1
JEE Main 2023 (Online) 10th April Morning Shift
+4
-1
Out of Syllabus

If A is a 3 $$\times$$ 3 matrix and $$|A| = 2$$, then $$|3\,adj\,(|3A|{A^2})|$$ is equal to :

A
$${3^{12}}\,.\,{6^{10}}$$
B
$${3^{11}}\,.\,{6^{10}}$$
C
$${3^{12}}\,.\,{6^{11}}$$
D
$${3^{10}}\,.\,{6^{11}}$$
2
JEE Main 2023 (Online) 10th April Morning Shift
+4
-1

For the system of linear equations

$$2x - y + 3z = 5$$

$$3x + 2y - z = 7$$

$$4x + 5y + \alpha z = \beta$$,

which of the following is NOT correct?

A
The system has infinitely many solutions for $$\alpha=-6$$ and $$\beta=9$$
B
The system has a unique solution for $$\alpha$$ $$\ne$$ $$-5$$ and $$\beta=8$$
C
The system is inconsistent for $$\alpha=-5$$ and $$\beta=8$$
D
The system has infinitely many solutions for $$\alpha=-5$$ and $$\beta=9$$
3
JEE Main 2023 (Online) 8th April Evening Shift
+4
-1

If $$A=\left[\begin{array}{cc}1 & 5 \\ \lambda & 10\end{array}\right], \mathrm{A}^{-1}=\alpha \mathrm{A}+\beta \mathrm{I}$$ and $$\alpha+\beta=-2$$, then $$4 \alpha^{2}+\beta^{2}+\lambda^{2}$$ is equal to :

A
12
B
10
C
19
D
14
4
JEE Main 2023 (Online) 8th April Evening Shift
+4
-1

Let S be the set of all values of $$\theta \in[-\pi, \pi]$$ for which the system of linear equations

$$x+y+\sqrt{3} z=0$$

$$-x+(\tan \theta) y+\sqrt{7} z=0$$

$$x+y+(\tan \theta) z=0$$

has non-trivial solution. Then $$\frac{120}{\pi} \sum_\limits{\theta \in \mathrm{s}} \theta$$ is equal to :

A
40
B
30
C
10
D
20
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