Which one of the following graphs represents the function $\mathrm{f}\left(\mathrm{x}\right) = \frac{\mathrm{x}}{\mathrm{x}}, \ne 0$

• 

• 

• 

• None of the above

Consider the following statements :

Statement I : x > sin(x) for all x > 0

Statement II : f (x) = x - sin(x) is an increasing function for all x > 0.

Which one of the following is correct in respect of the above statements ?

• Both Statement I and Statement II are true and Statement II is the correct explanation of Statement I

• Both Statement I and Statement II are true and Statement II is not the correct explanation of Statement I

• Statement I is true but Statement II is false

• Statement I is false but Statement II is true

If $\mathrm{f}\left(\mathrm{x}\right) = \frac{4\mathrm{x} + {\mathrm{x}}^4}{1 + 4{\mathrm{x}}^3} \mathrm{and} \mathrm{g}\left(\mathrm{x}\right) = \ln \left(\frac{1 + \mathrm{x}}{1 - \mathrm{x}}\right),$ then what is the value of f o g$\left(\frac{\mathrm{e} - 1}{\mathrm{e} + 1}\right)$ = ?

• 2

• 1

• 0

• $\frac{1}{2}$

Which one of the following can be considered as appropriate pair of values of regression coefficient of y on x and regression coefficient of x on y ?

• (1, 1)

• ( - 1, 1)

• $\left( - \frac{1}{2}, 2\right)$

• $\left(\frac{1}{3}, \frac{10}{3}\right)$

45.

It is given that $\overline{\mathrm{x}} = 10, \overline{\mathrm{y}} = 90, {\mathrm{\sigma }}_{\mathrm{x}} = 3, {\mathrm{\sigma }}_{\mathrm{y}} = 12 \mathrm{and} {\mathrm{r}}_{\mathrm{xy}} = 0.8$

The regression equation of x and y is :

• y = 3.2x + 58

• x = 3.2y + 58

• x = - 8 + 0.2y

• y = - 8 + 0.2x

The coefficient of correlation whenregression are 0.2 and 1.8 is :

• 0.36

• 0.2

• 0.6

• 0.9

What is the range of the function y = $\frac{x^2}{1 + x^2}$

where, x $\in \mathrm{ℝ}$

• [0, 1)

• [0, 1]

• (0, 1)

• (0, 1]

Consider the function

$\mathrm{f}\left(\mathrm{\theta }\right) = 4\left({\sin }^2\left(\mathrm{\theta }\right) + {\cos }^4\left(\mathrm{\theta }\right)\right)$

What is the maximum value of the function f($\mathrm{\theta }$)?

• 1

• 2

• 3

• 4

Consider the function

$\mathrm{f}\left(\mathrm{\theta }\right) = 4\left({\sin }^2\left(\mathrm{\theta }\right) + {\cos }^4\left(\mathrm{\theta }\right)\right)$

What is the minimum value of the function f($\mathrm{\theta }$)?

• 0

• 1

• 2

• 3

Consider the function

$\mathrm{f}\left(\mathrm{\theta }\right) = 4\left({\sin }^2\left(\mathrm{\theta }\right) + {\cos }^4\left(\mathrm{\theta }\right)\right)$

Consider the following statements :

$$\begin{gathered} 1. \mathrm{f}\left(\mathrm{\theta }\right) = 2 \mathrm{has} \mathrm{no} \mathrm{solution} \\ 2. \mathrm{f}\left(\mathrm{\theta }\right) = \frac{7}{2} \mathrm{has} \mathrm{a} \mathrm{solution} \\ \mathrm{Which} \mathrm{of} \mathrm{the} \mathrm{above} \mathrm{statements} \mathrm{is}/\mathrm{are} \mathrm{correct} ? \end{gathered}$$

• 1 only

• 2 only

• Both 1 and 2

• Neither 1 nor 2