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

The non-negative values of $b$ for which the function $\frac{16x^3}{3} - 4bx^2 + x$ has neither maximum nor minimum in the range $x>0$ is

A

0 < b < 1

B

1 < b < 2

C

b > 2

D

0 <= b < 1

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

Which one of the following is correct in respect of $f(x) = \frac{1}{\sqrt{|x| - x}}$ and $g(x) = \frac{1}{\sqrt{x - |x|}}$?

A

$f(x)$ has some domain and $g(x)$ has no domain

B

$f(x)$ has no domain and $g(x)$ has some domain

C

$f(x)$ and $g(x)$ have the same domain

D

$f(x)$ and $g(x)$ do not have any domain

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:

Given that $\int \frac{3 \cos x + 4 \sin x}{2 \cos x + 5 \sin x} dx = \frac{\alpha x}{29} + \frac{\beta}{29} \ln |2 \cos x + 5 \sin x| + c$

What is the value of $\alpha$ ?

A

7

B

13

C

17

D

26

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:

Given that $\int \frac{3 \cos x + 4 \sin x}{2 \cos x + 5 \sin x} dx = \frac{\alpha x}{29} + \frac{\beta}{29} \ln |2 \cos x + 5 \sin x| + c$

What is the value of $\beta$ ?

A

7

B

13

C

17

D

26

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