If $\sin \left(\mathrm{\theta }\right) = \frac{1}{2}$ and where, $\mathrm{\theta }$ is an obtuse angle, then $\cot \left(\mathrm{\theta }\right)$ is equal to

• $- \frac{1}{\sqrt{3}}$

• $- \sqrt{3}$

• $\frac{1}{\sqrt{3}}$

• $\sqrt{3}$

A man is standing on the horizontal plane. The angle of elevation of top of the pole is $\mathrm{\alpha }$. If he walks a distance double the height of the pole, then the elevation of the pole is $2\mathrm{\alpha }$. The value of $\mathrm{\alpha }$ is

• $\frac{\mathrm{\pi }}{12}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{6}$

The value of sin(50°) cos (10°) + cos(50°) sin(10°) is

• $\frac{1}{2}$

• $\sqrt{3}$

• $\frac{\sqrt{3}}{2}$

• 1

The least value of a, for which the function a $\frac{4}{\sin \left(\mathrm{x}\right)} + \frac{1}{1 - \sin \left(\mathrm{x}\right)}$ has at east one solution in the interval $\left(0, \frac{\mathrm{\pi }}{2}\right)$, is

• 9

• 4

• 5

• 1

155.

In $∆\mathrm{ABC}$, if 3a = b + c, then value of $\cot \left(\frac{\mathrm{B}}{2}\right)\cot \left(\frac{\mathrm{C}}{2}\right)$ will be

• 1

• 2

• $\sqrt{3}$

• $\sqrt{2}$

If sin(a) and cos(a) are the roots of the equation ax² + bx + c = 0, then

• a² - b² + 2ac = 0

• (a - c)² = b² + c²

• a² + b² - 2ac = 0

• a² + b² + 2ac = 0

In $∆\mathrm{ABC}$, if cot(A), cot(B) and cot(C) are in AP, then a², b² and c² are in

• HP

• AP

• GP

• None of the above

The maximum value of $3\cos \left(\mathrm{\theta }\right) + 4\sin \left(\mathrm{\theta }\right)$ is

• 3

• 4

• 5

• None of these

The period of $\sin \left(\mathrm{\theta }\right) - \sqrt{3}\cos \left(\mathrm{\theta }\right)$ is

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{2}$

• $\mathrm{\pi }$

• $2\mathrm{\pi }$

If $\cos \left(\mathrm{\theta }\right) = \frac{{\cos }^2\left(\mathrm{\alpha }\right) + {\cos }^2\left(\mathrm{\beta }\right) + {\cos }^2\left(\mathrm{\gamma }\right)}{{\sin }^2\left(\mathrm{\alpha }\right) + {\sin }^2\left(\mathrm{\beta }\right) + \sin \left(\mathrm{\gamma }\right)}$, where $\mathrm{\alpha }, \mathrm{\beta }, \mathrm{\gamma }$ are the angles made by a line with the positive directions of the axes of reference, then the measure of $\mathrm{\theta }$ is

• $60°$

• $90°$

• $30°$

• $45°$