Question
Find the Value of the following using binomial expansion: $(\sqrt{2}+\sqrt{3})^{6}+(\sqrt{2}-\sqrt{3})^{6}$
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Answer
$970$
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The students of standard $11$ have collected the data about profits (in crore Rs.) of $IT$ companies.
Find Karl Pearson's coefficient of skewness from these data and interpret it.
→Find Karl Pearson's coefficient of skewness from these data and interpret it.
|
Profit (crore₹)
|
$5-7$ | $7-9$ | $9-11$ | $11-13$ | $13-15$ | $15-17$ |
|
No. of companies
|
$5$ | $12$ | $20$ | $8$ | $3$ | $2$ |
Putting $a=1$ and $b=2$ in the expansion of $\left(\frac{a}{b}-\frac{2 b}{a}\right)^{4}$ verify both the sides.
→The frequency distribution of number of foreign tours of $100$ persons is as follows. Find the coefficient of skewness by Karl Pearson's method.
→| No. of foreign tours | $1$ | $2$ | $3-4$ | $5-8$ | $9--14$ | $15-25$ | $26-50$ |
| No. of persons | $8$ | $12$ | $18$ | $24$ | $18$ | $12$ | $8$ |
The following information is obtained for the time taken (in completed minutes) by each workers to carry out a certain job.
Find Karl Pearson’s coefficient from these data and interpret it.
Find Karl Pearson’s coefficient from these data and interpret it.
| Time taken (completed min.) | $5- 9$ | $10 -14$ | $15 – 19$ | $20 – 24$ | $25 -20$ |
| No. of workers | $3$ | $8$ | $4$ | $2$ | $1$ |
The data on weekly income of $40$ workers of a factory are as follows. Construct an appropriate continuous frequency distribution having $7$ classes.
$290,180,185,264,188,238,220,210,225,198,236,250$, $200,170,195,270,240,205,195,220,235,265,218,232$, $170,220,215,210,285,248,270,245,260,230,185$, $200,210,180,165,240 .$
→$290,180,185,264,188,238,220,210,225,198,236,250$, $200,170,195,270,240,205,195,220,235,265,218,232$, $170,220,215,210,285,248,270,245,260,230,185$, $200,210,180,165,240 .$
The observations of a data are obtained as follows. Prepare a frequency distribution using these data such that class length is $5$ and one of the classes is $30-34$.
$33,35,37,35,34,36,45,42,37,35,34,33,45,46,37,20,21$, $46,44,45,29,27,28,26,54,47,22,33,32,32,41,41,23,31$, $41,23,21,39,23,33,42,41,33,38,36,40,36,38,24,27 .$
→$33,35,37,35,34,36,45,42,37,35,34,33,45,46,37,20,21$, $46,44,45,29,27,28,26,54,47,22,33,32,32,41,41,23,31$, $41,23,21,39,23,33,42,41,33,38,36,40,36,38,24,27 .$
Write a short note on one dimensional diagrams.
Find the Value of the following using binomial expansion: $(1+\sqrt{3})^{7}+(1-\sqrt{3})^{7}$
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