Trigonometry · JEE Main previous year questions

2016 5 questions

1. Q12016 · 3 Apr 2016 · Shift 1

   A value of $\theta$ for which $\frac{2+3i\sin \theta }{1-2i\sin \theta }$ is purely imaginary, is :

   1. A.${\sin }^{-1}\left(\frac{\sqrt{3}}{4}\right)$
   2. B.${\sin }^{-1}\left(\frac{1}{\sqrt{3}}\right)$
   3. C.$\frac{\pi }{3}$
   4. D.$\frac{\pi }{6}$
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   Answer: B

2. Q162016 · 3 Apr 2016 · Shift 1

   For $x\in R$, $f(x)=\left|\log 2-\sin x\right|$ and $g(x)=f(f(x))$, then :

   1. A.$g\text{ is not differentiable at }x=0$
   2. B.$g^{\prime }(0)=\cos (\log 2)$
   3. C.$g^{\prime }(0)=-\cos (\log 2)$
   4. D.$g\text{ is differentiable at }x=0\text{ and }{g}^{\prime }(0)=-\sin (\log 2)$
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   Answer: B

3. Q192016 · 3 Apr 2016 · Shift 1

   If $0\le x<2\pi$, then the number of real values of $x$, which satisfy the equation $\cos x+\cos 2x+\cos 3x+\cos 4x=0$ is:

   1. A.$7$
   2. B.$9$
   3. C.$3$
   4. D.$5$
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   Answer: A

4. Q242016 · 3 Apr 2016 · Shift 1

   Consider : $f(x)={\tan }^{-1}\left(\sqrt{\frac{1+\sin x}{1-\sin x}}\right),x\in \left(0,\frac{\pi }{2}\right)$. A normal to $y=f(x)$ at $x=\frac{\pi }{6}$ also passes through the point:

   1. A.$\left(\frac{\pi }{6},0\right)$
   2. B.$\left(\frac{\pi }{4},0\right)$
   3. C.$(0,0)$
   4. D.$\left(0,\frac{2\pi }{3}\right)$
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   Answer: D

5. Q302016 · 3 Apr 2016 · Shift 1

   A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is $30^{\circ }$. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is $60^{\circ }$. Then the time taken (in minutes) by him, from B to reach the pillar, is :

   1. A.$6$
   2. B.$10$
   3. C.$20$
   4. D.$5$
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   Answer: D