The chapter Number Systems is the foundation of mathematics in Class 9. It introduces students to real numbers, irrational numbers, laws of exponents, and representation of numbers on the number line.
As per the syllabus prescribed by Central Board of Secondary Education (CBSE), this chapter plays a crucial role in building algebraic concepts for higher classes.
Top 10 Important Questions from Number Systems – Class 9
- Let x be a rational number and y be an irrational number.
Is (x+y) necessarily an irrational number? Give an example in support of your answer. - Represent √4.7 geometrically on the number line.
- Find the value of a and b if
$$
\frac{7+3\sqrt{5}}{3+\sqrt{5}} – \frac{7-3\sqrt{5}}{3-\sqrt{5}} = a + b\sqrt{5}.
$$ - Rationalize the denominator of
$$
\frac{3}{3 + \sqrt{5} – 2}.
$$ - On simplification, the expression
$$
\frac{5^{n+2} – 6 \times 5^{n+1}}{13 \times 5^n – 2 \times 5^{n+1}}$$ equal to……. - If $$10^x = 64$$
find the value of
$$\frac{10^{x+1}}{10^x}$$ - The value of
$$\frac{3 – 2\sqrt{2}}{3 + 2\sqrt{2}}$$ is ______. - If $$\frac{9^y \times 3^2\times (3^\frac{-y}{2})^{-2}-(27)^x }{3^{3x}\times 2^3} = \frac{1}{27}$$ prove that y- x = 1.
- Prove that $$\frac{1}{1 + y^{a-b}} + \frac{1}{1 + y^{b-a}} = 1.$$
- Locate √3 and √5 on the number line.