1
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83

Consider the following for the next two (02) items that follow:

Let $f(x) = \frac{x}{\ln x}; (x > 1)$

Consider the following statements :
1. $f''(e) = \frac{1}{e}$
2. $f(x)$ attains local minimum value at $x = e$
3. A local minimum value of $f(x)$ is $e$
Which of the statements given above are correct ?

A

1 and 2 only

B

2 and 3 only

C

1 and 3 only

D

1, 2 and 3

2
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83

Consider the following for the next two (02) items that follow:

Let $f(x)$ and $g(x)$ be two functions such that $g(x) = x - \frac{1}{x}$ and $f \circ g(x) = x^3 - \frac{1}{x^3}$.

What is $g[f(x) - 3x]$ equal to?

A

$x^3 - \frac{1}{x^3}$

B

$x^3 + \frac{1}{x^3}$

C

$x^2 - \frac{1}{x^2}$

D

$x^2 + \frac{1}{x^2}$

3
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83

Consider the following for the next two (02) items that follow:

Let $f(x)$ and $g(x)$ be two functions such that $g(x) = x - \frac{1}{x}$ and $f \circ g(x) = x^3 - \frac{1}{x^3}$.

What is $f''(x)$ equal to?

A

$\frac{-2}{x^3}$

B

$2x + \frac{2}{x^3}$

C

$6x + 3$

D

$6x$

4
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83

Consider the following for the next two (02) items that follow:

Let $f(x) = |x| + 1$ and $g(x) = [x] - 1$, where [.] is the greatest integer function.

Let $h(x) = \frac{f(x)}{g(x)}$.

Consider the following statements:

1. $f(x)$ is differentiable for all $x < 0$

2. $g(x)$ is continuous at $x = 0.0001$

3. The derivative of $g(x)$ at $x = 2.5$ is 1

Which of the statements given above are correct?

A

1 and 2 only

B

2 and 3 only

C

1 and 3 only

D

1, 2, and 3

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