1
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
$${t_2} > {t_3} > {t_1} > {t_4}$$
2
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
3
IIT-JEE 2004 Screening
MCQ (Single Correct Answer)
+2
-0.5
Given both $$\theta $$ and $$\phi $$ are acute angles and $$\sin \,\theta = {1 \over 2},\,$$ $$\cos \,\phi = {1 \over 3},$$ then the value of $$\theta + \phi $$ belongs to
A
$$\left( {{\pi \over 3},\left. {{\pi \over 2}} \right]} \right.$$
B
$$\left( {{\pi \over 2},{{2\pi } \over 3}} \right)$$
C
$$\left( {{{2\pi } \over 3},\left. {{{5\pi } \over 6}} \right]} \right.$$
D
$$\left( {{{5\pi } \over 6},\pi } \right]$$
4
IIT-JEE 2002 Screening
MCQ (Single Correct Answer)
+2
-0.5
The number of integral values of $$k$$ for which the equation $$7\cos x + 5\sin x = 2k + 1$$ has a solution is
A
4
B
8
C
10
D
12
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