Tag: division

Questions Related to division

How many rational numbers exist between any two distinct rational numbers?

  1. 2

  2. 3

  3. 11

  4. Infinite number of rational numbers


Correct Option: D
Explanation:

Infinite number of rational numbers exist between any two distinct rational numbers. We know that a rational number is a number which can be written in the form of $\frac { p }{ q } $ where p and q are integers and q $\neq $0.

If $n=2^3\times 3^4\times 7\times15^6$, then find the number of consecutive zeros in natural number n

  1. 6

  2. 3

  3. 2

  4. 1


Correct Option: B

1 $\div$ 28 is _______

  1. $28$

  2. $1$

  3. $0$

  4. $\cfrac {1}{28}$


Correct Option: D
Explanation:

$1\div 28=\dfrac { 1 }{ 28 } $

So correct answer will be option D

If a cellphone costs Rs.$999$. What is the cost of $12$ such cellphones?

  1. Rs.$26,356$

  2. Rs.$56,235$

  3. Rs.$13,568$

  4. Rs.$11,988$


Correct Option: D
Explanation:

By unitary method,


$1$ cellphone $=$ Rs. $999$
$12$ cellphones $=$ Rs. $999\times 12 =$ Rs.$11,988$

64 $\div$ 1 is ______

  1. 1

  2. 0

  3. 46

  4. 64


Correct Option: D
Explanation:

$64\div 1=\dfrac { 64 }{ 1 } =64$

So correct answer will be option D

State whether the statement is true or false.
$ \displaystyle \frac{4}{-9}   $ and $ \displaystyle \frac{-16}{36}   $ represent the same rational number?

  1. True

  2. False


Correct Option: A
Explanation:

Yes beacause
$ \displaystyle \frac{4}{-9}   $=$ \displaystyle \frac{4\times (-4)}{9\times(-4)}   $= $ \displaystyle \frac{-16}{36}   $ 


or $ \displaystyle \frac{-16}{36}   $= $ \displaystyle \frac{-16\div -4}{36\div -4}   $ =$ \displaystyle \frac{4}{-9}   $

Solve it 
$\dfrac {\left( {{{\left( {245 + 232} \right)}^2} - {{\left( {245 - 232} \right)}^2}} \right)}{\left( {245 + 232} \right)}$

  1. $4$

  2. $2$

  3. $232$

  4. none of these


Correct Option: D
Explanation:
$=\dfrac{{\left(245+232\right)}^{2}-{\left(245-232\right)}^{2}}{\left(245+232\right)}$
$=\dfrac{\left(245+232-245+232\right)\left(245+232+245-232\right)}{\left(245+232\right)}$
$=\dfrac{2\left(232\right)2\left(245\right)}{\left(245+232\right)}$
$=\dfrac{2,27,360‬}{477}=476.65$

Let $Q = \dfrac{x}{y}$ where $x$ and $y$ are real numbers. If both $x$ and $y$ are increased equally then

  1. $Q$ will increase

  2. $Q$ will decrease

  3. $Q$ will remain the same

  4. none of the above


Correct Option: D

The value of $0.\bar { 1 } +0.0\bar { 1 } +0.00\bar { 1 } $ is equal to 

  1. $\dfrac{407}{3300}$

  2. $\dfrac { 37 }{ 3000 } $

  3. $\dfrac { 4 }{ 3300 } $

  4. $\dfrac { 1343 }{ 10989 } $


Correct Option: A
Explanation:
$0.\bar{1}+0.0\bar{1}+0.00\bar{1}$

Let $x=0.11111...+0.01111...+0.00111....$

$\Rightarrow x=0.12333...$

$\therefore x=0.123333...$

$\Rightarrow 100x=12.333...$

$\Rightarrow 100x-x=12.333333...-0.123333...$

$\Rightarrow 99x=12.210000....$

$\Rightarrow 99x=12.21$

$\Rightarrow x=\dfrac{12.21}{99}$

$\Rightarrow x=\dfrac{1221}{9900}$

$\therefore x=\dfrac{407}{3300}$

 $\displaystyle \frac{3x}{2}-\frac{x}{4}=2$. Find value of x

  1. $2$

  2. $\dfrac85$

  3. $4$

  4. $\dfrac45$


Correct Option: B
Explanation:
$\cfrac { 3x }{ 2 } -\cfrac { x }{ 4 } =2$
$\cfrac { 6x-x }{ 4 } =2$
$\cfrac { 5x }{ 4 } =2$
$x=\cfrac { 4 }{ 5 } \times 2=\cfrac { 8 }{ 5 } $