1
AIEEE 2004
+4
-1
Let $$A = \left( {\matrix{ 0 & 0 & { - 1} \cr 0 & { - 1} & 0 \cr { - 1} & 0 & 0 \cr } } \right)$$. The only correct

statement about the matrix $$A$$ is

A
$${A^2} = 1$$
B
$$A=(-1)I,$$ where $$I$$ is a unit matrix
C
$${A^{ - 1}}$$ does not exist
D
$$A$$ is a zero matrix
2
AIEEE 2004
+4
-1
If $${a_1},{a_2},{a_3},.........,{a_n},......$$ are in G.P., then the value of the determinant

$$\left| {\matrix{ {\log {a_n}} & {\log {a_{n + 1}}} & {\log {a_{n + 2}}} \cr {\log {a_{n + 3}}} & {\log {a_{n + 4}}} & {\log {a_{n + 5}}} \cr {\log {a_{n + 6}}} & {\log {a_{n + 7}}} & {\log {a_{n + 8}}} \cr } } \right|,$$ is

A
$$-2$$
B
$$1$$
C
$$2$$
D
$$0$$
3
AIEEE 2003
+4
-1
If $$A = \left[ {\matrix{ a & b \cr b & a \cr } } \right]$$ and $${A^2} = \left[ {\matrix{ \alpha & \beta \cr \beta & \alpha \cr } } \right]$$, then
A
$$\alpha = 2ab,\,\beta = {a^2} + {b^2}$$
B
$$\alpha = {a^2} + {b^2},\,\beta = ab$$
C
$$\alpha = {a^2} + {b^2},\,\beta = 2ab$$
D
$$\alpha = {a^2} + {b^2},\,\beta = {a^2} - {b^2}$$
4
AIEEE 2003
+4
-1
If $$1,$$ $$\omega ,{\omega ^2}$$ are the cube roots of unity, then

$$\Delta = \left| {\matrix{ 1 & {{\omega ^n}} & {{\omega ^{2n}}} \cr {{\omega ^n}} & {{\omega ^{2n}}} & 1 \cr {{\omega ^{2n}}} & 1 & {{\omega ^n}} \cr } } \right|$$ is equal to

A
$${\omega ^2}$$
B
$$0$$
C
$$1$$
D
$$\omega$$
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