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
If $S_{n}=8\left[\left(\frac{3}{2}\right)^{n}-1\right]$, find $T_{n+1}$ and hence the value of $T_{2}+T_{3}$.
→There were $1250$ skilled and $400$ unskilled workers in a private company in the year $2011$ . There were $220$ female workers and of them, $140$ were unskilled. In the year $2012$, the number of skilled workers was $1475$ and of them, $1300$ were males. Out of $250$ unskilled workers, $200$ were males. In $2013$, there were $1700$ skilled and $50$ unskilled workers. Out of total workers, $250$ were females of them $240$ were skilled. In the year $2014$ , there were $2000$ workers and of them, $2\%$ were unskilled. Out of total workers, $300$ were females and of them, $10$ were unskilled. Present the above data in the form of table.
→Obtain the value of $(\sqrt{3}+\sqrt{2})^{4}+(\sqrt{3}-\sqrt{2})^{4}$ using binomial expansion method.
→Using all the letters of the word $\text{MAMAJI}$ once, how many words can be formed? If all these words are arranged in the order of dictionary; what will be the rank of the word $\text{‘MAMAJI’}$?
→
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 $x+S$.
→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 $h(x)=2 x+3, x \in \mathrm{B}$
Various measures for the frequency distributions of monthly salaries of two production firms are as follows. Compare the firms using coefficient of skewness by Bowley’s and Karl Pearson’s method :
→| Details | Mean | Median | First quartile | Third quartile | Standard deviation |
| Firm $A$ | $350$ | $344$ | $324$ | $356$ | $26$ |
| Firm $B$ | $360$ | $340$ | $330$ | $370$ | $38$ |
The mean and $S.d.$ of $50$ observations are respectively $30$ and $10$. In the calculation, two observations were taken $7$ and $3$ instead of $- 7$ and $- 9$, find the true values of mean and $S.d.$
→The total cost function for a factory is $y = 10 + 3x$ where $x = No$. of units produced and $y =$ total cost of producing $x$ units. The range, the quartile deviation, the mean deviation and standard deviation of daily production of the factory are $50, 5, 8$ and $10$ units respectively. Find the range quartile deviation mean deviation and standard deviation for total cost y from it.
→