1 Marks Question

Question 11 Mark

Which of the following quantities vary inversely as other$?$ The length $x$ of a journey by bus and price $y$ of the ticket.

Answer

If the length of a journey is more, the price of the ticket will also be more. Therefore, it is not in inverse variation.

View full question & answer→

Question 21 Mark

Fill in the blanks in the following so as to make the statement true: 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.

Answer

Two quantities are said to vary directly with each other if they increase (decrease) together in such a way that the ratio of the corresponding values remains same.

View full question & answer→

Question 31 Mark

Which of the following quantities vary directly with other$?$ Distance $x$ and time $y,$ speed remaining the same.

Answer

Speed is constant. Therefore, distance and time does not vary directly.

View full question & answer→

Question 41 Mark

Which of the following quantities vary inversely as other? Journey $(x\ km)$ undertaken by a car and the petrol $(y$ litres$)$ consumed by it.

Answer

If the length of the journey is more, the amount of petrol consumed by the car will also be more. Therefore, it is not in inverse variation.

View full question & answer→

Question 51 Mark

In which of the following tables $x$ and $y$ vary directly$?$

$a$	$1^2$	$2^2$	$3^2$	$4^2$	$5^2$
$b$	$1^3$	$2^3$	$3^3$	$4^3$	$5^3$

Answer

If $x$ and $y$ vary directly, the ratio of the corresponding values of $x$ and $y$ remains constant.
$\frac{\text{x}}{\text{y}}=\frac{1^{2}}{1^{3}}=1$
$\frac{\text{x}}{\text{y}}=\frac{2^{2}}{2^{3}}=\frac{1}{2}$
$\frac{\text{x}}{\text{y}}=\frac{3^{2}}{3^{3}}=\frac{1}{3}$
$\frac{\text{x}}{\text{y}}=\frac{4^{2}}{4^{3}}=\frac{1}{4}$
$\frac{\text{x}}{\text{y}}=\frac{5^{2}}{5^{3}}=\frac{1}{5}$In all the cases, the ratio is not the same. Therefore, $x$ and $y$ do not vary directly. Thus, in $(i)$ and $(ii), x$ and $y$ vary directly.

View full question & answer→

Question 61 Mark

In which of the following tables $x$ and $y$ vary directly$?$

$a$	$7$	$9$	$13$	$21$	$25$
$b$	$21$	$27$	$39$	$63$	$75$

Answer

If $x$ and $y$ vary directly, the ratio of the corresponding values of $x$ and $y$ remains constant.
$\frac{\text{x}}{\text{y}}=\frac{7}{21}=\frac{1}{3}$
$\frac{\text{x}}{\text{y}}=\frac{9}{27}=\frac{1}{3}$
$\frac{\text{x}}{\text{y}}=\frac{13}{39}=\frac{1}{3}$
$\frac{\text{x}}{\text{y}}=\frac{21}{63}=\frac{1}{3}$
$\frac{\text{x}}{\text{y}}=\frac{25}{75}=\frac{1}{3}$
In all the cases, the ratio is the same. Therefore, $x$ and $y$ vary directly.

View full question & answer→

Question 71 Mark

Which of the following quantities vary directly with other?Wages $(y)$ and number of hours $(x)$ of work.

Answer

The number of hours is directly related to the wages. Therefore, it is a direct variation.

View full question & answer→

Question 81 Mark

Which of the following quantities vary inversely as other$?$ The number of $x$ men hired to construct a wall and the time $y$ taken to finish the job.

Answer

If the number of men is more, the time taken to construct a wall will be less. Therefore, it is in inverse variation. Thus, only $(i)$ is in inverse variation.

View full question & answer→

Question 91 Mark

Which of the following quantities vary directly with other$?$ Weight of articles $(x)$ and their cost $(y).$

Answer

The number of articles is directly related to the weight of the articles. Therefore, they will vary directly with each other.

View full question & answer→

Question 101 Mark

Which of the following quantities vary directly with other$?$ Area of a land $(x)$ and its cost $(y).$

Answer

If the area of a land is large, its cost will also be high. Thus, it is a direct variation. Thus, the respective values in $(i), (ii), (iv)$ and $(vi)$ vary directly with each other.

View full question & answer→

Question 111 Mark

Which of the following quantities vary directly with other$?$ Number of articles $(x)$ and their price $(y).$

Answer

The number of articles is directly related to the price. Therefore, they will vary directly with each other.

View full question & answer→

Question 121 Mark

Fill in the blanks in the following so as to make the statement true: If $u = 3 v,$ then $u$ and $v$ vary _________ with each other.

Answer

because $u = 3v, u$ and $y$ vary directly with each other.

View full question & answer→

Question 131 Mark

Which of the following quantities vary directly with other? Speed $(x)$ and time $(y)$ (distance covered remaining the same).

Answer

Distance is constant. Therefore, speed and time does not vary directly.

View full question & answer→

Question 141 Mark

In which of the following tables $x$ and $y$ vary directly$?$

$a$	$2$	$3$	$4$	$5$	$6$
$b$	$6$	$9$	$12$	$17$	$20$

Answer

If $x$ and $y$ vary directly, the ratio of the corresponding values of $x$ and $y$ remains constant.
$\frac{\text{x}}{\text{y}}=\frac{2}{6}=\frac{1}{3}$
$\frac{\text{x}}{\text{y}}=\frac{3}{9}=\frac{1}{3}$
$\frac{\text{x}}{\text{y}}=\frac{4}{12}=\frac{1}{3}$
$\frac{\text{x}}{\text{y}}=\frac{5}{17}=\frac{5}{17}$
$\frac{\text{x}}{\text{y}}=\frac{6}{20}=\frac{3}{10}$ In all the cases, the ratio is not the same.
Therefore, $x$ and $y$ do not vary directly.

View full question & answer→

Question 151 Mark

In which of the following tables $x$ and $y$ vary directly$?$

$a$	$10$	$20$	$30$	$40$	$46$
$b$	$5$	$10$	$15$	$20$	$23$

Answer

If $x$ and $y$ vary directly, the ratio of the corresponding values of $x$ and $y$ remains constant.
$\frac{\text{x}}{\text{y}}=\frac{10}{5}=2$
$\frac{\text{x}}{\text{y}}=\frac{20}{10}=2$
$\frac{\text{x}}{\text{y}}=\frac{30}{15}=2$
$\frac{\text{x}}{\text{y}}=\frac{40}{20}=2$
$\frac{\text{x}}{\text{y}}=\frac{46}{23}=2$
In all the cases, the ratio is the same. Therefore, $x$ and $y$ vary directly.

View full question & answer→

Question 161 Mark

Fill in the blanks in the following so as to make the statement true:
$x$ and $y$ are said to vary directly with each other if for some positive number $k$ ________$ = k.$

Answer

$x$ and $y$ are said to vary directly with each other if $\frac{\text{x}}{\text{y}}=\text{k},$ where $k$ is a positive number.

View full question & answer→

Question 171 Mark

Which of the following quantities vary inversely as other?
The number of x men hired to construct a wall and the time y taken to finish the job.

Answer

If the number of men is more, the time taken to construct a wall will be less. Therefore, it is in inverse variation.
Thus, only (i) is in inverse variation.

View full question & answer→

Question 181 Mark

Which of the following quantities vary inversely as other?
The length x of a journey by bus and price y of the ticket.

Answer

If the length of a journey is more, the price of the ticket will also be more. Therefore, it is not in inverse variation.

View full question & answer→

Question 191 Mark

Which of the following quantities vary inversely as other?
Journey (x km) undertaken by a car and the petrol (y litres) consumed by it.

Answer

If the length of the journey is more, the amount of petrol consumed by the car will also be more. Therefore, it is not in inverse variation.

View full question & answer→

Question 201 Mark

Which of the following quantities vary directly with other?
Weight of articles (x) and their cost (y).

Answer

The number of articles is directly related to the weight of the articles. Therefore, they will vary directly with each other.

View full question & answer→

Question 211 Mark

Which of the following quantities vary directly with other?
Wages (y) and number of hours (x) of work.

Answer

The number of hours is directly related to the wages. Therefore, it is a direct variation.

View full question & answer→

Question 221 Mark

Which of the following quantities vary directly with other?
Speed (x) and time (y) (distance covered remaining the same).

Answer

Distance is constant. Therefore, speed and time does not vary directly.

View full question & answer→

Question 231 Mark

Which of the following quantities vary directly with other?
Number of articles (x) and their price (y).

Answer

The number of articles is directly related to the price. Therefore, they will vary directly with each other.

View full question & answer→

Question 241 Mark

Which of the following quantities vary directly with other?
Distance x and time y, speed remaining the same.

Answer

Speed is constant. Therefore, distance and time does not vary directly.

View full question & answer→

Question 251 Mark

Which of the following quantities vary directly with other?
Area of a land (x) and its cost (y).

Answer

If the area of a land is large, its cost will also be high. Thus, it is a direct variation.
Thus, the respective values in (i), (ii), (iv) and (vi) vary directly with each other.

View full question & answer→

Question 261 Mark

In which of the following tables x and y vary directly?

a	7	9	13	21	25
b	21	27	39	63	75

Answer

If x and y vary directly, the ratio of the corresponding values of x and y remains constant.
$\frac{\text{x}}{\text{y}}=\frac{7}{21}=\frac{1}{3}$
$\frac{\text{x}}{\text{y}}=\frac{9}{27}=\frac{1}{3}$
$\frac{\text{x}}{\text{y}}=\frac{13}{39}=\frac{1}{3}$
$\frac{\text{x}}{\text{y}}=\frac{21}{63}=\frac{1}{3}$
$\frac{\text{x}}{\text{y}}=\frac{25}{75}=\frac{1}{3}$
In all the cases, the ratio is the same. Therefore, x and y vary directly.

View full question & answer→

Question 271 Mark

In which of the following tables x and y vary directly?

a	2	3	4	5	6
b	6	9	12	17	20

Answer

If x and y vary directly, the ratio of the corresponding values of x and y remains constant.
$\frac{\text{x}}{\text{y}}=\frac{2}{6}=\frac{1}{3}$
$\frac{\text{x}}{\text{y}}=\frac{3}{9}=\frac{1}{3}$
$\frac{\text{x}}{\text{y}}=\frac{4}{12}=\frac{1}{3}$
$\frac{\text{x}}{\text{y}}=\frac{5}{17}=\frac{5}{17}$
$\frac{\text{x}}{\text{y}}=\frac{6}{20}=\frac{3}{10}$
In all the cases, the ratio is not the same. Therefore, x and y do not vary directly.

View full question & answer→

Question 281 Mark

In which of the following tables x and y vary directly?

a	1²	2²	3²	4²	5²
b	1³	2³	3³	4³	5³

Answer

If x and y vary directly, the ratio of the corresponding values of x and y remains constant.
$\frac{\text{x}}{\text{y}}=\frac{1^{2}}{1^{3}}=1$
$\frac{\text{x}}{\text{y}}=\frac{2^{2}}{2^{3}}=\frac{1}{2}$
$\frac{\text{x}}{\text{y}}=\frac{3^{2}}{3^{3}}=\frac{1}{3}$
$\frac{\text{x}}{\text{y}}=\frac{4^{2}}{4^{3}}=\frac{1}{4}$
$\frac{\text{x}}{\text{y}}=\frac{5^{2}}{5^{3}}=\frac{1}{5}$
In all the cases, the ratio is not the same.
Therefore, x and y do not vary directly. Thus, in (i) and (ii), x and y vary directly

View full question & answer→

Question 291 Mark

In which of the following tables x and y vary directly?

a	10	20	30	40	46
b	5	10	15	20	23

Answer

If x and y vary directly, the ratio of the corresponding values of x and y remains constant.
$\frac{\text{x}}{\text{y}}=\frac{10}{5}=2$
$\frac{\text{x}}{\text{y}}=\frac{20}{10}=2$
$\frac{\text{x}}{\text{y}}=\frac{30}{15}=2$
$\frac{\text{x}}{\text{y}}=\frac{40}{20}=2$
$\frac{\text{x}}{\text{y}}=\frac{46}{23}=2$
In all the cases, the ratio is the same. Therefore, x and y vary directly.

View full question & answer→

MATHS 1 Marks Question

Test yourself on this topic