1
JEE Main 2023 (Online) 13th April Morning Shift
+4
-1

For $$x \in \mathbb{R}$$, two real valued functions $$f(x)$$ and $$g(x)$$ are such that, $$g(x)=\sqrt{x}+1$$ and $$f \circ g(x)=x+3-\sqrt{x}$$. Then $$f(0)$$ is equal to

A
5
B
0
C
$$-$$3
D
1
2
JEE Main 2023 (Online) 12th April Morning Shift
+4
-1

Let $$\mathrm{D}$$ be the domain of the function $$f(x)=\sin ^{-1}\left(\log _{3 x}\left(\frac{6+2 \log _{3} x}{-5 x}\right)\right)$$. If the range of the function $$\mathrm{g}: \mathrm{D} \rightarrow \mathbb{R}$$ defined by $$\mathrm{g}(x)=x-[x],([x]$$ is the greatest integer function), is $$(\alpha, \beta)$$, then $$\alpha^{2}+\frac{5}{\beta}$$ is equal to

A
45
B
136
C
46
D
nearly 135
3
JEE Main 2023 (Online) 11th April Evening Shift
+4
-1

The domain of the function $$f(x)=\frac{1}{\sqrt{[x]^{2}-3[x]-10}}$$ is : ( where $$[\mathrm{x}]$$ denotes the greatest integer less than or equal to $$x$$ )

A
$$(-\infty,-2) \cup[6, \infty)$$
B
$$(-\infty,-3] \cup[6, \infty)$$
C
$$(-\infty,-2) \cup(5, \infty)$$
D
$$(-\infty,-3] \cup(5, \infty)$$
4
JEE Main 2023 (Online) 10th April Morning Shift
+4
-1

If $$f(x) = {{(\tan 1^\circ )x + {{\log }_e}(123)} \over {x{{\log }_e}(1234) - (\tan 1^\circ )}},x > 0$$, then the least value of $$f(f(x)) + f\left( {f\left( {{4 \over x}} \right)} \right)$$ is :

A
2
B
4
C
0
D
8
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