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Maths Solve The Following Question.1MARKS

Direct and Inverse Variations · Maharashtra Board STD 8 (MSBSHSE - Semi English Medium). 16 questions.

Questions

Solve The Following Question.1MARKS

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16 questions · self-marked practice — reveal the answer and mark yourself.

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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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