Question
Expand the following: $\left(\frac{3}{x}-\frac{x}{3}\right)^{6}$
✓
Answer
$\frac{729}{x^{6}}-\frac{486}{x^{4}}+\frac{135}{x^{2}}-20+\frac{\left(5 x^{2}\right)}{3}-\frac{\left(2 x^{4}\right)}{27}+\frac{x^{6}}{729}$
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 and standard deviation of the marks obtained by $100$ students in the test of $60$ marks are $40$ and $5.1$ respectively. Later on, it was known that one of the students scored $40$ Marks of but by mistake it was taken as $50$. Find the correct marks value of the standard deviation of the marks.
→For a geometric progression, the ratio of sum of the fifth and the third term to the difference of the fifth and the third term is $5 : 3.$ Find $r.$
→From the following data state which frequency distribution is close to symmetry.:
Frequency distribution $\mathrm{A}: \bar{x}=40, M=44, S=15$
Frequency distribution $\mathrm{B}: x=40, M=45, s=16$
→Frequency distribution $\mathrm{A}: \bar{x}=40, M=44, S=15$
Frequency distribution $\mathrm{B}: x=40, M=45, s=16$
The data regarding the number of mobile phones produced during last $60$ days by a mobile phone manufacturing company is given below. Distribute it into $10$ classes :
$\text{699 380 625 653 452 763 385 959 485 970 749 595 1029 500 499 453 525 621 465 565 103 785 286 1060 760 355 645 775 825 235 390 399 530 540 695 999 849 550 720 430 752 389 1075 701 875 552 351 265 199 370 1025 825 783 225 603 553 503 663 385 465}$
Obtain “less than’ and “more than’ type cumulative frequency distribution from it.
→$\text{699 380 625 653 452 763 385 959 485 970 749 595 1029 500 499 453 525 621 465 565 103 785 286 1060 760 355 645 775 825 235 390 399 530 540 695 999 849 550 720 430 752 389 1075 701 875 552 351 265 199 370 1025 825 783 225 603 553 503 663 385 465}$
Obtain “less than’ and “more than’ type cumulative frequency distribution from it.
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.
The following information is available on the talk time (in min.) noted for $70$ calls of a certain mobile phone user. Find the mean talk time.
→| Talk time (in min.) | Less than $4$ | Less than $8$ | Less than $12$ | Less than $16$ | Less than $20$ |
| No. of calls | $20$ | $42$ | $57$ | $65$ | $70$ |
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.
A banker counts $128$ notes in the first minute and there after he counts half the number of notes he counted in the previous minute. How many notes he would count in five minutes ?
→A machine is purchased in $Rs. 10,600.$ The depreciation on the machine is calculated at the rate of $10\%$ per annum. What will be the estimated value of the machine at the end of four years?
→A bus operator gets the following number of passengers in $10$ trips on a day. Find the quartile deviation and the coefficient of quartile deviation of number of passengers from the following data :
$19, 25, 35, 10, 24, 8, 12, 5, 20, 30$
→$19, 25, 35, 10, 24, 8, 12, 5, 20, 30$