NDA Mathematics 13 April 2025 | Application of Derivatives Question 37 | Mathematics

Consider the following for the two (02) items that follow:
The slope of the tangent to the curve y = f(x) at (x, f(x) ) is 4 for every real number x and the curve passes through the origin.

What is the nature of the curve?

A straight line passing through (1,4)

A straight line passing through (-14)

A parabola with vertex at origin and focus at (2,0)

A parabola with vertex at origin and focus at (1, 0)

NDA Mathematics 13 April 2025

MCQ (Single Correct Answer)

+2.5

-0.833

Consider the following for the two (02) items that follow:
Let the function f(x) = x ² + 9

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)?

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

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

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

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

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