Question
Using binomial expansion show that, $(\sqrt{7}+1)^{5}-$ $(\sqrt{7}-1)^{5}=632$
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Answer
$\mathrm{LHS}=\mathrm{RHS}$
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The data on retail price of a commodity for $50$ days are as follows. Classify the data iaking class length $1$ and the mid value of initial class $12.5$ into an appropriate continuous frequency distribution. (Price is per $kg$ in ).
$\text{13.25,14.20,13.75,14.10,14.00,12.85,13.40,14.20,15.30$, $15.40,16.10,15.80,15.60,15.10,14.85,14.75,15.25,16.45}$, $\text{16.40,16.55,17.10,16.90,16.80,17.00,16.40,16.50,16.60$, $16.65,16.70,16.85,17.00,17.25,17.50,17.45,17.60,17.75}$, $\text{17.40,17.35,17.45,17.50,17.60,17.50,17.65,17.25,18.10$, $17.00,17.20,17.50,17.80,17.90 .}$
→$\text{13.25,14.20,13.75,14.10,14.00,12.85,13.40,14.20,15.30$, $15.40,16.10,15.80,15.60,15.10,14.85,14.75,15.25,16.45}$, $\text{16.40,16.55,17.10,16.90,16.80,17.00,16.40,16.50,16.60$, $16.65,16.70,16.85,17.00,17.25,17.50,17.45,17.60,17.75}$, $\text{17.40,17.35,17.45,17.50,17.60,17.50,17.65,17.25,18.10$, $17.00,17.20,17.50,17.80,17.90 .}$
The frequency distribution of units of power consumed in an hour for different machines during a production process of factory is as follows. Find coefficient of skewness by Bowley’s method.
→| Units of power consumed | $10 – 15$ | $15 – 20$ | $20 – 25$ | $25 – 30$ | $30 – 35$ | $35 – 40$ |
| No. of machines | $5$ | $10$ | $15$ | $20$ | $25$ | $30$ |
The information of the salary of $200$ employees of company is given below. Find the standard deviation of the salary Of the employees :
→| Salary (thousand $Rs.$) | Less than $10$ | Less than $20$ | Less than $30$ | Less than $40$ | Less than $50$ | Less than $60$ | Less than$ 70$ |
| No. of persons | $5$ | $17$ | $47$ | $92$ | $142$ | $179$ | $200$ |
The commission paid on insurance policy amounts to agents in a branch of an insurance company during a month has the following frequency distribution.
Find the coefficient of skewness by Bowley's method.
→Find the coefficient of skewness by Bowley's method.
| Commission paid(thousand Rs.) | $10-12$ | $12-14$ | $14-16$ | $16-18$ | $18-20$ | $20-22$ | $22-24$ | $24-26$ | $26-28$ | $28-30$ |
| No. of companies | $4$ | $10$ | $16$ | $29$ | $52$ | $80$ | $32$ | $23$ | $17$ | $1$ |
Information regarding the age of persons living in two different regions is as under. Present it by using an appopriate diagram.
→| Age | Less than $15$ (Child) | $15$ to $35$ (Young) | $35$ to $60$ (Adult) | More than $60$ (Old) | Total |
| Region $A$ | $480$ | $360$ | $240$ | $120$ | $1200$ |
| Region $B$ | $350$ | $250$ | $200$ | $200$ | $1000$ |
Find the standard deviation of age of the persons from the following distribution of $125$ persons living in a society. Also find the coefficient of standard deviation.
→The following table shows the monthly expense for entertainment in a group of $100$ students. Find the median of this expense.
→| Expense $(₹)$ | Less than $200$ | $200-400$ | $400-600$ | $600-700$ | $700-800$ | $900$ and above |
| No. of students | $8$ | $23$ | $40$ | $17$ | $7$ | $5$ |
Putting $a=1$ and $b=2$ in the expansion of $\left(\frac{a}{b}-\frac{2 b}{a}\right)^{4}$ verify both the sides.
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