Class 9 Practice Level 3 - Number Systems - Set 2

Total questions: 15

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

Topic: Real Numbers

None

Which of the following expressions represents an irrational number?

Topic: Real Numbers

$\displaystyle 1\text{ }+\sqrt{2}$

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

$\displaystyle \frac{5}{7}$

$\displaystyle \frac{7}{11}$

None

$ \displaystyle \text{The product of }(4\text{ }+\sqrt{6})\text{ }and\text{ }(4\text{ }-\sqrt{6})\text{ is}:$

Topic: Real Numbers

None

$ \displaystyle \text{If }x\text{ }=~\sqrt{{11}}\text{ }and\text{ }y\text{ }=\text{ }5,\text{ }what\text{ }is\text{ }{{x}^{2}}+\text{ }{{y}^{2}}?$

Topic: Real Numbers

None

$ \displaystyle The\text{ }value\text{ }of~\frac{1}{{\sqrt{5}+2}}\text{ is:}$

Topic: Real Numbers

$ \displaystyle \sqrt{5}-2$

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

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

$ \displaystyle \frac{{\left( {2+\sqrt{5}} \right)}}{3}$

None

$ \displaystyle If\ \sqrt{a}\text{ }=\text{ }\frac{7}{4}\text{ },\text{ then a is}:$

Topic: Real Numbers

$ \displaystyle \frac{{49}}{{16}}$

$ \displaystyle \frac{{28}}{{16}}$

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

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

None

$\displaystyle If\text{ }\sqrt{a}\text{ }+\sqrt{b}\text{ }=\text{ }9\text{ }and\ \sqrt{a}\text{ }-\sqrt{b}\text{ }=3,$ then the value of a is:

Topic: Real Numbers

None

$ \displaystyle if\text{ }a\text{ }=\text{ }4\text{ }+\sqrt{3},\text{ }then\text{ }\frac{{1\text{ }}}{a}\text{ }is:$

Topic: Real Numbers

$ \displaystyle 4~-~\surd 3$

$ \displaystyle \frac{{4~-~\sqrt{3}}}{{13}}$

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

$ \displaystyle \frac{{4+~\sqrt{3}}}{{13}}$

None

$\displaystyle \text{If }x=3+\sqrt{5},\text{ then the }x-\frac{1}{x}\text{ is :}$

Topic: Real Numbers

$ \displaystyle \sqrt{5}-2$

$ \displaystyle \frac{{2-~2\surd 5~}}{{4~}}$

$ \displaystyle \frac{{9~+~5\surd 5~}}{{4~}}$

$ \displaystyle 4$

None

10.

$ \displaystyle \text{If }x\text{ }=\text{ }4\text{ }+\sqrt{7},\text{ then the value }of\text{ }{{x}^{2}}-\text{ }8x\text{ }+\text{ }13\text{ }is:$

Topic: Real Numbers

None

11.

$ \displaystyle \text{The product of }(6\text{ }+\sqrt{5})\text{ }and\text{ }(6\text{ }-\sqrt{5})\text{ }is:$

Topic: Real Numbers

None

12.

$ \displaystyle \text{if}\ a=3+\sqrt{7}\ and\ b=3-\sqrt{7},\text{then the value of }{{\text{a}}^{2}}+{{b}^{2}}\ is:$

Topic: Real Numbers

None

13.

$ \displaystyle \text{If }x\text{ }=\text{ }2+\sqrt{5},\text{ }then\text{ }{{x}^{2}}-\text{ }4x\text{ }-\text{ }1\text{ }is:$

Topic: Real Numbers

-1

None

14.

$\displaystyle \text{If }a\text{ }=\sqrt{{10}}\text{ }+\sqrt{6}\text{ }and\text{ }b\text{ }=\sqrt{{10}}-\sqrt{6},\text{ then the value of }ab\text{ }is:$

Topic: Real Numbers

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

None

15.

$\displaystyle \text{If }x\text{ }=\text{ }5\text{ }+\sqrt{3},\text{ then }{{x}^{2}}-\text{ }10x\text{ }+\text{ }13\text{ is}:$

Topic: Real Numbers

-9

-1

None

1 out of 15

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Class 9 Practice Level 3 - Number Systems - Set 2

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