A

1003024601

Level: 
A
Assume the password for the safe deposit box consists of four different letters from the set \( \{A;B;C;D;E;F;G;H\} \) and four different numbers from the set \( \{1;2;3;4;5;6;7\} \). How many different passwords are there?
\( \binom84 \cdot \binom74 \cdot 8! = 98\,784\,000 \)
\( \frac{8!}{4!}\cdot\frac{7!}{3!}\cdot8!=56\,899\,584\,000 \)
\( \left(\frac{8!}{4!}+\frac{7!}{3!}\right)\cdot8! = 101\,606\,400 \)
\( \left(\binom84+\binom74\right)\cdot8!=4\,233\,600 \)

1003019103

Level: 
A
There are \( 30 \) students in the class, one of them is Adam. The teacher picks randomly three students to be tested. What is the probability that Adam is among them?
\( \frac{\binom{29}2}{\binom{30}3}=0{.}1 \)
\( \frac{\binom{29}2}{\binom{30}2}\doteq 0{.}9333 \)
\( \frac{\binom{29}3}{\binom{30}3}=0{.}9 \)
\( \frac{\binom31\binom{27}2}{\binom{30}{3}}\doteq 0{.}2594 \)

1103019503

Level: 
A
Function \( f \) is given by the graph. Identify which of the following statements is true.
Function \( f \) has minimum at \( x=0 \) and maximum at \( x=5 \).
Function \( f \) has minimum at \( x=-5 \) and maximum at \( x=5 \).
Function \( f \) has minimum at \( x=-1 \) and maximum at \( x=4 \).
Function \( f \) has neither minimum nor maximum.

1003019502

Level: 
A
Suppose function \( f \) is given completely by the next table. \[ \begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-2&5& 9&0&-8&2&4 \\\hline f(x) &2&-3&0&-7&-1&5&4\\ \hline\end{array}\] Identify which of the following statements is true.
Function \( f \) has minimum at \( x= 0 \) and maximum at \( x= 2 \).
Function \( f \) has minimum at \( x= 0 \) and maximum at \( x= 9 \).
Function \( f \) has minimum at \( x= -8 \) and maximum at \( x= 2 \).
Function \( f \) has minimum at \( x= -8 \) and maximum at \( x= 9 \).

1003019501

Level: 
A
Suppose function \( f \) is given completely by the next table. \[ \begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-3&-2& -1&0&1&2&3 \\\hline f(x) &2&-3&1&0&1&-2&2\\ \hline\end{array}\] Identify which of the following statements is true.
Function \( f \) has minimum at \( x= -2\) and maximum at \( x= -3\) and at \( x= 3\).
Function \( f \) has minimum at \( x= -3\) and maximum at \( x= 2\).
Function \( f \) has minimum at \( x= -2\) and it has no maximum.
Function \( f \) has minimum at \( x= -3\) and maximum at \( x=3 \).