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. $f(x)$ is increasing in the interval $(e, \infty)$
2. $f(x)$ is decreasing in the interval $(1, e)$
3. $9 \ln 7 > 7 \ln 9$
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 $f(x) = |x| + 1$ and $g(x) = [x] - 1$, where [.] is the greatest integer function.

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

What is $\lim\limits_{x \to 0-} h(x) + \lim\limits_{x \to 0+} h(x)$ equal to?

A

$-\frac{3}{2}$

B

$-\frac{1}{2}$

C

$\frac{1}{2}$

D

$\frac{3}{2}$

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 $.

What is f(0.5) equal to ?
A
$\frac{1}{2}$
B
$\frac{2}{3}$
C
1
D
2
4
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 $f(x)=\frac{a^{x-1}+b^{x-1}}{2}$ and g(x) = x - 1.

What is $\displaystyle \lim _{x \rightarrow 1} \frac{f(x)-1}{g(x)}$ equal to?
A
$\frac{\ln (\mathrm{ab})}{4}$
B
$\frac{\ln (\mathrm{ab})}{2}$
C
In (ab)
D
In (ab)
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