1
AIEEE 2010
MCQ (Single Correct Answer)
+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
$$\, - 2$$
2
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
Let $$\cos \left( {\alpha + \beta } \right) = {4 \over 5}$$ and $$\sin \,\,\,\left( {\alpha - \beta } \right) = {5 \over {13}},$$ where $$0 \le \alpha ,\,\beta \le {\pi \over 4}.$$
Then $$tan\,2\alpha $$ =
A
$${56 \over 33}$$
B
$${19 \over 12}$$
C
$${20 \over 7}$$
D
$${25 \over 16}$$
3
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
A line $$AB$$ in three-dimensional space makes angles $${45^ \circ }$$ and $${120^ \circ }$$ with the positive $$x$$-axis and the positive $$y$$-axis respectively. If $$AB$$ makes an acute angle $$\theta $$ with the positive $$z$$-axis, then $$\theta $$ equals :
A
$${45^ \circ }$$
B
$${60^ \circ }$$
C
$${75^ \circ }$$
D
$${30^ \circ }$$
4
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
If the vectors $$\overrightarrow a = \widehat i - \widehat j + 2\widehat k,\,\,\,\,\,\overrightarrow b = 2\widehat i + 4\widehat j + \widehat k\,\,\,$$ and $$\,\overrightarrow c = \lambda \widehat i + \widehat j + \mu \widehat k$$ are mutually orthogonal, then $$\,\left( {\lambda ,\mu } \right)$$ is equal to :
A
$$(2, -3)$$
B
$$(-2, 3)$$
C
$$(3, -2)$$
D
$$(-3, 2)$$
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