For f to be a function, what is the domain of f, if $\mathrm{f}\left(\mathrm{x}\right) = \frac{1}{\sqrt{\left|\mathrm{x}\right| - \mathrm{x}}} ?$

• $\left( - \infty , 0\right)$

• $\left(0, \infty \right)$

• $\left( - \infty , \infty \right)$

• $\left( - \infty , 0\right)$

If f(x) is an even function, where f{x) $\ne$ 0, then which one of the following is correct ?

• f'(x) is an even function

• f'(x) is an odd function

• f'(x) may be an even or odd function depending on the type of function

• f'(x) is a constant function

Consider the following statements :

1. If the correlation coefficient r_xy = 0, then the two lines of regression are parallel to each other.
2. If the correlation coefficient ${\mathrm{r}}_{\mathrm{xy}} = + 1$, then the two lines of regression are perpendicular to each other. Which of the above statements is/are correct

• 1 only

• 2 only

• Both 1 and 2

• Neither 1 nor 2

If 4x - 5y + 33 = 0 and 20x - 9y = 107 are two lines of regression, then what are the values of $\overline{\mathrm{x}} \mathrm{and} \overline{\mathrm{y}}$ respectively

• 12 and 18

• 18 and 12

• 13 and 17

• 17 and 13

Consider the following expressions :

$$\begin{gathered} 1. \mathrm{x} + {\mathrm{x}}^2 - \frac{1}{\mathrm{x}} \\ 2. \sqrt{{\mathrm{ax}}^2 + \mathrm{bx} + \mathrm{x} - \mathrm{c} + \frac{\mathrm{d}}{\mathrm{x}} - \frac{\mathrm{e}}{{\mathrm{x}}^2}} \\ 3. 3{\mathrm{x}}^2 - 5\mathrm{x} +\hspace{0.17em}\mathrm{ab} \\ 4. \frac{2}{{\mathrm{x}}^2 - \mathrm{ax} + {\mathrm{b}}^3} \\ 5. \frac{1}{\mathrm{x}} - \frac{2}{\mathrm{x}\hspace{0.17em}+ 5} \\ \mathrm{Which} \mathrm{of} \mathrm{the} \mathrm{above} \mathrm{are} \mathrm{rational} \mathrm{expression} ? \end{gathered}$$

• 1, 4 and 5 only

• $1, 3, 4 \mathrm{and} 5 \mathrm{only}$

• 2, 4 and 5 only

• 1 and 2 only

What is the value of ${\log }_9\left(27\right) + {\log }_8\left(32\right) ?$

• $\frac{7}{2}$

• $\frac{19}{6}$

• 4

• 7

The sum of the binary numbers (11011)₂, (10110110), and (10011x0y)₂, is the binary number (101101101)₂. What are the values of x and y ?

• x = 1, y = 1

• x = 1, y = 0

• x = 0, y = 1

• x = 0, y = 0

If (0.2)^x = 2 and log₁₀(2) = 0.3010, then what is the value of x to the nearest tenth ?

•  - 10.0

•  - 0.5

• - 0.4

• - 0.2

$\mathrm{If} \mathrm{f}\left(\mathrm{x}\right) = \frac{\sqrt{\mathrm{x} - 1}}{\mathrm{x} - 4} \mathrm{defines} \mathrm{a} \mathrm{function} \mathrm{on} \mathrm{R}, \mathrm{then} \mathrm{what} \mathrm{is} \mathrm{its} \mathrm{domain} ?$

• $\left( - \infty , 4\right) \cup \left(4, \infty \right)$

• $[4, \infty )$

• $\left( 1, 4\right) \cup \left(4, \infty \right)$

• $\left[1, 4) \cup (4, \infty \right]$

For the function f(x) = $\left|\mathrm{x} - 3\right|$, which one of the following is not correct ?

• The function is not continuous at x = - 3

• The function is continuous at x = 3

• The function is differentiable at x = 0

• The function is differentiable at x = - 3