1
IIT-JEE 2007
MCQ (Single Correct Answer)
+3
-0.75
The number of solutions of the pair of equations $$$\,2{\sin ^2}\theta - \cos 2\theta = 0$$$ $$$2co{s^2}\theta - 3\sin \theta = 0$$$

in the interval $$\left[ {0,2\pi } \right]$$

A
zero
B
one
C
two
D
four
2
IIT-JEE 2006 Screening
MCQ (Single Correct Answer)
+3
-0.75
The values of $$\theta \in \left( {0,2\pi } \right)$$ for which $$2\,{\sin ^2}\theta - 5\,\sin \theta + 2 > 0,$$ are
A
$$\left( {0,{\pi \over 6}} \right)\, \cup \,\left( {{{5\pi } \over 6},2\pi } \right)$$
B
$$\,\left( {{\pi \over 8},{{5\pi } \over 6}} \right)$$
C
$$\left( {0,{\pi \over 8}} \right)\, \cup \,\left( {{\pi \over 6},{{5\pi } \over 6}} \right)$$ v
D
$$\,\left( {{{41\pi } \over {48}},\,\pi } \right)$$
3
IIT-JEE 2006
MCQ (Single Correct Answer)
+3
-0.75
Let $$\theta \in \left( {0,{\pi \over 4}} \right)$$ and $${t_1} = {\left( {\tan \theta } \right)^{\tan \theta }},\,\,\,\,{t_2} = \,\,{\left( {\tan \theta } \right)^{\cot \theta }}$$, $${t_3}\, = \,\,{\left( {\cot \theta } \right)^{\tan \theta }}$$ and $${t_4}\, = \,\,{\left( {\cot \theta } \right)^{\cot \theta }},$$then
A
$${t_1} > {t_2} > {t_3} > {t_4}$$
B
$${t_4} > {t_3} > {t_1} > {t_2}$$
C
$${t_3} > {t_1} > {t_2} > {t_4}$$
D
$${t_2} > {t_3} > {t_1} > {t_4}$$
4
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+2
-0.5
$$\cos \left( {\alpha - \beta } \right) = 1$$ and $$\,\cos \left( {\alpha + \beta } \right) = 1/e$$ where $$\alpha ,\,\beta \in \left[ { - \pi ,\pi } \right].$$
Paris of $$\alpha ,\,\beta $$ which satisfy both the equations is/are
A
0
B
1
C
2
D
4
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