A

9000148901

Level: 
A
The current Czech vehicle registration plate number has the form NLN-NNNN, where N stands for a digit from \(0\) to \(9\) and L stands for a letter from an alphabet containing \(26\) letters. How many different registration plates are possible?
\(26\cdot 10^{6}\)
\(10^{6}\)
\(15\cdot 10^{6} + 6\cdot 10^{5}= 156\cdot 10^{5}\)
\(16\cdot 10^{6}\)

9000148903

Level: 
A
A combination lock will open if a right choice of three numbers (from \(1\) to \(9\)) is selected. Suppose that we use a brute force attack to open the lock (we try all possibilities). To try one code takes \(20\) seconds. What is the maximal time (in seconds) required to open the lock by brute force?
\(20\cdot 9^{3}\, \mathrm{s}=14\:580\,\mathrm{s}\)
\(20\cdot \frac{9!} {6!}\, \mathrm{s}=10\:080\,\mathrm{s}\)
\(20\cdot \frac{9!} {3!\; 6!}\, \mathrm{s}=1\:680\,\mathrm{s}\)
\(20\cdot 9\cdot 3\, \mathrm{s}=540\,\mathrm{s}\)

9000148907

Level: 
A
A bowl contains \(12\) different gummy-bears and \(20\) different sweet-drops. Anne can choose either one sweet-drop or one gummy-bear. From the rest, Jane can choose one sweet-drop and two gummy-bears. Anne wants to provide a maximum of the possibilities for Jane's choice. What should Anne choose?
sweet-drop
gummy-bear
Both possibilities give the same result.

9000148908

Level: 
A
There are seven different yellow apples, eight different green apples and ten different red apples. How many ways are there to choose three apples, if we wish to have three apples of different colors?
\(10\cdot 8\cdot 7=560\)
\(\frac{10\cdot 8\cdot 7} {2}=280 \)
\((10 + 8 + 7)\cdot 2=50\)
\(10 + 8 + 7=25\)

9000148906

Level: 
A
Each candidate in a tender is fluent in at least one out of two required languages (English and French). There are \(20\) candidates fluent in English and \(14\) candidates fluent in French. From these amounts \(10\) candidates are fluent in both languages. How many candidates are there in the tender?
\(24\)
\(34\)
\(14\)
\(44\)

9000150101

Level: 
A
Evaluate the following integral on \(\mathbb{R}\). \[ \int \left (\cos x -\sin x\right )\, \mathrm{d}x \]
\(\sin x +\cos x + c,\ c\in \mathbb{R}\)
\(\sin x -\cos x + c,\ c\in \mathbb{R}\)
\(-\sin x +\cos x + c,\ c\in \mathbb{R}\)
\(-\sin x -\cos x + c,\ c\in \mathbb{R}\)