**MCQs Questions for Class 10 Maths Chapter 1 Real Numbers**

In this 21^{st} century, Multiple Choice Questions (MCQs) play a vital role to prepare for a competitive examination. CBSE board has also brought a major change in its board exam patterns. Now-a-days, a total of 10 MCQs questions are asked in the class 10 board examination.

In most of the competitive examinations, only MCQ questions are asked. So, for getting ready for the competitive examinations, we have to practice for MCQs questions to solve. It strengthens the critical thinking and problem solving skills.

In future, if you want to prepare for competitive examination and to crack it, then you should more focus on the MCQ questions. Thus, from the board examinations point of view and competitive examinations point of view, you should practice more on multiple choice questions.

Thus, let’s solve these MCQs Questions to make our foundation very strong.

**MCQs Questions for Class 10 Maths Chapter 1 Real
Numbers**

**1.** For an
integer m, every odd integer is of the form

(A) m

(B) m + 1

(C) 2m

(D) 2m + 1

**Answer:
D**

**2.** HCF of 8, 9 and 25 is

(A) 8

(B) 9

(C) 25

(D) 1

**Answer:
D**

**3.** If
two positive integers a and b are written as a = p^{3}q^{2} and
b = pq^{3}, where p and q are prime numbers, then HCF (a, b) is:

(A)
pq

(B) pq^{2}

(C) p^{3}q^{3 }

(D) p^{2}q^{2}

**Answer:
B**

**4.** Which of the following is not irrational?

(A) (2 – √3)2

(B) (√2 + √3)2

(C) (√2 – √3)(√2 + √3)

(D)2√7/7

**Answer:
C**

**5.**
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

**Answer:
A**

**6.**
The product of a rational and irrational number is

(A) rational

(B) irrational

(C) both of above

(D) none of above

**Answer:
B**

**7.**
If HCF (a, b) = 12 and a × b = 1800, then LCM (a, b) is

(A) 3600

(B) 900

(C) 150

(D) 90

**Answer:
C**

**8.** If
the HCF of 65 and 117 is expressible in the form 65 m – 117, then the value of
m is

(A) 4

(B) 2

(C) 1

(D) 3

**Answer: B**

**9.**
The sum of a rational and irrational number is

(A) rational

(B) irrational

(C) both of above

(D) none of above

**Answer: B**

**10. **If
m^{n} = 32, where m and n are positive integers, then the value of
(n)^{mn} is

(A) 9765625

(B) 9775625

(C) 9785625

(D) 9865625

**Answer: A**

**11.** The
largest number which divides 70 and 125, leaving remainders 5 and 8,
respectively, is

(A) 13

(B) 65

(C) 875

(D) 1750

**Answer: A**

**12.**
The product of two different irrational numbers is always

(A) rational

(B) irrational

(C) both of above

(D) none of above

**Answer: B**

**13.**
Given that LCM of (91, 26) = 182, then HCF of (91, 26) is

(A) 13

(B) 26

(C) 7

(D) 9

**Answer: A**

**14.** If
two positive integers p and q can be expressed as p = ab^{2} and q
= a^{3}b, where a and b are prime numbers, then LCM of (p, q) is

(A) ab

(B) a^{2}b^{2}

(C) a^{3}b^{2}

(D) a^{3}b^{3}

**Answer: C**

**15.**
If b = 3, then any integer can be expressed as a =

(A) 3q, 3q+ 1, 3q + 2

(B) 3q

(C) 3q+ 1

(D) none of the above

**Answer: A**

**16.**
If A = 2n + 13 and B = n + 7, where n is a natural number, then HCF of A and B

(A) 2

(B) 1

(C) 3

(D) 4

**Answer: B**

**17.** The
values of the remainder r, when a positive integer a is divided by 3 are:

(A) 0, 1,
2,
3

(B) 0, 1

(C) 0, 1,
2

(D) 2, 3, 4

**Answer: C**

**18.**
The product of three consecutive positive integers is divisible by

(A) 4

(B) 6

(C) no common factor

(D) only 1

**Answer: B**

**19.**
n² – 1 is divisible by 8, if n is

(A) an integer

(B) a natural number

(C) an odd natural number

(D) an even natural number

**Answer: C**

**20.** A
rational number in its decimal expansion is 327.7081. What would be the prime
factors of q when the number is expressed in the p/q form?

(A) 2 and
3

(B) 3 and 5

(C) 2, 3
and
5

(D) 2 and 5

**Answer: D**

**21.**
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**

**22.**
The LCM of 2³ × 3² and 2² × 3³ is

(A) 2³

(B) 3³

(C) 2³ × 3³

(D) 2² × 3²

**Answer: C**

**23.** The
HCF of 441, 567 and 693 is

(A) 1

(B) 441

(C)
126

(D) 63

**Answer: D**

**24.**
Express 98 as a product of its primes.

(A) 2² × 7

(B) 2² × 7²

(C) 2 × 7²

(D) 2^{3} × 7

**Answer: C**