C

1003041603

Level: 
C
There are \( 30 \) students in a class, of them are \( 14 \) girls and the rest are boys. The teacher selects two students for weekly routine help. If selection is done at random, what is the probability that these students are not two girls? Round the result to two decimal places.
\( \frac{\binom{16}2+\binom{16}1\cdot\binom{14}1}{\binom{30}2}\doteq 0{.}79 \)
\( \frac{\binom{16}2}{\binom{30}2}\doteq 0{.}28 \)
\( \frac{\binom{14}2}{\binom{30}2}\doteq 0{.}21 \)
\( \frac{\binom{16}1\cdot\binom{14}1}{\binom{30}2}\doteq 0{.}51 \)

1003041602

Level: 
C
A box contains \( 50 \) transistors and \( 4 \) of them are lower quality. From all transistors \( 5 \) are selected at random for inspection. What is the probability that of lower quality is at most one of the selected transistors? Round the result to two decimal places.
\( \frac{\binom{46}5 + \binom{46}4\cdot\binom41}{\binom{50}5}\doteq 0{.}96 \)
\( \frac{\frac{46!}{41!}+\frac{46!}{42!}}{\frac{50!}{45!}}\doteq 0{.}66 \)
\( \frac{\binom{46}5 + \binom{46}4}{\binom{50}5}\doteq 0{.}72 \)
\( \frac{\frac{46!}{41!}+\frac{46!}{42!}\cdot \frac{4!}{3!}}{\frac{50!}{45!}}\doteq 0{.}71 \)

1003049204

Level: 
C
Let \( f(x)=|x| \). Identify which of the statements is false.
\( \forall a\text{, }b\in\mathbb{R}\colon f(a+b)=f(a)+f(b) \)
\( \forall a\text{, }b\in\mathbb{R}\colon f(a\cdot b)=f(a)\cdot f(b) \)
\( \forall a\in\mathbb{R}\text{, }b\in\mathbb{R}\setminus\{0\}\colon f(\frac ab)=\frac{f(a)}{f(b)} \)
\( \forall a\in\mathbb{R}\colon f(a)=f(-a) \)

1003049203

Level: 
C
Identify which of the statements is false.
\( \forall a\text{, }b\in\mathbb{R}\colon |a+b|=|a|+|b| \)
\( \forall a\text{, }b\in\mathbb{R}\colon |a\cdot b|=|a|\cdot|b| \)
\( \forall a\in\mathbb{R}\text{, }b\in\mathbb{R}\setminus\{0\}\colon|\frac ab|=\frac{|a|}{|b|} \)
\( a\in\mathbb{R}\colon |a|=|-a| \)

1003028402

Level: 
C
Let \( f(x)=\frac{2x-4}{x^2-4} \). Which of the statements about the domain and the range of the function \( f \) is true?
\( -2\notin D(f) \wedge -2\in H(f) \)
\( -2\in D(f) \wedge -2\notin H(f) \)
\( -2\in D(f) \wedge -2\in H(f) \)
\( -2\notin D(f) \wedge -2\notin H(f) \)
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