Inverse Proportionality

Q. If the increase in one quantity, leads to a decrease in other, then the quantities are in _________ .

1. direct proportion
2. inverse proportion
3. direct and inverse proportion
4. None of the above

Q. Number of taps(inlet) required for filling a tank with water and time taken to fill are ______.

1. in inverse proportion.
2. in direct proportion.
3. in continous proportion.
4. not in proportion.

Q.

Question 52

If p and q are in inverse propotion, i.e. pq = k (constant), then (p + 2) and (q - 2) are also in inverse proportion.

Q.

The variables x and y vary inversely, and y = 8 when x = 3. Find the equation of inverse variation between x and y.

1. xy =24

2. y = 24 x

3. x = 24 y

4. xy = 12

Q.

Which of the following are in inverse proportion?

1. The population of a country and the area of land per person.

2. The time taken for a fixed journey and the speed of the vehicle.

3. Area of cultivated land and the crop harvested.

4. The time taken for a journey and the distance travelled in a uniform speed.

Q. A hostel has a provision for 225 students for 40 days. After 15 days, 25 more students join the hostel. How long will the provision last at the same rate?

1. 26.5 days
2. 24.5 days
3. 32.5 days
4. 22.5 days

Q. Ramesh takes 5 seconds to complete the race with speed 20 m/s. Suresh's speed is 5 m/s more than Ramesh, time taken by Suresh to complete same race is

1. 4 seconds
2. 4.5 seconds
3. 2.5 seconds
4. 5 seconds

Q.

If d varies directly as t²., then we can write dt² = k, where k is some constant. State whether the statement is true (T) or false (F).

1. True
2. False

Q.

Are $x$ and $y$ in inverse proportion?

1. Yes

2. No

Q.

Suppose that $y$ varies jointly with $w$ and $x$ and inversely with $z$ and $y=360$ when $w=8$, $x=25$ and $z=5$. How do you write the equation that models the relationship. Then find $y$ when $w=4$, $x=4$ and $z=3$?

Q.

From the below table, which of the following conclusions can be drawn ?

1. $x$ and $y$ are directly proportional

2. $x$ and $y$ are inversely proportional

3. $x$ and $\frac{1}{y}$ are directly proportional

4. All of the these

Q.

In a map, a distance of 10 km on land is equal to $\frac{1}{10}cm$. If two places are $5\frac{1}{2}cm$ apart on the map, then what is the actual distance between them?

1. $\frac{2}{11}km$

2. 50 km

3. 550 km

4. 100 km

Q. Given that x and y are in inverse proportion, and $y_1,y_2$ are values of y corresponding to the values $x_1,x_2$ of x, respectively. Which of the following is correct?

1. $x_1{y}_2=x_2{y}_1$
2. $x_1{y}_1=x_2{y}_2$
3. $x_1{x}_2=y_1{y}_2$
4. $\frac{x_1}{y_1}=\frac{x_2}{y_2}$

Q.

Which of the following are inversely proportional?

1. Driving speed and time

2. Number of people working in a family and the total income of the family

3. Food intake versus weight of the person

4. Depth of oil in a cylinder and the area of the cylinder’s base

Q.
$\mathrm{A\; \alpha \; B}$ such as $\frac{A}{B}=5$ and $\mathrm{P\; \alpha }\frac{1}{Q}$
such as $P\times Q=36$. Match the values accordingly.

1. $P_1=8$
2. $A_1=36.2$
3. $P_2=20$
4. $A_2=23.9$

Q. If $\frac{a}{(a+b)(a+c)}=\frac{1}{a+b+c+d}$ then show that a, b, c, d are in proportion.

Q.

For the data in the table, tell whether $y$ varies directly with $x$.

If it does, write an equation for the direct variation.

$x$	$0$	$1$	$2$	$3$
$y$	$0$	$4$	$8$	$12$

1. No

2. Yes, $y=4x$

3. Yes, $y=0.25x$

4. yes, $y=x+4$

Q. A and B are inversely related and the proportionality constant is 16. Find B if A = 8.

1. 18
2. 14
3. 6
4. 2

Q.

What are real-life examples of inverse proportion?

Q.

If $y$ varies directly with $x$, and if $y=12$ when $x=3$, how do you write the direct variation equation?

Q. If $A_1\times B_1=A_2\times B_2$, then A and B are in proportion and if $\frac{P_1}{Q_1}=\frac{P_2}{Q_2}$, then P and Q are in proportion.

1. direct
2. inverse
3. continued
4. indirect

Q. Match the given length of a rectangle to corresponding breadth so that the area is equal to $72c{m}^2$.

1. 8 cm
2. 4 cm
3. 6 cm
4. 3 cm

Q.

Consider a rectangle of area one square metre. What is the relation between the length and the breadth of the rectangle in terms of proportion?

1. Data insufficient

2. No relation

3. Directly proportional

4. Inversely proportional

Q. Given that x and y are in inverse proportion, and $y_1,y_2$ are values of y corresponding to the values $x_1,x_2$ of x respectively. Which of the following is correct?

1. =

2. x₁y₁=x₂y₂

3. x₁y₂=x₂y₁

4. x₁x₂=y₁y₂

Q. Which of the following statements is/are correct?
1. f(x) is increasing in the interval [-1, 2].
2. f(x) is decreasing in the interval (2, 3].
Select the correct answer using the code given below

1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2

Q. A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?

Q. A and B are in direct proportion, when A increases, B also increases.

1. False
2. True