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UPSC NDA 2 2016 Mathematics Solved Paper

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Consider the following function for the next two (02) items that follow:
f(x)={

3x2+12x−1	−1≤x≤2
37−x	2<x≤3.

[NDA II 2016]

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Question : 77

Total: 120

Which of the following statements are correct?
1. f(x) is continuous at x=2.
2. f(x) attains greatest value at x=2.
3. f(x) is differentiable at x=2.
Select the correct answer using the code given below:

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

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