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

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
Change Language

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

$6x$

3
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the next items that follow:

Let a function f be defined on ℝ - {0} and $\rm 2 f(x)+f\left(\frac{1}{x}\right)=x+3 $.

If f is differentiable, then what is f'(0.5) equal to?
A
$\frac{1}{4}$
B
$\frac{2}{3}$
C
2
D
4
4
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
If f(x) = |ln|x|| where 0 < x < 1, then what is f'(0.5) equal to ?
A
-2
B
-1
C
0
D
2
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