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 $f(x)$ 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

$6x$

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 $f(x) = |x| + 1$ 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

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 $f(x) = |x| + 1$ 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

$\frac{3}{2}$

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 $\varphi(a) = \int_{a}^{a + 100 \pi} |\sin x| dx$

What is $\varphi(a)$ equal to?

A

0

B

$a$

C

100$a$

D

200

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