A vertical pole MN is standing at a point N on the ground. A, B, C are three points on the ground such that N lies on segment AC. If angles of elevation of the top M of the pole from A, B, C are 30°, 45° and 65° respectively, then \(AB : BC\) equals
An aeroplane flying at a constant speed, parallel to the horizontal ground, \(\sqrt{3}\) km above it, is observed at an elevation of 60° from a point on the ground. If, after five seconds, its elevation from the same point is 30°, then the speed (in km h⁻¹) of the aeroplane is
Question nos. 687 to 689Column-1 represents a condition to form trigonometric equation. Column-2 represents the value of \(\sin\theta + \cos\theta\) and Column-3 represents the general value of \(\theta\) satisfying the trigonometric equation.Column-1Column-2Column-3(I) If \(2^{\sin\theta}\), \(\sqrt{2}\) and \(2^{\cos\theta}\) are three terms of a decreasing G.P.(i) \(\dfrac{\sqrt{3}+1}{2}\)(P) \(\theta = 2n\pi - \dfrac{\pi}{2}\)(II) If \(\cos\theta\), \(\sec\theta\) and \(\cot\theta\) are three positive numbers in H.P.(ii) \(\sqrt{2}\)(Q) \(\theta = 2n\pi + \dfrac{\pi}{6}\)(III) If \(2\log\sec\theta\), \(\log 2\) and \(2\log\text{cosec}\,\theta\) are in A.P.(iii) \(-1\)(R) \(\theta = 2n\pi + \dfrac{\pi}{2}\)(IV) If G.M. of \((2+\sin\theta)\), \((3+\sin\theta)\) and \((4+\sin\theta)\) is equal to cube root of 6.(iv) \(1\)(S) \(\theta = 2n\pi + \dfrac{\pi}{4}\)689. Which of the following options is the only correct combination?