IIT-JEE 2006 | Trigonometric Functions & Equations Question 35 | Mathematics

IIT-JEE 2006

MCQ (Single Correct Answer)

-1

Let $$\theta \in\left(0, \frac{\pi}{4}\right)$$ and $$t_{1}=(\tan \theta)^{\tan \theta}, t_{2}=(\tan \theta)^{\cot \theta}, t_{3}=(\cot \theta)^{\tan \theta}$$ and $$t_{4}=(\cot \theta)^{\cot \theta}$$, then

$$t_{1}>t_{2}>t_{3}>t_{4}$$

$$t_{4}>t_{3}>t_{1}>t_{2}$$

$$t_{3}>t_{1}>t_{2}>t_{4}$$

$$t_{2}>t_{3}>t_{1}>t_{4}$$

IIT-JEE 2006

MCQ (Single Correct Answer)

-1

If $0<\theta<2 \pi$, then the intervals of values of $\theta$ for which $2 \sin ^2 \theta-5 \sin \theta+2>0$, is

$\left(0, \frac{\pi}{6}\right) \cup\left(\frac{5 \pi}{6}, 2 \pi\right)$

$\left(\frac{\pi}{8}, \frac{5 \pi}{6}\right)$

$\left(0, \frac{\pi}{8}\right) \cup\left(\frac{\pi}{6}, \frac{5 \pi}{6}\right)$

$\left(\frac{41 \pi}{48}, \pi\right)$

IIT-JEE 2005 Screening

MCQ (Single Correct Answer)

-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

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)

-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

$$\left( {{\pi \over 3},\left. {{\pi \over 2}} \right]} \right.$$

$$\left( {{\pi \over 2},{{2\pi } \over 3}} \right)$$

$$\left( {{{2\pi } \over 3},\left. {{{5\pi } \over 6}} \right]} \right.$$

$$\left( {{{5\pi } \over 6},\pi } \right]$$

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