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Division - class-VIII

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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 } $

Find the remainder when $105!$ is divided by $214.$ 

  1. $168$

  2. $108$

  3. $196$

  4. $172$


Correct Option: B

Evaluate: $625\div 125$

  1. $125$

  2. $25$

  3. $31$

  4. $5$


Correct Option: D
Explanation:
The natural number $625$ can be divided by another natural number $125$ as follows:

$625\div 125=\dfrac { 625 }{ 125 } =5$

Hence, $625\div 125=5$

$\displaystyle  50 -\frac { 1 }{ 4 }\times  ........ =0$ 

  1. $\displaystyle \frac { 199 }{ 4 }$

  2. $\displaystyle \frac { 1 }{ 4 }$

  3. 200

  4. 0


Correct Option: C
Explanation:

50-x/4=0

50=x/4
x=50*4
x=200
hence option C is correct..

$\displaystyle 40-  \frac { 1 }{ 2 }\times ........ = 1 $ 

  1. $\displaystyle \frac { 79 }{ 2 }$

  2. 79

  3. $\displaystyle \frac { 2 }{ 79 }$

  4. $78$


Correct Option: D
Explanation:

40-x/2=1

40-1=x/2
39=x/2
x=39*2
x=78

Evaluate: $625\div 5=$

  1. $125$

  2. $25$

  3. $234$

  4. $35$


Correct Option: A
Explanation:
The natural number $625$ can be divided by another natural number $5$ as follows:

$625\div 5=\dfrac { 625 }{ 5 } =125$

Hence, $625\div 5=125$

Evaluate: $625\div 25$

  1. $125$

  2. $25$

  3. $35$

  4. $10$


Correct Option: B
Explanation:
The natural number $625$ can be divided by another natural number $25$ as follows:

$625\div 25=\dfrac { 625 }{ 25 } =25$

Hence, $625\div 25=25$

$\frac {171\tfrac {3}{4}\times 171\tfrac {3}{4}-91\tfrac {3}{4}\times 91\tfrac {3}{4}}{171\tfrac {3}{4}+91\tfrac {3}{4}}$ is equal to

  1. $263\frac {1}{2}$

  2. $90\frac {1}{4}$

  3. $80$

  4. $80\frac {3}{4}$


Correct Option: C
Explanation:

If $a=171\frac {3}{4}, b=91\frac {3}{4}$, then given expression is


$\dfrac {a^2-b^2}{a+b}=\dfrac {(a+b)(a-b)}{(a + b)}=a-b=171\frac {3}{4}-91\frac {3}{4}=80$

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