NDA 2019 Paper 1 | Application of Derivatives Question 32 | Mathematics

A given quantity of metal is to be case into a half cylinder (i.e. with a rectangular base and semicircular ends). If the total surface area is to be minimum, then the ratio of the height of the half cylinder to the diameter of the semicircular ends is

$$\pi$$ : ($$\pi$$ + 2)

($$\pi$$ + 2) : $$\pi$$

1 : 1

None of these

NDA 2019 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

The minimum distance from the point (4, 2) to y² = 8x is equal to

$$\sqrt 2 $$

2$$\sqrt 2 $$

3$$\sqrt 2 $$

NDA 2019 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

What is the minimum value of a²x + b²y where xy = c² ?

abc

2abc

3abc

4abc

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)?

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

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

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

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

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