1
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1 If the system of linear equations.

$$8x + y + 4z = - 2$$

$$x + y + z = 0$$

$$\lambda x - 3y = \mu$$

has infinitely many solutions, then the distance of the point $$\left( {\lambda ,\mu , - {1 \over 2}} \right)$$ from the plane $$8x + y + 4z + 2 = 0$$ is :

A
$$3\sqrt 5$$
B
4
C
$${{26} \over 9}$$
D
$${{10} \over 3}$$
2
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1 Let A be a 2 $$\times$$ 2 matrix with det (A) = $$-$$ 1 and det ((A + I) (Adj (A) + I)) = 4. Then the sum of the diagonal elements of A can be :

A
$$-$$1
B
2
C
1
D
$$- \sqrt2$$
3
JEE Main 2022 (Online) 25th July Evening Shift
+4
-1 The number of real values of $$\lambda$$, such that the system of linear equations

2x $$-$$ 3y + 5z = 9

x + 3y $$-$$ z = $$-$$18

3x $$-$$ y + ($$\lambda$$2 $$-$$ | $$\lambda$$ |)z = 16

has no solutions, is

A
0
B
1
C
2
D
4
4
JEE Main 2022 (Online) 25th July Morning Shift
+4
-1 The number of $$\theta \in(0,4 \pi)$$ for which the system of linear equations

\begin{aligned} &3(\sin 3 \theta) x-y+z=2 \\ &3(\cos 2 \theta) x+4 y+3 z=3 \\ &6 x+7 y+7 z=9 \end{aligned}

has no solution, is :

A
6
B
7
C
8
D
9
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