1
JEE Main 2023 (Online) 13th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$B=\left[\begin{array}{lll}1 & 3 & \alpha \\ 1 & 2 & 3 \\ \alpha & \alpha & 4\end{array}\right], \alpha > 2$$ be the adjoint of a matrix $$A$$ and $$|A|=2$$. Then $$\left[\begin{array}{ccc}\alpha & -2 \alpha & \alpha\end{array}\right] B\left[\begin{array}{c}\alpha \\ -2 \alpha \\ \alpha\end{array}\right]$$ is equal to :

A
32
B
$$-$$16
C
0
D
16
2
JEE Main 2023 (Online) 13th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Fractional part of the number $$\frac{4^{2022}}{15}$$ is equal to

A
$$\frac{8}{15}$$
B
$$\frac{4}{15}$$
C
$$\frac{1}{15}$$
D
$$\frac{14}{15}$$
3
JEE Main 2023 (Online) 13th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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
4
JEE Main 2023 (Online) 13th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

For the differentiable function $$f: \mathbb{R}-\{0\} \rightarrow \mathbb{R}$$, let $$3 f(x)+2 f\left(\frac{1}{x}\right)=\frac{1}{x}-10$$, then $$\left|f(3)+f^{\prime}\left(\frac{1}{4}\right)\right|$$ is equal to

A
13
B
$$\frac{29}{5}$$
C
$$\frac{33}{5}$$
D
7
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