1
JEE Main 2024 (Online) 30th January Evening Shift
MCQ (Single Correct Answer)
+4
-1

If the domain of the function $$f(x)=\log _e\left(\frac{2 x+3}{4 x^2+x-3}\right)+\cos ^{-1}\left(\frac{2 x-1}{x+2}\right)$$ is $$(\alpha, \beta]$$, then the value of $$5 \beta-4 \alpha$$ is equal to

A
9
B
12
C
11
D
10
2
JEE Main 2024 (Online) 30th January Morning Shift
MCQ (Single Correct Answer)
+4
-1

If the domain of the function $$f(x)=\cos ^{-1}\left(\frac{2-|x|}{4}\right)+\left\{\log _e(3-x)\right\}^{-1}$$ is $$[-\alpha, \beta)-\{\gamma\}$$, then $$\alpha+\beta+\gamma$$ is equal to :

A
11
B
12
C
9
D
8
3
JEE Main 2024 (Online) 29th January Morning Shift
MCQ (Single Correct Answer)
+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
$$[0,1]$$
4
JEE Main 2024 (Online) 27th January Evening Shift
MCQ (Single Correct Answer)
+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
$$\mathbf{R}-\left\{-\frac{5}{2}\right\}$$
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