Maths : Real Numbers : Book Back, Exercise, Example Numerical Question with Answers, Solution : Exercise 2.9: One Mark Multiple Choose the correct Answers

**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 = 5/2^{6}

[ **Answer: **(1) 5/64 ]

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

[ **Answer: **(4) π]

6.
An irrational number between 2 and 2.5 is

(1)
√11

**(2) √5 **

(3)
√2.5

(4)
√8

**Solution**: 2^{2} = 4 and 2.5^{2}
= 6.25

[ **Answer: **(2) √5]

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.

[ **Answer: **(2) 3/10]

8.
If 1/7 = then the value of 5/7 is

**Solution**:

[ **Answer:** (2) ]

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…

[ **Answer: (1) **]

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

[ **Answer: **(4) √13]

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

[ **Answer:** (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

[ **Answer: **(2) 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

[ **Answer:** (2) 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**:
(2√5 - √2)^{2}
= (2√5)^{2} – 2 × 2√5 × √2 +√2^{2}

=
4×5 – 4√10
+ 2 = 22 - 4√10

[ **Answer**: (2) 22-4√10 ]

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

(1)
10^{3} / 3^{3}

(2)
10^{5} / 3^{5}

(3)
10^{2} / 3^{2}

**(4) 10 ^{6} / 3^{6}**

**Solution**:

[ **Answer: **(4) 10^{6} / 3^{6 }]

19.
If √9^{x =}^{3}√9^{2}
, then* x *= ______

(1)
2 / 3

**(2) 4 / 3**

(3)
1 / 3

(4)
5/ 3

**Solution**: (9^{x})^{1/2} = (9^{2})^{1/3}

⇒ 9^{x/2} = 9^{2/3 }

⇒ *x*/3 = 2/3

3*x* = 4

*x*= 4/3

[ **Answer**: (2) 4 / 3 ]

20.
The length and breadth of a rectangular plot are 5×10^{5} and 4×10^{4}
metres respectively. Its area is ______.

(1)
9×10^{1} *m*^{2}

(2)
9×10^{9} *m*^{2}

**(3) 2×10 ^{10} m^{2} **

(4)
20×10^{20} *m*^{2}

**Solution**:

** l **=5 × 10

Area = *l* × *b*
= 5 × l0^{5} ×
4 × l0^{4} = 20 x 10^{5+4 }= 20 × 10^{9} = 2.0 x 10^{1}
× 10^{9}

= 2 × 10^{10 }*m*^{2}

[ **Answer: **(3) 2×10^{10} *m*^{2
}]

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