1
JEE Main 2023 (Online) 15th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let the determinant of a square matrix A of order $m$ be $m-n$, where $m$ and $n$

satisfy $4 m+n=22$ and $17 m+4 n=93$.

If $\operatorname{det}(n \operatorname{adj}(\operatorname{adj}(m A)))=3^{a} 5^{b} 6^{c}$ then $a+b+c$ is equal to :
A
96
B
84
C
109
D
101
2
JEE Main 2023 (Online) 13th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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
3
JEE Main 2023 (Online) 13th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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

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 $$a=b=6$$
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