MCQ Questions For Class 10 Real Numbers

Real Numbers Class 10 MCQ is one of the best strategies to prepare for the CBSE Class 10 Board exam. If you want to complete a grasp concept or work on one’s score, there is no method except constant practice. Students can improve their speed and accuracy by doing more MCQ on Real Numbers class 10, which will help them all through their board test.

Real Numbers Class 10 MCQ Questions with Answer

Class 10 Math MCQ with answers are given here to chapter 1 Real Numbers. These MCQs are based on the latest CBSE board syllabus and relate to the latest Class 10 Mathematics syllabus. By Solving these Class 10 MCQs, you will be able to analyze all of the concepts quickly in the chapter and get ready for the Class 10 Annual exam.

Learn Real Numbers Class 10 MCQ with answers pdf free download according to the latest CBSE and NCERT syllabus. Students should prepare for the examination by solving CBSE Class 10 Mathematics Real Numbers MCQ with answers given below.

Question 1. For P ∈ N, 3^4P – 2^4P is always divisible by ____     
(a) 15
(b) 5
(c) 13
(d) Both (b) and (c)
(e) None of these

Question 2. The greatest number of 5 digits exactly divisible by 15, 24 and 36 is ____
(a) 99620
(b) 99720
(c) 99968
(d) 99960
(e) None of these

Question 3. For any odd natural number n,(√3)⁴ⁿ + (√2)⁴ⁿ) is always divisible by ______ 
(a) 5
(b) 7
(c) 17
(d) 13
(e) None of these

Question 4. If I is a positive integer then (I)2 will be in the form of ———— 
(a) 4m for some integer m
(b) 8m for some integer m
(c) 4m+1 for some integer m
(d) Both (a) and (c)
(e) None of these

Question 5. Which one among the following statements is true?
(a) The remainder when the square of any number is divided by 4 is 1 or 0.
(b) There is no natural number for which 4 ends with digit zero.
(c) A positive integer n is prime, if no prime p less than or equal to n divides n.
(d) All the above
(e) None of these

Question 6. The unit value of 100 100 6 – 5 is ______ 
(a) 0
(b) 1
(c) 2
(d) 3
(e) None of these

Question 7. If LCM and HCF of two numbers are equal, then the numbers will be _________
(a) Composite
(b) Prime
(c) Equal
(d) Co-prime
(e) None of these

Question 8. If the product of two numbers is 149058 and HCF of these numbers is 21 then how many pairs of these numbers are possible? 
(a) 1
(b) 2
(c) 3
(d) 4
(e) None of these

Question 9. Which among the following statements is not true? 
(a) The square of any odd integer is of the form 4q + 1, for some integer q.
(b) For any odd integer p, p² – 1 is divisible by 8.
(c) If p and q are both odd positive integers/ then p² + q² is even and divisible by 4.
(d) For any natural number n, n 12 cannot end with the digit 0 or 5.
(e) None of these

Question 10. For any natural number n, 2 (2n + 1)² – 1 is always divisible by ______ 
(a) 2
(b) 4
(c) 8
(d) All the above
(e) None of these

Question 11. If 14 (1 x 2 x 3 x 4 x 5 …………….A 10 x 14) and B 19 (1 x 2 x 3 x 4 x 5 …………….10 x 19) then which one of the following is/are correct? 
(i) B – A is a prime number.
(ii) B + A is a composite number.
(iii) A is a composite number.
(iv) B is a prime number.
(a) Both (i) and (ii)
(b) Both (ii) and (iii)
(c) Both (iii) and (iv)
(d) All (i), (ii), (iii) and (iv)
(e) None of these

Question 12. Which of the following statements is always true?
(a) The sum or difference of a rational and an irrational number is rational.
(b) Every irrational number is a surd.
(c) The product or quotient of a non-zero rational number and an irrational number is irrational.
(d) All the above
(e) None of these

Question 13. The decimal expansion of the rational number 12879 /1250 will terminate after: 
(a) One decimal places
(b) Two decimal places
(c) Three decimal places
(d) Four decimal places
(e) None of these

Question 14. Find the greatest prime factor in 527527. 
(a) 17
(b) 11
(c) 13
(d) 31
(e) None of these

Question 15. In a seminar, the numbers of participants in science, English and Mathematics are 144, 180 and 192 respectively. Find the minimum number of rooms required if in each room the same number of participants are to be seated and all of them being in the same subject. 
(a) 38
(b) 40
(c) 43
(d) 45
(e) None of these

Question 16. Without actually performing the Song division, choose which among the following rational numbers will not have a terminating decimal expansion. 
(a) 123 /16
(b) 351 /2⁷ x 5⁸ x 7¹⁸
(c) 32 / 28 x 59
(d) 833 /49 2 
(e) None of these

Question 17. The largest number that divides 588, 1999 and 1650 leaving 3, 10 and 12 respectively is ______
(a) 117
(b) 109
(c) 27
(d) 43
(e) None of these

Question 18. If p is a single digit natural number and the unit digits of 4 p and p are same, then how many possibilities p can assume?
(a) 2
(b) 3
(c) 4
(d) 5
(e) None of these

Question 19. The sum of exponents of prime factors in the primefactorisation of 196 is     
(a) 3
(b) 4
(c) 5
(d) 2

Question 20. The rational number of the form p/ q , q ≠ 0, p and q are positive integers , which represents 0.⁻134 i.e., (0.1343434….) is     
(a) 134/ 999
(b) 134/ 990
(c) 133/ 999
(d) 133/ 990

Question 21. The value of (27)^3p – (13)^3p ends in ______ (where p is a natural number)
(a) 0
(b) 4
(c) 6
(d) Either (b) or (c)
(e) None of these

Question 22. If P 1 3 5 7………….21 andQ 2 4 6 8 10…………22 then HCF of P and Q is ________
(a) 12375
(b) 14175
(c) 825
(d) 925
(e) None of these

Question 23. The decimal expansion of the rational number 33/2² .5 will terminate after     
(a) one decimal place
(b) two decimal places
(c) three decimal places
(d) more than 3 decimal places

Question 24. The least number which is a perfect square and is divisible by each of 16, 20 and 24 is     
(a) 240
(b) 1600
(c) 2400
(d) 3600

Question 25. When 2256 is divided by 17, then remainder would be       
(a) 1
(b) 16
(c) 14
(d) None of these

Question 26. The sum of three non-zero prime numbers is 100. One of them exceeds the other by 36. Then, the largest number is     
(a) 73
(b) 91
(c) 67
(d) 57

Question 27. For some integer q, every odd integer is of the form     
(a) q
(b) q + 1
(c) 2q
(d) 2q + 1

Question 28. What is the largest number that divides 70 and 125, leaving remainders 5 and 8 respectively?     
(a) 13
(b) 9
(c) 3
(d) 585

Whoever needs to take the CBSE Class 10 Board Exam should look at this MCQ. To the Students who will show up in CBSE Class 10 Mathematics Board Exams, It is suggested to practice more and more questions. Aside from the sample paper you more likely had solved. These Real Numbers class 10 MCQ are ready by the subject specialists themselves.

Question 29. The least number which when divided by 15, leaves a remainder of 5, when divided by 25, leaves a remainder of 15 and when divided by 35, leaves a remainder of 25, is     
(a) 515
(b) 525
(c) 1040
(d) 1050

Question 30. Consider the following statements: For any integer n,       
I. n² + 3 is never divisible by 17.
II. n² + 4 is never divisible by 17.
Then,
(a) both I and II are true
(b) both I and II are false
(c) I is false and II is true
(d) I is true and II is false

Question 31. If n is an even natural number, then the largest natural number by which n (n + 1) (n + 2) is divisible is     
(a) 6
(b) 8
(c) 12
(d) 24

Question 32. Which of the following will have a terminating decimal expansion?       
(a) 77/ 210
(b) 23/ 30
(c) 125 /441
(d) 23/ 8

Question 33. Which of the following statement(s) is/are not correct?         
(a) 7³/5⁴  is a non-terminating repeating decimal.
(b) If a = 2 +√ 3 and b = √2 –√ 3 , then a + b is irrational.
(c) If 19 divides a³, then 19 divides a, where a is a positive integer.
(d) Product of L.C.M. and H.C.F. of 25 and 625 is 15625.

Question 34. The number 3¹³ – 3¹⁰ is divisible by     
(a) 2 and 3
(b) 3 and 10
(c) 2, 3 and 10
(d) 2, 3 and 13

Question 35. Which of the following statement is true?       
(a) Every point on the number line represents a rational number.
(b) Irrational numbers cannot be represented by points on the number line.
(c) 22/ 7 is a rational number.
(d) None of these.

Question 36. The largest non-negative integer k such that 24k divides 13! is       
(a) 2
(b) 3
(c) 4
(d) 5

Question 37. Which of the following statement(s) is/are not correct?       
(a) There are infinitely many even primes.
(b) Let ‘a’ be a positive integer and p be a prime number such that a² is divisible by p, then a is divisible by p.
(c) Every positive integer different from 1 can be expressed as a product of non-negative power of 2 and an odd number.
(d) If ‘p’ is a positive prime, then √p is an irrational number.

Question 38. I. The L.C.M. of x and 18 is 36. II. The H.C.F. of x and 18 is 2. What is the number x ?       
(a) 1
(b) 2
(c) 3
(d) 4

Question 39. Which of the following statement(s) is/are not correct?       
(a) Every integer is a rational number.
(b) The sum of a rational number and an irrational number is an irrational number.
(c) Every real number is rational.
(d) Every point on a number line is associated with a real number.

Question 40. If p₁ and p₂ are two odd prime numbers such that p₁ > p₂, then p₁ ² – p₂² is     
(a) an even number
(b) an odd number
(c) an odd prime number
(d) a prime number

Question 41. When a natural number x is divided by 5, the remainder is 2. When a natural number y is divided by 5, the remainder is 4. The remainder is z when x + y is divided by 5. The value of 2z −5/3  is     
(a) –1
(b) 1
(c) –2
(d) 2

Question 42. If a = 2³ × 3, b = 2 × 3 × 5, c = 3ⁿ × 5 and L.C.M. (a, b, c) = 2³ × 3² × 5, then n =     
(a) 1
(b) 2
(c) 3
(d) 4

Question 43. A number lies between 300 and 400. If the number is added to the number formed by reversing the digits, the sum is 888 and if the unit’s digit and the ten’s digit change places, the new number exceeds the original number by 9. Then, the number is       
(a) 339
(b) 341
(c) 378
(d) 345

Question 44. What is the largest number that divides 245 and 1029, leaving remainder 5 in each case?     
(a) 15
(b) 16
(c) 9
(d) 5

Question 45. Given that 1/7= 0.142857 7 , which is a repeating decimal having six different digits. If x is the sum of such first three positive integers n such that 1/n= 0.^—abcdef n, where a, b, c, d, e and f are different digits, then the value of x is       
(a) 20
(b) 21
(c) 41
(d) 42

Question 46. Given that L.C.M. (91, 26) = 182, then H.C.F. (91, 26) is       
(a) 13
(b) 26
(c) 17
(d) 9

Question 47. The value of ^—0.235 is :     
(a) 233/ 900
(b) 233/ 990
(c) 235/ 999
(d) 235/ 990

Question 48. A class of 20 boys and 15 girls is divided into n groups so that each group has x boys and y girls. Values of x, y and n respectively are       
(a) 3, 4 and 8
(b) 4, 3 and 6
(c) 4, 3 and 7
(d) 7, 4 and 3

Question 49. For some integer m, every even integer is of the form       
(a) m
(b) m + 1
(c) 2m
(d) 2m + 1

Question 50. If m = n² – n, where n is an integer, then m² – 2m is divisible by     
(a) 20
(b) 24
(c) 30
(d) 16

Question 51. The unit digit in the expression 55⁷²⁵ + 73⁵⁸¹⁰ + 22⁸⁵³ is       
(a) 0
(b) 4
(c) 5
(d) 6

Question 52. Which of the following statement(s) is/are always true?       
(a) The sum of two distinct irrational numbers is rational.
(b) The rationalising factor of a number is unique.
(c) Every irrational number is a surd.
(d) None of these

Question 53. The product of unit digit in (7⁹⁵ – 3⁵⁸) and (7⁹⁵ + 3⁵⁸) is         
(a) 8
(b) lies between 3 and 7
(c) 6
(d) lies between 3 and 6

Question 54. On dividing a natural number by 13, the remainder is 3 and on dividing the same number by 21, the remainder is 11. If the number lies between 500 and 600, then the remainder on dividing the number by 19 is       
(a) 4
(b) 6
(c) 9
(d) 13

Question 55. If p, q are two consecutive natural numbers, then H.C.F. (p, q) is       
(a) p
(b) q
(c) 1
(d) pq

Question 56. Product of two co-prime numbers is 117. Their L.C.M. should be       
(a) 1
(b) 117
(c) equal to their H.C.F.
(d) Lies between 1 to 117

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