Tag: maths

Questions Related to maths

$54.327\times 357.2\times 0.0057$ is the same as.

maths calculating and mental strategies 3 written methods dividing decimals division of decimals

  1. $5.4327\times 3.572\times 5.7$

  2. $5.4327\times 3.572\times 0.57$

  3. $54327\times 3572\times 0.0000057$

  4. $5432.7\times 3.572\times 0.000057$

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Correct Option: A
Explanation:
Given expression is $54.327\times 357.2\times 0.0057$
$\Rightarrow$  Number of decimal places in the given expression = $8$
$\Rightarrow$   Number of decimal places in (A) = 8
$\Rightarrow$   Number of decimal places in (B) = 9 
$\Rightarrow$   Number of decimal places in (C)= 7
$\therefore$    The expression in $(A)$ is the same as the given Expression.

Simplify $\left[\displaystyle\frac{(0.333)^3}{(0.111)^2}-\frac{(0.222)^4}{(0.111)^3}\right]$.

maths calculating and mental strategies 3 written methods dividing decimals division of decimals

  1. $1.331$

  2. $1.221$

  3. $1.484$

  4. $1.551$

Show answer
Correct Option: B
Explanation:
Given, $[\dfrac{(0.333)^3}{(0.111)^2} - \dfrac{(0.222)^4}{(0.111)^3}]$
We can solve like 
= $[\dfrac{0.333 \times 0.333 \times 0.333}{0.111 \times 0.111} - \dfrac{0.222 \times 0.222 \times 0.222 \times 0.222}{0.111 \times 0.111 \times 0.111}]$
= ${3 \times 3 \times 0.333} - 2 \times  2 \times 2 \times 0.222$
= $2.997 - 1.776$
= $1.221$

Divide $125.625$ by $0.5$

maths calculating and mental strategies 3 written methods dividing decimals division of decimals

  1. $251.25$

  2. $2512.5$

  3. $25125$

  4. $25.125$

Show answer
Correct Option: A
Explanation:

Division of $125.625$ by $0.5$ is

$\dfrac{125.625}{0.5}$ $=251.25$
Hence, the answer is $251.25$

Find the product:
$\displaystyle 0.05\times 0.09\times 5$

maths calculating and mental strategies 3 written methods dividing decimals division of decimals

  1. $0.025$

  2. $0.225$

  3. $0.005$

  4. $0.0225$

Show answer
Correct Option: D
Explanation:
Multiply the numbers without decimal point
i.e. $5\times 9\times 5=225$
$0.05$ have decimal point after $2$ digits
$0.09$ have decimal point after $2$ digits
So, the product will have decimal point after $2+2=4$ digits
Thus, the product of $0.05\times 0.09 \times 5=0.0225$

Solve the given expression:
$\displaystyle 9.826\div 10$

maths calculating and mental strategies 3 written methods dividing decimals division of decimals

  1. $98.26$

  2. $982.6$

  3. $0.09826$

  4. $0.9826$

Show answer
Correct Option: D
Explanation:
Denominator is one power of $410$
So, the number of digits after decimal point will increase by $1$ 
The division of $9.826$ by $10$ is 
$\therefore \dfrac{9.826}{10}$ $=0.9826$


select the missing number based on the given
$27: 65 :: 54: $____

maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

  1. $130$

  2. $127$

  3. $126$

  4. $125$

Show answer
Correct Option: A
Explanation:

$let\> the\> missing\> number\> be \>x \\ then\> (\frac{27}{65})=(\frac{54}{x})\\  \>x=(\frac{54\times 65}{27})\\= 130$

A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains $25$%. The percentage of water in the mixture is

maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

  1. $4$%

  2. $6\frac { 1 }{ 4 } $%

  3. $20$%

  4. $25$%

Show answer
Correct Option: C
Explanation:

According to the question,

Let's assume milkman has $100$ liter of milk, If he added $x$ liter of water, the percentage of water in the mixture$=\dfrac {x}{(100+x)}\times 100$

The milk gain $25$%, he must have added $25$ liter water in $100$ liter of milk. Then the percentage of water in the mixture$=\dfrac {25}{(100+25)}\times 100=20\%$


In the new mixture, If the milk is $80$% then $80$% of total mixture should be $100$ liter
$(100+x)\times \dfrac{80}{100}=100$
$8x=200$
$x=25$

Then, the percentage of water in the mixture $=\dfrac {25}{(100+25)}\times 100=20\%$

The value of 0.037, where 0.037 stands for the number 0.0373737........, is _________.

maths decimal fraction written methods dividing decimals division of decimals

  1. 37/1000

  2. 37/990

  3. 1/37

  4. 1/27

Show answer
Correct Option: A

If the area of a parallelogram is $144 \operatorname { cm } ^ { 2 }$ and its base is $9 cm$. then its height is 

maths perimeter and area of rectilinear figures parallelogram and rectangle area of parallelogram area of a parallelogram

  1. $8 cm$

  2. $12 cm$

  3. $24 cm$

  4. $16 cm$

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Correct Option: D
Explanation:

Area of parallelogram $=base\times height$


$\Rightarrow$ $144{cm}^{2}=9cm\times 10cm$


$\Rightarrow$ $h$ in $cm=\cfrac{144{cm}^{2}}{9cm}$

$\therefore$ $h=16cm$

Hence height $=16cm$

Area of the parallelogram formed by the pairs of lines $x^{2}+xy-^{2}=0$ and $x^{2}+xy-y^{2}-3x-4y+1=0$ is

maths perimeter and area of rectilinear figures parallelogram and rectangle area of parallelogram area of a parallelogram

  1. $\sqrt {5}$

  2. $\dfrac {1}{\sqrt {5}}$

  3. $2\sqrt {5}$

  4. $\dfrac {2}{\sqrt {5}}$

Show answer
Correct Option: C