1
JEE Main 2022 (Online) 27th July Evening Shift
+4
-1

Let $$A=\left(\begin{array}{rr}4 & -2 \\ \alpha & \beta\end{array}\right)$$.

If $$\mathrm{A}^{2}+\gamma \mathrm{A}+18 \mathrm{I}=\mathrm{O}$$, then $$\operatorname{det}(\mathrm{A})$$ is equal to _____________.

A
$$-$$18
B
18
C
$$-$$50
D
50
2
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1

Let $$A=\left(\begin{array}{cc}1 & 2 \\ -2 & -5\end{array}\right)$$. Let $$\alpha, \beta \in \mathbb{R}$$ be such that $$\alpha A^{2}+\beta A=2 I$$. Then $$\alpha+\beta$$ is equal to

A
$$-$$10
B
$$-$$6
C
6
D
10
3
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1

$$\text { Let } A=\left[\begin{array}{l} 1 \\ 1 \\ 1 \end{array}\right] \text { and } B=\left[\begin{array}{ccc} 9^{2} & -10^{2} & 11^{2} \\ 12^{2} & 13^{2} & -14^{2} \\ -15^{2} & 16^{2} & 17^{2} \end{array}\right] \text {, then the value of } A^{\prime} B A \text { is: }$$

A
1224
B
1042
C
540
D
539
4
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
$${{10} \over 3}$$
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