NUMBER SYSTEMS

1 Which of the following is a rational number?
(a) ` 1+\sqrt{5}` (b) ` 2\sqrt{3}`
(c) 0 (d) π
Very Short Answer Questions ( 1 mark)
2 Q. Which of the following is a rational number?
(a) ` 1+\sqrt{5}` (b) ` 2\sqrt{3}`
(c) 0 (d) π
2Q.Which of the following is irrational?
(a) ` \sqrt{\frac{4}{9}` (b) `\frac{\sqrt{12}}{\sqrt{3}`
(c) ` \sqrt{81` (d) ` \sqrt5`
1Q.If ` x=2+\sqrt{3}` then ` \frac{1}{x}` is equal to
(a) ` 2+\frac{1}{\sqrt{3}}` (b) ` \frac{1}{2-\sqrt{3}}`
(c) ` 2-\sqrt{3}` (d) `\frac{1}{2}+\sqrt{3}`
3Q.An irrational number between `\sqrt{2}` and `\sqrt{3}` is
(a) ` \frac{\sqrt{2}+\sqrt{3}}{2}` (b) ` -\frac{\sqrt{2}+\sqrt{3}}{2}`
(c) ` \sqrt{2}\times \sqrt{3}` (d) `\sqrt{5}`
4Q.If ` 5^{2y}=25` then `5^{-y}` is equal to
(a) ` \frac{-1}{5}` (b) `\frac{1}{50}`
(c)`\frac{1}{625}` (d) `\frac{1}{5}`
Fill in the blanks:
5Q. `\sqrt{6}\times \sqrt{8}` = __________
6Q. The decimal expansion of the number `\sqrt{3}` is __________ and __________
7Q. __________ is a whole number but not a natural number.
` \2sqrt[81]^{{0.50}` = __________
8Q. Between two distinct rational number there lie __________ rational numbers.
9Q. The sum and difference of rational and irrational number is always __________ numbers.
10Q. Every rational number is a __________ number.
11Q. Find a rational number between ` \frac{-2}{3}` and `\frac{1}{4}` .
12Q. Express ` 0.\overline{7}` in the form `\frac{p}{q}`, where p and q are integers and q ≠ 0.
13Q. Find the value of ` 0.\overline{23}+0.\overline{22}` in the form `\frac{p}{q}`, where p & q are integres and q ≠ 0.
14Q. Find the value of x, if `5^{x-3}.3^{2x-8}=225`
15Q. Find the value of ` \left[4-5\left( 4-5 \right)^{4} \right]^3`
16Q. Write first five whole numbers in `\frac{p}{q}` form, where p and q are integers and q ≠ 0.
17Q. Find two irrational numbers between ` \sqrt{25}` and ` \sqrt{27}`.
18Q. Write two numbers whose decimal expansions are terminating.
19Q. Find the value of `\left( 256 \right)^0.16\times \left( 256 \right)^0.09`
20Q. Evaluate ` \left( \frac{3}{5} \right)^3\times \left( \frac{5}{3} \right)^5`
21Q. What can be the maximum number of digits in the repeating block of digits in the decimal expansion of ` \frac{5}{7}`.