${\int }_1^3\frac{\sqrt{4 - \mathrm{x}}}{\sqrt{\mathrm{x}} + \sqrt{4 - \mathrm{x}}}\mathrm{dx}$ is equal to

• 1

• 3

• 2

• 0

The area bounded between the parabola y² = 4x and the line y = 2x - 4 is equal to

• $\frac{17}{3} \mathrm{sq} \mathrm{unit}$

• $\frac{19}{3} \mathrm{sq} \mathrm{unit}$

• 9 sq unit

• 15 sq unit

The differential equation of the family of circles passing through the orign and having their centres on the x-axis is

• ${\mathrm{y}}^2 = {\mathrm{x}}^2 +\hspace{0.17em}2\mathrm{xy}\frac{\mathrm{dy}}{\mathrm{dx}}$

• ${\mathrm{y}}^2 = {\mathrm{x}}^2 -\hspace{0.17em}2\mathrm{xy}\frac{\mathrm{dy}}{\mathrm{dx}}$

• ${\mathrm{x}}^2 = {\mathrm{y}}^2 +\hspace{0.17em}\mathrm{xy}\frac{\mathrm{dy}}{\mathrm{dx}}$

• ${\mathrm{x}}^2 = {\mathrm{y}}^2 +\hspace{0.17em}3\mathrm{xy}\frac{\mathrm{dy}}{\mathrm{dx}}$

24.

A population grows at the rate of 10% of the population per year. How long does it take for the population to double?

• 20log(2) yr

• 10log(2)yr

• 5log(2) yr

• None of the above

If ${\int }_0^1\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} = 5, \mathrm{then} \mathrm{the} \mathrm{value} \mathrm{of} ... + {\int }_0^1{\mathrm{x}}^9\mathrm{f}\left({\mathrm{x}}^{10}\right)\mathrm{dx}$ is equal to

• 125

• 625

• 275

• 55

If $\overrightarrow{\mathrm{a}} . \overrightarrow{\mathrm{b}} = \left|\overrightarrow{\mathrm{a}}\right|\left|\overrightarrow{\mathrm{b}}\right|$, then the angle between $\overrightarrow{\mathrm{a}} \mathrm{and} \overrightarrow{\mathrm{b}}$ is

• 45°

• 180°

• 90°

• 60°

If $\overrightarrow{\mathrm{a}} +\hspace{0.17em}2\overrightarrow{\mathrm{b}} +\hspace{0.17em}3\overrightarrow{\mathrm{c}} = \overrightarrow{0}$, then $\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}} + \overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}} + \overrightarrow{\mathrm{c}} \times \overrightarrow{\mathrm{a}}$ is equal to

• $2\left(\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}}\right)$

• $3\left(\overrightarrow{\mathrm{c}} \times \overrightarrow{\mathrm{a}}\right)$

• $\overrightarrow{0}$

• $6\left(\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}}\right)$

If the volume of the parallelopiped with $\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}} \mathrm{and} \overrightarrow{\mathrm{c}}$ as coterminous edges is 40 cu unit, then the volume of the parallelopiped having $\overrightarrow{\mathrm{b}} + \overrightarrow{\mathrm{c}}, \overrightarrow{\mathrm{c}} + \overrightarrow{\mathrm{a}} \mathrm{and} \overrightarrow{\mathrm{a}} + \overrightarrow{\mathrm{b}}$ as coterminous edges in cubic unit is

• 80

• 120

• 160

• 40