Inverse Variations

Q. A map is given with a scale of $2$ cm $=1,000$ km. What is the actual distance between the two places in km, if the distance in the map is $2.5$ cm?

Q. If y is inversely proportional to cube of x, and $x=5$ when $y=1$, find the value of $y$, when $x=3$

1. $\frac{125}{27}$
2. $\frac{125}{3}$
3. $\frac{5}{27}$
4. $\frac{5}{3}$

Q. If $y$ varies inversely as the square of $x$, and $x=4$ when $y=3$, then value of $y$, when $x=2$ is .

1. $12$
2. $8$
3. $6$

Q.

In an experiment with a sonometer, a tuning fork of frequency $256\mathrm{Hz}$ resonates with a length of $25\mathrm{cm}$ and another tuning fork resonates with a length of $16\mathrm{cm}$. The tension of the string remains constant. The frequency of the second tuning fork is

1. $163.84\mathrm{Hz}$

2. $400\mathrm{Hz}$

3. $320\mathrm{Hz}$

4. $204.8\mathrm{Hz}$

Q. Which of the following is true for $X\propto \frac{1}{Y}$

1. $X=\frac{Y}{k}$, where k = constant
2. $X\times Y=k$, where k = constant
3. $X=\frac{Y}{k}$, where k = Variable
4. $X\times Y=k$, where k = Variable

Q.

If the cost of $10kg$ of wheat is $Rs170.50$, then :

Cost of $8kg$ of wheat will be $Rs\_\_\_\_$

Q. When one quantity decreases as another increases, they are said to be inversely proportional.

1. True
2. False

Q. The time taken to cover a certain distance increases as the speed increases.

1. True
2. False

Q. An empty tank is filled using 5 pipes in 60 minutes. How many more same type of pipes are needed if the tank is to be filled in 30 minutes?

1. 5
2. 7.5
3. 10
4. 12

Q. A pond is dug in 4 days and requires 12 men. If there is an inverse relationship between the number of men required to dig a well and the number of days, calculate the number of men required to dig the well in 1 day.

1. 12
2. 48
3. 36
4. 49

Q. The frequency of a vibrating guitar string and its length have an inverse relationship. If a guitar string, 0.65 m long, vibrates four times per second, then the frequency of a string of length 0.5 metres is times per second.

Q. The cost of producing a chocobar varies inversely with the number of chocobars produced. If 400 chocobars are produced, then the cost is $\$2$ each. If 1600 chocobars are produced, then the cost(in cents) of one bar is .

Q.

Sophia planned on distributing 5 candies each to 20 of her classmates on her birthday, upon arrival to class she discovered 5 more of her classmates present than she had anticipated. If each of the classmates should get equal number of candies, then each will get

candies.

Q. Two brothers John and Robert started from school to reach their home through the same path. John started running at 5 km/hr and reached home in 1 hr. If Robert was running at 6 km/hr, by how much time John arrived late than Robert?

1. $\frac{1}{6}$ hr
2. $\frac{5}{6}$ hr
3. $\frac{7}{6}$ hr
4. $\frac{6}{5}$ hr

Q. In a class, number of desk and number of students are tabulated as follows: Number of desks Number of students

10	15	20
20	30	40

Find the proportional number of desk for 50 students.

1. 50
2. 25
3. 21
4. 30

Q. Which of the following follows indirect variations between X and Y?

1. X	3	4	5	6
   Y	20	15	12	10

2. X	9	6	3	2
   Y	10	15	30	45

3. X	2	4	6	8
   Y	12	6	4	3

4. X	2	4	5	6
   Y	50	25	20	25

Q. A quantity $y$ varies inversly with $x$ and if $y=8$, $x=5$, then for $x=10$, the value of $y=$

1. 3
2. 4
3. 5

Q.

If$x,y$ and $z$ are in proportion, then

1. $x^2=yz$

2. $y^2=xz$

3. $z^2=xy$

4. $x=y=z$

Q. The length, $l$, of an object is inversely proportional to the square of its height, $h$. When the height of that object is 5 units, its length is 4.8 units. What would be the length of the object if its height were reduced by 20% ?

1. $9.5$ units
2. $11.75$ units
3. $7.5$ units