Online Test for 9th Class Maths

Chapter 1 NUMBER SYSTEMS

Topics Covered: Rational numbers, Irrational numbers, Locating irrational numbers on the number line, Real numbers and their decimal expansions, Representing real numbers on the number line, Operations on real numbers, Rationalisation of denominator, Laws of exponents for real numbers Mathematics for class 9 MCQs Chapter 1 Number systems.

  • Total Questions =10
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Class 9 Maths Online Quiz : Number Systems

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Q. 1. $\frac{1}{\sqrt{9}-\sqrt{8}}$ is equal to

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Q. 2. Every rational number is

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Q. 3. Value of $\sqrt[4]{(81)^{-2}}$ is

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Q. 4. Which of the following is equal to $x$ ?

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Q. 5. The value of $1.999 \ldots$ in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$, is

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Q. 6. Which of the following is irrational?

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Q. 7. Between two rational numbers

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Q. 8. After rationalising the denominator of $\frac{7}{3 \sqrt{3}-2 \sqrt{2}}$, we get the denominator as

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Q. 9. The product of any two irrational numbers is

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Q. 10. A rational number between $\sqrt{2}$ and $\sqrt{3}$ is



Main Concepts and Foarmule

Rational Number:
A number is called a rational number, if it can be written in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.

Irrational Numbers:
A number which cannot be expressed in the form $\frac{p}{q}$ (where $p$ and $q$ are integers and $q \neq 0$ ) is called an irrational number.

Real Numbers :
All rational numbers and all irrational numbers together make the collection of real numbers.

Decimal Expansion of a Rational Number:
Decimal expansion of a rational number is either terminating or non-terminating recurring, while the decimal expansion of an irrational number is non-terminating non-recurring. - If $r$ is a rational number and $s$ is an irrational number, then $r+s$ and $r-s$ are irrationals. Further, if $r$ is a non-zero rational, then $r s$ and $\frac{r}{s}$ are irrationals.

Note: If $r$ is a rational number and $s$ is an irrational number, then-
1. $r+s$ and $r-s$ are irrational numbers
2. Also, If $r$ a non-zero rational number then $rs$ and $\frac{r}{s}$ are irrational numbers


For positive real numbers $a$ and $b$ :
(i) $\sqrt{ab}=\sqrt{a}\sqrt{b}$
(ii) $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$
(iii) $(\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b})=a-b$
(iv) $(a+\sqrt{b})(a-\sqrt{b})=a^2-b$
(v) $(\sqrt{a}+\sqrt{b})^2=a+2\sqrt{ab}+b$

If $p$ and $q$ are rational numbers and $a$ is a positive real number, then-
(i) $a^pa^q=a^{p+q}$
(ii) ${\left(a^p\right)}^q=a^{pq}$
(iii) $\frac{a^p}{a^q}=a^{p-q}$
(iv) $a^pb^p=(ab)^p$