Two quantities $x$ and $y$ are said to vary directly with each other if for some rational number $k$ , $x y = k$ . State whether the statement is true (T) or false (F).

True

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False

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Solution

The correct option is B False
Direct Proportion
Two quantities a and b are said to be in direct proportion if they increase or decrease together. In other words, the ratio of their corresponding values remains constant. This means that,
$\frac{a}{b} = k$
where $k$ is a positive number, then the quantities $a$ and $b$ are said to vary directly.
In such a case if the values $b_{1}, b_{2}$ of $b$ corresponding to the values $a_{1}, a_{2}$ of $a$ , respectively then it becomes;
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}}$
The direct proportion is also known as direct variation.
Two quantities $x$ and $y$ are said to vary directly with each other if for some rational number $k$ , $x y = k$ is false.
In direct proportion, $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}}$
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = k$
Hence, the statement is false.

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Question 43

Two quantities x and y are said to vary directly with each other if for some rational number k, xy =k.

Q. Fill in the blanks in each of the following so as to make the statement true:
(i) Two quantities are said to vary.... with each other if they increase (decrease) together in such a way that the ratio of the corresponding values remains same.
(ii) x and y are said to vary directly with each other if for some positive number k,...... = k.
(iii) If u = 3 v, then u and v vary .... with each other.

Question 21

Both x and y are said to vary___with each other, if for some positive number k, xy=k.

Fill in the blanks in each of the following so as to make the statement true.
(i) Two quantities are said to vary ___ with each other if they increase (decrease) together in such a way that the ratio of the corresponding values remains same.
(ii) x and y are said to vary directy with each other if for some positive number k,___ = k.
(iii) If u= 3 v, then u and v vary___ with each other.

Question 43

Two quantities x and y are said to vary directly with each other if for some rational number k, xy =k.

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Two quantities x and y are said to vary directly with each other if for some rational number k, xy=k. State whether the statement is true (T) or false (F).

Two quantities $x$ and $y$ are said to vary directly with each other if for some rational number $k$ , $x y = k$ . State whether the statement is true (T) or false (F).