Variables Changing That Are Not in Proportion

Q.

Question 4

The number of teeth and the age of a person vary
(a) directly with each other
(b) inversely with each other
(c) neither directly nor inversely with each other
(d) sometimes directly and sometimes inversely with each other

Q. The relation between $x$ and $y$ is $y=2x+3$.

Here $y$ varies _______.

1. Not in proportion with $x$
2. Directly with $x$
3. inversely with $x$
4. (a) and (b) above.

Q. In the equation $a(b+a)=10$, $a$ is _____

1. Directly proportional to $b$
2. Inversely proportional to $b$
3. Not proportional to $b$
4. (b) and (c) above.

Q.

What is the constant of proportionality in the equation $\mathrm{y}=2.5\mathrm{x}$?

Q.

$\text{In the equation}x(y+4)=1,y\text{is}$

1. Directly proportional to x

2. Not proportional to x
3. Inversely proportional to x
4. Can't say

Q.

Question 48

​​​​​​​Sate weather the given statement is true or false.

If d varies directly as $t^2$, then we can write $d{t}^2=k,$ where k is some constant.

Q. In which of the following relation, $y$ not varies proportionally with $x$ ?

1. $x=12y$
2. $\frac{x}{y}=8$
3. $\frac{5}{x}=y$
4. $x(y+4)=7$

Q. In which of the following relation, $x$ and $y$ are not in proportion?

1. $xy=12$
2. $\frac{x}{y}=3$
3. $y=x+6$
4. $\frac{x}{y}=\frac{1}{2}$

Q.

Suppose $y$ varies directly with $x\text{and}y=72\text{when}x=6.$ What direct variation equation relates $x$ and $y$? What is the value of $y$ when$x=10$

1. $y=\frac{1}{12}x;120$

2. $y=12x;120$

3. $y=6x;62$

4. $y=\frac{1}{6}x;43.2$

Q. The quantities x and y are inversely related and the constant of proportionality is 8. Find y if x = 4.

1. 4
2. 2
3. 5
4. 1

Q.

In the equation y = x + 3, y is directly proportional to x.

1. True

2. False

Q. If X and Y are inversely related, then which of the following is correct?

1. X+Y=Constant
2. X-Y=Constant
3. XxY=Constant
4. X/Y=Constant

Q. If two quantities x and y are given to be inversely related, then what is the constant of proportionality?

1. x - y
2. x + y
3. x
4. x × y

Q.

$\text{In the equation}x(y+4)=1,y\text{is}$

1. Not proportional to x

2. Inversely proportional to x

3. Can't say

4. Directly proportional to x

Q.

Determine the type of proportionality between variables x and y in the equation y = $x^2$ - 2.

1. Inversely proportional

2. Both directly and inversely

3. Neither directly nor inversely

4. Directly proportional

Q.

In the equation, y = 4$x$, x and y are in inverse proportion.

1. True

2. False

Q. The number of pipes used to fill a drum will be inversely proportional to the time taken to fill the drum.

1. True
2. False

Q.

State true or false. In the equation t = a - 5, the variable t is directly proportional to variable a.

1. False

2. True

Q. The variable $x$ is inversely proportion to $y$. If $x$ increases by $p\%$, then by what per cent will $y$ decrease?

Q. The quantities x and y are inversely related and the constant of proportionality is 8. Find y if x = 4.

1. 4
2. 2
3. 5
4. 1

Q.

Question 46

Length of a side of a square and its area vary directly with each other.

Q.

$\text{In the equation}x(y+4)=1,y\text{is}$

1. Directly proportional to x

2. Not proportional to x
3. Inversely proportional to x
4. Can't say

Q. Find the value of $z$ in the given equation:
$\frac{z}{6}\left(\frac{3}{2}\right)-7=-2(3z-4)$.

1. $-\frac{12}{5}$
2. $-\frac{4}{25}$
3. $\frac{4}{25}$
4. $\frac{12}{5}$

Q. It is given that $l$ varies directly as $m$.
(i) Write an equation which relates $l$ and $m$.
(ii) Find the constant of proportion (k), when $l$ is $6$, then $m$ is $18$.
(iii) Find $l$, when $m$ is $33$.( take constant of proportion as 1/3)
(iv) Find $m$, when $l$ is $8$.
[3 marks]

Q. The number of pipes used to fill a drum will be inversely proportional to the time taken to fill the drum.

1. True
2. False

Q.

In the equation y = x + 3, y is directly proportional to x.

1. True

2. False

Q.

$\text{In the equation}x(y+4)=1,y\text{is}$

1. Directly proportional to x

2. Not proportional to x
3. Inversely proportional to x
4. Can't say