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

If $f(x)=ax-b$ and $g(x)=cx+d$ are such that $f(g(x))=g(f(x))$, then which one of the following holds?

A

$f(d) = g(b)$

B

$f(b)+g(d)=0$

C

$f(a)+g(c)=2a$

D

$f(d)+g(b)=2d$

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

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

A

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

B

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

C

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

D

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

4
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 $h(x) = \frac{f(x)}{g(x)}$.

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

EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12