Tag: maths

Quizzes (518) Questions (9324)

Questions Related to maths

Multiple choice maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

Choose the rational number which does not lie between rational numbers $\dfrac{3}{5}$ and $\dfrac{2}{3}$.

  1. $\dfrac{46}{75}$
  2. $\dfrac{47}{75}$
  3. $\dfrac{49}{75}$
  4. $\dfrac{50}{75}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

All the options have denominator $75$. Hence, let us convert into equivalent fractions having denominator $75$. 
$\dfrac{3}{5} $ $=\dfrac{3\times 15}{5\times 15} $ $=\dfrac{45}{75}$

$\dfrac{2}{3}$ $=\dfrac{2\times 25}{3\times 25}$ $=\dfrac{50}{75}$

Hence, $\dfrac{50}{75}$ does not lie between the given numbers.

Multiple choice maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

Rationalising the denominator of $\dfrac {5}{\sqrt 3-\sqrt 5}$ is -

  1. $(\frac {5}{2}(\sqrt 3+\sqrt 5)$
  2. $(-\frac {5}{2}(\sqrt 3+\sqrt 5)$
  3. $(\frac {5}{2}(\sqrt 3-\sqrt 5)$
  4. $(-\frac {5}{2}(\sqrt 3-\sqrt 5)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

here, $\dfrac {5}{\sqrt 3-\sqrt 5}$

$=\dfrac {5}{\sqrt 3-\sqrt 5}\times \dfrac {\sqrt 3+\sqrt 5}{\sqrt 3+\sqrt 5}$

$=\dfrac {5(\sqrt 3+\sqrt 5)}{3-5}$


$=-\dfrac {5}{2}(\sqrt 3+\sqrt 5)$

Multiple choice maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

The rational number lies between $\dfrac{3}{7}$ and $\dfrac{2}{3}$ is

  1. $\dfrac{2}{5}$
  2. $\dfrac{4}{7}$
  3. $\dfrac{3}{7}$
  4. $\dfrac{3}{3}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Converting the fractions to decimals or common denominators helps locate a rational number between 3/7 (approx 0.428) and 2/3 (approx 0.667). Option B, 4/7, is approximately 0.571, which correctly lies between these two values.

Multiple choice maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

A train of length 180 m crosses a man standing on a platform in 12 seconds and cross another train coming from opposite direction in 12 sec. If the second train running at 2/3 rd speed of the firstthen find the length of the second train?

  1. 56

  2. 120

  3. 20

  4. 44
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Length of the first train$=180m$


 Time taken by  the train to cross the man standing on the platform$=12s$


Speed of the first train$=\dfrac{180}{12}$

                                      $=15m/s$

Speed of the second train$=\dfrac{2}{3}\times15$

                                            $=10m/s$

Relative speed$=15+10$

                          $=25m/s$
 
Let the length of the train be $y$ metres.

$Distance =Speed\times time$

$y+180=25\times12$

$y+180=300$

$y=300-180$
$y=120$
So, the length of the second train$=120m$

Multiple choice maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

 Rational numbers between $\displaystyle \frac{3}{8}$ and $\displaystyle \frac{7}{12}$ are

  1. $\displaystyle \frac{3}{8}, \frac{41}{96}, \frac{23}{48}, \frac{7}{12}$
  2. $\displaystyle \frac{3}{8}, \frac{41}{196}, \frac{23}{48}, \frac{7}{12}$
  3. $\displaystyle \frac{3}{8}, \frac{41}{96}, \frac{23}{148}, \frac{7}{12}$

  4. none of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A rational number between two numbers $ a $ and $ b = \dfrac {(a +

b)}{2} $
So, a rational number between $\dfrac {3}{8} $ and $ \dfrac {7}{12}$

$ = \dfrac {\dfrac {3}{8} + \dfrac {7}{12}}{2} = \dfrac {23}{48} $

Now, another rational number between $ \dfrac {3}{8} $ and $ \dfrac {23}{48} $

$= \dfrac {\dfrac {3}{8} + \dfrac {23}{48}}{2} = \dfrac {41}{96} $ 

Hence, required two rational numbers between $\dfrac {3}{8} $ and $ \dfrac {7}{12} $ are $\dfrac {3}{8} ,\dfrac {41}{96}, \dfrac {23}{48}, \dfrac {7}{12}$

Multiple choice maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

__________ are rational numbers between between 5 and -2.

  1. $\displaystyle 5, \frac{33}{4},\ \frac{3}{2}, -\frac{1}{4}, -2$
  2. $\displaystyle \frac{13}{4},\ \frac{3}{2}, -\frac{1}{4} $
  3. $\displaystyle 5, \frac{13}{4},\ \frac{13}{2}, -\frac{1}{4}, -2$

  4. none of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A rational number between two numbers $ a $ and $ b = \dfrac {(a + b)}{2} $

So, a rational number between $ 5 $ and $ - 2 = \dfrac

{( 5 - 2 )}{2} = \dfrac {3}{2} $


Now, another rational number between $ 5 $ and $ \dfrac {3}{2} =

\dfrac {( 5 + \dfrac {3}{2})}{2} = \dfrac {13}{4} $

Another rational number between $ \dfrac {3}{2} $ and $ -2 =

\dfrac {( \dfrac {3}{2}) - 2}{2} = -\dfrac {1}{4} $

 $ \therefore \dfrac {13}{4},  \dfrac {3}{2}, - \dfrac {1}{4} $  are the rational numbers between $ 5 $ and $ -2 $

Multiple choice maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

________ are rational numbers between $\displaystyle \frac{1}{3}$ and $\displaystyle \frac{1}{4}$

  1. $\displaystyle \frac{1}{3}, \frac{7}{64}, \frac{13}{48}, \frac{1}{4}$
  2. $\displaystyle \frac{1}{3}, \frac{7}{24}, \frac{13}{48}, \frac{1}{4}$
  3. $\displaystyle \frac{1}{3}, \frac{7}{24}, \frac{13}{68}, \frac{1}{4}$

  4. none of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A

rational number between two numbers $ a $ and $ b = \frac {(a +

b)}{2} $

So, a

rational number between $\frac {1}{3} $ and $ \frac {1}{4} = \frac {(\frac {1}{3} + \frac {1}{4})}{2} = \frac {7}{24} $

Now, another rational number between $ \frac {7}{24} $ and $ \frac {1}{4} = \frac {(\frac {7}{24} + \frac {1}{4})}{2} = \frac {13}{48} $



Hence, required two rational numbers between $\frac {1}{3} $ and $ \frac {1}{4} $ are $\frac {1}{3} ,\frac {7}{24}, \frac {13}{48}, \frac {1}{4}$

Multiple choice maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

 ________ are rational numbers between $\displaystyle -\dfrac{3}{4}$ and $\displaystyle \dfrac{1}{2}.$

  1. $\dfrac{-7}{16}, \dfrac{-1}{8}, \dfrac{9}{16}$
  2. $\dfrac{-15}{16}, \dfrac{-1}{8}, \dfrac{3}{16}$
  3. $\dfrac{-7}{16}, \dfrac{-1}{8}, \dfrac{3}{16}$

  4. none of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
A rational number between two numbers $ a $ and $ b = \dfrac {(a + b)}{2} $ 

So,
a rational number between $ - \dfrac {3}{4} $ and $ \dfrac {1}{2} $
$= \dfrac {-\dfrac {3}{4} + \dfrac {1}{2}}{2} = - \dfrac {1}{8} $

Now,
another rational number between $ - \dfrac {3}{4} $ and $ - \dfrac {1}{8} $
$=\dfrac {- \dfrac {3}{4} - \dfrac {1}{8}}{2} = - \dfrac {7}{16} $ 

Another rational number between $ - \dfrac {1}{8} $ and $ \dfrac {1}{2} =$

$\dfrac { - \dfrac {1}{8} + \dfrac {1}{2}} {2} =  \dfrac {3}{16} $ 

Hence, required three rational numbers between $ - \dfrac {3}{4} $ and $  \dfrac {1}{2} $ are $ - \dfrac {3}{4}, - \dfrac {7}{16},  - \dfrac {1}{8}, \dfrac {3}{16}, \dfrac {1}{2} $
Multiple choice maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

The rational number lying between the numbers $\displaystyle \frac{1}{3}$ and $\displaystyle \frac{3}{4}$ are

  1. $\displaystyle \frac{97}{300}$,$\displaystyle \frac{299}{500}$
  2. $\displaystyle \frac{99}{300}$,$\displaystyle \frac{301}{400}$
  3. $\displaystyle \frac{95}{300}$,$\displaystyle \frac{301}{400}$
  4. $\displaystyle \frac{117}{300}$,$\displaystyle \frac{287}{400}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To insert rational numbers between $2$ numbers, we will arrange the options and check if they are in ascending order.
$\dfrac { 1 }{ 3 } { ? }\dfrac { 117 }{ 300 } \ \Longrightarrow 300<351\ \qquad \dfrac { 3 }{ 4 } { ? }\dfrac { 287 }{ 400 } \ \Longrightarrow 1200>1148$
They are in ascending order, i.e., $\dfrac { 1 }{ 3 } ,\dfrac { 117 }{ 300 } ,\dfrac { 287 }{ 400 } ,\dfrac { 3 }{ 4 } $
From the given options only option $D$ satisfies this condition. Hence, $D$ is the answer.

Multiple choice maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

Let a, b, c be positive integers such that $\frac {a\sqrt 2+b}{b\sqrt 2+c}$ is a rational number, then which of the following is always an integers?

  1. $\frac {2a^2+b^2}{2b^2+c^2}$
  2. $\frac {a^2+b^2-c^2}{a+b-c}$
  3. $\frac {a^2 _2b^2}{b^2+2c^2}$
  4. $\frac {a^2+b^2+c^2}{a+c-b}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For (a*sqrt(2)+b)/(b*sqrt(2)+c) to be rational, the irrational parts must cancel. This implies a/b = b/c, so b^2 = ac. Testing option D: (a^2+b^2+c^2)/(a+c-b) is a standard algebraic identity related to this condition.