NDA 2016 Paper 2 | Application of Derivatives Question 10 | Mathematics

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?

f(x) is a strictly decreasing function in (0, x)

f(x) is a strictly increasing function in (0, x)

f(x) is neither increasing nor decreasing in (0, x)

f(x) is not decreasing in (0, x)

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?

f(x) is increasing in $$\left( { - \infty ,{1 \over 2}} \right)$$ and decreasing in $$\left( {{1 \over 2},\infty } \right)$$

f(x) is decreasing in $$\left( { - \infty ,{1 \over 2}} \right)$$ and increasing in $$\left( {{1 \over 2},\infty } \right)$$

f(x) is increasing in ($$-$$ $$\infty$$, 1) and decreasing in (1, $$\infty$$)

f(x) is decreasing in ($$-$$ $$\infty$$, 1) and increasing in (1, $$\infty$$)

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?

f(x) has local minima at more than one point in ($$-$$ $$\infty$$, $$\infty$$)

f(x) has local maxima at more than one point in ($$-$$ $$\infty$$, $$\infty$$)

f(x) has local minima at one point only in ($$-$$ $$\infty$$, $$\infty$$)

f(x) has neither maxima nor minima in ($$-$$ $$\infty$$, $$\infty$$)

NDA 2017 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

Which one of the following is correct in respect of the function

$$f(x) = x(x - 1)(x + 1)$$ ?

The local maximum value is larger than local minimum value

The local maximum value is smaller than local minimum value

The function has no local maximum

The function has no local minimum

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