1
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
$$\alpha = {a^2} + {b^2},\,\beta = {a^2} - {b^2}$$
2
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
$$\omega$$
3
AIEEE 2003
+4
-1
If the system of linear equations
$$x + 2ay + az = 0;$$ $$x + 3by + bz = 0;\,\,x + 4cy + cz = 0;$$
has a non - zero solution, then $$a, b, c$$.
A
satisfy $$a+2b+3c=0$$
B
are in A.P
C
are in G.P
D
are in H.P.
4
AIEEE 2002
+4
-1
If $$a>0$$ and discriminant of $$\,a{x^2} + 2bx + c$$ is $$-ve$$, then
$$\left| {\matrix{ a & b & {ax + b} \cr b & c & {bx + c} \cr {ax + b} & {bx + c} & 0 \cr } } \right|$$ is equal to
A
$$+ve$$
B
$$\left( {ac - {b^2}} \right)\left( {a{x^2} + 2bx + c} \right)$$
C
$$-ve$$
D
$$0$$
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