Question
Find the values of the following using binomial expansion: $(\sqrt{2}-3)^{5}-(\sqrt{2}+3)^{5}$
✓
Answer
$-1686$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The mean number of units produced by $100$ workers of a factory per day is $60$ units and its standard deviation is $10$ units. Later on, it was noticed that two workers have actually produced $30$ and $20$ units respectively but it was registered as $5$ and $45$ units respectively. By considering this, find corrected mean and corrected standard deviation of the number of units produced by the workers.
→In the year $201$3, there were $1200$ students studying in a school and of them, $400$ were girls, $5O$ girls were not residing in hostel. In all $600$ boys were residing in hostel. In the year $2014$, there is an increase of $20\%$ in the number of boys and the number of girls increased by $30\%$. During this year, $260$ boys and $100$ girls were not residing in hostel.
In the year $2015, 140$ boys and $100$ girls were newly admitted in the school and all of them resided with the hostel students. Present above data in a tabular form.
In the given data three attributes are :
$(1)$ Year $: 2013, 2014, 2015$
$(2)$ Residence : Hostel, Not in hostel
$(3)$ Sex: Boys, Girls
→In the year $2015, 140$ boys and $100$ girls were newly admitted in the school and all of them resided with the hostel students. Present above data in a tabular form.
In the given data three attributes are :
$(1)$ Year $: 2013, 2014, 2015$
$(2)$ Residence : Hostel, Not in hostel
$(3)$ Sex: Boys, Girls
The information about marks of students from two commerce classes of standard $11$ of a school is as follows. Find the coefficient of skewness by Karl Pearson's and Bowley's method.
→| Weight (kg) | 65 | 60 | 54 | 52 | 50 | 48 | 46 | 45 |
| No. of persons | 2 | 5 | 7 | 8 | 6 | 4 | 5 | 3 |
Discuss advantages and disadvantages of direct inquiry.
The workers in a factory are working in two shifts. Total number of workers is $5000$ . There are $2000$ workers in the first shift. In this shift, among the local workers, the number of male workers is $1200$ and the number of female workers is $300$ . In the second shift, among the local workers, the number of male workers is $2000$ and the number of female workers is $600$ . There are total $1200$ female workers in the factory, of them $500$ female workers are working in the first shift. Present the data in a tabular form.
→The frequency distribution of number of $LED$ bulbs sold in an electric store is given below. Find the coefficient of skewness by Karl Pearson's method.
→| No. of typing errors | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ |
| No. of pages | $10$ | $15$ | $23$ | $9$ | $23$ | $12$ | $8$ |
State the difference between primary and secondary data.
The mean and $S.d$. of $9$ observations are respectively $0$ and $2$. In the calculation, if two observations were taken $- 2$ and $3$, instead of $- 5$ and $4$, then find the true values of mean and $S.d.$
→The monthly income (in thousand $Rs$) of $130$ persons living in a certain area is as follows :
Find the median of income.
→| Income (thousand $Rs)$ | Less than $4$ | $4- 8$ | $8- 12$ | $12 – 20$ | $20 – 28$ | $28 – 36$ |
| No. of Persons | $6$ | $14$ | $31$ | $35$ | $28$ | $16$ |