The sum of angles of elevation of the top of a tower from two points distant a and b from the base and in the same straight line with it is 90°. Then, the height of the tower is

• ${\mathrm{a}}^2\mathrm{b}$

• ab²

• $\sqrt{\mathrm{ab}}$

• ab

If 1° = $\mathrm{\alpha }$. radians, then the approximate value of cos(60° 1') is

• $\frac{1}{2} + \frac{\mathrm{\alpha }\sqrt{3}}{120}$

• $\frac{1}{2} - \frac{\mathrm{\alpha }}{120}$

• $\frac{1}{2} - \frac{\mathrm{\alpha }\sqrt{3}}{120}$

• $\frac{1}{2} + \frac{\mathrm{\alpha }}{120}$

$\cos \left(\mathrm{A}\right) = \frac{3}{4} \Rightarrow 32\sin \left(\frac{\mathrm{A}}{2}\right)\sin \left(\frac{5\mathrm{A}}{2}\right) = ?$

• 7

• 8

• 13

• 11

$\mathrm{In} \mathrm{a} ∆\mathrm{ABC}, \mathrm{if} \frac{\cos \left(\mathrm{A}\right)}{\mathrm{a}} = \frac{\cos \left(\mathrm{B}\right)}{\mathrm{b}} = \frac{\cos \left(\mathrm{C}\right)}{\mathrm{c}}, \mathrm{then} ∆\mathrm{ABC} \mathrm{is}$

• right angled

• isosceles right angled

• equilateral

• Scalene

235.

The angle of elevation of a stationary cloud from a point 2500m above a lake is 15° and from the same point the angle of depression of its reflection in the lake is 45°. The height(in metres) of the cloud above the lake, given that cot(15°) = 2 + $\sqrt{3}$, is

• 2500

• $2500\sqrt{2}$

• $2500\sqrt{3}$

• 5000

$\mathrm{The} \mathrm{minimum} \mathrm{value} \mathrm{of} 27{\tan }^2\left(\mathrm{\theta }\right) + 3{\cot }^2\left(\mathrm{\theta }\right) \mathrm{is}$

• 15

• 18

• 24

• 30

$\cos \left(36°\right) - \cos \left(72°\right) = ?$

• 1

• $\frac{1}{2}$

• $\frac{1}{4}$

• $\frac{1}{8}$

In an acute angled triangle, cot(B)cot(C) + cot(A)cot(C) + cot(A)cot(B) = ?

• - 1

• 0

• 1

• 2

$\mathrm{x} = \log \left(\frac{1}{\mathrm{y}} + \sqrt{1 + \frac{1}{{\mathrm{y}}^2}}\right) \Rightarrow \mathrm{y} = ?$

• $\tanh \left(\mathrm{x}\right)$

• $\coth \left(\mathrm{x}\right)$

• $\mathrm{sech}\left(\mathrm{x}\right)$

• $\mathrm{csch}\left(\mathrm{x}\right)$

The period of f(x) = $\cos \left(\frac{\mathrm{x}}{3}\right) + \sin \left(\frac{\mathrm{x}}{2}\right)$ is

• $2\mathrm{\pi }$

• $4\mathrm{\pi }$

• $8\mathrm{\pi }$

• $12\mathrm{\pi }$