If $\mathrm{P}\left(\mathrm{A}\right) = \frac{1}{2}, \mathrm{P}\left(\mathrm{B}\right) = \frac{1}{3} \mathrm{and} \mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right) = \frac{1}{4}$, then the value of $\mathrm{P}\left(\frac{\mathrm{B}}{\mathrm{A}}\right)$ wll be

• 1

• 0

• $\frac{1}{2}$

• $\frac{1}{3}$

Six boys and six girls sit in a row. The probability that the boys and girls sit alternately will be

• $\frac{1}{462}$

• $\frac{1}{924}$

• $\frac{1}{2}$

• None of these

In a regular hexagon, 3 vertices out of 6 are randomly chosen. The probability that the triangle formed out of these three vertices will be an equilateral triangle, is

• $\frac{1}{2}$

• $\frac{1}{5}$

• $\frac{1}{10}$

• $\frac{1}{20}$

If two lines of regression are 3x + 12y = 19 and 9x + 3y = 46, then the value of r_xy will be

• 0.289

• - 0.289

• 0.209

• None of these

5.

The brain of any computer system is

• ALU

• memory

• CPU

• control unit

Which of the following is not an output device ?

• Projector

• Speaker

• Printer

• Mouse

The full form of IP is

• Interface Program

• Internet Protocol

• Internet Program

• Interface Protocol

If $\mathrm{x} = 9^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.} 9^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$9$}\right.} 9^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$27$}\right.} ... \infty$, $\mathrm{y} = 4^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.} 4^{\raisebox{1ex}{$- 1$}\!\left/ \!\raisebox{-1ex}{$9$}\right.} 4^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$27$}\right.} ... \infty$ and $\mathrm{z} = \sum _{\mathrm{r} = 1}^{\infty }{\left(1 + \mathrm{i}\right)}^{- \mathrm{r}}$, then arg (x + yz) will be

• $- {\tan }^{-1}\left(\frac{2}{\sqrt{3}}\right)$

• $- {\tan }^{-1}\left(\frac{\sqrt{2}}{3}\right)$

• $\mathrm{\pi } - {\tan }^{-1}\left(\frac{\sqrt{2}}{3}\right)$

• 0

If a, b, c are in arithmetic progression, then $\frac{\mathrm{a}}{\mathrm{bc}}, \frac{1}{\mathrm{c}}, \frac{2}{\mathrm{b}}$ will be in

• arithmetic proression

• geometric progression

• harmonic progresssion

• None of the above

If G is the geometric mean of x and y, then $\frac{1}{{\mathrm{G}}^2 - {\mathrm{x}}^2} + \frac{1}{{\mathrm{G}}^2 - {\mathrm{y}}^2}$ will be

• - G²

• $- \frac{1}{{\mathrm{G}}^2}$

• $\frac{1}{{\mathrm{G}}^2}$

• G²