**Real Numbers**Symbol to represent set of Real Numbers |

**(MCQs)**

**Q1: Which of the following has a non-terminating decimal expansion?**

(a) 77/210

(b) 23/8

(c) 17/8

(d) 35/50

**Q2(CBSE 2010): The decimal expansion of 141/120 will terminate after how many places of decimals?**

(a) 1

(b) 2

(c) 3

(d) will not terminate

**Q3: HCF of 84 and 270 is**

(a) 8

(b) 6

(c) 4

(d) 2

**Q4(CBSE 2010): If p, q are two consecutive natural numbers, then HCF(p, q) is:**

(a) q

(b) p

(c) 1

(d) pq

**Q5: If HCF if 60 and 168 is 12, what is the LCM**

(a) 480

(b) 240

(c) 420

(d) 840

**Q6(CBSE 2010): How many prime factors are there in prime factorisation of 5005 ?**

(a) 2

(b) 4

(c) 6

(d) 7

**Q7(CBSE 2010): A rational number can be expressed as a terminating decimal if the denominator has factors**

(a) 2, 3 or 5

(b) 2 or 3

(c) 3 or 5

(d) 2 or 5

**Q8(CBSE 2010): If p, q are two prime numbers, then LCM(p, q) is :**

(a) 1

(b) p

(c) q

(d) pq

**Q9: Let x = p/q be a rational number such that prime factorization of q is NOT in the form of 2**

^{n}5^{m}, where m and n are non-negative integers. Then x has a decimal representation which is:(a) terminating

(b) Non-terminating, repeating

(c) Non-terminating, non-repeating

(d) None of these

**Q10(CBSE 2010): Euclid’s division lemma states that for any two positive integer ‘a’ and ‘b’ there exists 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

**Q11(CBSE 2010): Which of the following is not an irrational number?**

(a) 5 - √3

(b) 5 + √3

(c) 4 + √2

(d) 5 + √9

**Q12**

**(CBSE 2011)**: Which of the following numbers has terminating decimal expansion?(a) 37/45

(b) 21/(2

^{3}5

^{6})

(c) 17/49

(d) 89/(2

^{2}3

^{2})

**Q13: The mathematician who gave the term '**

*algorithm*'?(a) Euclid

(b) Gold Bach

(c) Khwarizmi

(d) Gauss

**Q14: The decimal expansion of Ď**

(a) is terminating.

(b) is non-terminating and repeating

(c) is non-terminating and non-repeating

(d) None of these

**Answers**:

1: (a) 77/210

[

**Hint**: For a rational number in the form p/q, such that the prime factors of q are

__not__of the form 2

^{n}5

^{m}, where n and m are non-negative integers. Then the rational number has a decimal expansion which is non terminating repeating (recurring).]

2: (c) 3 [

**Hint**: Rational form of number p/q, where q = 2

^{3}5

^{2}]

3: (b) 6

4: (c) 1

5: (d) 840 [

**Hint**: LCM × HCF = Product of two numbers]

6: (b) 4 [

**Hint**: 5005 = 5×7×11×13]

7: (d) 2 or 5

8: (d) pq

9: (b) Non-terminating, repeating

10: (c) 0 ≤ r < b

11:(d) 5 + √9 [

**Hint**: √9 = 3, 5 + √9 = 8, a rational number]

12: (b) 21/(2

^{3}5

^{6}) [Hint: for rational number x = p/q, if factors are in the form of 2

^{n}5

^{m}, where n and m are non-negative integers, the rational number has a decimal expansion of terminating type.]

13: (c) Khwarizmi

14: (c) is non-terminating and non-repeating

☛ See also CH1: Real Numbers (Study Points)

CH 1: Real Numbers (NCERT Ex 1.1)

CH 1: Real Numbers (Euclid's Division Lemma - Q & A)

CH 1: Problems on Euclid's Division Algorithm

CH 1: Real Numbers (Problems and Answers)

CH 1: Real Numbers (NCERT Ex 1.2)

CH 1: Real Numbers (NCERT Exemplar Ex 1.1 Q1-3)

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