Direct And Inverse Proportions Test

Result

Direct And Inverse Proportions Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

State 'T' for true and 'F' for false and choose the correct option with the help of the table given below.

(i) If p and q are in inverse proportion, then (p + 1) and (q + 1) are in direct proportion.

(ii) If x and y are in direct proportion, then (x - 2) and (y - 2) are also in direct proportion.

(iii) Two quantities x and y are said to be vary inversely with each other if x/y = k, where k is a positive constant.

(iv) When distance is kept fixed, then speed varies inversely with time.

(i) (ii) (iii) (iv)

A F F F T

B T T F F

C T T T F

D F F T T

A
A

B
B

C
C

D
D

Solution

(i) If p and q are in inverse proportion, then (p + 1) and (q + 1) are in direct proportion.

⇒ This statement is false, because if p and q are in inverse proportion, then we cannot say anything certainly about (p + 1) and (q + 1) whether they are directly proportional or inversely proportional.

(ii) If x and y are in direct proportion, then (x - 2) and (y - 2) are also in direct proportion.

⇒ This statement is false because if x and y are in inverse proportion, then we cannot say anything certainly about (x - 2) and (y - 2) whether they are directly proportional or inversely proportional.

(iii) Two quantities x and y are said to be vary inversely with each other if x/y = k ,where k is a positive constant.

⇒ This statement is false because two quantities x and y are said to vary directly with each other if x/y = k, where k is a positive constant.

(iv) When distance is kept fixed, then speed varies inversely with time.

⇒ This statement is true because Distance = Speed x Time. Thus, if distance remains constant, then time and speed vary inversely.

Question 2

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Fill in the blanks with the help of the table given below.

(i) The area and the length of a rectangle vary ___A____ with each other.
(ii) If two quantities x and y vary directly with each other, then the ___B____ of their corresponding value remains constant.
(iii) Given p and q are in direct proportion, if p is doubled, then the value of q will be ____C_____.

	A	B	C
P	directly	ratio	doubled
Q	inversely	product	halved
R	directly	product	doubled
S	inversely	ratio	halved

S

R

Q

P

Solution

(i) The area and the length of a rectangle vary ___A____ with each other.
⇒ Area of a rectangle = Length × Breadth

So, the area of a rectangle is directly proportional to its length.

(ii) If two quantities x and y vary directly with each other, then the ___B____ of their corresponding value remains constant.

⇒ The ratio of x to y is constant.

If two quantities x and y vary directly with each other, then the ratio of their corresponding value remains constant.

(iii) Given p and q are in direct proportion, if p is doubled, then the value of q will be doubled.

Question 3
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x and y are inversely proportional to each other, and when x = 18, y = 6. Which of the following is not a possible pair of corresponding values of x and y?

A
9 and 5

B
3 and 36

C
27 and 4

D
9 and 12a

Solution

For inverse proportionality,
x₁y₁ = x₂y₂

1) 18 × 6 = 9 × 5
But, 108 ≠ 45

2) 18 × 6 = 3 × 36
108 = 108

3) 18 × 6 = 27 × 4
108 = 108

4) 18 × 6 = 9 × 12
108 = 108