CBSE Questions for Class 9 Maths Number Systems Quiz 3 - MCQExams.com

Rationalise the denominator of :
$$\displaystyle\ \frac{2}{\sqrt{6}-\sqrt{2}}$$
  • $$\displaystyle\ \frac{\sqrt{6}-\sqrt{2}}{2}$$
  • $$\displaystyle\ \frac{\sqrt{6}\sqrt{2}}{2}$$
  • $$\displaystyle\ \frac{\sqrt{6}+\sqrt{2}}{2}$$
  • None of these
Write the simplest rationalization factor of the following surds :
$$2\sqrt{2}$$
  • $$\sqrt{3}$$
  • $$\sqrt{8}$$
  • $$\sqrt{2}$$
  • $$\sqrt{4}$$
State whether true or false.
$$\displaystyle \sqrt{2}+\sqrt{3}=\sqrt{5}$$
  • True
  • False
State whether true or false.
$$\displaystyle \frac{2}{7}$$ is a rational number.
  • True
  • False
$$\sqrt 7$$ is
  • A rational number
  • An irrational number
  • Not a real number
  • Terminating decimal
Are the square roots of all positive integers irrational?
  • True
  • False
State whether the following statement are true or false? Justify your answers.
Every irrational number is a real number.
  • True
  • False
The decimal expansion of the number $$\sqrt {2}$$ is 
  • A finite decimal
  • $$1.4121$$
  • Non-Terminating, Recurring
  • Non-Terminating, Non-Recurring
A number that can be expressed in the form $$\displaystyle\frac{a}{b}$$, where $$a$$ and $$b$$ are integers and $$b$$ is not equal to zero is called
  • a fraction
  • an integer
  • a rational number
  • a real number
Which of the following statement is false?
  • Every fraction is a rational number
  • Every rational number is a fraction
  • Every integer is a rational number
  • All the above
Write two irrational numbers between $$0.2$$ and $$0.21$$.
  • $$0.2010010001...$$
  • $$0.2020020002...$$
  • $$0.2010010001$$
  • $$0.2020020002$$
If we divide a positive integer by another positive integer, what is the resulting number ?
  • Always a natural number
  • Always an integer
  • A rational number
  • An irrational number
Find two irrational numbers between $$0.5$$ and $$0.55$$.
  • $$0.5010010001...$$
  • $$0.5020020002...$$
  • $$0.50101010101...$$
  • $$0.50202020202...$$
Conjugate surd of $$\displaystyle a-\sqrt{b}$$  is:
  • $$\displaystyle a+\sqrt{b}$$
  • $$\displaystyle \sqrt{a}-b$$
  • $$\displaystyle \sqrt{a}-\sqrt{b}$$
  • $$\displaystyle \sqrt{a}+b$$
The rationalising factor of $$\displaystyle 5+2\sqrt{6}$$ is
  • $$\displaystyle -2\sqrt{6}-5$$
  • $$\displaystyle \sqrt{6}-10$$
  • $$\displaystyle 6-2\sqrt{5}$$
  • $$\displaystyle 5-2\sqrt{6}$$
State true or false.
The three rational number between $$5$$ and $$6$$ are $$ \displaystyle\frac{21}{4},\frac{22}{4},\frac{23}{4}$$.
  • True
  • False
Simplify $$(32)^{\displaystyle \frac {-2}{5}}\, \div\, (125)^{\displaystyle \frac {-2}{3}}$$
  • $$\displaystyle \frac {4}{25}$$
  • $$\displaystyle \frac {25}{4}$$
  • $$\displaystyle \frac {2}{5}$$
  • $$\displaystyle \frac {5}{2}$$
A rational number between $$\displaystyle \frac{1}{4}$$ and $$\displaystyle \frac{1}{3}$$ is
  • $$\displaystyle \frac{7}{24}$$
  • $$\displaystyle \frac{16}{48}$$
  • $$\displaystyle \frac{13}{48}$$
  • All the above
$$\left ( \displaystyle \frac {16}{81} \right )^{\displaystyle \frac {3}{4}}$$ = ..........
  • $$\displaystyle \frac {9}{2}$$
  • $$\displaystyle \frac {2}{9}$$
  • $$\displaystyle \frac {8}{27}$$
  • $$\displaystyle \frac {27}{8}$$
If p: every fraction is a rational number
   q: every rational number is a fraction
then which of the following is correct?
  • p is true and q is false.
  • p is false and q is true.
  • Both p and q are true.
  • Both p and q are false.
$$\displaystyle \frac{-2}{-19}$$ is a
  • Positive rational number.
  • Negative rational number.
  • Either positive or negative number.
  • Has neither a positive numerator nor a negative number
The value of $$(3^{0} - 4^{0})\, \times\, 5^2$$ is
  • $$25$$
  • $$0$$
  • $$-25$$
  • none of these
Evaluate: $$(0.04)^{-1.5} $$
  • $$25$$
  • $$125$$
  • $$250$$
  • $$625$$
$$\displaystyle \frac{-5}{0}$$ is a ........
  • Positive rational number.
  • Negative rational number.
  • Either positive or negative rational number.
  • Neither positive nor negative rational number.
The value of $$[ (-2)^{(-2)} ]^{(-3)}$$ is
  • 64
  • 32
  • cannot be determined
  • none of these
Which of the following is a rational number (s)?
  • $$\displaystyle \frac{-2}{9}$$
  • $$\displaystyle \frac{4}{-7}$$
  • $$\displaystyle \frac{-3}{17}$$
  • All the three given numbers
A rational number is defined as a number that can be expressed in the form $$\dfrac{p}{q}$$ where $$p$$ and $$q$$ are integers and 
  • $$q=0$$
  • $$q=1$$
  • $$q\neq 1$$
  • $$q\neq 0$$
Evaluate: $$(256)^{0.16}\, \times\, (256)^{0.09}$$
  • $$4$$
  • $$16$$
  • $$64$$
  • $$256.25$$
The value of $$(8^{-25}\, -\, 8^{-26})$$ is
  • $$7\, \times\, 8^{-25}$$
  • $$7\, \times\, 8^{-26}$$
  • $$8\, \times\, 8^{-26}$$
  • None of these
The reciprocal of a positive rational number is positive.
  • True
  • False
  • Cannot be determined
  • None
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