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Number Systems Test - 25

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Number Systems Test - 25
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  • Question 1
    1 / -0
    Simplify and give reasons:
    323×(3031)\cfrac { { 3 }^{ -2 } }{ 3 } \times \left( { 3 }^{ 0 }-{ 3 }^{ -1 } \right)
    Solution

  • Question 2
    1 / -0
    Simplify and give reasons:
    [(32 ) 2]2\left[ { \left( \cfrac { 3 }{ 2 }  \right)  }^{ -2 } \right] ^{ 2 }
    Solution
    we know that,

    (am)n=amn\because (a^m)^n=a^{mn}

    so,

    ((32)2)2=(32)4((\dfrac32)^{-2})^2=(\dfrac32)^{-4}
    we also know

    (ab)m=(ba)m\because (\dfrac{a}{b})^{-m}=(\dfrac{b}{a})^m

    =(23)4=(\dfrac23)^4

    =1681=\dfrac{16}{81}
















  • Question 3
    1 / -0
    Simplify:
    [(35 ) 2÷(45 ) 3]×(35 ) 2\left[ { \left( \cfrac { 3 }{ 5 }  \right)  }^{ -2 }\div { \left( \cfrac { 4 }{ 5 }  \right)  }^{ -3 } \right] \times { { \left( \cfrac { 3 }{ 5 }  \right)  } }^{ -2 }
    Solution

  • Question 4
    1 / -0
    Which irrational number is plotted on the number line in figure?

    Solution
    According to the given figure,

    the red dot is closer to 1.751.75 and out of the options only 3\sqrt3 is only one near to 1.751.75 .
    The irrational number is plotted on the number line
    3=1.732\sqrt {3}=1.732.

    Hence, option CC is correct.
  • Question 5
    1 / -0
    Classify the following numbers as rational or irrational:  1275\displaystyle \frac{\sqrt{12}}{\sqrt{75}}.
    Solution
    12 75 =23 53 =25\dfrac { \sqrt { 12 }  }{ \sqrt { 75 }  } =\dfrac { 2\sqrt { 3 }  }{ 5\sqrt { 3 }  } =\dfrac { 2 }{ 5 } , which is a rational number. 
    Hence, the correct answer will be option AA.
  • Question 6
    1 / -0
    22\displaystyle\frac{2}{\sqrt{2}} is equal to:
    Solution
    To find 22\dfrac{2}{\sqrt2},

    Multiply numerator and denominator by 2\sqrt2we get, 

    22\dfrac{2}{\sqrt2} =2×22×2=\dfrac{2 \times \sqrt2 }{\sqrt2 \times \sqrt2}

    =222= \dfrac{2\sqrt2 }{2}  =2= \sqrt2

    Hence, option BB is correct.
  • Question 7
    1 / -0
    Which one of the following is an irrational number?
    Solution

    Step 1: Simplifying the following options.\textbf{Step 1: Simplifying the following options.}
                    The numbers which are non-repeating and non-terminating are irrational numbers.\text{The numbers which are non-repeating and non-terminating are irrational numbers.}
                    Option A : π=3.141... is an irrational number.\text{Option A : }\pi = 3.141... \text{ is an irrational number.}
                    Option B : 9=3 is a rational number.\text{Option B : }\sqrt{9} = 3 \text{ is a rational number.}
                    Option C : 14 is a rational number.\text{Option C : }\dfrac{1}{4} \text{ is a rational number.}
                    Option D : 15 is a rational number.\text{Option D : }\dfrac{1}{5} \text{ is a rational number.}
                    Option A : π is an irrational number.\therefore \text{Option A : }\pi \text{ is an irrational number.}
    Hence, option A is the correct answer.\textbf{Hence, option A is the correct answer.}
  • Question 8
    1 / -0
    p0p^{0} is equal to
    Solution
    As we can see that pp is raised to power 00. It means that there is no term of pp

     So, p0=1p^{0}=1
    Any real number when raised to the power 00 gives 11.
  • Question 9
    1 / -0
    Simplify the following using law of exponents.
    210×242^{10}\times 2^4
    Solution
    we know that,

    am×an=am+n\because a^m \times a^n=a^{m+n}

    so,
    210×242^{10}\times 2^4

    =210+4=2^{10+4}

    =214=2^{14}
  • Question 10
    1 / -0
    Evaluate 20+302^0+3^0
    Solution

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