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1

IIT-JEE 2005 Screening

MCQ (Single Correct Answer)
$$\cos \left( {\alpha - \beta } \right) = 1$$ 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
2

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)
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
$$\left( {{{5\pi } \over 6},\pi } \right]$$
3

IIT-JEE 2002 Screening

MCQ (Single Correct Answer)
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
4

IIT-JEE 2001 Screening

MCQ (Single Correct Answer)
If $$\alpha + \beta = \pi /2$$ and $$\beta + \gamma = \alpha ,$$ then $$\tan \,\alpha \,$$ equals
A
$$2\left( {\tan \beta + \tan \gamma } \right)$$
B
$$\,\tan \beta + \tan \gamma $$
C
$$\tan \beta + 2\tan \gamma $$
D
$$2\tan \beta + \tan \gamma $$

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