C

2000003203

Level: 
C
A deltoid is composed of two isosceles triangles that have a common base. See the picture. Find the measures of the deltoids interior angles.
\( \alpha=36^{\circ};~\beta=134^{\circ};~\gamma=56^{\circ};~\delta=134^{\circ}\)
\( \alpha=36^{\circ};~\beta=100^{\circ};~\gamma=56^{\circ};~\delta=100^{\circ}\)
\( \alpha=56^{\circ};~\beta=134^{\circ};~\gamma=56^{\circ};~\delta=134^{\circ}\)
\( \alpha=36^{\circ};~\beta=128^{\circ};~\gamma=56^{\circ};~\delta=128^{\circ}\)

2000003109

Level: 
C
In the morning at \(7\,\mathrm{a.m.}\) we measured \(3^\circ\mathrm{C}\), at \(10\,\mathrm{a.m.}\) we measured \(12^\circ \mathrm{C}\). How many degrees was at \(9\,\mathrm{a.m.}\), if we assume that the temperature rose linearly?
\(9^\circ\mathrm{C}\)
\(10^\circ\mathrm{C}\)
\(8^\circ\mathrm{C}\)
\(6^\circ\mathrm{C}\)

2010000306

Level: 
C
Evaluate the following integral on the interval \((0;+\infty)\). \[ \int x^{3}\ln x\, \mathrm{d}x \]
\(\frac{x^4}{4}\ln x -\frac{x^4} {16}+ c,\ c\in \mathbb{R}\)
\(\frac{x^3}{3}\ln x -\frac{x^3} {9}+ c,\ c\in \mathbb{R}\)
\(\frac{x^2}{2}\ln x -\frac{x^2} {4}+ c,\ c\in \mathbb{R}\)
\(x\ln x -x+ c,\ c\in \mathbb{R}\)

2010000305

Level: 
C
Evaluate the following integral on the interval \((0;+\infty)\). \[ \int \log_2 x\, \mathrm{d}x \]
\(x\log_2x -\frac{x} {\ln 2}+ c,\ c\in \mathbb{R}\)
\(\log_2 x -\frac{x} {\ln 2}+ c,\ c\in \mathbb{R}\)
\(x\log_2 x -x+ c,\ c\in \mathbb{R}\)
\(x\log_2 x +\frac{x} {\ln 2}+ c,\ c\in \mathbb{R}\)

2010000304

Level: 
C
Solve the indefinite integral \[ \int\mathrm{e}^{\cos ⁡x}\sin ⁡x\,\mathrm{d}x \] of a real-valued function.
\( -\mathrm{e}^{\cos ⁡x} +c \), \( c\in\mathbb{R} \)
\(- \mathrm{e}^{\cos ⁡x}\cdot\cos ⁡x+c \), \( c\in\mathbb{R} \)
\( \mathrm{e}^{\sin ⁡x}\cdot\cos ⁡x+c \), \( c\in\mathbb{R} \)
\( \mathrm{e}^{\cos ⁡x}\cdot\sin ⁡x+c \), \( c\in\mathbb{R} \)

2010000210

Level: 
C
Insert \(3\) numbers between the roots of the equation \( 5x^2 -26x+5=0\) such that the resulting sequence is a part (\(5\) terms) of an increasing arithmetic sequence with the common difference \(d\). Choose the incorrect statement about the common difference \(d\).
\(d\) is a fraction smaller than \(1\)
\( d>0\)
\(d\) is a fraction greater than \(1\)
\(d\) is a rational number