1
NDA 2016 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Let $$f(x) = \left\{ {\matrix{ {3{x^2} + 12x - 1,} & { - 1 \le x \le 2} \cr {37 - x,} & {2 < x \le 3} \cr } } \right.$$
Which of the following statements is/are correct?

I. f(x) is increasing in the interval {$$-$$1, 2}.

II. f(x) is decreasing in the interval {2, 3}.

Select the correct answer using the code given below.
A
Only I
B
Only II
C
Both I and II
D
Neither I nor II
2
NDA 2016 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Let $$f(x) = \left\{ {\matrix{ {3{x^2} + 12x - 1,} & { - 1 \le x \le 2} \cr {37 - x,} & {2 < x \le 3} \cr } } \right.$$
Which of the following statements are correct?

I. f(x) is continuous at x = 2.

II. f(x) attains greatest value at x = 2.

III. f(x) is differentiable at x = 2.

Select the correct answer using the code given below.
A
I and II
B
II and III
C
I and III
D
I, II and III
3
NDA 2016 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Let $$f(x) = \left\{ {\matrix{ {{{{e^x} - 1} \over x},} & {x > 0} \cr {0,} & {x = 0} \cr } } \right.$$ be a real valued function. Which one of the following statements is correct?
A
f(x) is a strictly decreasing function in (0, x)
B
f(x) is a strictly increasing function in (0, x)
C
f(x) is neither increasing nor decreasing in (0, x)
D
f(x) is not decreasing in (0, x)
4
NDA 2016 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the function $$f(x) = |x - 1| + {x^2}$$, where x$$\in$$R.
Which one of the following statements is correct?
A
f(x) is increasing in $$\left( { - \infty ,{1 \over 2}} \right)$$ and decreasing in $$\left( {{1 \over 2},\infty } \right)$$
B
f(x) is decreasing in $$\left( { - \infty ,{1 \over 2}} \right)$$ and increasing in $$\left( {{1 \over 2},\infty } \right)$$
C
f(x) is increasing in ($$-$$ $$\infty$$, 1) and decreasing in (1, $$\infty$$)
D
f(x) is decreasing in ($$-$$ $$\infty$$, 1) and increasing in (1, $$\infty$$)
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