JEE Main 2014 · 9 Apr · Shift 1 · Mathematics Q84

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MathematicsSingle correct+4 / -1Question 84 of 90

A line in the 3-dimensional space makes an angle $\theta\left(0<\theta\le\dfrac\pi2\right)$ with both the $x$ and $y$ axes. Then the set of all values of $\theta$ is the interval :

\left(0,\dfrac\pi4\right]

\left[\dfrac\pi6,\dfrac\pi3\right]

\left[\dfrac\pi4,\dfrac\pi2\right]

\left(\dfrac\pi3,\dfrac\pi2\right)

Answer and worked solution

Official answer: C

$\cos^2\theta+\cos^2\theta+\cos^2\gamma=1$ , so $\cos^2\gamma=1-2\cos^2\theta\ge0$ . This needs $\cos\theta\le\frac1{\sqrt2}$ , i.e. $\theta\in\left[\dfrac\pi4,\dfrac\pi2\right]$ .

Topics:Direction cosines and ratios

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JEE Main 2014 · 9 Apr · Shift 1, Mathematics question 84