1
AIEEE 2004
MCQ (Single Correct Answer)
+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
$$ - {3 \over {\sqrt {130} }}$$
2
AIEEE 2004
MCQ (Single Correct Answer)
+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
$${2 \over 3}$$
3
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
The period of $${\sin ^2}\theta $$ is
A
$${\pi ^2}$$
B
$$\pi $$
C
$$2\pi $$
D
$$\pi /2$$
4
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
The number of solution of $$\tan \,x + \sec \,x = 2\cos \,x$$ in $$\left[ {0,\,2\,\pi } \right]$$ is
A
2
B
3
C
0
D
1
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