1
AIEEE 2005
+4
-1
If $${a^2} + {b^2} + {c^2} = - 2$$ and

f$$\left( x \right) = \left| {\matrix{ {1 + {a^2}x} & {\left( {1 + {b^2}} \right)x} & {\left( {1 + {c^2}} \right)x} \cr {\left( {1 + {a^2}} \right)x} & {1 + {b^2}x} & {\left( {1 + {c^2}} \right)x} \cr {\left( {1 + {a^2}} \right)x} & {\left( {1 + {b^2}} \right)x} & {1 + {c^2}x} \cr } } \right|,$$

then f$$(x)$$ is a polynomial of degree

A
$$1$$
B
$$0$$
C
$$3$$
D
$$2$$
2
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
3
AIEEE 2004
+4
-1
Let $$A = \left( {\matrix{ 1 & { - 1} & 1 \cr 2 & 1 & { - 3} \cr 1 & 1 & 1 \cr } } \right).$$ and $$10$$ $$B = \left( {\matrix{ 4 & 2 & 2 \cr { - 5} & 0 & \alpha \cr 1 & { - 2} & 3 \cr } } \right)$$. if $$B$$ is

the inverse of matrix $$A$$, then $$\alpha$$ is

A
$$5$$
B
$$-1$$
C
$$2$$
D
$$-2$$
4
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
$$0$$
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