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

Let the domains of the functions $f(x)=\log _4 \log _3 \log _7\left(8-\log _2\left(x^2+4 x+5\right)\right)$ and $\mathrm{g}(x)=\sin ^{-1}\left(\frac{7 x+10}{x-2}\right)$ be $(\alpha, \beta)$ and $[\gamma, \delta]$, respectively. Then $\alpha^2+\beta^2+\gamma^2+\delta^2$ is equal to :

A
15
B
13
C
16
D
14
2
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
3
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
4
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
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