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UPSC NDA I 2014 Mathematics Paper

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For the next three (03) items that follow:
Let f(x) be a function in 1≤x<∞ by

f(x)={

2−x	for	1≤x≤2
3x−x2	for	x>2

[NDA I 2014]

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Question : 99

Total: 120

Consider the following statements :
1. The function is continuous at every point in the interval [1,∞).
2. The function is differentiable at x=1.5. Which of the above statements is/are correct?

1 only
2 only
Both 1 and 2
Neither 1 nor 2

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