1
WB JEE 2024
+1
-0.25

If $$A=\left(\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right)$$ and $$\theta=\frac{2 \pi}{7}$$, then $$A^{100}=A \times A \times \ldots .(100$$ times) is equal to

A
$$\left(\begin{array}{cc} \cos 2 \theta & -\sin 2 \theta \\ \sin 2 \theta & \cos 2 \theta \end{array}\right)$$
B
$$\left(\begin{array}{cc} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right)$$
C
$$\left(\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right)$$
D
$$\left(\begin{array}{cc} 0 & -1 \\ 1 & 0 \end{array}\right)$$
2
WB JEE 2024
+1
-0.25

$$\text { If }\left|\begin{array}{lll} x^k & x^{k+2} & x^{k+3} \\ y^k & y^{k+2} & y^{k+3} \\ z^k & z^{k+2} & z^{k+3} \end{array}\right|=(x-y)(y-z)(z-x)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right) \text {, then }$$

A
k = $$-$$3
B
k = 3
C
k = 1
D
k = $$-$$1
3
WB JEE 2024
+1
-0.25

If $$\left[\begin{array}{ll}2 & 1 \\ 3 & 2\end{array}\right] \cdot A \cdot\left[\begin{array}{cc}-3 & 2 \\ 5 & -3\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$$, then $$A=$$

A
$$\left[\begin{array}{ll}1 & 1 \\ 1 & 0\end{array}\right]$$
B
$$\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]$$
C
$$\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right]$$
D
$$\left[\begin{array}{ll}0 & 1 \\ 1 & 1\end{array}\right]$$
4
WB JEE 2024
+2
-0.5

Let $$A=\left(\begin{array}{ccc}1 & -1 & 0 \\ 0 & 1 & -1 \\ 1 & 1 & 1\end{array}\right), B=\left(\begin{array}{l}2 \\ 1 \\ 7\end{array}\right)$$

Then for the validity of the result $$\mathrm{AX}=\mathrm{B}, \mathrm{X}$$ is

A
$$\left(\begin{array}{c}-1 \\ 1 \\ 7\end{array}\right)$$
B
$$\left(\begin{array}{l}1 \\ 2 \\ 4\end{array}\right)$$
C
$$\left(\begin{array}{c}3 \\ 1 \\ -1\end{array}\right)$$
D
$$\left(\begin{array}{l}4 \\ 2 \\ 1\end{array}\right)$$
EXAM MAP
Medical
NEET