1
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
2
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
$$\left[\begin{array}{ll}0 & 1 \\ 1 & 1\end{array}\right]$$
3
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
$$\left(\begin{array}{l}4 \\ 2 \\ 1\end{array}\right)$$
4
WB JEE 2024
+2
-0.5

Let $$A=\left[\begin{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{array}\right]$$, then

A
$$\mathrm{A}$$ is a null matrix
B
$$\mathrm{A}$$ is skew symmetric matrix
C
$$\mathrm{A}^{-1}$$ does not exist
D
$$\mathrm{A}^2=\mathrm{I}$$
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