1
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1
Out of Syllabus

Let the matrix $$A=\left[\begin{array}{lll}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{array}\right]$$ and the matrix $$B_{0}=A^{49}+2 A^{98}$$. If $$B_{n}=A d j\left(B_{n-1}\right)$$ for all $$n \geq 1$$, then $$\operatorname{det}\left(B_{4}\right)$$ is equal to :

A
$$3^{28}$$
B
$$3^{30}$$
C
$$3^{32}$$
D
$$3^{36}$$
2
JEE Main 2022 (Online) 27th July Evening Shift
+4
-1
Out of Syllabus

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
3
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
4
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
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