1
JEE Main 2025 (Online) 4th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $f, g:(1, \infty) \rightarrow \mathbb{R}$ be defined as $f(x)=\frac{2 x+3}{5 x+2}$ and $g(x)=\frac{2-3 x}{1-x}$. If the range of the function fog: $[2,4] \rightarrow \mathbb{R}$ is $[\alpha, \beta]$, then $\frac{1}{\beta-\alpha}$ is equal to

A
56
B
2
C
29
D
68
2
JEE Main 2025 (Online) 3rd April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $f$ be a function such that $f(x)+3 f\left(\frac{24}{x}\right)=4 x, x \neq 0$. Then $f(3)+f(8)$ is equal to
A
13
B
11
C
10
D
12
3
JEE Main 2025 (Online) 3rd April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the domain of the function $f(x)=\log _7\left(1-\log _4\left(x^2-9 x+18\right)\right)$ is $(\alpha, \beta) \cup(\gamma, o)$, then $\alpha+\beta+\gamma+\hat{o}$ is equal to

A
17
B
15
C
16
D
18
4
JEE Main 2025 (Online) 3rd April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
$$ \text { If the domain of the function } f(x)=\log _e\left(\frac{2 x-3}{5+4 x}\right)+\sin ^{-1}\left(\frac{4+3 x}{2-x}\right) \text { is }[\alpha, \beta) \text {, then } \alpha^2+4 \beta \text { is equal to } $$
A
4
B
3
C
7
D
5
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