Tag: maths

Questions Related to maths

State true or false.
$10cm$ in kilometre is $0.0001km$

maths fraction one fraction, many forms use of decimals in measure of length decimal fractions in the units of currency, length, weight, capacity

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

As we know,


$1$ m $= 100$ m


$1$ km $= 1000$ m

Given, $10$ cm

So, $10$ cm $= \dfrac{10}{100}$ m$= 0.1$ m

$0.1$ m = $\dfrac{0.1}{1000}$ km $= 0.0001$ km

So, $10$ cm $= 0.0001$ km

State true or false.

$9$ paise is equal to Rs.$0.09$.

maths fraction one fraction, many forms use of decimals in measure of length decimal fractions in the units of currency, length, weight, capacity

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

As we know,

1 Rs = 100 paisa

Given, 9 paisa
So, 9 paisa = $\frac{9}{100}$ Rs
= 0.09 Rs

Fill in the banks: 
$1765$ grams $=................... kg$

maths fraction one fraction, many forms use of decimals in measure of length decimal fractions in the units of currency, length, weight, capacity

  1. $1.765$

  2. $1.65$

  3. $1.55$

  4. $1.25$

Show answer
Correct Option: A
Explanation:

$1$ kg $= 1000$ gm


So, $1765$ grams $= \dfrac{1765}{1000}$ kg


$= 1.765$ kg 

Let $D$ represent a repeating decimal. If $P$ denotes the $r$ figures of $D$ which do not repeat themselves, and $Q$ denotes the $s$ figures which do repeat themselves, then the incorrect expression is

maths fraction one fraction, many forms use of decimals in measure of length decimal fractions in the units of currency, length, weight, capacity

  1. $D = P.QQQ....$

  2. $10^{r}D = P.QQQ...$

  3. $10^{r + s}D = PQ .QQQ .....$

  4. $10^{r}(10^{s} - 1)D = Q(P - 1)$

  5. $10^{r} . 10^{2s}D = PQ.QQQ...$

Show answer
Correct Option: D
Explanation:

$D = .PQQQ .... = .a _{1} ...a _{r}b _{1} ...b _{x}b _{1} ...b _{s} ...$ So $(a), (b), (c)$ and $(e)$ are all correct choices. To check that $(d)$ is incorrect, we have
$10^{r + s}D - 10^{r}D = PQ - P. \therefore 10^{r}(10^{s} - 1)D = P(Q - 1)$.

$2+\dfrac {1}{2}$ In the decimal form

maths fraction one fraction, many forms use of decimals in measure of length decimal fractions in the units of currency, length, weight, capacity

  1. $2.5$

  2. $1.5$

  3. $3.5$

  4. $2$

Show answer
Correct Option: A
Explanation:

$2+\dfrac{1}{2}$

As $\dfrac{1}{2}=0.5$
So $2+0.5=2.5$

If the standard deviation of $x _{1},x _{2},.....x _{n}$ is 3.5, then the standard deviatiuon of $-2x _{1}-3,-2x _{2}-3....,-2x _{n}-3$ is

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

  1. -7

  2. -4

  3. 7

  4. 1.75

Show answer
Correct Option: C

If $\sigma$ $f _i$ $x _i$  = 20 and $\sigma$ $f _i$ = 4, what is the mean of the data.

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

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

  2. $80$

  3. $16$

  4. $5$

Show answer
Correct Option: A
Explanation:
$\sigma fixi=20$
and $\sigma fi=4$

Hence, Mean $=\dfrac{\sigma fi}{\sigma fixi}=\dfrac{4}{20}=\dfrac{1}{5}$

Hence Option $A$ is correct

The variance of the data $6,\ 8,\ 10,\ 12\,,14\,,\ 16,\ 18,\ 20,\ 22,\ 24$ is

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

  1. $15$

  2. $20$

  3. $30$

  4. $33$

Show answer
Correct Option: D
Explanation:
Mistake :$14$ is not given
Mean $\bar x=\dfrac{6+8+10+12+14+16+18+20+22+24}{10}=\dfrac{150}{10}=15$
Variance$=\dfrac{1}{n} \sum\limits _{i=1}^n(x _{i}-\bar x)^2$
$\implies \dfrac{1}{10}((6-15)^2+(8-15)^2+(10-15)^2+(12-15)^2+(14-15)^{2}+(16-15)^2+(18-15)^2+(20-15)^2$
$+(22-15)^2+(24-15)^2$

$\implies \dfrac{81+49+25+9+1+1+9+25+49+81}{10}$

$\implies \dfrac{330}{10}=33$

The variate x and u are related by $\displaystyle u= \frac{x-a}{h}$ then correct relation between $\displaystyle \sigma _{x}:and:\sigma _{u}$

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

  1. $\displaystyle \sigma _{x}= h\sigma _{u}$

  2. $\displaystyle \sigma _{x}= h+\sigma _{u}$

  3. $\displaystyle \sigma _{u}= h\sigma _{x}$

  4. $\displaystyle \sigma _{u}= h+\sigma _{x}$

Show answer
Correct Option: A
Explanation:

Given $\displaystyle u =\frac{x}{h}-\frac{a}{h}$
Since,S.D. is not depend on change of origin but it is depend on change of scale.
$\displaystyle \therefore \sigma _{u}=\frac{\sigma _{x}}{h}$
$\Rightarrow h\sigma _{u}=\sigma _{x}$

Standard deviation of a collection of data is $2\sqrt{2}$. If each value in a data set  is multipled by $3$, then the standard deviation of the new data is.

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

  1. $\sqrt{12}$

  2. $4\sqrt{2}$

  3. $6\sqrt{2}$

  4. $9\sqrt{2}$

Show answer
Correct Option: C
Explanation:
The standard deviation would also be multiplied by $3$.
Because the mean would also be $3x$ larger, the differences from the mean would be $3x$ larger too.
It is the same idea as if you were looking at your data set through an enlarging lens- everything would be $3x$ bigger, not only the data values, but also the mean, the differences from the mean, but just everything!
$\therefore$ the standard deviation becomes $2\sqrt{2}\times 3=6\sqrt{2}$