1
JEE Main 2023 (Online) 13th April Evening Shift
+4
-1
Out of Syllabus

Let for $$A = \left[ {\matrix{ 1 & 2 & 3 \cr \alpha & 3 & 1 \cr 1 & 1 & 2 \cr } } \right],|A| = 2$$. If $$\mathrm{|2\,adj\,(2\,adj\,(2A))| = {32^n}}$$, then $$3n + \alpha$$ is equal to

A
11
B
9
C
12
D
10
2
JEE Main 2023 (Online) 13th April Evening Shift
+4
-1

If the system of equations

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

$$2 x-5 y+\lambda z=\mu$$

$$x+2 y-5 z=7$$

has infinitely many solutions, then $$(\lambda+\mu)^{2}+(\lambda-\mu)^{2}$$ is equal to

A
916
B
912
C
920
D
904
3
JEE Main 2023 (Online) 13th April Morning Shift
+4
-1

For the system of linear equations

$$2 x+4 y+2 a z=b$$

$$x+2 y+3 z=4$$

$$2 x-5 y+2 z=8$$

which of the following is NOT correct?

A
It has infinitely many solutions if $$a=3, b=8$$
B
It has infinitely many solutions if $$a=3, b=6$$
C
It has unique solution if $$a=b=8$$
D
It has unique solution if $$a=b=6$$
4
JEE Main 2023 (Online) 13th April Morning Shift
+4
-1

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
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