1
AP EAPCET 2021 - 19th August Morning Shift
+1
-0

The rank of the matrix $$\left[\begin{array}{ccc}4 & 2 & (1-x) \\ 5 & k & 1 \\ 6 & 3 & (1+x)\end{array}\right]$$ is 1 , then,

A
$$k=\frac{5}{2}, x=\frac{1}{5}$$
B
$$k=\frac{5}{2}, x \neq \frac{1}{5}$$
C
$$k=\frac{1}{5}, x=\frac{5}{2}$$
D
$$k \neq \frac{5}{2}, x=\frac{1}{5}$$
2
AP EAPCET 2021 - 19th August Morning Shift
+1
-0

If $$a_1, a_2, \ldots . a_9$$ are in GP, then $$\left|\begin{array}{lll}\log a_1 & \log a_2 & \log a_3 \\ \log a_4 & \log a_5 & \log a_6 \\ \log a_7 & \log a_8 & \log a_9\end{array}\right|$$ is equal to

A
$$\log \left(a_1, a_2, \ldots a_n\right)$$
B
1
C
$$\left(\log a_9\right)^9$$
D
0
3
AP EAPCET 2021 - 19th August Morning Shift
+1
-0

If $$\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+3 \hat{\mathbf{j}}-\hat{\mathbf{k}}$$ and $$\mathbf{c}=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$$, then the value of $$\left|\begin{array}{ccc}\mathbf{a} \cdot \mathbf{a} & \mathbf{a} \cdot \mathbf{b} & \mathbf{a} \cdot \mathbf{c} \\ \mathbf{b} \cdot \mathbf{a} & \mathbf{b} \cdot \mathbf{b} & \mathbf{b} \cdot \mathbf{c} \\ \mathbf{c} \cdot \mathbf{a} & \mathbf{c} \cdot \mathbf{b} & \mathbf{c} \cdot \mathbf{c}\end{array}\right|$$ is equal to

A
2020
B
2025
C
2030
D
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