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.

9000145410

Level: 
A
Identify a true statement about the function \(f(x) = \frac{1} {4}x^{4} - x^{3}\).
The local minimum of \(f\) is at \(x = 3\).
The function \(f\) has neither local minimum nor local maximum.
The function \(f\) has a local minimum at \(x = 0\).
The function \(f\) has two local extrema. These extrema are at \(x = 3\) and \(x = 0\).