Tag: maths

Questions Related to maths

Nehal purchased $7$ kg $200$ g of sugar, $9$ kg $395$ g of rice. What is the total weight which Nehal carried?

maths how much does it weigh? define weight and units of weight using decimals in weight conversion of length measurement (length) basic operations with same units operations involving units of length

  1. $10$ kg $375$ g

  2. $16$ kg $595$ g

  3. $20$ kg $495$ g

  4. $24$ kg $765$ g

Show answer
Correct Option: B
Explanation:
Total weight carried$=\left( 7.200+9.395 \right) ㎏=16.595㎏$
$=16㎏$ $595 gm$

Chris sold 112 kg 342 g of newspapers and 195 kg of magazines. Find the total quantity of articles sold.

maths how much does it weigh? define weight and units of weight using decimals in weight conversion of length measurement (length) basic operations with same units operations involving units of length

  1. $200$ kg $143$ g

  2. $256$ kg $246$ g

  3. $307$ kg $342$ g

  4. $384$ kg $342$ g

Show answer
Correct Option: C
Explanation:
Total quantity of articles sold$=\left( 112.342+195 \right) ㎏=307.342㎏$
$=307$ ㎏ $342$ gm

How many spherical bullets can be made out of a solid cube of lead whose edge measures $44\space cm$, each bullet being $4\space cm$ in diameter.

maths how much does it weigh? define weight and units of weight using decimals in weight conversion of length measurement (length) basic operations with same units operations involving units of length

  1. $2451$

  2. $2541$

  3. $2304$

  4. $2536$

Show answer
Correct Option: B
Explanation:

Number of spherical bullets formed $ = \dfrac {Volume  of 

cube}{Volume   of   one   spherical  bullet} $





Volume of a cube of edge a $ = {a}^{3} $





 Volume of a sphere of radius 'r' $ = \dfrac { 4 }{ 3 } \pi { r }^{ 3 } $





As the diameter of the sphere is $4$ cm, its radius r $ = 2$ cm





Hence, number of spherical bullets formed $ = \dfrac {44 \times 44 \times 44}{\dfrac {4}{3}

\times \dfrac {22}{7} \times 2 \times 2 \times 2} = 2541 $

A hemispherical tank of radius $1\displaystyle\frac{3}{4}m$ is full of water. It is connected with a pipe which empties it at the rate of $7\space litres$ per second. How much time will it take to empty the tank completely?

maths how much does it weigh? define weight and units of weight using decimals in weight conversion of length measurement (length) basic operations with same units operations involving units of length

  1. $26.74\space min.$

  2. $26.54\space min.$

  3. $26.4\space min.$

  4. $26\space min.$

Show answer
Correct Option: A
Explanation:

Suppose the pipe takes $x$ seconds to empty the tank. 

Then, 
The volume of the water that flows out of the tank in $x$ seconds =Volume of the hemispherical tank

The volume of the water that flows out of the tank $x$ in seconds= Volume of the hemispherical shell of radius $175cm$

$\Rightarrow 7000x=\cfrac { 2 }{ 3 } \times \cfrac { 22 }{ 7 } \times 175\times 175\times 175$

$\Rightarrow x=\cfrac { 2 }{ 3 } \times \cfrac { 22 }{ 7 } \times \cfrac { 175\times 175\times 175 }{ 7000 } =1604.16seconds$

$\Rightarrow x=\cfrac { 1604.16 }{ 60 } =26.74\quad minutes$

If the coefficient of variation and standard deviation of a distribution are 50% and 20 respectively, then its mean is

maths measures of dispersion coefficient of variance variance and standard deviation statistics and probability range and mean deviation

  1. 40

  2. 30

  3. 20

  4. none of these

Show answer
Correct Option: A
Explanation:

Given $\sigma = 20$, coefficient of variation $=50$ %
We know coefficient of variation $=\cfrac{\sigma }{\bar{x}}\times 100=50$
$\Rightarrow \bar{x} = 2\times \sigma = 40$

The sum of squares of deviations for $10$ observations taken from mean $50$ is $250 $. Then Co-efficient of variation is

maths measures of dispersion coefficient of variance variance and standard deviation statistics and probability range and mean deviation

  1. $10\%$

  2. $40\%$

  3. $50\%$

  4. None

Show answer
Correct Option: A
Explanation:
$\sum(x-\overline{x})^2=250$, $\overline{x}=50$
$\Rightarrow$  Standard deviation $(\sigma)=\sqrt{\dfrac{250}{10}}=\sqrt{25}=5$
$\Rightarrow$  Coefficient of variation $=\sqrt{\dfrac{\sum(x-\overline{x})^2}{n}}$
                                             $=\dfrac{\sigma}{Mean}\times 100$

                                             $=\dfrac{5}{50}\times 100$

                                             $=10\%$

The Coefficient of Variation is given by:

maths measures of dispersion coefficient of variance variance and standard deviation statistics and probability range and mean deviation

  1. $\dfrac{Mean}{\ Standard \ \ deviation } \times 100$

  2. $\dfrac{\ Standard \ \ deviation }{Mean}$

  3. $\dfrac{Standard \ \ deviation }{Mean }\times 100$

  4. $\dfrac{Mean}{Standard \ Deviation}$

Show answer
Correct Option: C
Explanation:

The coefficient of variation (CV) is a standardized measure of dispersion 

. It is defined as the ratio of the standard deviation to the mean.
$CV\quad =\quad \cfrac { \sigma  }{ Mean }\times100 $

If mean of a series is 40 and variance 1486, then coefficient of variation is 

maths measures of dispersion coefficient of variance variance and standard deviation statistics and probability range and mean deviation

  1. $0.9021$

  2. $0.9637$

  3. $0.8864$

  4. $0.9853$

Show answer
Correct Option: B
Explanation:

If mean of the given dist. be $\bar{x}$ and S.D be $\sigma $
then given $\bar{x} = 40, \sigma^2 = 1486$
$\therefore$ Coefficient of variation $=\cfrac{\sigma}{\bar{x}}=\cfrac{\sqrt{1486}}{40}=.9637$

If the coefficient of variation and standard deviation of a distribution are 50% and 20 respectively, the its mean is

maths measures of dispersion coefficient of variance variance and standard deviation statistics and probability range and mean deviation

  1. 40

  2. 30

  3. 20

  4. None of these

Show answer
Correct Option: A
Explanation:

We know if a distribution having mean $\bar{x}$ and standard deviation $\sigma$
then coefficient of variation $=\cfrac{\sigma}{\bar{x}}\times 100$
$\therefore \cfrac{20}{\bar{x}}\times 100=50\Rightarrow \bar{x} = 40$
Hence required mean is $=40$

The sum of the squares of deviation of 10 observations from their mean 50 is 250, then coefficient of varition is

maths measures of dispersion coefficient of variance variance and standard deviation statistics and probability range and mean deviation

  1. 10%

  2. 40%

  3. 50%

  4. None of these

Show answer
Correct Option: A
Explanation:

Given $\displaystyle \Sigma \left ( x _{i}-\overline{x} \right )^{2}=250$,$n=10,\overline{x}=50$

Now, $\sigma=\sqrt{\dfrac{1}{n}\Sigma \left ( x _{i}-\overline{x} \right )^{2}}$

$= \sqrt{\dfrac{1}{10}\times 250}=5$ 
Hence coefficient of variation $\displaystyle =\dfrac{\sigma }{\overline{x}}\times 100=\dfrac{5}{50}\times 100=10$%