1
AIEEE 2010
+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
$${25 \over 16}$$
2
AIEEE 2009
+4
-1
Let A and B denote the statements

A: $$\cos \alpha + \cos \beta + \cos \gamma = 0$$

B: $$\sin \alpha + \sin \beta + \sin \gamma = 0$$

If $$\cos \left( {\beta - \gamma } \right) + \cos \left( {\gamma - \alpha } \right) + \cos \left( {\alpha - \beta } \right) = - {3 \over 2},$$ then:

A
A is false and B is true
B
both A and B are true
C
both A and B are false
D
A is true and B is false
3
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
$${{\left( {1 + \sqrt 7 } \right)} \over 4}$$
4
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
$$2\left( {{a^2} + {b^2}} \right)$$
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