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A is proportional to B. B is inversely proportional to C. C is proportional to the square of D. D is directly proportional to the cube root of E. Assuming positive integers, if A increases then E
- a)Increases
- b)Decreases
- c)Cannot say
- d)Could increase or decrease
Correct answer is option 'B'. Can you explain this answer?
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Solution:
Given, A is proportional to B, B is inversely proportional to C, C is proportional to the square of D and D is directly proportional to the cube root of E.
Let's assume the proportionality constant for each relation as k.
Therefore,
A ∝ B => A = kB
B ∝ 1/C => B = k/C
C ∝ D² => C = kD²
D ∝ E^(1/3) => D = kE^(1/3)
Substituting the values of B, C and D in terms of A and E, we get:
A = k(kE^(1/3))/C²
Simplifying the equation, we get:
A ∝ E^(1/3)/C²
We can see that A is directly proportional to E^(1/3) and inversely proportional to C².
Now, if A increases, the value of E^(1/3)/C² should decrease. This means that E^(1/3) should decrease or C² should increase.
Since C is proportional to D², if C increases, D also increases.
But D is directly proportional to the cube root of E. So, if D increases, E should also increase.
Hence, if A increases, E should also increase.
Therefore, the correct answer is option (b) Decreases is incorrect and the answer is (a) Increases.
Given, A is proportional to B, B is inversely proportional to C, C is proportional to the square of D and D is directly proportional to the cube root of E.
Let's assume the proportionality constant for each relation as k.
Therefore,
A ∝ B => A = kB
B ∝ 1/C => B = k/C
C ∝ D² => C = kD²
D ∝ E^(1/3) => D = kE^(1/3)
Substituting the values of B, C and D in terms of A and E, we get:
A = k(kE^(1/3))/C²
Simplifying the equation, we get:
A ∝ E^(1/3)/C²
We can see that A is directly proportional to E^(1/3) and inversely proportional to C².
Now, if A increases, the value of E^(1/3)/C² should decrease. This means that E^(1/3) should decrease or C² should increase.
Since C is proportional to D², if C increases, D also increases.
But D is directly proportional to the cube root of E. So, if D increases, E should also increase.
Hence, if A increases, E should also increase.
Therefore, the correct answer is option (b) Decreases is incorrect and the answer is (a) Increases.
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A is proportional to B. B is inversely proportional to C. C is proportional to the square of D. D is directly proportional to the cube root of E. Assuming positive integers, if A increases then Ea)Increasesb)Decreasesc)Cannot sayd)Could increase or decreaseCorrect answer is option 'B'. Can you explain this answer?
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