1
AIEEE 2012
+4
-1
The equation $${e^{\sin x}} - {e^{ - \sin x}} - 4 = 0$$ has:
A
infinite number of real roots
B
no real roots
C
exactly one real root
D
exactly four real roots
2
AIEEE 2010
+4
-1
If $$\alpha$$ and $$\beta$$ are the roots of the equation $${x^2} - x + 1 = 0,$$ then $${\alpha ^{2009}} + {\beta ^{2009}} =$$
A
$$\, - 1$$
B
$$\, 1$$
C
$$\, 2$$
D
$$\, - 2$$
3
AIEEE 2009
+4
-1
The quadratic equations $${x^2} - 6x + a = 0$$ and $${x^2} - cx + 6 = 0$$ have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is
A
1
B
4
C
3
D
2
4
AIEEE 2009
+4
-1
If $$\,\left| {z - {4 \over z}} \right| = 2,$$ then the maximum value of $$\,\left| z \right|$$ is equal to :
A
$$\sqrt 5 + 1$$
B
2
C
$$2 + \sqrt 2$$
D
$$\sqrt 3 + 1$$
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