CBSE Questions for Class 9 Maths Number Systems Quiz 1 - MCQExams.com

State whether the statement is true (T) or false (F).
If $$\dfrac{p}{q}$$ is a rational number, then $$p$$ cannot be equal to zero.
  • True
  • False
State whether the statement is true (T) or false (F).
If $$\dfrac{x}{y}$$ is a rational number, then $$y$$ is always a whole number.
  • True
  • False

State true or false.

Zero is the smallest rational number.
  • True
  • False
$$5^{0}=5$$
  • True
  • False
If $$x$$ be any non-zero integer and $$m,n$$ be positive integers, then $$x^m \times x^n$$ is equal to
  • $$x^m$$
  • $$x^{m+n}$$
  • $$x^n$$
  • $$x^{m-n}$$
If $$y$$ is any non-zero integer, then $$y^0$$ is equal to ....
  • $$1$$
  • $$0$$
  • $$-1$$
  • Not found
$$(-2)^{0}=2$$
  • True
  • False
$$(-6)^{0}=-1$$
  • True
  • False

Find the positive rational number out of the following.
  • $$\dfrac{-4}{9}$$
  • $$\dfrac{-16}{36}$$
  • $$\dfrac{-20}{-45}$$
  • $$\dfrac{28}{-63}$$
State whether the following statement is true (T) or false (F):
$$3^0 = (1000)^0$$.
  • True
  • False
State true or false:
All terminating decimal numbers are rational numbers.
  • True
  • False
$$\sqrt 3$$  is
  • an irrational number
  • a rational number
  • a composite number
  • a prime number
$$ \dfrac{2}{7} $$ is an irrational number.
  • True
  • False
State, in each case, whether true or false:
$$ \dfrac{5}{11} $$ is a rational number
  • True
  • False
State, in each case, whether true or false:
All rational numbers are real numbers.
  • True
  • False
The number obtained on rationalizing the denominator of $$\dfrac {1}{\sqrt {7} - 2}$$ is
  • $$\dfrac {\sqrt {7} + 2}{3}$$
  • $$\dfrac {\sqrt {7} - 2}{3}$$
  • $$\dfrac {\sqrt {7} + 2}{5}$$
  • $$\dfrac {\sqrt {7} + 2}{45}$$
After rationalising the denominator of $$\dfrac{7}{3\sqrt{3}-2\sqrt{2}}$$, we get the denominator of the resultant equivalent expression as:
  • $$5$$
  • $$13$$
  • $$19$$
  • $$35$$
The number obtained on rationalising the denominator of $$\dfrac{1}{\sqrt{9}-\sqrt{8}}$$ is ?
  • $$\dfrac{1}{3+2\sqrt{2}}$$
  • $$3-2\sqrt{2}$$
  • $$3+2\sqrt{2}$$
  • $$\dfrac{1}{2}\left ( 3-2\sqrt{2} \right )$$
Which of the following is irrational number?
  • $$\sqrt{\dfrac{8}{18}}$$
  • $$\sqrt{\dfrac{12}{3}}$$
  • $$\sqrt{\dfrac{28}{8}}$$
  • $$\sqrt{81}$$
$$\sqrt {10}\times \sqrt {15}$$ is equal to
  • $$\sqrt {25}$$
  • $$5\sqrt {6}$$
  • $$6\sqrt {5}$$
  • $$10\sqrt {5}$$
The product of any two irrational numbers
  • Is always an irrational number
  • Is always a rational number
  • Is always an integer
  • Can be rational or irrational
The decimal expansion of $$\pi $$ is :
  • terminating
  • non-terminating and non-recurring
  • non-terminating and recurring
  • doesnt exist
The product of a non-zero rational number with an irrational number is always :
  • Irrational number
  • Rational number
  • Whole number
  • Natural number
Rationalise the denominator and find the equivalent of : $$\displaystyle\ \frac{2\sqrt{3}}{\sqrt{2}}$$
  • $$\sqrt{12}$$
  • $$\sqrt{3}$$
  • $$\sqrt{6}$$
  • $$\sqrt{2}$$
Find conjugate of:
$$3-\sqrt{5}$$
  • $$3+\sqrt{5}$$
  • $$3-\sqrt{5}$$
  • $$3\sqrt{5}$$
  • None of these
Rationalise the denominator of:
(i) $$\displaystyle\ \frac{1}{2-\sqrt{3}}$$
  • $$2+\sqrt{7}$$
  • $$2+\sqrt{2}$$
  • $$2+\sqrt{3}$$
  • $$2+\sqrt{5}$$
Is zero a rational number? Can you write it in the form $$\dfrac{p}{q}$$, where $$p$$ and $$q$$ are integers and $$ q\ne 0$$?
  • True
  • False
Classify the result as rational or irrational:
$$(3+\sqrt{23})-\sqrt{23}$$.
  • Rational number
  • Irrational number
  • Data Insufficient
  • None of the above
Write the simplest rationalization factor of the following surds :
$$4\sqrt[3]{3}$$
  • $$\sqrt[3]{9}$$
  • $$\sqrt[2]{9}$$
  • $$\sqrt{9}$$
  • $$\sqrt{3}$$
A number is an irrational if and only if its decimal representation is:
  • non terminating
  • non terminating and repeating
  • non terminating and non repeating
  • terminating
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