Every rational number is:

1

(a)

a natural number

(b)

an integer

(c)

a real number

(d)

a whole number

Two rational numbers between \(\frac { 2 }{ 3 } \) and \(\frac { 5 }{ 3 } \)are:

1

(a)

1/6 and 2/6

(b)

1/2 and 2/7

(c)

5/6 and 7/6

(d)

2/3 and 4/3

A terminating decimal is:

1

(a)

natural number

(b)

a whole number

(c)

a rational number

(d)

an integer

A number is an irrational if and only if its decimal representation is:

1

(a)

non-terminating

(b)

non-terminating and repeating

(c)

non terminating and non repeating

(d)

terminating

Which of the following is a rational number?

1

(a)

\(\sqrt { 5 } \)

(b)

\(\pi \)

(c)

0.101 001 0001 00001...

(d)

0.853 853 853....

Which of the following is an irrational number?

1

(a)

\(3.\overline { 3 } \)

(b)

3.763

(c)

\(3.\overline { 763 } \)

(d)

3.101 1001 10001...

The value of \(2.\overline { 9 } \) in the form \(\frac { p }{ q } \) where p and q are integers and \(q\neq 0\), is

1

(a)

\(\frac { 2999 }{ 1000 } \)

(b)

\(\frac { 19 }{ 10 } \)

(c)

3

(d)

\(\frac { 26 }{ 9 } \)

If \(x=\frac { \sqrt { 7 } }{ 5 } \) and \(\frac { 5 }{ x } =p\sqrt { 7 } \) , then the value of p is:

1

(a)

\(\frac { 5 }{ \sqrt { 7 } } \)

(b)

\(\frac { 25 }{ 7 } \)

(c)

\(\frac { 7 }{ 25 } \)

(d)

\(\frac { \sqrt { 7 } }{ 5 } \)

If a = 2 and b = 3, then the value of b^a is

1

(a)

4

(b)

9

(c)

2

(d)

3

The value of \(\sqrt { \left( { 3 }^{ -2 } \right) } \)

1

(a)

1/9

(b)

9

(c)

-3

(d)

1/3

Is \(\frac{\sqrt{98}}{\sqrt{2}}\) a rational number or not?

1

(a)

\(\frac{\sqrt{98}}{\sqrt{2}}\)=\(\frac{\sqrt{98}}{\sqrt{2}}\) = √49 = 7
So, it is a rational number.

Express the rational number \(0.\bar{9}\) in the form \(\frac{p}{q}\), where p and q are integers and q≠0.

1

(a)

Let, x = 0.999...
⇒ 10x = 9.999...
⇒ 10x - x = (9.999...)-(0.999...)
⇒ 9x = 9
⇒ x = 1

Calculate the value of \(2.\bar{9}\) in the form of \(\frac{p}{q}\), where p and q are integers and q≠0.

1

(a)

Let x = \(2.\bar{9}\)  = 2.9999...
⇒ 10x = 29.999...
⇒ 10x-x = (29.999...)-(2.999...)
9x = 27
x = \(\frac{27}{9}\) = 3

Simplify: √72+√800-18.

1

(a)

√72 + √800-√18
=\(\sqrt{36\times2}+\sqrt{400\times2}-\sqrt{9\times2}\)
= 6√2 + 20√2 - 3√2 = 23√2

Find the value of [(16)^1/2]^1/2

1

(a)

[(16)^1/2]^1/2 = \([(4^{2})^{\frac{1}{2}}]^\frac{1}{2}=[4]^{\frac{1}{2}}\)
= 2

Find two rational numbers between 3/4 and 5/9.

2

(a)

Give three rational numbers between -3 and -2.

2

(a)

Simplify: (5²)^-7

2

(a)

Simplify: \(\frac { { 23 }^{ -10 } }{ { 23 }^{ 7 } } \)

2

(a)

Rationalize \(\frac { 5 }{ \sqrt { 3 } -\sqrt { 5 } } \left( -\frac { 5 }{ 2 } \right) \)

2

(a)

State whether the following statements are true or false.Give reasons for your answers.
(i) Every natural number is a whole number.
(ii) Every integer is a whole number.
(iii) Every rational number is a whole number.

3

(a)

Write the following in decimal form and say what kind of decimal expansion each has:
\(\frac { 2 }{ 11 } \)

3

(a)

Express the following in the form p/q, where p and q are integers and \(q\neq 0\)
\(0.\overline { 47 } \)

3

(a)

Classify the following numbers as rational or irrational: \(\frac { 2\sqrt { 7 } }{ 7\sqrt { 7 } } \)

3

(a)

If \(x=\frac { \sqrt { 3 } -1 }{ \sqrt { 3 } +1 } \) and \(y=\frac { 3+2\sqrt { 2 } }{ 3-2\sqrt { 2 } } \) , then find the the value of x+y

3

(a)

Find four rational numbers between \(\frac { 3 }{ 7 } \)and \(\frac { 5 }{ 7 } \)

5

(a)

If x = 3-2√2, find the value of √x+\(\frac{1}{\sqrt{x}}\)

5

(a)