NDA Mathematics 13 April 2025 | Application of Derivatives Question 38 | Mathematics

Consider the following statements:
I. f(x) is an increasing function.
II. f(x) has local maximum at x = 0
Which of the statements given above is/are correct?

I only

II only

Both I and II

Neither I nor II

NDA Mathematics 1st September 2024

MCQ (Single Correct Answer)

+2.5

-0.833

Direction : Consider the following for the items that follow :

Let f(x) = cos2x + x on [-π/2, π/2].

What is the greatest value of f(x)?

$\rm \frac{\sqrt3}{2}-\frac{\pi}{12}$

$\rm \frac{\sqrt3}{2}+\frac{\pi}{12}$

$\rm \frac{\sqrt3}{2}+\frac{\pi}{9}$

$\rm \frac{\sqrt3}{2}+\frac{\pi}{6}$

NDA Mathematics 1st September 2024

MCQ (Single Correct Answer)

+2.5

-0.833

Direction : Consider the following for the items that follow :

Let f(x) = cos2x + x on [-π/2, π/2].

What is the least value of f(x)?

$-\left(1+\frac{\pi}{2}\right)$

$-\left(\frac{1}{2}+\frac{\pi}{2}\right)$

$-\left(1+\frac{\pi}{4}\right)$

$-2\left(\frac{1}{2}-\frac{\pi}{4}\right)$

NDA Mathematics 21 April 2024

MCQ (Single Correct Answer)

+2.5

-0.83

The non-negative values of $b$ for which the function $\frac{16x^3}{3} - 4bx^2 + x$ has neither maximum nor minimum in the range $x>0$ is

0 < b < 1

1 < b < 2

b > 2

0 <= b < 1

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