Class 9 Practice Level 3 – Number Systems – set -1

Total questions: 15

$ \displaystyle \text{If }a=2+\sqrt{3}\text{ and }b=2-\sqrt{3}\text{ then the value of }{{a}^{2}}+{{b}^{2}}\text{ is}:$

Topic: Real Numbers

None

Which of the following is the sum of an irrational and a rational number?

Topic: Real Numbers

$ \displaystyle 3+\sqrt{2}$

$ \displaystyle 3-\sqrt{2}$

$ \displaystyle \sqrt{2}\times \sqrt{2}$

$ \displaystyle \frac{1}{2}+\frac{3}{2}$

None

The product of $ \displaystyle \left( {3+\sqrt{5}} \right)$ and $ \displaystyle \left( {3-\sqrt{5}} \right)$

Topic: Real Numbers

None

$ \displaystyle \text{If x }=\text{ }\sqrt{\text{7}}\text{ and y }=\text{ 3, what is }{{\text{x}}^{\text{2}}}+\text{ }{{\text{y}}^{\text{2}}}?$

Topic: Real Numbers

None

The value of $ \displaystyle \frac{1}{{\sqrt{2}-1}}$ is:

Topic: Real Numbers

$ \displaystyle \sqrt{2}+1$

$ \displaystyle \sqrt{2}-1$

$ \displaystyle 2+\sqrt{2}$

$ \displaystyle 2-\sqrt{2}$

None

$ \displaystyle \text{If }\sqrt{\text{a}}\text{ =}\frac{5}{3}\text{, then a is:}$

Topic: Real Numbers

$ \displaystyle \frac{{25}}{9}$

$ \displaystyle \frac{{15}}{9}$

$ \displaystyle \frac{{25}}{6}$

$ \displaystyle \frac{{16}}{9}$

None

$\displaystyle \text{If }\sqrt{a}+\sqrt{b}=7\text{ and }\sqrt{a}-\sqrt{b}=1\text{, then the value of }a\text{ is:}$

Topic: Real Numbers

None

$\displaystyle \text{If }a=3+2\sqrt{2}\text{, then }\frac{1}{a}\text{ is :}$

Topic: Real Numbers

$ \displaystyle 3-2\sqrt{2}$

$ \displaystyle 2-2\sqrt{2}$

$ \displaystyle 2-32$

$ \displaystyle \frac{{\left( {3-2\sqrt{2}} \right)}}{7}$

None

$\displaystyle \text{If }x=2+\sqrt{3},\text{then }x-\frac{1}{x}is:$

Topic: Real Numbers

$ \displaystyle \sqrt{3}-1$

$ \displaystyle \sqrt{3}+1$

$ \displaystyle 2\sqrt{3}$

None

10.

$\displaystyle \text{If }x=3+2\sqrt{{2 ,}}\text{ then the value of }{{x}^{2}}-6x+5\text{ }is:$

Topic: Real Numbers

None

11.

The product of $ \displaystyle \left( {5+\sqrt{7}} \right)$ and $ \displaystyle \left( {5-\sqrt{7}} \right)$ is:

Topic: Real Numbers

None

12.

$ \displaystyle \text{If }x=1+\sqrt{2}\text{, then }{{x}^{2}}-2x-1\text{ }is:$

Topic: Real Numbers

-1

None

13.

$ \displaystyle \text{If }a=2+\sqrt{5}\text{ and }b=2-\sqrt{5},\text{then the value of }{{a}^{2}}+{{b}^{2}}\text{ is}:$

Topic: Real Numbers

None

14.

$ \displaystyle \text{If }a=\sqrt{6}+\sqrt{5}\text{ and }b=\sqrt{6}-\sqrt{5},\text{then the value of }ab\text{ is}:$

Topic: Real Numbers

$ \displaystyle 2+\sqrt{{30}}$

None

15.

$\displaystyle x=3+\sqrt{2},\text{ then }{{x}^{2}}-6x+7\text{ is}$

Topic: Real Numbers

-1

None

1 out of 15

Class 9 Practice Level 3 – Number Systems – set -1

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