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

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## 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 = ( 2 ^{m} * 5^{m} ) , 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 = ( 2**p/q is non terminating repeating decimal .

^{m}* 5^{m}),**Q4. What are the factors of the number : a**

^{2n}– b^{2n}?[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.

a

^{2n}– b

^{2n}is divisible by both ( a-b) and (a+b) because ( a-b ) and ( a+b )are factors of ( a

^{2n}– b

^{2n})

**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. (a**

^{n}+ b^{n}) 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.

( a

^{n}+b

^{n}) is never divisible by (a-b).

**Q8.**

**(a**

^{n}+ b^{n})**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 = 2

^{3}* 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 = 2^{2}*19^{1}

Sum of exponents of prime factors of 76 is 2+1 = 3**Q12. If a = d ^{3}t and r = dt^{2} 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 = d**[ a and r are prime number?^{3}t and r = bdt^{2}then LCM of the numbers ‘a’ and ‘r’ is ?[a] d*t

[b] b*d

^{3}*t

^{3}

[c] 2dt

[d] dtb

**Answer and Explanation :**Option

**[ b ]**

**“b*d**is the correct answer of the above question.

^{3}*t^{3}“a = d*d*d*t

r = b*d*t*t*t

LCM of a and r = b*d

^{3}*t

^{3}

**Q14. The numbers a ,b, c are expressed in terms of prime factors a follows :-**

**a = 2**

b= 3 * 5

c = 2

LCM of a,b,c is 2

Find the Values of n, m and r

^{2}* 5^{3}b= 3 * 5

c = 2

^{3}* 5^{2}LCM of a,b,c is 2

^{n}*3^{m}* 5^{r}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 = 2

^{2}* 5

^{3}= 2*2*5*5*5

b= 3 * 5 = 3 * 5

c = 2

^{3}* 5

^{2}= 2*2*2 *5*5

LCM of a,b,c = 2

^{3}*3

^{1}* 5

^{3}

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. 61**

^{n}-56^{n}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.

a

^{n}-b

^{n}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=Q

^{2}

[c] a

^{2}b

^{2}=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

Q

^{2}= 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 /(2^{4} * 5^{1} ) = 3 / ( 2^{3} * 5^{1} )

6/80 can be expressed in the the form N/ 2^{m} * 5^{n} .So we can say that 6/80 is a terminating rational number.**Q24. For n = 2 ^{6} * 3^{2} * 5^{3}, 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.