1
JEE Main 2025 (Online) 24th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $f(x)=\frac{2^{x+2}+16}{2^{2 x+1}+2^{x+4}+32}$. Then the value of $8\left(f\left(\frac{1}{15}\right)+f\left(\frac{2}{15}\right)+\ldots+f\left(\frac{59}{15}\right)\right)$ is equal to

A
108
B
92
C
118
D
102
2
JEE Main 2025 (Online) 23rd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $f(x)=\log _{\mathrm{e}} x$ and $g(x)=\frac{x^4-2 x^3+3 x^2-2 x+2}{2 x^2-2 x+1}$. Then the domain of $f \circ g$ is

A
$(0, \infty)$
B
$[1, \infty)$
C
$\mathbb{R}$
D
$[0, \infty)$
3
JEE Main 2025 (Online) 22nd January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $\mathrm{A}=\{1,2,3,4\}$ and $\mathrm{B}=\{1,4,9,16\}$. Then the number of many-one functions $f: \mathrm{A} \rightarrow \mathrm{B}$ such that $1 \in f(\mathrm{~A})$ is equal to :

A
151
B
139
C
163
D
127
4
JEE Main 2024 (Online) 9th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the range of the function $$f(x)=\frac{1}{2+\sin 3 x+\cos 3 x}, x \in \mathbb{R}$$ be $$[a, b]$$. If $$\alpha$$ and $$\beta$$ ar respectively the A.M. and the G.M. of $$a$$ and $$b$$, then $$\frac{\alpha}{\beta}$$ is equal to

A
$$\pi$$
B
$$\sqrt{\pi}$$
C
$$\sqrt{2}$$
D
2
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