Question

1.   If ‘x’ and ‘y’ are in an inverse variation then which of the following is correct?

A. x – y = constant

B. x + y = constant

C. xy = constant

D.  above all


2.   If ‘A’ can finish a work in ‘n’ days then part of work finished in 1 day is:

A. 1 – n

B. 1/n

C. n – 1

D. none of these


3.   If an increase in one quantity brings about a corresponding decrease in the other and vice versa, then the two quantities vary:

A. directly

B. inversely

C. sometimes directly and sometimes inversely

D. none of these.


4.   Which of the following is not a case of direct variation?

A. Number of sheets of some kind are incresed when their total weight its increased

B. More quentity of petrol is required to travel more distance with a fixed speed

C. More fees would be collected if number of students increased in a class

D. Time taken will be less if number of workers are increased to complete the same work.


5.   Which of the following is a case of direct variation;

A. If the length of radius is increased the circumference will be increased

B. If number of students is a hostel are increased then the fixed food provision will last for less days

C. For fixed duration, more the periods, lesser will be the duration of one period

D. In case of a cylindrical vessel, lesser the diameter more is the level of water in it.


6. If x = 15 and y = 1/30, then x and y are:

A. Directly proportional

B. Inversely proportional

C. Neither directly nor inversely proportional

D. Cannot be determined


7. If the weight of 12 sheets of thick paper is 40 grams, how many sheets of the same paper would weigh 2500 grams?

A. 750

B. 800

C. 850

D. 950


8. The scale of a map is given as 1:300. Two cities are 4 km apart on the map. The actual distance between them is:

A. 1000 km

B. 1100 km

C. 1200 km

D. 1300 km


9. If two quantities are inversely proportional, then which one is true?

A. x1/y1 = x2/y2

B. x1/x2 = y1/y2

C. x1/x2 = y2/y1

D. x1.x2 = y1.y2


10. 6 pipes are required to fill a tank in 1 hour 20 minutes. If we use 5 such types of pipes, how much time it will take to fill the tank?

A. 120 minutes

B. 96 minutes

C. 80 minutes

D. 85 minutes


11. If two quantities depends on each other in such a way that the change in one results in a corresponding change in the other, then the two quantities are said to be in

A. Direct variation

B. Indirect variation

C. Variation

D. Above all

12. A farmer has enough food to feed 30 animals in his cattle for 4 days, How long would the food last if there were 10 less animals in his farm?

A. 6 days

B. 5 days

C. 8 days

D. 12 days


13. The ratio of girls to boys in a class is 2 : 3. The actual strength of the class is:

A. 12

B.. 15

C. 16

D. 18


14. A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm. What is the actual length of the bacteria, If the photograph is enlarged 20,000 times.

A. 3 cm

B. 4 cm

C. 6 cm

D. 2 cm


15. Both X and y are in direct proportion then
1/x and 1/y are in

A. Direct proportion

B. Inverse proportion

C. Neither in direct nor in inverse proportion

D. None of these


16. Which of the following quantities vary inversely with each other

A. Distance travelled and cab fare

B. Area of land and its cost

C. Number of workers and amount of work done

D. Number of workers and time taken to finish the job


17. Which of them is correct

A. Speed of moving body and distance travelled by it in a particular time vary directly

B. Speed of a mooving body and time taken to cover a particular distance vary inversely with each other

C. Distance travelled and time taken by a mooving body (speed remains constant) vary directly with each other

D. Above all​

Answer 1

Answer:

Step-by-sTEP

OPTION A

Answer 2

Answer:

1) (c) xy = constant

2) (b) $\frac{1}{n}$

3) (b) inversely

4) (d) Time taken will be less if number of workers are increased to complete the same work.

5) (a) If the length of radius is increased the circumference will be increased.

6) (b) Inversely proportional

7) (a) 750

8) (c) 1200 km

9) (c) $\frac{x_{1} }{x_{2} } = \frac{y_{2} }{y_{1} }$

10) (b) 96 minutes

11) (a) direct variation

12 (a) 6 days

13 (b) 15

14 (d) 2 cm

15) (b) Inverse proportion

16) (d) Number of workers and time taken to finish the job

17) (d) Above all

Step-by-step explanation:

1. If ‘x’ and ‘y’ are in an inverse variation then which of the following is correct?

Solution:

In inverse variation of x and y, x and y = constant

In direct variation of x and y, = constant

2. If ‘A’ can finish a work in ‘n’ days then part of work finished in 1 day is

$\frac{1}{n}$ day

3. If an increase in one quantity brings about a corresponding decrease in the other and vice versa, then the two quantities vary inversely.

4. Which of the following is not a case of direct variation?

Time taken will be less if number of workers are increased to complete the same work.

5. Which of the following is a case of direct variation;

If the length of radius is increased the circumference will be increased

6. If x = 15 and y = 1/30, then x and y are:

Solution:

x = 15    y = 1/30

$\frac{1}{15} = \frac{1}{2*30} \\y = \frac{1}{2x}\\ y \alpha \frac{1}{x}$

Therefore, x and y are Inversely proportional

7. If the weight of 12 sheets of thick paper is 40 grams, how many sheets of the same paper would weigh 2500 grams?

Solution:

x be the weight of one sheet.

$12 * x = 40\\\\x = \frac{40}{12} \\\\x = 3.33 grams$

Total weight of sheet = 2500 grams

To find the number of sheet

$Number of Sheet = \frac{2500}{3.33}$

= 750 Sheets

750 sheets of the same paper would weigh 2500 grams.

8. The scale of a map is given as 1:300. Two cities are 4 km apart on the map. The actual distance between them is:

Solution:

Distance of map = x cm

Actual distance = y cm

1 : 300 = x : y

$\frac{1}{300} = \frac{x}{y}$

Given x = 4 km

$\frac{1}{300} = \frac{4}{y}$

y = 4 km × 300

y = 1200 km

The actual distance = 1200 km

9. If two quantities are inversely proportional, then which one is true?

Solution:

$x \alpha \frac{1}{y}\\ x = k \frac{1}{y}\\ xy = k\\x_{1} y_{1} = x_{2}y_{2}\\ \frac{x_{1} }{x_{2} } = \frac{y_{2} }{y_{1} }$

10. 6 pipes are required to fill a tank in 1 hour 20 minutes. If we use 5 such types of pipes, how much time it will take to fill the tank?

Solution:

The time required to fill 6 pipes = 1 hour 20 minutes

1 hour 20 minutes = 80 minutes

Let the number of pipe = 5

The time taken to fill 5 pipes = x

By using inverse proportion:

80 × 6 = (x) × 5

x = 96 minutes

The time taken to fill 5 pipes is 96 minutes

11. If two quantities depends on each other in such a way that the change in one results in a corresponding change in the other, then the two quantities are said to be in

(a) Direct variation

12. A farmer has enough food to feed 30 animals in his cattle for 4 days, How long would the food last if there were 10 less animals in his farm?

Solution:

A farmer have food to feed 30 animals in his cattle for 4 days

To find the food last if there was 10 animals less in his farm

Therefore, the number of animals = 20

30 × 4 = 20 × (x)

x = 6 days

The food last if there were 10 less animals in his farm is 6 days

13. The ratio of girls to boys in a class is 2 : 3. The actual strength of the class is:

Solution:

The ratio given = 2 : 3

The total number of students should be multiple of 5(2+3)

In the answers given, only 15 is the multiple of 5

Answer = (b) 15

14. A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm. What is the actual length of the bacteria, If the photograph is enlarged 20,000 times.

Solution:

A bacteria enlarged 50,000 times attains a length of 5 .

To find the actual length of the bacteria, If the photograph is enlarged 20,000 times.

$\frac{5}{50000} = \frac{x}{20000}$

x = 2 cm

Therefore, the enlarged length = 2 cm

15. Both X and y are in direct proportion then 1/x and 1/y are in

(b) Inverse proportion

16. Which of the following quantities vary inversely with each other

Number of workers and time taken to finish the job

If more number of workers are there to do the work therefore it will take less time to complete. It is inversely proportional to each other.

17. Which of them is correct ?

$Speed = \frac{Distance}{Time}$

Speed is inversely proportional to time.

Distance is directly proportional to speed

Speed is inversely to time

Therefore, all the above statement is true.

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