1
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1 Let A be a 3 $$\times$$ 3 invertible matrix. If |adj (24A)| = |adj (3 adj (2A))|, then |A|2 is equal to :

A
66
B
212
C
26
D
1
2
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1 The ordered pair (a, b), for which the system of linear equations

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

5x $$-$$ 8y + 9z = 3

2x + y + az = $$-$$1

has no solution, is :

A
$$\left( {3,{1 \over 3}} \right)$$
B
$$\left( { - 3,{1 \over 3}} \right)$$
C
$$\left( { - 3, - {1 \over 3}} \right)$$
D
$$\left( {3, - {1 \over 3}} \right)$$
3
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1 The system of equations

$$- kx + 3y - 14z = 25$$

$$- 15x + 4y - kz = 3$$

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

is consistent for all k in the set

A
R
B
R $$-$$ {$$-$$11, 13}
C
R $$-$$ {13}
D
R $$-$$ {$$-$$11, 11}
4
JEE Main 2022 (Online) 25th June Morning Shift
+4
-1 Let A be a 3 $$\times$$ 3 real matrix such that

$$A\left( {\matrix{ 1 \cr 1 \cr 0 \cr } } \right) = \left( {\matrix{ 1 \cr 1 \cr 1 \cr } } \right);A\left( {\matrix{ 1 \cr 0 \cr 1 \cr } } \right) = \left( {\matrix{ { - 1} \cr 0 \cr 1 \cr } } \right)$$ and $$A\left( {\matrix{ 0 \cr 0 \cr 1 \cr } } \right) = \left( {\matrix{ 1 \cr 1 \cr 2 \cr } } \right)$$.

If $$X = {({x_1},{x_2},{x_3})^T}$$ and I is an identity matrix of order 3, then the system $$(A - 2I)X = \left( {\matrix{ 4 \cr 1 \cr 1 \cr } } \right)$$ has :

A
no solution
B
infinitely many solutions
C
unique solution
D
exactly two solutions
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