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# Exercise 2.9: One Mark Multiple Choose the correct Answers

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Real Numbers

Exercise 2.9

1. If n is a natural number then √n is

(1) always a natural number.

(2) always an irrational number.

(3) always a rational number

(4) may be rational or irrational

[ Answer: (4) may be rational or irrational ]

2. Which of the following is not true?.

(1) Every rational number is a real number.

(2) Every integer is a rational number.

(3) Every real number is an irrational number.

(4) Every natural number is a whole number.

Solution: Real numbers contain rationals and irrationals.

[ Answer: (3) Every real number is an irrational number]

3. Which one of the following, regarding sum of two irrational numbers, is true?

(1) always an irrational number.

(2) may be a rational or irrational number.

(3) always a rational number.

(4) always an integer.

[ Answer: (2) may be a rational or irrational number]

4. Which one of the following has a terminating decimal expansion?.

(1) 5/64

(2) 8/9

(3) 14/15

(4) 1/12

Solution: 5/64 = 5/26

5. Which one of the following is an irrational number

(1) √25

(2) √(9 /4)

(3) 7/11

(4) π

Solution: π represents a irrational number

6. An irrational number between 2 and 2.5 is

(1) √11

(2) √5

(3) √2.5

(4) √8

Solution: 22 = 4 and 2.52 = 6.25

7. The smallest rational number by which 1/3 should be multiplied so that its decimal expansion terminates with one place of decimal is

(1) 1/10

(2) 3/10

(3) 3

(4) 30

Solution: 3/10 is the small number.

8. If 1/7 =  then the value of 5/7 is

Solution:

9. Find the odd one out of the following.

(1) √32 × √2

(2) √27 / √3

(3) √72 × √8

(4) √54 / √18

Solution:

√72 × √8 = √[9×8] × √8 = 3×8 = 24;

√32 × √2 = √[16×2] × √2 = 4×2=8;

√27 ÷ √3 = √[9×3] × √3 = 3×3=9;

√54 ÷ √18 = √[3×18] × √18 = √3×18=18√3;

[Answer: (4) √54 ÷ √18 ]

10.

Solution: 0.343434… + 0.344444…

11. Which of the following statement is false?

(1) The square root of 25 is 5 or −5

(2) – √25 = −5

(3) √25 = 5

(4) √25 = ± 5

[ Answer: (4) √25 = ± 5]

12. Which one of the following is not a rational number?

(1) √[8/18]

(2) 7/3

(3) √0. 01

(4) √13

Solution:

√(8/18) = √(4/9) = 2/3 is a rational number;

7/3 is a rational number

√0.01 - √(1/100)=1/10 is a rational number

√13 is not a rational number

13. √27+ √12 =

(1) √39

(2) 5√6

(3) 5√3

(4) 3√5

Solution: √27 + √12 = √[9×3] + √[4×3] = 3√3 + 2√3 = 5√3

14. If √80 = k√5, then k =

(1) 2

(2) 4

(3) 8

(4) 16

Solution: √80 = √[16×5] = 4√5 = k√5 k=4

15. 4√7×2√3=

(1) 6√10

(2) 8√21

(3) 8√10

(4) 6√21

Solution: 4√7 × 2√3 = 8 × √[7×3] = 8√21

16. When written with a rational denominator, the expression 2√3 / 3√2 can be simplified as

(1) √2 / 3

(2) √3 / 2

(3) √6  / 3

(4) 2  / 3

Solution: 2√3 / 3√2 = 2√3 × √2 / 3√2 × √2 = 2√6 / 3×2 = 2√6 / 6 = √6/3

[ Answer: (3) √6  / 3]

17. When (2√5 − √2)2 is simplified, we get

(1) 4√5+2√2

(2) 22-4√10

(3) 8-4√10

(4) 2√10-2

Solution: (25 - 2)2 = (25)2 – 2 × 25 × 2 +22

= 4×5 – 410 + 2 = 22 - 410

18. ( 0. 000729 )-3/4 × (0.09 )-3/4 = ______

(1) 103 / 33

(2) 105  / 35

(3) 102  / 32

(4) 106 / 36

Solution:

[ Answer: (4) 106 / 36 ]

19. If √9x = 3√92 , then x = ______

(1) 2 / 3

(2) 4 / 3

(3) 1 / 3

(4) 5/ 3

Solution: (9x)1/2 = (92)1/3

9x/2 = 92/3

x/3 = 2/3

3x = 4

x= 4/3

[ Answer: (2) 4 / 3 ]

20. The length and breadth of a rectangular plot are 5×105 and 4×104 metres respectively. Its area is ______.

(1) 9×101 m2

(2) 9×109 m2

(3) 2×1010 m2

(4) 20×1020 m2

Solution:

l =5 × 105 metres; b = 4 × 104 metres

Area = l × b = 5 × l05 × 4 × l04 = 20 x 105+4 = 20 × 109 = 2.0 x 101 × 109

= 2 × 1010 m2