1
JEE Main 2024 (Online) 6th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The function $$f(x)=\frac{x^2+2 x-15}{x^2-4 x+9}, x \in \mathbb{R}$$ is

A
both one-one and onto.
B
onto but not one-one.
C
neither one-one nor onto.
D
one-one but not onto.
2
JEE Main 2024 (Online) 5th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$f, g: \mathbf{R} \rightarrow \mathbf{R}$$ be defined as :

$$f(x)=|x-1| \text { and } g(x)= \begin{cases}\mathrm{e}^x, & x \geq 0 \\ x+1, & x \leq 0 .\end{cases}$$

Then the function $$f(g(x))$$ is

A
neither one-one nor onto.
B
one-one but not onto.
C
both one-one and onto.
D
onto but not one-one.
3
JEE Main 2024 (Online) 5th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$A=\{1,3,7,9,11\}$$ and $$B=\{2,4,5,7,8,10,12\}$$. Then the total number of one-one maps $$f: A \rightarrow B$$, such that $$f(1)+f(3)=14$$, is :

A
120
B
180
C
240
D
480
4
JEE Main 2024 (Online) 1st February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If the domain of the function

$f(x)=\frac{\sqrt{x^2-25}}{\left(4-x^2\right)}+\log _{10}\left(x^2+2 x-15\right)$ is $(-\infty, \alpha) \cup[\beta, \infty)$, then $\alpha^2+\beta^3$ is equal to :
A
140
B
175
C
125
D
150
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