9th_Maths_Chapter_1_MCQ_Quiz_Number

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) $a^pb^p=(ab)^p$

Q. 1. Value of $(256)^{0.16} \times(256)^{0.09}$ is
	4
	16
	64
	256.25

Q. 2. Value of $\sqrt[4]{(81)^{-2}}$ is
	$\frac{1}{9}$
	$\frac{1}{3}$
	9
	$\frac{1}{81}$

Q. 3. Which of the following is equal to $x$ ?
	$x^{\frac{12}{7}}-x^{\frac{5}{7}}$
	$\sqrt[12]{\left(x^{4}\right)^{\frac{1}{3}}}$
	$\left(\sqrt{x^{3}}\right)^{\frac{2}{3}}$
	$x^{\frac{12}{7}} \times x^{\frac{7}{12}}$

Q. 4. Which of the following is irrational?
	0.14
	$0.14 \overline{16}$
	$0 . \overline{1416}$
	$0.4014001400014 \ldots$

Q. 5. The product $\sqrt[3]{2} \cdot \sqrt[4]{2} \cdot \sqrt[12]{32}$ equals
	$\sqrt{2}$
	2
	$\sqrt[12]{2}$
	$\sqrt[12]{32}$

Online Test for 9th Class Maths

Chapter 1 NUMBER SYSTEMS

Class 9 Maths Online Quiz : Number Systems

Main Concepts and Foarmule

Q. 7. Decimal representation of a rational number cannot be
	terminating
	non-terminating
	non-terminating repeating
	non-terminating non-repeating

Q. 10. Which of the following is not equal to $\left[\left(\frac{5}{6}\right)^{\frac{1}{5}}\right]^{-\frac{1}{6}}$ ?
	$\left(\frac{5}{6}\right)^{\frac{1}{5}-\frac{1}{6}}$
	$\frac{1}{\left[\left(\frac{5}{6}\right)^{\frac{1}{5}}\right]^{\frac{1}{6}}}$
	$\left(\frac{6}{5}\right)^{\frac{1}{30}}$
	$\left(\frac{5}{6}\right)^{-\frac{1}{30}}$

Q. 6. $\sqrt[4]{\sqrt[3]{2^{2}}}$ equals
	$2^{-\frac{1}{6}}$
	$2^{-6}$
	$2^{\frac{1}{6}}$
	$2^{6}$

Q. 9. After rationalising the denominator of $\frac{7}{3 \sqrt{3}-2 \sqrt{2}}$, we get the denominator as
	13
	19
	5
	35