Trigonometry · JEE Main previous year questions

2018 3 questions

1. Q292018 · 16 Apr 2018 · Shift 1

   A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If it takes 18 min. for the angle of depression of the car to change from $30^{\circ }$ to $45^{\circ }$ ; then after this, the time taken (in min.) by the car to reach the foot of the tower, is :

   1. A.$9\left(1+\sqrt{3}\right)$
   2. B.$18\left(1+\sqrt{3}\right)$
   3. C.$18\left(\sqrt{3}-1\right)$
   4. D.$\frac{9}{2}\left(\sqrt{3}-1\right)$
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   Answer: A

2. Q282018 · 8 Apr 2018 · Shift 1

   If sum of all the solutions of the equation $8\cos x\cdot \left(\cos \left(\frac{\pi }{6}+x\right)\cdot \cos \left(\frac{\pi }{6}-x\right)-\frac{1}{2}\right)=1$ in $[0,\pi ]$ is $\mathrm{k}\pi$, then k is equal to

   1. A.$\frac{20}{9}$
   2. B.$\frac{2}{3}$
   3. C.$\frac{13}{9}$
   4. D.$\frac{8}{9}$
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   Answer: C

3. Q292018 · 8 Apr 2018 · Shift 1

   PQR is a triangular park with $\mathrm{PQ}=\mathrm{PR}=200\mathrm{m}$. A T.V. tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P, Q and R are respectively $45^{\circ }$, $30^{\circ }$ and $30^{\circ }$, then the height of the tower (in m) is :

   1. A.$50\sqrt{2}$
   2. B.$100$
   3. C.$50$
   4. D.$100\sqrt{3}$
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   Answer: B