Number System - CBSE

which of the following is a rational number

•  $\sqrt{2}$  

•  $\sqrt{3}$  

•  $\sqrt{0}$  

•  $\sqrt{5}$  

 $\frac{p}{q}$  form of  $0.\overline{6}$   is 

•  $\frac{2}{33}$  

•  $\frac{2}{3}$  

•  $\frac{1}{3}$  

•  $\frac{11}{13}$  

Decimal value of   $4\ \frac{1}{8}$   is

• 4.1515151515...............

• 4.152

• 4.125

• 4.215151515..........

The Value of  $\left(\sqrt{3}+11\right)\left(\sqrt{3}-11\right)$   is

• - 140

• 128

• 140

• - 118

The value of   $\left(\sqrt{5}+\sqrt{3}\right)^2$    is

•  $8+2\sqrt{15}$  

•  $2+2\sqrt{2}$  

•  $8+2\sqrt{30}$  

•  $2\sqrt{15}-8$  

For positive real numbers a and b, which is not true?

• $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$

• $\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}$

• $\left(a+\sqrt{b}\right)\left(a-\sqrt{b}\right)=a^2-b$

• $\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)=a^2-b$

The number of rational numbers between  $\sqrt{5}$     and    $\sqrt{7}$   is 

• 2

• 30

• infinitely many

• One

On rationalising the denominator of    $\frac{1}{\sqrt{3}}$     , we get

•  $3$  

•  $\frac{\sqrt{3}}{3}$  

•  $-\frac{\sqrt{3}}{3}$  

•  $\sqrt{3}$  

The Value of   $81^{\frac{1}{2}}$    is  

• 3

• 27

• 9

• 81

On rationalising the denominator of ,     $\frac{1}{\sqrt{8}-\sqrt{7}}$        we get

•  $\frac{\sqrt{7}-\sqrt{8}}{15}$  

•  $\sqrt{8}+\sqrt{7}$  

•  $\frac{\sqrt{8}+\sqrt{7}}{-1}$  

•  $\sqrt{8}-\sqrt{7}$