Class 10 Maths important MCQs for Chapter 1- Real Numbers are provided here with answers and detailed solutions.

Important Multiple Choice Questions (MCQs) from Real Numbers are provided here for students who are preparing for the CBSE Class 10 Board Exam. Detailed solutions are also provided for all questions. These MCQs will help students clear all the fundamental concepts and prepare effectively for the Class 10 Maths exam.

## Q1.If there are two positive integers a and b then there exists unique integers q and r satisfying

(1) a= bq – r

(2) a= bq + r

(3) a= br – q

(4) a= br – q

## Answer

Answer : bq + r

## Q2.The prime factorisation of natural numbers is unique except

(1) Not for the order of its factors

(2) For the order of its factors

(3) None

(4) Both a and b

## Answer

Answer : for the order of its factors

## Q3.The product of the smallest power of each common prime factor in the numbers is the

(1) HCF

(2) LCM

(3) None

(4) Both a and b

## Answer

Answer : HCF

## Q4.The product of the greatest power of each prime factor involved in the numbers is the

(1) LCM

(2) HCF

(3) None

(4) Both a and b

## Answer

Answer : LCM

## Q5.For any two positive integers a and b

(1) HCF (a, * LCM (a, = a*b

(2) HCF (a, b) * LCM (a, b) = a/b

(3) None

(4) Both a and b

## Answer

Answer : HCF (a, * LCM (a, = a*b

## Q6.The HCF of 96 and 404 is

(1)4

(2)2

(3)8

(4)6

## Answer

Answer : 4

## Q7.The LCM of 96 and 404 is

(1)404

(2)96

(3)969

(4)9696

## Answer

Answer : 9696

## Q8.The HCF of 6, 72 and 120 is

(1)3

(2)2

(3)12

(4)6

## Answer

Answer : 6

## Q9.The LCM of 6, 72 and 120 is

(1)120

(2)72

(3) None

(4)360

## Answer

Answer : 360

## Q10.√2, √3, √15, are the

(1) Irrational number

(2) Rational numbers

(3) Composite numbers

(4) Prime numbers

## Answer

Answer : irrational numbers

## Q11.Π is the

(1) Irrational number

(2) Rational number

(3) Composite numbers

(4) Prime numbers

## Answer

Answer : irrational number

## Q12.Let p be the prime number, if p divides a2then (a is the positive integer)

(1) p divides a

(2) a divides p

(3) None

(4) Both a and b

## Answer

Answer : p divides a

## Q13.√2 is rational

(1) False

(2) True

(3) Not confirm

(4) Both a and b

## Answer

Answer : false

## Q14.√3 is irrational

(1) False

(2) True

(3) None

(4) Both a and b

## Answer

Answer : true

## Q15.The sum or difference of a rational and irrational number is

(1) Irrational

(2) Rational

(3) Not confirm

(4) Both a and b

## Answer

Answer : irrational

## Q16.The product and quotient of a non zero rational and irrational number is

(1) Irrational

(2) Rational

(3) None

(4) Both a and b

## Answer

Answer : irrational

## Q17.(5 – √3) is

(1) Irrational

(2) Rational

(3) Not confirm

(4) Both a and b

## Answer

Answer : irrational

## Q18.3√2 is rational

(1) False

(2) True

(3) None

(4) Both a and b

## Answer

Answer : false

## Q19.Every composite number can be expressed as a product of primes and this

(1) Factorisation is unique

(2) Factorisation is not unique

(3) None

(4) Both a and b

## Answer

Answer : factorisation is unique

## Q20.The set of natural numbers denoted by N is

(1) {…. -2, -1, 0, 1, 2, 3, ….}

(2) {0, 1, 2, 3, 4,}

(3) {2, 4, 6, 8,}

(4) {1, 2, 3, 4, ….}

## Answer

Answer : {1, 2, 3, 4,}

## Q21.Set of natural numbers contains all the integers

(1) negative integers

(2) positive integers

(3) all the whole numbers

(4) both a and b

## Answer

Answer : positive integers

## Q22.The set of natural numbers is the proper subset of

(1) set of integers

(2) set of whole numbers

(3) none

(4) both a and b

## Answer

Answer : both a and b

## Q23.The set of natural number contain all the whole numbers except

(1)0

(2)1

(3) none

(4) both a and b

## Answer

Answer : 0

## Q24.The addition of two natural numbers is the again

(1) positive integer

(2) natural number

(3) zero

(4) both a and b

## Answer

Answer : both a and b

## Q25.The addition of two natural numbers is also natural number which is called as

(1) commutative property

(2) associative property

(3) distributive property

(4) closure property

## Answer

Answer : closure property

## Q26.The addition and multiplication are associative in case of natural numbers is the property of

(1) associative property

(2) closure property

(3) distributive property

(4) commutative property

## Answer

Answer : associative property

## Q27.when we reverse the order of natural numbers in case of addition and multiplication then the answer will not be changed. The property is called as

(1) commutative property

(2) closure property

(3) distributive property

(4) associative property

## Answer

Answer : commutative property

## Q28.the property in which natural numbers are distributed over addition is called as

(1) commutative property

(2) distributive property

(3) associative property

(4) closure property

## Answer

Answer : distributive property

## Q29.The additive identity of set of natural numbers is

(1)0

(2)1

(3) does not exist

(4) both 0 and 1

## Answer

Answer : does not exist

## Q30.The multiplicative identity of set of natural numbers is

(1)1

(2)0

(3) does not exist

(4) both 0 and 1

## Answer

Answer : 1

## Q31.The set of whole numbers is the set of natural numbers which includes also

(1) rational numbers

(2) negative integers

(3) none of the above

(4) zero

## Answer

Answer : zero

## Q32.The set whole numbers are

(1) {0, 1, 2, 3, 4,}

(2) {1, 2, 3, 4,}

(3) {1, 3, 5, 7, …}

(4) {…-2, -1, 0, 1, 2, …}

## Answer

Answer : {0, 1, 2, 3, 4, …}

## Q33.The numbers which does not includes to set of whole numbers are

(1) 2.3, 4.5

(2) 1/3, 1/5

(3) natural numbers

(4) both a and b

## Answer

Answer : both a and b

## Q34.All the natural numbers are

(1) whole numbers

(2) positive integers

(3) both a and b

(4) negative integers

## Answer

Answer : both a and b

## Q35.The set of whole numbers is the proper subset of

(1) natural numbers

(2) integers

(3) both a and b

(4) rational numbers

## Answer

Answer : integers

## Q36.The set of whole numbers does not include

(1) fractions

(2) negative integers

(3) a, b and c

(4) decimals

## Answer

Answer : a, b and c

## Q37.The set of natural numbers is the subset of

(1) integers

(2) whole numbers

(3) both a and b

(4) rational numbers

## Answer

Answer : both a and b

## Q38.The set of natural numbers also called as

(1) set of whole numbers

(2) set of integers

(3) set of counting numbers

(4) set of rational numbers

## Answer

Answer : set of counting numbers

## Q39.the set of natural numbers N and set of whole numbers W are the proper subsets of

(1) set of prime numbers

(2) set of rational numbers

(3)set of integers

(4) set of composite numbers

## Answer

Answer : set of integers

## Q40.Every natural number is a

(1) positive integer

(2) whole number

(3) both a and b

(4) rational number

## Answer

Answer : both a and b

## Q41.Except zero all the whole numbers are

(1) natural numbers

(2) integers

(3) odd numbers

(4) prime numbers

## Answer

Answer : natural numbers

## Q42.The number expressed in the form of p/q where p and q both are integers and q is not equal to zero then p/q is a

(1) rational number

(2) irrational number

(3) even number

(4) prime number

## Answer

Answer : rational number

## Q43.The rational numbers include

(1) natural numbers

(2) whole numbers

(3) a, b and c

(4) integers

## Answer

Answer : a, b and c

## Q44.The rational numbers are also called as

(1) composite numbers

(2) decimals

(3) both a and c

(4) fractions

## Answer

Answer : both a and c

## Q45.Every integer is a rational number is

(1) always false

(2) always true

(3) can’t say

(4) both a and b

## Answer

Answer : always true

## Q46.The only one whole number which is not rational is

(1)3

(2)1

(3) both a and c

(4)0

## Answer

Answer : 0

## Q47.Every rational number is an integer

(1) always false

(2) always true

(3) can’t say

(4) sometimes true

## Answer

Answer : sometimes true

## Q48.There are rational numbers between any two given rational numbers.

(1) few

(2) infinitely many

(3) can’t say

(4) five

## Answer

Answer : infinitely many

## Q49.The umbers which are not written in the form of p/q where p and q are integers and q is not equal to zero are called

(1) irrational numbers

(2) rational numbers

(3) none

(4) both a and b

## Answer

Answer : irrational numbers

## Q50.√3 is a

(1) irrational number

(2) rational number

(3) none

(4) both a and b

## Answer

Answer : irrational number

## Q51.π is a

(1) irrational number

(2) rational number

(3) none

(4) both a and b

## Answer

Answer : irrational number

## Q52.The sum or difference of rational and an irrational number is

(1) irrational

(2) rational

(3) none

(4) both a and b

## Answer

Answer : irrational

## Q53.The product or quotient of a nonzero rational numbers with an irrational number is

(1) irrational

(2) rational

(3) none

(4) a and b

## Answer

Answer : irrational

## Q54.If we add, subtract, multiply or divide two irrationals the result may be

(1) irrational

(2) rational

(3) none

(4) both a and b

## Answer

Answer : both a and b

## Q55.Prime numbers are those which are having factors

(1) itself

(2) one

(3) none

(4) one and itself

## Answer

Answer : one and itself

## Q56.1 is a prime number true or false

(1) false

(2) true

(3) none

(4) both a and b

## Answer

Answer : false

## Q57.0 is the prime number

(1) false

(2) true

(3) none

(4) both a and b

## Answer

Answer : false

## Q58.0 and 1 are

(1) only not prime

(2) neither prime nor composite

(3) none

(4) only not composite

## Answer

Answer : neither prime nor composite

## Q59.2 is the first and only one_________prime number.

(1) even

(2) odd

(3)c) composite

(4) both and b

## Answer

Answer : even

## Q60.2,3,5,7,11,13,17… all are

(1) even numbers

(2) composite numbers

(3) prime numbers

(4) odd numbers

## Answer

Answer : prime numbers

Class 10 Maths important MCQs for Chapter 1- Real Numbers are provided here with answers and detailed solutions.

Important Multiple Choice Questions (MCQs) from Real Numbers are provided here for students who are preparing for the CBSE Class 10 Board Exam. Detailed solutions are also provided for all questions. These MCQs will help students clear all the fundamental concepts and prepare effectively for the Class 10 Maths exam.

## Q1.If there are two positive integers a and b then there exists unique integers q and r satisfying

(1) a= bq – r

(2) a= bq + r

(3) a= br – q

(4) a= br – q

## Answer

Answer : bq + r

## Q2.The prime factorisation of natural numbers is unique except

(1) Not for the order of its factors

(2) For the order of its factors

(3) None

(4) Both a and b

## Answer

Answer : for the order of its factors

## Q3.The product of the smallest power of each common prime factor in the numbers is the

(1) HCF

(2) LCM

(3) None

(4) Both a and b

## Answer

Answer : HCF

## Q4.The product of the greatest power of each prime factor involved in the numbers is the

(1) LCM

(2) HCF

(3) None

(4) Both a and b

## Answer

Answer : LCM

## Q5.For any two positive integers a and b

(1) HCF (a, * LCM (a, = a*b

(2) HCF (a, b) * LCM (a, b) = a/b

(3) None

(4) Both a and b

## Answer

Answer : HCF (a, * LCM (a, = a*b

## Q6.The HCF of 96 and 404 is

(1)4

(2)2

(3)8

(4)6

## Answer

Answer : 4

## Q7.The LCM of 96 and 404 is

(1)404

(2)96

(3)969

(4)9696

## Answer

Answer : 9696

## Q8.The HCF of 6, 72 and 120 is

(1)3

(2)2

(3)12

(4)6

## Answer

Answer : 6

## Q9.The LCM of 6, 72 and 120 is

(1)120

(2)72

(3) None

(4)360

## Answer

Answer : 360

## Q10.√2, √3, √15, are the

(1) Irrational number

(2) Rational numbers

(3) Composite numbers

(4) Prime numbers

## Answer

Answer : irrational numbers

## Q11.Π is the

(1) Irrational number

(2) Rational number

(3) Composite numbers

(4) Prime numbers

## Answer

Answer : irrational number

## Q12.Let p be the prime number, if p divides a2then (a is the positive integer)

(1) p divides a

(2) a divides p

(3) None

(4) Both a and b

## Answer

Answer : p divides a

## Q13.√2 is rational

(1) False

(2) True

(3) Not confirm

(4) Both a and b

## Answer

Answer : false

## Q14.√3 is irrational

(1) False

(2) True

(3) None

(4) Both a and b

## Answer

Answer : true

## Q15.The sum or difference of a rational and irrational number is

(1) Irrational

(2) Rational

(3) Not confirm

(4) Both a and b

## Answer

Answer : irrational

## Q16.The product and quotient of a non zero rational and irrational number is

(1) Irrational

(2) Rational

(3) None

(4) Both a and b

## Answer

Answer : irrational

## Q17.(5 – √3) is

(1) Irrational

(2) Rational

(3) Not confirm

(4) Both a and b

## Answer

Answer : irrational

## Q18.3√2 is rational

(1) False

(2) True

(3) None

(4) Both a and b

## Answer

Answer : false

## Q19.Every composite number can be expressed as a product of primes and this

(1) Factorisation is unique

(2) Factorisation is not unique

(3) None

(4) Both a and b

## Answer

Answer : factorisation is unique

## Q20.The set of natural numbers denoted by N is

(1) {…. -2, -1, 0, 1, 2, 3, ….}

(2) {0, 1, 2, 3, 4,}

(3) {2, 4, 6, 8,}

(4) {1, 2, 3, 4, ….}

## Answer

Answer : {1, 2, 3, 4,}

## Q21.Set of natural numbers contains all the integers

(1) negative integers

(2) positive integers

(3) all the whole numbers

(4) both a and b

## Answer

Answer : positive integers

## Q22.The set of natural numbers is the proper subset of

(1) set of integers

(2) set of whole numbers

(3) none

(4) both a and b

## Answer

Answer : both a and b

## Q23.The set of natural number contain all the whole numbers except

(1)0

(2)1

(3) none

(4) both a and b

## Answer

Answer : 0

## Q24.The addition of two natural numbers is the again

(1) positive integer

(2) natural number

(3) zero

(4) both a and b

## Answer

Answer : both a and b

## Q25.The addition of two natural numbers is also natural number which is called as

(1) commutative property

(2) associative property

(3) distributive property

(4) closure property

## Answer

Answer : closure property

## Q26.The addition and multiplication are associative in case of natural numbers is the property of

(1) associative property

(2) closure property

(3) distributive property

(4) commutative property

## Answer

Answer : associative property

## Q27.when we reverse the order of natural numbers in case of addition and multiplication then the answer will not be changed. The property is called as

(1) commutative property

(2) closure property

(3) distributive property

(4) associative property

## Answer

Answer : commutative property

## Q28.the property in which natural numbers are distributed over addition is called as

(1) commutative property

(2) distributive property

(3) associative property

(4) closure property

## Answer

Answer : distributive property

## Q29.The additive identity of set of natural numbers is

(1)0

(2)1

(3) does not exist

(4) both 0 and 1

## Answer

Answer : does not exist

## Q30.The multiplicative identity of set of natural numbers is

(1)1

(2)0

(3) does not exist

(4) both 0 and 1

## Answer

Answer : 1

## Q31.The set of whole numbers is the set of natural numbers which includes also

(1) rational numbers

(2) negative integers

(3) none of the above

(4) zero

## Answer

Answer : zero

## Q32.The set whole numbers are

(1) {0, 1, 2, 3, 4,}

(2) {1, 2, 3, 4,}

(3) {1, 3, 5, 7, …}

(4) {…-2, -1, 0, 1, 2, …}

## Answer

Answer : {0, 1, 2, 3, 4, …}

## Q33.The numbers which does not includes to set of whole numbers are

(1) 2.3, 4.5

(2) 1/3, 1/5

(3) natural numbers

(4) both a and b

## Answer

Answer : both a and b

## Q34.All the natural numbers are

(1) whole numbers

(2) positive integers

(3) both a and b

(4) negative integers

## Answer

Answer : both a and b

## Q35.The set of whole numbers is the proper subset of

(1) natural numbers

(2) integers

(3) both a and b

(4) rational numbers

## Answer

Answer : integers

## Q36.The set of whole numbers does not include

(1) fractions

(2) negative integers

(3) a, b and c

(4) decimals

## Answer

Answer : a, b and c

## Q37.The set of natural numbers is the subset of

(1) integers

(2) whole numbers

(3) both a and b

(4) rational numbers

## Answer

Answer : both a and b

## Q38.The set of natural numbers also called as

(1) set of whole numbers

(2) set of integers

(3) set of counting numbers

(4) set of rational numbers

## Answer

Answer : set of counting numbers

## Q39.the set of natural numbers N and set of whole numbers W are the proper subsets of

(1) set of prime numbers

(2) set of rational numbers

(3)set of integers

(4) set of composite numbers

## Answer

Answer : set of integers

## Q40.Every natural number is a

(1) positive integer

(2) whole number

(3) both a and b

(4) rational number

## Answer

Answer : both a and b

## Q41.Except zero all the whole numbers are

(1) natural numbers

(2) integers

(3) odd numbers

(4) prime numbers

## Answer

Answer : natural numbers

## Q42.The number expressed in the form of p/q where p and q both are integers and q is not equal to zero then p/q is a

(1) rational number

(2) irrational number

(3) even number

(4) prime number

## Answer

Answer : rational number

## Q43.The rational numbers include

(1) natural numbers

(2) whole numbers

(3) a, b and c

(4) integers

## Answer

Answer : a, b and c

## Q44.The rational numbers are also called as

(1) composite numbers

(2) decimals

(3) both a and c

(4) fractions

## Answer

Answer : both a and c

## Q45.Every integer is a rational number is

(1) always false

(2) always true

(3) can’t say

(4) both a and b

## Answer

Answer : always true

## Q46.The only one whole number which is not rational is

(1)3

(2)1

(3) both a and c

(4)0

## Answer

Answer : 0

## Q47.Every rational number is an integer

(1) always false

(2) always true

(3) can’t say

(4) sometimes true

## Answer

Answer : sometimes true

## Q48.There are rational numbers between any two given rational numbers.

(1) few

(2) infinitely many

(3) can’t say

(4) five

## Answer

Answer : infinitely many

## Q49.The umbers which are not written in the form of p/q where p and q are integers and q is not equal to zero are called

(1) irrational numbers

(2) rational numbers

(3) none

(4) both a and b

## Answer

Answer : irrational numbers

## Q50.√3 is a

(1) irrational number

(2) rational number

(3) none

(4) both a and b

## Answer

Answer : irrational number

## Q51.π is a

(1) irrational number

(2) rational number

(3) none

(4) both a and b

## Answer

Answer : irrational number

## Q52.The sum or difference of rational and an irrational number is

(1) irrational

(2) rational

(3) none

(4) both a and b

## Answer

Answer : irrational

## Q53.The product or quotient of a nonzero rational numbers with an irrational number is

(1) irrational

(2) rational

(3) none

(4) a and b

## Answer

Answer : irrational

## Q54.If we add, subtract, multiply or divide two irrationals the result may be

(1) irrational

(2) rational

(3) none

(4) both a and b

## Answer

Answer : both a and b

## Q55.Prime numbers are those which are having factors

(1) itself

(2) one

(3) none

(4) one and itself

## Answer

Answer : one and itself

## Q56.1 is a prime number true or false

(1) false

(2) true

(3) none

(4) both a and b

## Answer

Answer : false

## Q57.0 is the prime number

(1) false

(2) true

(3) none

(4) both a and b

## Answer

Answer : false

## Q58.0 and 1 are

(1) only not prime

(2) neither prime nor composite

(3) none

(4) only not composite

## Answer

Answer : neither prime nor composite

## Q59.2 is the first and only one_________prime number.

(1) even

(2) odd

(3)c) composite

(4) both and b

## Answer

Answer : even

## Q60.2,3,5,7,11,13,17… all are

(1) even numbers

(2) composite numbers

(3) prime numbers

(4) odd numbers

## Answer

Answer : prime numbers

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