B

2000003306

Level: 
B
A rectangle with the sides of \( 4\,\mathrm{cm} \) and \( 6\,\mathrm{cm} \) is rotated around its longer side thus giving rise to a solid. Find the volume of such a solid?
\( 96\pi\,\mathrm{cm}^3 \)
\( 48\pi\,\mathrm{cm}^3 \)
\( 96\,\mathrm{cm}^3 \)
\( 144\pi\,\mathrm{cm}^3 \)

2000003303

Level: 
B
The volume of a regular quadrilateral pyramid is \( 432\,\mathrm{cm} ^3\) and the base edge of the pyramid has the length equal to \( 12\,\mathrm{cm} \). The height of the pyramid is:
\( 9\,\mathrm{cm} \)
\( 3\,\mathrm{cm} \)
\( 36\,\mathrm{cm} \)
\( 27\,\mathrm{cm} \)

2000003301

Level: 
B
The axial section of a cylinder is a square with the diagonal length of \( 5\sqrt{2}\,\mathrm{cm} \). The lateral surface area of the cylinder is equal to:
\( 25\pi\,\mathrm{cm}^2 \)
\( 25\,\mathrm{cm}^2 \)
\( 25\sqrt{2}\,\mathrm{cm}^2 \)
\( 25\sqrt{2}\pi\,\mathrm{cm}^2 \)

2010002009

Level: 
B
Differentiate the following function. \[ f(x) =\ln \left (\frac{2x} {2 - x}\right ) \]
\(f^{\prime}(x) = \frac{2} {(2-x)x} ,\ x\in \left (0,2\right )\)
\(f^{\prime}(x) = \frac{2} {(2-x)x} ,\ x\in \mathbb{R}\setminus \left \{0,2\right \}\)
\(f^{\prime}(x) = \frac{2-x} {2x},\ x\in \left (0,2\right )\)
\(f^{\prime}(x) = \frac{2-x} {2x},\ x\in \mathbb{R}\setminus \left \{0,2\right \}\)

2010002008

Level: 
B
Differentiate the following function. \[ f(x) =\ln \left(3x^{2} - 5x \right) \]
\(f^{\prime}(x) = \frac{6x-5} {3x^{2}-5x},\ x\in \left (-\infty ,0\right )\cup \left (\frac{5}{3},\infty \right )\)
\(f^{\prime}(x) = \frac{6x-5} {3x^{2}-5x},\ x\in \mathbb{R}\setminus \left \{0,\frac{5} {3}\right \}\)
\(f^{\prime}(x) = \frac{1} {3x^{2}-5x},\ x\in \left (-\infty ,0\right )\cup \left (\frac{5}{3},\infty \right )\)
\(f^{\prime}(x) = \frac{1} {3x^{2}-5x},\ x\in \mathbb{R}\setminus \left \{0,\frac{5} {3}\right \}\)

2010002007

Level: 
B
Differentiate the following function. \[ f(x) = \frac{\sqrt{x} +2} {2-\sqrt{x} } \]
\(f'(x) = \frac{2} {\sqrt{x}}\frac{1}{(2-\sqrt{x})^{2}}, \ x \in (0 ,4)\cup (4,\infty) \)
\(f'(x) = \frac{\sqrt{x}} {2(2-\sqrt{x})^2}, \ x \in (0 ,4) \cup (4,\infty) \)
\(f'(x) = \frac{1} {(2-\sqrt{x})^2}, \ x \in (0 ,4) \cup (4,\infty) \)
\(f'(x) = \frac{1} {x(2-\sqrt{x})^2}, \ x \in (0 ,4) \cup (4,\infty) \)

2010002006

Level: 
B
Differentiate the following function. \[ f(x) = \frac{2-x^{2} } {4x} \]
\(f'(x) = \frac{-x^{2}-2} {4x^{2}} , \ x\in \mathbb{R} \setminus \{0\}\)
\(f'(x) = \frac{-x} {2} ,\ x\in \mathbb{R} \setminus \{0\}\)
\(f'(x) = \frac{2-x^{2}} {4x^{2}} ,\ x\in \mathbb{R} \setminus \{0\}\)
\(f'(x) = \frac{-x-2} {4x^{2}} ,\ x\in \mathbb{R} \setminus \{0\}\)