1
AIEEE 2006
+4
-1
If $$0 < x < \pi$$ and $$\cos x + \sin x = {1 \over 2},$$ then $$\tan x$$ is
A
$${{\left( {1 - \sqrt 7 } \right)} \over 4}$$
B
$${{\left( {4 - \sqrt 7 } \right)} \over 3}$$
C
$$- {{\left( {4 + \sqrt 7 } \right)} \over 3}$$
D
$${{\left( {1 + \sqrt 7 } \right)} \over 4}$$
2
AIEEE 2004
+4
-1
If $$u = \sqrt {{a^2}{{\cos }^2}\theta + {b^2}{{\sin }^2}\theta } + \sqrt {{a^2}{{\sin }^2}\theta + {b^2}{{\cos }^2}\theta }$$
then the difference between the maximum and minimum values of $${u^2}$$ is given by
A
$${\left( {a - b} \right)^2}$$
B
$$2\sqrt {{a^2} + {b^2}}$$
C
$${\left( {a + b} \right)^2}$$
D
$$2\left( {{a^2} + {b^2}} \right)$$
3
AIEEE 2004
+4
-1
Let $$\alpha ,\,\beta$$ be such that $$\pi < \alpha - \beta < 3\pi$$.
If $$sin{\mkern 1mu} \alpha + \sin \beta = - {{21} \over {65}}$$ and $$\cos \alpha + \cos \beta = - {{27} \over {65}}$$ then the value of $$\cos {{\alpha - \beta } \over 2}$$
A
$${{ - 6} \over {65}}\,\,$$
B
$${3 \over {\sqrt {130} }}$$
C
$${6 \over {65}}$$
D
$$- {3 \over {\sqrt {130} }}$$
4
AIEEE 2004
+4
-1
A line makes the same angle $$\theta$$, with each of the $$x$$ and $$z$$ axis.
If the angle $$\beta \,$$, which it makes with y-axis, is such that $$\,{\sin ^2}\beta = 3{\sin ^2}\theta ,$$ then $${\cos ^2}\theta$$ equals
A
$${2 \over 5}$$
B
$${1 \over 5}$$
C
$${3 \over 5}$$
D
$${2 \over 3}$$
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