1
JEE Main 2022 (Online) 27th June Morning Shift
+4
-1

Let the system of linear equations
$$x + 2y + z = 2$$,
$$\alpha x + 3y - z = \alpha$$,
$$- \alpha x + y + 2z = - \alpha$$
be inconsistent. Then $$\alpha$$ is equal to :

A
$${5 \over 2}$$
B
$$-$$$${5 \over 2}$$
C
$${7 \over 2}$$
D
$$-$$$${7 \over 2}$$
2
JEE Main 2022 (Online) 26th June Evening Shift
+4
-1

If the system of equations

$$\alpha$$x + y + z = 5, x + 2y + 3z = 4, x + 3y + 5z = $$\beta$$

has infinitely many solutions, then the ordered pair ($$\alpha$$, $$\beta$$) is equal to :

A
(1, $$-$$3)
B
($$-$$1, 3)
C
(1, 3)
D
($$-$$1, $$-$$3)
3
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
4
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
$$\left( {3, - {1 \over 3}} \right)$$
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