CBSE Class 10 Mathematics Real Numbers MCQs Set 03

Mathematics Objective Questions and Answers: Chapter 01 Real Numbers

Explore reliable objective questions for Chapter 01 Real Numbers tailored for Class 10 learners. Utilizing these Mathematics multiple-choice formats ensures thorough preparation and strengthens problem-solving speed for upcoming school assessments.

Download Chapter 01 Real Numbers MCQs with Answers

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Question : The smallest number which when increased by 17 is exactly divisible by both 520 and 468 is:
a) 4697
b) 4663
c) 4656
d) 4680
Answer : B

Question : What is the smallest number which when increased by 5 is completely divisible by 8, 11 and 24?
a) 259
b) 355
c) 255
d) None of these
Answer : A

Question : Find the least number that when divided by 16, 18 and 20 leaves a remainder of 4 in each case, but is completely divisible by 7.
a) 2800
b) 2882
c) 2884
d) None of these
Answer : C

Question : What least number should be subtracted from 1856 so that remainder when divided by 7, 12 and 16 is 4?
a) 170
b) 172
c) 174
d) None of these
Answer : B

Question : The L. C. M. of two numbers is 48. The numbers are in the ratio 2 : 3. The sum of the numbers is.
a) 40
b) 42
c) 44
d) None of these
Answer : A

Question : L. C. M. of two prime numbers x & y (x > y) is 161. The value of 3y – x is.
a) -1
b) -2
c) -3
d) None of these
Answer : B

Question : Find the greatest number that will divide 43, 91 & 183 so as to leave the same remainder in each case.
a) 4
b) 3
c) 2
d) None of these
Answer : A

Question : The least multiple of 7 which leaves a remainder of 4 when divided by 6, 9, 12 and 18 is.
a) 362
b) 365
c) 364
d) None of these
Answer : C

Question : The greatest number which can divide 1356, 1868, 2764 leaving same remainder 12 in each case is?
a) 63
b) 64
c) 65
d) None of these
Answer : B

Question : The H.C.F & L.C.M of two numbers are 13 and 455 respectively. If one of the numbers lies b/w 75 and 125, find the numbers.
a) 91
b) 95
c) 97
d) None of these
Answer : A

Question : If the L.C.M of the polynomials (y – 3)a (2y + 1)b (y + 13)7 and (y – 3)4(2y + 1)9 (y + 13)c is (y –3)6 (2y + 1)10 (y+ 13)7, then the least value of a + b + c is.
a) 16
b) 18
c) 20
d) None of these
Answer : A

Question : The H.C.F of the polynomials 9(x + a)p (x – b)q (x + c)r and 12(x + a) p+3 (x- b)q – 3 (x + c)r + 2 is 3(x+ a)6 (x –b)6 (x + c)6, then the value of p + q – r is.
a) 10
b) 11
c) 9
d) None of these
Answer : C

Question : If the H.C.F of 8x3ya and 12xby2 in 4xayb, then find the maximum value of a + b.
a) 6
b) 4
c) 8
d) None of these
Answer : B

Question : How many integers (a, b) exist such that the product of a, b and H.C.F (a, b) = 1080.
a) 12
b) 9
c) 10
d) None of these
Answer : B

Question : Find the smallest number that leaves a remainder of 4 on division by 5, 5 on division by 6, 6 on division by 7, 7 on division by 8 and 8 on division by 9?
a) 9125
b) 20779
c) 9711
d) 2519
Answer : D

Question : There are two numbers such that a>b, H.C.f (a, b) = h and Lcm (a, b) = l, what is the L.C.M of a – b and b.
a) (a b)b /h
b) a – b
c) b/h
d) None of these
Answer : A

Question : How many pairs of positive integers x, y exist such that H.C.F of x, y = 35 and the sum of x & y = 1085?
a) 10
b) 2
c) 3
d) 15
Answer : D

Question : How many pairs of positive integers x, y exist such that H.C.F (x, y) + L.C.M (x, y) = 91?
a) 8
b) 2
c) 6
d) None of these
Answer : A

Question : The smallest prime number is: 
a) 0
b) 1
c) 2
d) 3 
Answer : C
 
Question : The sum of first five prime numbers is:
a) 26
b) 15
c) 39
d) 28 
Answer : D
 
Question : Total prime numbers between 1 and 100 are: 
a) 31
b) 25
c) 22
d) 20 
Answer : D
 
Question : The unit’s digit obtained on simplifying 207×781×39×94 is: 
a) 9
b) 1
c) 7
d) 2 
Answer : D
 
Question : The number √3 is a/an: 
a) integer
b) rational number
c) irrational number
d) None of these 
Answer : C
 
Question : The HCF and LCM of 6, 72 and 120 is: 
a) 8, 360
b) 6, 340
c) 6, 360
d) None of these 
Answer : C
 
Question : The total number of even prime numbers is: 
a) 0
b) 1
c) 2
d) None of these 
Answer : B
 
Question : 22/7 is a: 
a) prime number
b) an integer
c) a rational number
d) an irrational number 
Answer : C
 
Question : The sum of two numbers is 37 and their product is 342. The numbers are: 
a) 18, 19
b) 23, 14
c) 24, 13
d) 28, 9  
Answer : A
 
Question : A number is as bigger than 22 as much it is smaller than 72. The number is: 
a) 92
b) 47
c) 24
d) None of these  
Answer : B
 
Question : If HCF and LCM of two numbers are 4 and 9696, then the product of two numbers is: 
a) 9696
b) 24242
c) 38784
d) 4848 
Answer : C
 
Question : 5 √2 √3 is: 
a) a natural number
b) an integer
c) a rational number
d) an irrational number
Answer : D
 
Question :
Rea
 
a) 12
b) 9
c) 8
d) 6  
Answer : D
 
Question : The number .211 2111 21111 211111… is a:
a) terminating decimal
b) non-terminating repeating decimal
c) non-terminating decimal which is non-repeating
d) None of these 
Answer : C
 
Question : If mn = 32 , where m and n are positive integers, then the value of nmn is:
a) 32
b) 25
c) 510
d) 525 
Answer : C
 
Question : Any one of the numbers a, a +2 and a + 4 is a multiple of:
a) 2
b) 3
c) 5
d) 7 
Answer : B
 
Question : If p is a prime number and p divides k2 , then p divides:
a) 2k2
b) k
c) 3k
d) None of these 
Answer : B
 
Question : If the HCF of 85 and 153 is expressible in the form of 85n -153 then, the value of n is:
a) 3
b) 2
c) 4
d) 1  
Answer : B
 
Question : Given that LCM (91, 26) = 182 then, HCF (91, 26) is:
a) 13
b) 26
c) 7
d) 9
Answer : A
 
Question : Out of the four numbers
Re
 the rational number is :
a) i
b) ii
c) iii
d) iv
Answer : B

Question : C10M: A is the first letter for
a) Apple
b) Mobile Phone
c) Glass
d) Aeroplane
Answer : Aeroplane

Question :  √5 is
a) an irrational number
b) a rational number
c) none of these
d) an integer
Answer : an irrational number

Question : The decimal expansion of irrational number is
a) non-terminating non-repeating
b) terminating
c) non-terminating repeating
d) none of these
Answer : non-terminating non-repeating

Question :  The decimal expansion of number 29/22 X 5X7 is
a) non-terminating repeating
b) none of these
c) terminating
d) non-terminating non-repeating
Answer : non-terminating repeating

Question :  If two positive integers a and b are written as a = x 4 y2 and b = x2 y3, a, b are prime numbers, then HCF (a, b) is
a) x2 y2
b) x2 y
c) xy
d) x4 y3
Answer :  x2 y2

Question :  If two positive integers a and b are written as a = xy2 and b = x 3 y, a, b are prime numbers, then LCM
a) x3 y2
b) none of these
c) xy
d) x2 y2
Answer :  x3 y2

Question : The product of LCM and HCF of two numbers m and n is
a) m x n
b) none of these
c) m - n
d) m + n
Answer : m x n

Question : The largest number which divides 615 and 963 leaving remainder 6 in each case is
a) 82
b) 95
c) 87
d) 93
Answer : 82

Question : If the HCF of 65 and 117 is expressible in the form 65m –117, then the value of m is
a) 2
b) 4
c) 11
d) 3
Answer : 2

Question : The product of a non-zero rational and an irrational number is
a) always irrational
b) one
c) rational or irrational
d) always rational
Answer : always irrational

Question : The product of two irrational numbers is
a) rational or irrational
b) one
c) always rational
d) always irrational
Answer : rational or irrational

Question : The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is
a) 2520
b) 504
c) 100
d) 10
Answer : 2520

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

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

Question : A ……… is a proven statement used for proving another statement.
a) axiom
b) theorem
c) lemma
d) algorithm

Question : The product of non-zero rational ad an irrational number is
a) always rational
b) always irrational
c) rational or irrational
d) one

Question : The HCF of smallest composite number and the smallest prime number is
a) 0
b) 1
c) 2
d) 3

Question : Given that HCF(1152, 1664) = 128 the LCM(1152, 1664) is
a) 14976
b) 1664
c) 1152
d) none of these

Question : The HCF of two numbers is 23 and their LCM is 1449. If one of the numbers is 161, then the other number is
a) 23
b) 207
c) 1449
d) none of these

Question : Which one of the following rational number is a non-terminating decimal expansion:
a) 33/50
b) 66/180
c) 6/15
d) 41/1000

Question : A number when divided by 61 gives 27 quotient and 32 as remainder is
a) 1679
b) 1664
c) 1449
d) none of these

Question : The product of L.C.M and H.C.F. of two numbers is equal to
a) Sum of numbers
b) Difference of numbers
c) Product of numbers
d) Quotients of numbers

Question : L.C.M. of two co-prime numbers is always
a) product of numbers
b) sum of numbers
c) difference of numbers
d) none

Question : What is the H.C.F. of two consecutive even numbers
a) 1
b)2
c) 4
d) 8

Question : What is the H.C.F. of two consecutive odd numbers
a) 1
b) 2
c) 4
d) 8

Question : The missing number in the following factor tree is
a) 2
b) 6
c) 3
d) 9

""CBSE-Class-10-Mathematics-Real-Numbers

Question :  π is
a) a natural number
b) not a real number
c) a rational number
d) an irrational number

Question : The decimal expansion of  π
a) is terminating
b) is non terminating and recurring
c) is non terminating and non recurring
d) does not exist.

Question :  For some integer q, every even integer is of the form
a) q
b) q + 1
c) 2q
d) none of these

Question : Which of the following is a rational number?
a) √36
b) √12
c) √14
d) √21

Question : If a and b are positive integers, then HCF (a, b) x LCM (a, b) =
a) a x b
b) a + b
c) a – b
d) a/b

Question : If the HCF of two numbers is 1, then the two numbers are called
a) composite
b) relatively prime or co-prime
c) perfect
d) irrational numbers

Question : The decimal expansion of 93 /1500 will be
a) terminating
b) non-terminating
c) non-terminating repeating
d) non-terminating non-repeating.

Question :  √3 is
a) a natural number
b) not a real number
c) a rational number
d) an irrational number

Question : The HCF of 52 and 130 is
a) 52
b) 130
c) 26
d) 13

Question : For some integer q, every odd integer is of the form
a) q
b) q + 1
c) 2q
d) none of these

Question :  Which of the following is not a rational number?
a) √6
b) √9
c) √25
d) √36

Question : Euclid’s division lemma state that for any positive integers a and b, there exist unique integers q and r such that a = bq + r where r must satisfy
a) 1< r < b
b) 0 < r <= b
c) 0 <= r < b
d) 0 < r < b

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

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

Question : n2 – 1 is divisible by 8, if n is
a) an integer
b) a natural number
c) an odd integer
d) an even integer

Question : If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is
a) 4
b) 2
c) 1
d) 3

Question : The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is
a) 13
b) 65
c) 875
d) 1750

Question : If two positive integers a and b are written as a = x3y2 and b = xy3 ; x, y are prime numbers, then HCF (a, b) is
a) xy
b) xy2
c) x3y3
d) x2y2

Question : If two positive integers p and q can be expressed as p = ab2 and q = a3b; a, b being prime numbers, then LCM (p, q) is
a) ab
b) a2b2
c) a3b2
d) a3b3

Question : The product of a non-zero rational and an irrational number is
a) always irrational
b) always rational
c) rational or irrational
d) one

Question : The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is
a) 10
b) 100
c) 504
d) 2520

Question : The decimal expansion of the rational number 14587 1250 will terminate after:
a) one decimal place
b) two decimal places   
c) three decimal places
d) four decimal places

Question : The decimal expansion of the rational number 2 33 2 .5 will terminate after
a) one decimal place
b) two decimal places
c) three decimal places
d) more than 3 decimal places

1. Natural numbers

1, 2, 3, 4,... etc, are called natural numbers denoted by N.

2. Whole numbers
All natural numbers together with zero are called whole numbers denoted by W.
W = 0, 1, 2, 3, 4,....

3. Integers (Z)
... – 4, – 3, – 2, –1, 0, 1, 2, 3, 4, ....
(i) – 1, –2, – 3, – 4,..... are called negative integers.
(ii) 1, 2, 3, 4, ... are called positive integers.
Note: Zero is neither positive not negative.

4. The numbers of the form a/b, where a and b are natural numbers are called fractions.
e.g., 3/5 , 7/11 , 13/213 , .... etc.

5. The numbers of the form p/q, where p and q are integers and q ¹ 0 are called rational numbers.
e.g., -3/5 , 7/-11 , -13/-213 , .... etc.

6. If the denominator of a rational number has no prime factors other than 2 (or) 5 then and only then it is expressible as a terminating decimal.

7. Every rational number is always expressible in the form of terminating (or) a repeating decimal.

8. Numbers which when expressed in decimal form are expressible neither in terminating nor in repeating decimals are known as irrational numbers.
e.g., π, √2, 0.232332333... etc.

9. Some results on irrational numbers
(a) The – ve of an irrational number is an irrational number.
(B) The sum of a rational and an irrational number is an irrational number
(C) The product of a non-zero rational number with an irrational number is always an irrational number.

10. Real numbers
The totality of all rational and all irrational numbers forms the set R of all real numbers.

11. Properties of all real numbers
(a) Closure property of addition
The sum of two real numbers is always a real number.
(b) Commutative law of addition a + b = b + a, ∀ real numbers ‘a’ and ‘b’.
(c) Associative law for addition (a + b) + c = a + (b + c), ∀ real numbers a, b and c.
(d) Existence of additive identity
zero is the additive identity a + 0 = 0 + a = a, ∀ real numbers a.
(e) Existence of additive inverse
for each real number ‘a’ there exists a real number ‘–a’ such that
a + (–a) = (–a) + a = 0
(f) Closure property for multiplication
The product of two real numbers is a real numbers.
(g) Commutative law of multiplication ab = ba, ∀ real numbers a and b.
(h) Associative law of multiplication (ab)c = a(bc), ∀ real numbers a, b and c.
(i) Existence of multiplicative identity
1 is called the multiplicative identity.
1. a = a. 1 = a, ∀ real numbers a.
(j) Existence of multiplicative inverse
Every non-zero real number ‘a’ has its multiplicative inverse 1/a.
(k) Distributive law of multiplication over addition a(b+c) = ab + ac, ∀ real number a, b and c.

12. Zero is a real number which has no multiplicative inverse.

Question. A rational number between 1/4 and 1/3 is
(A) 7/24
(B) 0.29
(C) 13/48
(D) all the above

Answer: D

Question. An irrational number is
(A) a terminating and non-repeating decimal
(B) a nonterminating and non-repeating decimal
(C) a terminating and repeating decimal
(D) a nonterminating and repeating decimal

Answer: B

 

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Multiple Choice Questions (MCQs) for Class 10 Mathematics Chapter 01 Real Numbers

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