1
AIEEE 2011
+4
-1
If $$A = {\sin ^2}x + {\cos ^4}x,$$ then for all real $$x$$:
A
$${{13} \over {16}} \le A \le 1$$
B
$$1 \le A \le 2$$
C
$${3 \over 4} \le A \le {{13} \over {16}}$$
D
$${{3} \over {4}} \le A \le 1$$
2
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
$${25 \over 16}$$
3
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
4
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
$${{\left( {1 + \sqrt 7 } \right)} \over 4}$$
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