.

Reason (R): HCF (a, b) × LCM (a, b) = a × b.

 
 
 
 

23. HCF of 52 × 32 and 35 × 53 is:

 
 
 
 

24. 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?

 
 
 
 

25. Decompose 32760 into prime factors, we get factors as

 
 
 
 

26. The sum of exponents of prime factors in the prime factorisation of 250 is

 
 
 
 

27. In a school there are two sections, section A and section B of class X. There are 45 students in section A and 36 students in section B. The minimum numbers of books required for their class library so that they can be distributed equally among the students of section A or section B are

 
 
 
 

28. Two natural numbers whose difference is 66 and the least common multiple is 360, are:

 
 
 
 

29. Let p be a prime number and k be a positive integer. If p divides k2, then which of these is Definitely divisible by p?

 

k 7k k3
 
 
 
 

30. Two numbers are in the ratio of 15:11. If their H.C.F. is 13, then numbers will be

 
 
 
 

Question 1 of 30