In how many ways can 5 keys be put in a ring ?

• 4!

• 5!

• $\frac{4!}{2}$

• $\frac{5!}{2}$

The value of ${\left(\sqrt{5} + 1\right)}^5 - {\left(\sqrt{5} - 1\right)}^5$ is

• 232

• 352

• 452

• 532

The sum of the series $\frac{1}{2 . 3} + \frac{1}{4 . 5} + \frac{1}{6 . 7} + ...$ is

• $\log \left(\frac{\mathrm{e}}{2}\right)$

• $\log \left(\frac{2}{\mathrm{e}}\right)$

• $\frac{\mathrm{e}}{2}$

• $\frac{2}{\mathrm{e}}$

4.

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 the tangent at the point $\left(2\sec \left(\mathrm{\theta }\right), 3\tan \left(\mathrm{\theta }\right)\right)$ of the hyperbola $\frac{{\mathrm{x}}^2}{4} - \frac{{\mathrm{y}}^2}{9} = 1$ is parallel to 3x - y + 4 = 0, then the value of $\mathrm{\theta }$ is

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{2}$

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

• $60°$

• $90°$

• $30°$

• $45°$

The value of $\underset{\mathrm{x}\to 0}{\lim }\frac{\sin \left({\mathrm{x}}^4\right) - {\mathrm{x}}^4\cos \left({\mathrm{x}}^4\right) + {\mathrm{x}}^{20}}{{\mathrm{x}}^4\left({\mathrm{e}}^{2{\mathrm{x}}^4} - 1 - 2{\mathrm{x}}^4\right)}$ is equal to

• 0

• $- \frac{1}{6}$

• $\frac{1}{6}$

• Does not exist

ISP stands for

• Instructions Set Processor

• Information Standard Processing

• Interchange Standard Protocol

• Interrupt Service Procedure

The 8-bit encoding format used to store data in a computer is known as

• ASCII

• ANCI

• EBCDIC

• USCII