# MCQ Questions for Class 10 Maths with Answers Chapter 1 Real Numbers

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#### MCQ Questions for Class 10 Maths with Answers Chapter 1 Real Numbers with Answers

These MCQ Questions for Class 10 Maths Chapter 1 Real Numbers are prepared according to the latest pattern. It is very helpful for students who wants to do quick revision of all the concepts related to linear equations.

#### Class 10 Maths Chapter 1 Real Numbers MCQs

Q.1. The product of a rational and irrational number is
(a) rational
(b) irrational
(c) both of above
(d) none of above

Q.2. HCF of 8, 9, 25 is
(a) 8
(b) 9
(c) 25
(d) 1

Q.3. The largest number that will divide 398, 436 and 542 leaving remainders 7,11 and 15 respectively is
(a) 17
(b) 11
(c) 34
(d) 45

Answer (a) Algorithm, 398 – 7 = 391; 436 – 11 = 425; 542 – 15 = 527; HCF of 391, 425, 527 = 17

Q.4. The sum of two irrational numbers is always
(a) irrational
(b) rational
(c) rational or irrational
(d) one

Q.5. The decimal form of 129/225775 is
(a) terminating
(b) non-termining
(c) non-terminating non-repeating
(d) none of the above

Q.6. Which of the following is not irrational?
(a) (2 – √3)2
(b) (√2 + √3)2
(c) (√2 -√3)(√2 + √3)
(d)2√7/7

Q.7. The product of two different irrational numbers is always
(a) rational
(b) irrational
(c) both of above
(d) none of above

Q.8. If b = 3, then any integer can be expressed as a =
(a) 3q, 3q+ 1, 3q + 2
(b) 3q
(c) none of the above
(d) 3q+ 1

Q.9. The sum of a rational and irrational number is
(a) rational
(b) irrational
(c) both of above
(d) none of above

Q.10. Which number is divisible by 11?
(a) 1516
(b) 1452
(c) 1011
(d) 1121

Q.11. The set A = {0,1, 2, 3, 4, …} represents the set of
(a) whole numbers
(b) integers
(c) natural numbers
(d) even numbers

Q.12. LCM of the given number ‘x’ and ‘y’ where y is a multiple of ‘x’ is given by
(a) x
(b) y
(c) xy
(d) 𝑥𝑦

Q.13. The product of three consecutive positive integers is divisible by
(a) 4
(b) 6
(c) no common factor

Q.14. There are 312, 260 and 156 students in class X, XI and XII respectively. Buses are to be hired to take these students to a picnic. Find the maximum number of students who can sit in a bus if each bus takes equal number of students
(a) 52
(b) 56
(c) 48
(d) 63

Answer (a) HCF of 312, 260, 156 = 52

Q.15. Express 98 as a product of its primes
(a) 2² × 7
(b) 2² × 7²
(c) 2 × 7²
(d) 23 × 7

Q.16. Three farmers have 490 kg, 588 kg and 882 kg of wheat respectively. Find the maximum capacity of a bag so that the wheat can be packed in exact number of bags.
(a) 98 kg
(b) 290 kg
(c) 200 kg
(d) 350 kg

Answer (a) HCF of 490 kg, 588 kg and 882 kg = 98 kg

Q.17. m² – 1 is divisible by 8, if m is
(a) an even integer
(b) an odd integer
(c) a natural number
(d) a whole number

Q.18. For some integer p, every even integer is of the form
(a) 2p + 1
(b) 2p
(c) p + 1
(d) p

Q.19. There is a circular path around a sports field. Priya takes 18 minutes to drive one round of the field. Harish takes 12 minutes. Suppose they both start at the same point and at the same time and go in the same direction. After how many minutes will they meet ?
(a) 36 minutes
(b) 18 minutes
(c) 6 minutes
(d) They will not meet

Q.20. For some integer p, every odd integer is of the form
(a) 2p + 1
(b) 2p
(c) p + 1
(d) p

Q.21. The LCM of two numbers is 1200. Which of the following cannot be their HCF?
(a) 600
(b) 500
(c) 400
(d) 200

Answer (b) We know that LCM of two or more numbers is always divisible by their HCF. 1200 is divisible by 600, 200 and 400 but not by 500.

Q.22. If n = 23 × 34 × 54 × 7, then the number of consecutive zeros in n, where n is a natural number, is
(a) 2
(b) 3
(c) 4
(d) 7

Answer (b) If any number ends with the digit 0, it should be divisible by 10, i.e. it will be divisible by 2 and 5.
Prime factorization of n is given as 23 × 34 × 54 × 7.
It can be observed that there is (2 × 5) × (2 × 5) × (2 × 5)
⇒ 10 × 10 × 10 = 1000
Thus, there are 3 zeros in n.

Q.23. If two positive integers m and n are expressible in the form m = pq3 and n = p3q2 where p, q are
prime numbers, then HCF (m, n) =

A. pq
B. pq2
C. p3q3
D. p2q3

Answer (b) We know that HCF = Product of the smallest power of each common prime factor in the numbers.
So, HCF(a, b) = pq2

Q.24. If the LCM of a and 18 is 36 and the HCF of a and 18 is 2, then a =
(a) 2
(b) 3
(c) 4
(d) 1

Answer (c) We know that for any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × b.
Here LCM = 36, HCF = 2 and b = 18
Then, 2 × 36 = a × 18
a = (2 × 36) / 18
a = 4

Q.25. If HCF (26, 169) = 13, then LCM (26, 169) =
(a) 26
(b) 52
(c) 338
(d) 13

Answer (c) We know that for any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × b.
Here HCF = 13, a = 26 and b = 169
Then,
13 × LCM = 26 × 169
LCM = (26 × 169) / 13
LCM = 338