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$M_{ o }=50$ seconds
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Obtain an exclusive continuous frequency distribution from the following data.
→|
Less than weight (kg.)
|
$30$
|
$35$
|
$40$
|
$45$
|
$50$
|
$55$
|
$60$
|
$65$
|
$70$
|
|
Cumulative frequency
|
$0$
|
$17$
|
$25$
|
$40$
|
$48$
|
$54$
|
$57$
|
$59$
|
$60$
|
The price indices obtained for the first ten months of a year are $115,118,122,120,121,128,132,126,123, 125.$ Find the percentage of indices included in the range $x+S$.
→From the following measures obtained for the frequency distributions of sales (in lakh Rs.) of potatoes by two merchants in a month, determine which distribution is more close to symmetry.
Kush bought a motorcycle for $₹ 70,000$. If its cost reduces by $15 \%$ every year, what will be the value of the motorcycle at the end of the fourth year ?
→If the three positive numbers $k + 4, 4k -2$ and $7k + 1$ are in $G.P.$, find $K.$
→The data about weight (in grams) of mangoes from a tree are as follows. Moreover, the minimum weight for these mangoes is $410$ grams. Find the mean weight of mangoes.
→Verify whether relations between the elements of the sets given below are
functions or not.
(1) $\mathrm{A}=\{1,2,3,4\}, \mathrm{B}=\{3,5,7,9\}$, and relation is $f(x)=2 x+1, x \in \mathrm{A}$
(2) $\mathrm{P}=\left\{-\frac{1}{2}, 0,1\right\}, \mathrm{S}=\{10\}$, and rule is $k(x)=10, x \in \mathrm{P}$
(3) $\mathrm{A}=\{2,5,6\}, \mathrm{B}=\left\{1, \frac{3}{2}, \frac{9}{5}, \frac{11}{7}, \frac{13}{6}\right\}$, and rule is $y=\frac{2 x-1}{x+1}, x \in \mathrm{A}$
(4) $\mathrm{B}=\{-1,0,1,3\}, \mathrm{C}=\{-5,-3,-1,1,3\}$, and rule is $h(x)=2 x+3, x \in \mathrm{B}$
→(1) $\mathrm{A}=\{1,2,3,4\}, \mathrm{B}=\{3,5,7,9\}$, and relation is $f(x)=2 x+1, x \in \mathrm{A}$
(2) $\mathrm{P}=\left\{-\frac{1}{2}, 0,1\right\}, \mathrm{S}=\{10\}$, and rule is $k(x)=10, x \in \mathrm{P}$
(3) $\mathrm{A}=\{2,5,6\}, \mathrm{B}=\left\{1, \frac{3}{2}, \frac{9}{5}, \frac{11}{7}, \frac{13}{6}\right\}$, and rule is $y=\frac{2 x-1}{x+1}, x \in \mathrm{A}$
(4) $\mathrm{B}=\{-1,0,1,3\}, \mathrm{C}=\{-5,-3,-1,1,3\}$, and rule is $h(x)=2 x+3, x \in \mathrm{B}$
Find the quartile deviation of advertisement expenditure using following frequency distribution of advertising expenditure of $50$ companies :
→| Advertisement cost (thousand $Rs$. ) | $0 – 5$ | $5 – 15$ | $15 – 30$ | $30 – 40$ | $40 – 60$ | $60 -100$ | Total |
| No. of companies | $3$ | $8$ | $15$ | $10$ | $8$ | $6$ | $50$ |
Obtain the middle term in the expansion of $\left(2 x+\frac{3}{x}\right)^{4}$
→The monthly pocket expense (in $Rs$) of $15$ students of a hostel are respectively $45,30,50,60,36,48,40,66$, $57,72,60,30,35,27,39 .$ Find
$(1)$ Range and Quartile deviation and
$(2)$ Coefficient of range and coefficient of quartile deviation
$(3)$ If it is decided to reduce the monthly pocket expense of each student by $Rs 5$, what will be effect of this change on measures of range and quartile deviation?
$(4)$ If the monthly pocket expense of each student is decided to make half, find the new values of range and quartile deviation. Give reason for this change.
→$(1)$ Range and Quartile deviation and
$(2)$ Coefficient of range and coefficient of quartile deviation
$(3)$ If it is decided to reduce the monthly pocket expense of each student by $Rs 5$, what will be effect of this change on measures of range and quartile deviation?
$(4)$ If the monthly pocket expense of each student is decided to make half, find the new values of range and quartile deviation. Give reason for this change.