A

9000139707

Level: 
A
A Morse code utilized dots and dashes to encode letters of an alphabet. Find the number of signals of the length from \(1\) to \(4\) which can be obtained from dots and dashes.
\(2 + 2^{2} + 2^{3} + 2^{4}=30\)
\(1 + 2 + 3! + 4!=33\)
\(\frac{4!} {3!\, 2!}=2\)
\(2 \cdot 1 + 2 \cdot 2 + 2 \cdot 3 + 2 \cdot 4=20\)

9000139505

Level: 
A
The average mass of twelve oranges is \(120\, \mathrm{g}\). To this amount we add another six oranges with the average mass \(150\, \mathrm{g}\). Find the change in the average mass of oranges.
The average mass increases by \(10\, \mathrm{g}\).
The average mass increases by \(8.3\, \mathrm{g}\).
The average mass increases by \(25\, \mathrm{g}\).
The average mass decreases by \(8.3\, \mathrm{g}\).

9000139708

Level: 
A
The shelf contains \(15\) books. From this amount, \(9\) books are in English and \(6\) books in other languages. Find the number of possibilities how to rearrange the books on the shelf, if all English books have to be on the left and the other on the right.
\(9!\, 6!=261\:273\:600\)
\(9^{6}=531\:441\)
\(\frac{9!} {6!}=504\)
\(\frac{9!} {6!\, 3!}=84\)

9000139507

Level: 
A
The average mass of five melons is \(2\: 400\, \mathrm{g}\). We have to add another melon such that the new average value of all six melons will be \(2\: 420\, \mathrm{g}\). Find the mass of the sixth melon.
\(2\: 520\, \mathrm{g}\)
\(2\: 540\, \mathrm{g}\)
\(2\: 480\, \mathrm{g}\)
\(2\: 460\, \mathrm{g}\)

9000139501

Level: 
A
Ten apples in a box have average mass \(200\, \mathrm{g}\). We remove one apple of the mass \(200\, \mathrm{g}\) from the box. What is the change in the average mass of the apples from the box?
The average mass of the apples does not change.
The average mass of the apples decreases by \(20\, \mathrm{g}\).
The average mass of the apples increases by \(20\, \mathrm{g}\).
There is not enough information to solve this problem.

9000140002

Level: 
A
Solve the following equation with unknown \(x\) and a real parameter \(a\in\mathbb{R}\setminus\{0\}\). \[ \frac{x+a} {a} = ax - 1\]
\(\begin{array}{cc} \hline \text{Parameter} & \text{Solution set}\\ \hline a\in\{-1;1\} & \emptyset \\ a\notin\{-1;0;1\} & \left\{\frac{2a}{(a-1)(a+1)}\right\} \\\hline \end{array}\)
\(\begin{array}{cc} \hline \text{Parameter} & \text{Solution set}\\ \hline a=-1 & \emptyset \\ a\notin\{-1;0\} & \left\{\frac{2a}{(a-1)(a+1)}\right\} \\\hline \end{array}\)
\(\begin{array}{cc} \hline \text{Parameter} & \text{Solution set}\\ \hline a\in\{-1;1\} & \mathbb{R} \\ a\notin\{-1;0;1\} & \left\{\frac{2a}{(a-1)(a+1)}\right\} \\\hline \end{array}\)

9000139504

Level: 
A
The average salary of five employees is \(3\: 000\, \mathrm{Euro}\). This group of the employees is expanded by one new person. The salary of the new person is \(2\: 400\, \mathrm{Euro}\). Find the change in the average salary of this group.
The average salary decreases by \(100\, \mathrm{Euro}\).
The average salary decreases by \(480\, \mathrm{Euro}\).
The average salary increases by \(400\, \mathrm{Euro}\).
The average salary increases by \(480\, \mathrm{Euro}\).

9000140003

Level: 
A
Solve the following equation with unknown \(x\) and a real parameter \(a\in\mathbb{R}\setminus\{0\}\). \[ax - \frac{2} {a^{2}} = \frac{4x+1} {a} \]
\(\begin{array}{cc} \hline \text{Parameter} & \text{Solution set}\\ \hline a=-2 & \mathbb{R} \\ a=2 & \emptyset \\ a\notin\{-2;0;2\} & \left\{\frac1{a(a-2)}\right\} \\\hline \end{array}\)
\(\begin{array}{cc} \hline \text{Parameter} & \text{Solution set}\\ \hline a=-2 & \mathbb{R}\setminus\{1\} \\ a=2 & \emptyset \\ a\notin\{-2;0;2\} & \left\{\frac1{a(a-2)}\right\} \\\hline \end{array}\)
\(\begin{array}{cc} \hline \text{Parameter} & \text{Solution set}\\ \hline a=-2 & \emptyset \\ a=2 & \mathbb{R} \\ a\notin\{-2;0;2\} & \left\{\frac1{a(a-2)}\right\} \\\hline \end{array}\)

9000139506

Level: 
A
There are eight mandarins of average mass \(90\, \mathrm{g}\) in the box. We got two another mandarins and add them to the box. The new average mass of the mandarins in the box is \(92\, \mathrm{g}\). Find the average mass of the two added mandarins.
\(100\, \mathrm{g}\)
\(92\, \mathrm{g}\)
\(96\, \mathrm{g}\)
\(106\, \mathrm{g}\)

9000139303

Level: 
A
A DJ's playlist contains \(18\) songs. In this list there are \(7\) rap songs, \(5\) oldies and \(6\) rock songs. The opening part should consist of one rap song, two oldies and one rock song. The order of the songs does not matter. Find the number of possible ways how to put the opening together.
\(420\)
\(120\)
\(320\)
\(520\)