In Chapter 1 of Mathematics Class 9, we cover number comparison, notation systems, and number evaluations. All questions are crucial from an exam perspective.
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1. Value of $\sqrt[4]{(81)^{-2}}$ is
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2. The product $\sqrt[3]{2} \cdot \sqrt[4]{2} \cdot \sqrt[12]{32}$ equals
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3. A rational number between $\sqrt{2}$ and $\sqrt{3}$ is
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4. Between two rational numbers
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5. Which of the following is irrational?
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6. $\sqrt{10} \times \sqrt{15}$ is equal to
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7. Which of the following is not equal to $\left[\left(\frac{5}{6}\right)^{\frac{1}{5}}\right]^{-\frac{1}{6}}$ ?
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8. 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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9. The value of $\frac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}$ is equal to
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10. $2 \sqrt{3}+\sqrt{3}$ is equal to
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11. $\sqrt[4]{\sqrt[3]{2^{2}}}$ equals
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12. $\frac{1}{\sqrt{9}-\sqrt{8}}$ is equal to
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13. After rationalising the denominator of $\frac{7}{3 \sqrt{3}-2 \sqrt{2}}$, we get the denominator as
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14. The decimal expansion of the number $\sqrt{2}$ is
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15. Which of the following is equal to $x$ ?
Rational Number: A number is called a rational number if it can be expressed in the form of $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$. Irrational Number: A number that cannot be written in the form of $\frac{p}{q}$ (where $p$ and $q$ are integers and $q \neq 0$) is called an irrational number. Real Numbers: The collection of all rational and irrational numbers is called real numbers. Decimal Expansion of Real Numbers: The decimal expansion of a rational number is either terminating or non-terminating recurring, while the decimal expansion of an irrational number is non-terminating and non-recurring. Note: If $r$ is a rational number and $s$ is an irrational number then- 1. $r+s$ and $r-s$ are irrational numbers. 2. Additionally, if $r$ is a non-zero rational number then $rs$ and $\frac{r}{s}$ are irrational numbers.
Chapter 1: Number System in Class 9 Mathematics strengthens students' foundational knowledge in math. It includes all basic concepts and important questions useful for exams.