Real Numbers Class 10 MCQ with Answers – Maths Class 10 MCQ Online Test are covered in this Article. Real Numbers Class 10 MCQ Test contains 40 questions. Answers to MCQs on Real Numbers Class 10 MCQ with Answers Maths are available at the end of the last question. These MCQ have been made for Class 10 students to help check the concept you have learnt from detailed classroom sessions and application of your knowledge.
| Board | CBSE |
| Textbook | Maths (NCERT) |
| Class | Class 10 |
| Chapter | Chapter 1 Real Numbers |
| Category | MCQ Questions for Class 10 Maths with Answers |
Real Numbers Class 10 MCQ with Answers – Maths Class 10 MCQ Online Test
1. If LCM (88,121) =968, then HCF (88,121) is
(a)10
(b) 12
(c)13
(d)11
Answer
Answer: (d)11
Explanation: We know that LCM(a, b)×HCF(a, b)= a ×b
968×HCF(a, b)=88×121
HCF(a, b)= 88×121/968
= 11
2. The product of two same irrational number is
(a)irrational
(b) rational
(c) both rational and irrational
(d) none of the above
Answer
Answer: (b) rational
Explanation: Let √2 be any irrational number.
Then,
√2× √2 = 2
2 is a rational number.
So, product of two same irrational number is rational.
3. Express 200 as a product of its primes
(a)22 ×5×5
(b) 23 ×52
(c) 23 ×53
(d) 22 ×53
Answer
Answer: (b) 23 ×52
Explanation: 200 = 2×2×2×5×5
= 23 ×52
4. Which of the following is a prime number
(a)5×2×3×4×7×9+9
(b) 1×37
(c) 10×10×20
(d) 13×15×11+11×124
Answer
Answer: (b) 1×37
Explanation: Prime number: Prime numbers are those numbers which does not have factors other than 1 and itself.
1×37 =37
So, 1×37 is a prime number as its factors are only 1 and 37.
5. A rational number can be written in the form
(a) where p and q are integers and q=0
(b) where p and q are integers and q≠0
(c) where p and q are integers and q=0, p=0
(d) None of the above
Answer
Answer: (b) where p and q are integers and q≠0
Explanation: Rational number: A rational number can be represented in the form where p and q are
integers and q≠0.
Example: 7 is a rational number, we can represent 7 as
7 = 7/1 = 49/7
6. The least number that is divisible by all the numbers from 1 to 7 (both inclusive)
(a) 480
(b) 420
(c) 540
(d) 600
Answer
Answer: (b) 420
Explanation: LCM (1,2,3,4,5,6,7) will be the least number.
LCM of 1=1
LCM of 2=1×2
LCM of 3=1×3
LCM of 4=1×2×2
LCM of 5=1×5
LCM of 6=1×2×3
LCM of 7=1×7
LCM (1,2,3,4,5,6,7) = 1×2×2×3×5×7
= 420
7. The largest number which divides 80 and 126 leaving remainders 10 and 0 respectively
(a)14
(b)10
(c)12
(d) 13
Answer
Answer: (a)14
Explanation: Numbers when divides 80 and 126 leaves remainders 10 and 0,
80-10=70
126-0=126
Then HCF of 70 and 126 is 70=2×5×7
126=2×3×3×7
HCF (70,126)=14
So, the largest number is 14.
8. Fundamental theorem of arithmetic states that every composite number can be expressed as product of
(a) primes in a unique way
(b) composites in unique way
(c) either prime or composite in unique way
(d) neither primes nor composites
Answer
Answer: (a) primes in a unique way
Explanation: Fundamental Theorem of Arithmetic:
Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.
Real Numbers Class 10 MCQ with Answers – Maths Class 10 MCQ Online Test
9. 225/1600 has decimal expansion
(a) terminating
(b) non terminating
(c)both (a) and (b)
(d) None of the above
Answer
Answer: (a) terminating
Explanation: If the denominator has factors 2 and 5 then it has terminating decimal expansion.
1600=2×2×2×2×2×2×5×5
Denominator has factors 2 and 5, so it is a terminating decimal expansion.
10. The least number that is divisible by all the numbers from 1 to 10 (both inclusive)
(a)4800
(b)4020
(c)540
(d) 2520
Answer
Answer: (d) 2520
Explanation: LCM (1,2,3,4,5,6,7,8,9,10) = 2×2×2×3×3×5×7
=2520
11. Which of the following is a rational number
(a) (3+2√5)
(b) (2√3) √3
(c) (8 √5)/5
(d) (4+2√3) (4+2√3)
Answer
Answer: (b) (2√3) √3
Explanation: On solving,
(2√3) √3 =2×3 = 6
6 is a rational number.
12. The set A = { 1,2,3,4…..} and B = { 1,3,5,7,9……} represents
(a) Natural numbers and odd numbers
(b) Natural numbers and even numbers
(c) Whole numbers and odd numbers
(d) natural numbers and whole numbers
Answer
Answer: (a) Natural numbers and odd numbers
Explanation:
Natural numbers: Natural numbers are those numbers which includes all positive integers from 1 to infinity.
Odd numbers: Odd numbers are those numbers which are not divisible by 2.
13. The product of irrational number and non zero rational number is
(a) rational
(b) irrational
(c) both rational and irrational
(d) none of the above Correct option(b)
Answer
Answer: (b) irrational
Explanation: Let 2 is a rational number and √5 is an irrational number.
Then, 2×√5 =2√5 , which is an irrational number.
14. If LCM (y,150) =1050 and HCF (y ,150) =10. Then value of m is:
(a) y=37
(b) y=250
(c) y=70
(d) y=110
Answer
Answer: (c) y=70
Explanation: We know that
LCM×HCF = Product of the two numbers
1050×10 = 150×y
y=70
15.Express 81 as a product of its primes
(a) 33
(b) 25
(c) 34
(d) 33
Answer
Answer: (c) 34
Explanation: 81 = 3×3×3×3
= 34
16. If LCM (16,24) =48, then find HCF (16 ,24)
(a) 4
(b) 8
(c) 7
(d) 10
Answer
Answer: (b) 8
Explanation: We know that
LCM×HCF = Product of the two numbers
48×HCF(16,24) = 16×24
HCF(16,24) = 8
Real Numbers Class 10 MCQ with Answers – Maths Class 10 MCQ Online Test
17. Which of the following has non terminating repeating decimal expansion
(a) 43.123456789
(b) 0.120120012000120000. . .
(c) 43.12345678912345678912345…….
(d) 44.567
Answer
Answer: (c) 43.12345678912345678912345…….
Explanation: 43.123456789123456789……. it has non terminating repeating expansion, it is a rational number in the form p/q and q has factors other than 2 and 5.
18. Which of the following has non terminating repeating decimal expansion
(a) 225/1600
(b) 60/150
(c) 11/162
(d) 9/125
Answer
Answer: (c) 11/162
Explanation: If the denominator has factors other than 2 and 5 then it has a non-terminating repeating decimal expansion.
162 = 2×3×3×3×3
Since, the denominator has factor other than 2 and 5 which is 3. Thus, 11/162 has non terminating repeating decimal expansion.
19. What will be the prime factors of 336×336
(a)214× 31×7
(b) 28× 32×72
(c) 211×3× 72
(d) 212×3×7
Answer
Answer: (b) 28× 32×72
Explanation: 336×336
336=2×2×2×2×3×7
336=2×2×2×2×3×7
336×336=2×2×2×2×2×2×2×2××3×3×7×7
= 28× 32×72
20. The least number that is divisible by all the numbers from 1 to 6 (both inclusive)
(a) 90
(b) 24
(c) 40
(d) 60
Answer
Answer: (d) 60
Explanation: LCM (1,2,3,4,5,6) = 2×2×3×5
=60
21. 23.2̅3̅2̅3̅ represents
(a) terminating decimal expansion
(b) non terminating decimal expansion
(c) non terminating repeating decimal expansion
(d) None
Answer
Answer: (c) non terminating repeating decimal expansion
Explanation: 23.2̅3̅ =23.23232323…… it has non terminating repeating decimal expansion. It is in p/q form where q has factors other than 2 and 5.
22. 2√3+(5√5) √5 is a/an
(a) rational number
(b) irrational number
(c) either rational or irrational
(d) both rational and irrational
Answer
Answer: (b) irrational number
Explanation: Let us assume that 2√3+(5√5) √5 is rational.
That is, we can find coprime a and b (b ≠0) such that 2√3+(5√5) √5
Therefore, 2√3+(5√5) √5 = a/b
Rearranging this equation,
we get 2√3 +25=a/b
2√3 = a/b – 25
Since a and b are integers, we get a/b – 25 is rational, and so 2√3 is rational.
But this contradicts the fact that 2√3 is irrational.
This contradiction has arisen because of our incorrect assumption that 2√3+(5√5) √5 is rational. So, we conclude that
2√3+(5√5) √5 is irrational.
23. If LCM (a,b)=120 and a×b=600, then HCF(a,b) is
(a)5
(b)7
(c)9
(d)None
Answer
Answer: (a)5
Explanation: LCM(a, b) ×HCF(a, b)=a ×b
120×HCF(a, b)=600
HCF(a, b)=5
24. 1240 can be expressed as
(a)24×51×311
(b)23×52×311
(c)23×51×311
(d)23×51×312
Answer
Answer: (c)23×51×311
Explanation: 1240=2×2×2×5×31
=23×51×311
Real Numbers Class 10 MCQ with Answers – Maths Class 10 MCQ Online Test
25. For any two positive integers p and q ,LCM(p,q) ×HCF(p,q)=
(a) 1
(b) p× q
(c) p/q
(d) 0
Answer
Answer: (b) p× q
Explanation: For any two positive integers p and q,
LCM(p, q) ×HCF(p, q)=p ×q
26. If two positive integers are written as a=4m6n7 and b=2m5n6, m and n are prime numbers then HCF(a,b) is
(a)22m6n7
(b)21m5n6
(c) m6n7
(d)m5n6
Answer
Answer: (b)21m5n6
Explanation: HCF of two numbers is the number which divides both the numbers completely.
In given question, it can be observed that 2m5n6 is the common factor of both a and b which completely divides a and b.
27. The ratio between LCM and HCF of 10,20 and 30 is
(a)6:1
(b)1:6
(c)5:1
(d)2:3
Answer
Answer: (a)6:1
Explanation: LCM (10,20,30) = 2×2×3×5
=60
HCF (10,20,30) = 2×5
=10
LCM (10,20,30): HCF (10,20,30) 0 =60:10
=6:1
28. A number that is divisible by 2 is known as
(a) odd number
(b) even number
(c) whole number
(d) natural number
Answer
Answer: (b) even number
Explanation: An even number is a number that can be divided by 2.
29. If two positive integers are written as a=4m3n4p and b=2m2n3q , m and n are prime numbers then LCM(a,b) is
(a)22m3n4pq
(b)21m5n6p
(c) m6n7q
(d)8pqm5n7
Answer
Answer: (a)22m3n4pq
30. A rational number can be represented in the form of p/q, where
(a) q=0
(b) q≠0
(c) q = 0 to infinity
(d) q =p
Answer
Answer: (b) q≠0
Explanation: A rational number is a number that can be represented in the form of p/q , where q≠0.
31. The decimal expansion of rational number 22678/(24× 53) will terminate after
(a) two digits
(b) four digits
(c) one digit
(d) three digits
Answer
Answer: (d) three digits
Explanation: 22678/(24× 53) = 22678/(16×125) = 11.339
22678/(24× 53) after 3 digits.
32. The ratio between HCF and LCM of 4,2 and 20 is
(a)1:10
(b)2:5
(c)10:1
(d)1:1
Answer
Answer: (a)1:10
Explanation: LCM (4,2,20) =20
HCF (4,2,20) = 2
HCF (4,2,20) : LCM (4,2,20)= 2:20
= 1:10
Real Numbers Class 10 MCQ with Answers – Maths Class 10 MCQ Online Test
33. Composite numbers are those numbers which has factors other than.
(a) 1 and 2
(b) 2 and 3
(c) 1 and itself
(d) 2 and itself
Answer
Answer: (c) 1 and itself
Explanation: Composite numbers are those numbers which has factors other than 1 and itself.
34. Which of the following is not irrational
(a) (2√5) × (2√5)
(b) 7√6-2√3
(c) 2×8
(d) 2√3
Answer
Answer: (a) (2√5) × (2√5)
Explanation: (2√5) × (2√5) = (4√5× √5)
= 20
20 is not an irrational number.
35. Which of the following has non terminating non repeating decimal expansion
(a) π
(b) 60/150
(c) 67/(24×53×3)
(d) 22/(24×5)
Answer
Answer: (a) π
Explanation: Irrational numbers has non terminating non repeating decimal expansion.
Ï€ is an irrational number. So, it has non terminating non repeating decimal expansion.
36. If LCM/; (a, b)=35 and HCF (a, b) =12 then a× b is
(a)80
(b)70
(c)420
(d)500
Answer
Answer: (c)420
Explanation: LCM(a, b) ×HCF(a, b)=a ×b
35×12=a ×b
a× b=420
37. Which of the following has terminating decimal expansion
(a) π
(b) 10/130
(c) 67/(24×53×3)
(d) 2/(24×5)
Answer
Answer: (d) 2/(24×5)
Explanation: If the denominator has factors 2 and 5 then it has a terminating decimal expansion.
(24×5) = 2×2×2×2×2×5
Since, the denominator has factors 2 and 5. Thus, 2/(24×5) has terminating decimal expansion.
38. LCM of 45 and 78 is
(a)1070
(b)1170
(c)1270
(d)1180
Answer
Answer: (b)1170
Explanation: LCM of 45 = 3×3×5
LCM of 78 = 2×3×13
LCM (45, 78) = 2×3×3×5×13
= 1170
39. If LCM (77, s) =270 and HCF (77 ,s) =77. Then value of 77×s is:
(a)20790
(b)25009
(c) 22200
(d)23441
Answer
Answer: (a)20790
Explanation: LCM (77, s) ×HCF (77,s)=77×s
270×77 = 77×s
77×s = 20790
40. Which of the following is not an integer
(a)-22
(b)78/2
(c) 0
(d) 22/3
Answer
Answer: (d) 22/3
Explanation: An integer is a whole number that can be positive, negative or zero.
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