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

• $60°$

• $90°$

• $30°$

• $45°$

If a = 2, b = 3 and c = 5in $∆$BC, then $\angle$C is to equal

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{6}$

• None of these

If f : $\mathrm{R} \to \mathrm{R}$ be the signum function and g : $\mathrm{R} \to \mathrm{R}$ be the greatest integer function, then $\sin \left\{\mathrm{\pi }\left(\left(\mathrm{fog}\right)\left(\frac{1}{2}\right)\right)\right\}$ is equal to

• 1

• $\frac{\sqrt{3}}{2}$

• 0

• $\frac{1}{\sqrt{2}}$

The number of solution of $\tan \left(5\mathrm{\pi cos}\left(\mathrm{\theta }\right)\right) = \cot \left(5\mathrm{\pi sin}\left(\mathrm{\theta }\right)\right) \mathrm{for} \mathrm{\theta } \mathrm{in} \left(0, 2\mathrm{\pi }\right)$ will be

• 28

• 14

• 4

• 2

AB is a vertical pole. The end A is on the ground level. C is the middle point of AB and P is a point on the ground level. The portion BC subtends an angle $\mathrm{\beta }$ at P. If AP = nAB, then $\tan \left(\mathrm{\beta }\right)$ is equal to

• $\frac{\mathrm{n}}{2{\mathrm{n}}^2 + 1}$

• $\frac{\mathrm{n}}{{\mathrm{n}}^2 + 1}$

• $\frac{\mathrm{n}}{\mathrm{n} + 1}$

• None of these