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Question

Which one of the following, drawn on a linear scale, represents the circle shown in the figure above?

Select the CORRECT option 

The correct answer is
A

To determine which graph on a linear scale represents the given circle plotted on a logarithmic scale, we need to understand the transformation from logarithmic to linear scale.

The given graph is plotted in a logarithmic scale as shown below:

In the given image, axes are labeled as \(\log_{10}(X)\) and \(\log_{10}(Y)\). The figure is a circle, which suggests a constant ratio of \(X\) to \(Y\) when transformed.

To convert from log scale to linear scale:

  • If \(P = \log_{10}(X)\), then \(X = 10^P\).
  • If \(Q = \log_{10}(Y)\), then \(Y = 10^Q\).

In a logarithmic plot, a circle implies an equation of form:

\((\log_{10}(X) - a)^2 + (\log_{10}(Y) - b)^2 = r^2\)

Transforming this to a linear scale results in a geometrical figure like a geometric progression or ratio, potentially a distorted circle or ellipse depending on the axis scales.

Now, consider the given options in the linear scale:

Among the options, option A resembles a distorted circle (or ellipse), which aligns well with the transformation behavior from a logarithmic circle. The other shapes (represented in options B, C, and D) do not maintain the circle-like proportion when transformed.

Thus, the correct answer is:

A

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Important Questions from Data Interpetation (Notes)

  1. The population of a town over the years 2000-2007 is shown in the given figure.

    It can be inferred that during 2000-2007,

  2. The areas (in km²) under forests in four countries A, B, C and D for the years 2014 and 2024 are shown in the given bar chart:

    The minimum percentage of deforestation during 2014-2024 was in country

  3. Find the average amount collected from the sales of Bengali dishes, Punjabi dishes and Gujarati dishes.
  4. The amount collected by selling Chinese dishes is approximately what percentage more than the amount collected by selling Bengali dishes?
  5. The number of questions asked in shift I from the topic Profit-Loss is what percent more than the number of questions asked in shift II from the topic Average?
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