X and Y are two variables whose values at any time are related to each other as shown in Fig. (i). X is known to vary periodically with reference to time as shown in Fig. (ii). Which of the following curves depicts correctly the dependence of Y on time?

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Q: 147 (IAS/1995)
X and Y are two variables whose values at any time are related to each other as shown in Fig. (i). X is known to vary periodically with reference to time as shown in Fig. (ii).
Which of the following curves depicts correctly the dependence of Y on time?

question_subject: 

Logic/Reasoning

question_exam: 

IAS

stats: 

0,6,6,3,1,6,2

keywords: 

{'curves': [0, 1, 0, 0], 'dependence': [0, 1, 0, 2], 'variables': [0, 1, 1, 1], 'time': [2, 6, 15, 23], 'iv': [6, 110, 77, 8], 'values': [0, 2, 1, 3]}

The question is asking us to understand how the variables X and Y are related at any given time, as shown in Fig. (i), and to figure out how Y varies over time, based on the given periodic variation of X over time in Fig. (ii).

Option 1: This cannot be our choice because it shows a constant Y value over time which is not in line with the described relation.

Option 2: This might be tempting but it incorrectly predicts a symmetrical change in Y`s value over time, which would imply X and Y are directly proportional, which is not given.

Option 3: This is the correct option because it accurately represents how a change in X`s value influences Y`s value over time, acknowledging the relationship shown in Fig. (i). As X periodically increases and decreases, Y correspondingly oscillates around a particular value, but not symmetrically.

Option 4: This shows an inversely proportional relationship between Y and X, which doesn`t align with the described relationship between the two variables.

So, knowing the relationship between X and Y, along with X`s variation over time, allows us to predict the variation of Y over time, leading us to correctly choose option 3.