1
JEE Main 2024 (Online) 4th April Evening Shift
+4
-1

Let $$A=\left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right]$$ and $$B=I+\operatorname{adj}(A)+(\operatorname{adj} A)^2+\ldots+(\operatorname{adj} A)^{10}$$. Then, the sum of all the elements of the matrix $$B$$ is:

A
$$-$$110
B
22
C
$$-$$124
D
$$-$$88
2
JEE Main 2024 (Online) 4th April Morning Shift
+4
-1

Let $$\alpha \in(0, \infty)$$ and $$A=\left[\begin{array}{lll}1 & 2 & \alpha \\ 1 & 0 & 1 \\ 0 & 1 & 2\end{array}\right]$$. If $$\operatorname{det}\left(\operatorname{adj}\left(2 A-A^T\right) \cdot \operatorname{adj}\left(A-2 A^T\right)\right)=2^8$$, then $$(\operatorname{det}(A))^2$$ is equal to:

A
16
B
36
C
49
D
1
3
JEE Main 2024 (Online) 4th April Morning Shift
+4
-1

If the system of equations

\begin{aligned} & x+(\sqrt{2} \sin \alpha) y+(\sqrt{2} \cos \alpha) z=0 \\ & x+(\cos \alpha) y+(\sin \alpha) z=0 \\ & x+(\sin \alpha) y-(\cos \alpha) z=0 \end{aligned}

has a non-trivial solution, then $$\alpha \in\left(0, \frac{\pi}{2}\right)$$ is equal to :

A
$$\frac{5 \pi}{24}$$
B
$$\frac{11 \pi}{24}$$
C
$$\frac{7 \pi}{24}$$
D
$$\frac{3 \pi}{4}$$
4
JEE Main 2024 (Online) 1st February Evening Shift
+4
-1
Let the system of equations $x+2 y+3 z=5,2 x+3 y+z=9,4 x+3 y+\lambda z=\mu$ have infinite number of solutions. Then $\lambda+2 \mu$ is equal to :
A
22
B
17
C
15
D
28
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