Maths Chapter 1 Real Numbers Class 10 MCQ With Answers

These Questions about the Real Numbers Class 10 Mcq Questions are designed on the basis of Latest Syllabus.

Class 10 Real Numbers

Unit 1 – Number System Of Class 10 Maths Contains of first Chapter : Real Numbers In this Chapter MCQ are most important. Its important to know that Euclid’s Division Lemma has been deleted from the syllabus. And the questions based on “Prove That x is irrational” such type of questions has also been removed from syllabus.

Real Numbers Class 10 MCQ

Q1. Which one of the following equation is true for Euclid’s division Lemma? (a = Dividend , b= Divisor , q = quotient , r= remainder )
[a] a= bq +r
[b] a=rq + b
[c] b=rq + a
[d] b=qa + r

Answer and Explanation : Option [ a ] “a = bq + r “ is the correct answer of the above question.
Euclid’s Division Lemma : Given positive integers a and b there exists whole numbers q and r satisfying : a= bq+r.

Q2. What is the product of HCF and LCM of the two numbers 45 and 30 ?
[a] 1250
[b] 1260
[c] 1350
[d] 1620

Answer and Explanation : Option [ c ] “1350 “ is the correct answer of the above question.
HCF * LCM = product of two numbers .
HCF * LCM = 45 * 30 = 1350.

Q3. If q = ( 2m * 5m ) , which one of the following is true for p/q ?
[a] p/q is non zero decimal
[b] p/q is terminating decimal
[c] p/q is non terminating and non repeating decimal
[d] p/q is non terminating repeating decimal

Answer and Explanation : Option [ d ] ” p/q is non terminating repeating decimal” is the correct answer of the above question.
If q = ( 2m * 5m ), p/q is non terminating repeating decimal .

Q4. What are the factors of the number : a2n – b2n?
[a] a+b
[b] a-b
[c] a+b and a-b
[d] 2a+b

Answer and Explanation : Option [ c ] “a+b and a-b” is the correct answer of the above question.
a2n – b2n is divisible by both ( a-b) and (a+b) because ( a-b ) and ( a+b )are factors of ( a2n – b2n )

Q5. Any prime Number greater than 3 can be expressed in which one of the following equation ?
[a] (7k +0)
[b] ( 6k +1 ) or (6k -1)
[c] (6k+2 )
[d] (7k +6 )

Answer and Explanation : Option [ b ] “( 6k +1 ) or (6k -1) “ is the correct answer of the above question.

Q6. Find the Greatest Common Divisor of the numbers : 6 and 7?
[a] 49
[b] 42
[c] 24
[d] 36

Answer and Explanation : Option [ b ] “42 “ is the correct answer of the above question.
Greatest Common Divisor is the other name of HCF. So HCF of 6 and 7 is 42.

Q7. (an + bn ) is never divisible by which one of the following factor ?
[a] a+b
[b] 2a+b
[c] a+2b
[d] a-b

Answer and Explanation : Option [ d ] “a-b “ is the correct answer of the above question.
( an+bn ) is never divisible by (a-b).

Q8. (an + bn ) is exactly divisible by which one of the following factor for?( Note n = odd )
[a] a+2b
[b] 2a+b
[c] a-b
[d] a+b

Answer and Explanation : Option [ d ] ” a+b “ is the correct answer of the above question.

Q9. What is the total number of factor of composite number 55 ?
[a] 2
[b] 1
[c] 3
[d] 4

Answer and Explanation : Option [ d ] ” 4″ is the correct answer of the above question.
Factors of 55 are : 1,5,11,55

Q10. What is the power of 7 in the prime factorisation of 56 ?
[a] 1
[b] 2
[c] 3
[d] 4

Answer and Explanation : Option [ a ] ” 1″ is the correct answer of the above question.
56 = 23 * 7 . The power of 7 is 1.

Q11. What is the sum of exponents of the prime factors in the prime factorization of 76 ?
[a] 1
[b] 2
[c] 3
[d] 4

Answer and Explanation : Option [ c ] “3” is the correct answer of the above question.
76 = 22*191
Sum of exponents of prime factors of 76 is 2+1 = 3

Q12. If a = d3t and r = dt2 then HCF of the numbers ‘a’ and ‘r’ is ? [ a and r are prime number
[a] d*t
[b] d+t
[c] d
[d] t

Answer and Explanation : Option [ a ] “d*t” is the correct answer of the above question.
a = d*d*d*t
r = d*t*t*t
HCF of a and r is d * t — Common factors d and t

Q13. If a = d3t and r = bdt2 then LCM of the numbers ‘a’ and ‘r’ is ? [ a and r are prime number?
[a] d*t
[b] b*d3*t3
[c] 2dt
[d] dtb

Answer and Explanation : Option [ b ] “b*d3*t3 is the correct answer of the above question.
a = d*d*d*t
r = b*d*t*t*t
LCM of a and r = b*d3*t3

Q14. The numbers a ,b, c are expressed in terms of prime factors a follows :-
a = 22 * 53
b= 3 * 5
c = 23 * 52
LCM of a,b,c is 2n *3m * 5r
Find the Values of n, m and r

[a] 2 , 4, 6
[b] 3 , 1, 3
[c] 3 , 1 , 1
[d] 1, 3 , 3

Answer and Explanation : Option [ b ] “3 , 1, 3” is the correct answer of the above question.
a = 22 * 53 = 2*2*5*5*5
b= 3 * 5 = 3 * 5
c = 23 * 52 = 2*2*2 *5*5
LCM of a,b,c = 23 *31 * 53
n = 3
m = 1
r = 3

Q15. If HCF of 56 and 96 is 8 . then LCM of these two numbers is ____?
[a] 672
[b] 650
[c] 620
[d] 669

Answer and Explanation : Option [ a ] “672 “ is the correct answer of the above question.
HCF * LCM = a*b
8 * LCM = 56*96
LCM = 5376/8 = 672

Q16. 4.262626262626262626262…….. is _______ ?
[a] rational number
[b] irrational number
[c] integer
[d] whole number

Answer and Explanation : Option [ a ] ” rational number” is the correct answer of the above question.

Q17. 61n -56n is divisible by ______________ ?
[a] 56
[b] 61
[c] 117
[d] 5

Answer and Explanation : Option [ d ] “5” is the correct answer of the above question.
an-bn is divisible by a-b

Q18. LCM of the two numbers (a,b) is equal to HCF of these numbers = Q, find the relation between the two numbers?
[a] ab=Q
[b] ab=Q2
[c] a2b2=Q
[d] a+b = Q

Answer and Explanation : Option [ a ] ” ab = Q” is the correct answer of the above question.
HCF * LCM = a*b
Q * Q = ab
Q2 = ab

Q19. The LCM of two numbers is 12 . HCF of these two number is 12. One of the two number is 4. Find the other number .
[a] 36
[b] 56
[c] 66
[d] 77

Answer and Explanation : Option [ a ] “36 “ is the correct answer of the above question.
LCM = 12
HCF = 12
a = 4
b = ?
Solution:
LCM * HCF =a*b
12 * 12 = 4 * b
36 = b

Q20. HCF of 56 and 96 is ?
[a] 7
[b] 8
[c] 9
[d] 10

Answer and Explanation : Option [ b ] “8” is the correct answer of the above question.
Using Long Division Method , HCF of 56 and 96 is 8

Q21. Product of two number is 300,000. LCM of the two number is 3000. What is the HCF of two numbers ?
[a] 50
[b] 100
[c] 500
[d] 700

Answer and Explanation : Option [ b ] ” 100″ is the correct answer of the above question.
LCM * HCF = Product of two numbers
3000 * HCF = 300,000
HCF = 300,000/3000 = 100

Q22. The LCM of two numbers if 100. Which of the following cannot be their HCF ?
[a] 300
[b] 500
[c] 700
[d] 100

Answer and Explanation : Option [ c ] “700 “ is the correct answer of the above question.
For HCF and LCM of two number , the remainder is zero when LCM is divided by the HCF of two number.
Note : LCM of two number is completely divided by HCF of the numbers.

Q23. Which of the rational number have terminating decimal ?
[a] 2/36
[b] 6/80
[c] 9/63
[d] 1/3

Answer and Explanation : Option [ b ] “6/80 “ is the correct answer of the above question.
6/ 80 = 6 /(24 * 51 ) = 3 / ( 23 * 51 )
6/80 can be expressed in the the form N/ 2m * 5n .So we can say that 6/80 is a terminating rational number.

Q24. For n = 26 * 32 * 53, the number of consecutive zeroes in n (at last) is _______ ?
[a] 3
[b] 4
[c] 5
[d] 6

Answer and Explanation : Option [ a ] “3” is the correct answer of the above question.
Power of 2 is 6 and power of 5 is 3 therefore 3 pair of 2 and when multiplied result in 3 zeros ( 5*5*5*2*2*2 = 1000 ) . Therefore 3 zeros at last.