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UPSC NDA I 2024 Mathematics Paper

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Consider the following for the next two (02) items that follow :

Let

f(x)=|x|+1

and

g(x)=[x]-1

, where [.] is the greatest integer function.

Let

h(x)=\;\frac{f(x)}{g(x)}

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Question : 87 of 120

Marks: +1, -0

Consider the following statements :

f(x)

is differentiable for all

x < 0

g(x)

is continuous at

x=0.0001

3. The derivative of

g(x)

x=2.5

Which of the statements given above are correct?

1 and 2 only
2 and 3 only
1 and 3 only
1,2 and 3

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