1
JEE Main 2024 (Online) 29th January Morning Shift
+4
-1

If $$f(x)=\left\{\begin{array}{cc}2+2 x, & -1 \leq x < 0 \\ 1-\frac{x}{3}, & 0 \leq x \leq 3\end{array} ; g(x)=\left\{\begin{array}{cc}-x, & -3 \leq x \leq 0 \\ x, & 0 < x \leq 1\end{array}\right.\right.$$, then range of $$(f o g)(x)$$ is

A
$$[0,1)$$
B
$$[0,3)$$
C
$$(0,1]$$
D
$$[0,1]$$
2
JEE Main 2024 (Online) 27th January Evening Shift
+4
-1

Let $$f: \mathbf{R}-\left\{\frac{-1}{2}\right\} \rightarrow \mathbf{R}$$ and $$g: \mathbf{R}-\left\{\frac{-5}{2}\right\} \rightarrow \mathbf{R}$$ be defined as $$f(x)=\frac{2 x+3}{2 x+1}$$ and $$g(x)=\frac{|x|+1}{2 x+5}$$. Then, the domain of the function fog is :

A
$$\mathbf{R}-\left\{-\frac{7}{4}\right\}$$
B
$$\mathbf{R}$$
C
$$\mathbf{R}-\left\{-\frac{5}{2},-\frac{7}{4}\right\}$$
D
$$\mathbf{R}-\left\{-\frac{5}{2}\right\}$$
3
JEE Main 2024 (Online) 27th January Morning Shift
+4
-1
The function $f: \mathbf{N}-\{1\} \rightarrow \mathbf{N}$; defined by $f(\mathrm{n})=$ the highest prime factor of $\mathrm{n}$, is :
A
one-one only
B
neither one-one nor onto
C
onto only
D
both one-one and onto
4
JEE Main 2023 (Online) 13th April Evening Shift
+4
-1

The range of $$f(x)=4 \sin ^{-1}\left(\frac{x^{2}}{x^{2}+1}\right)$$ is

A
$$[0,2 \pi]$$
B
$$[0,2 \pi)$$
C
$$[0, \pi)$$
D
$$[0, \pi]$$
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