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Question

The following functions represent the distance (y) of bus stand of 5 cities from their respective center points with respect to time taken (x).

Function for City 1: y=2x+3

Function for City 2: y=2x3+3

Function for City 3: y=3x23

Function for City 4: Between x = 0 and x = 5,
slope = 4. After x = 5,
slope keeps increasing.

Function for City 5: Between x = 0 and x = 6,
slope = 2.5. For all values of
x 7, slope = 2.5

How many functions of the given ones are linear?

A
2
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B
3
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C
4
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D
5
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Solution

The correct option is B 3
For a function to be linear, the higest power (degree) of both the variables should be unity.

Let us consider function for City 1:

y=2x+3

Both the variables have power equal to 1. So, it is a linear function.

Let us consider function for City 2:

y=2x3+3

Both the variables have power equal to 1. So, it is a linear function.

Let us consider function for City 3:

y=3x23

Power of x is 2 here. So, it is not a linear function.



Let us consider function for City 4:

For a function to be linear, its slope should be constant. In this function, for x = 0 to x = 5, slope = 4. But, slope keeps increasing after x = 5. So, it is not a linear function.

Let us consider function for City 5:

For x = 0 to x = 6, slope = 2.5. For a function to be linear, the slope should be constant. For x ≥ 7, slope is constant. So, it is a linear function.

So, in total functions for City 1, 2, and 5 are linear ones.

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