C

1003086108

Level: 
C
The solution set of the equation \( 1 + \sin x \cdot \cos 2x = \sin x + \cos 2x \) for \( x\in\mathbb{R} \) is:
\( \bigcup\limits_{k\in\mathbb{Z}}\left\{\frac{\pi}2+2k\pi;k\pi\right\} \)
\( \bigcup\limits_{k\in\mathbb{Z}}\left\{\frac{\pi}2+2k\pi\right\} \)
\( \bigcup\limits_{k\in\mathbb{Z}}\left\{k\pi\right\} \)
\( \bigcup\limits_{k\in\mathbb{Z}}\left\{2k\pi\right\} \)

1003086107

Level: 
C
The solution set of the equation \( 2\mathrm{tg}^2x + 4\cos^2x = 7 \) for \( x\in\mathbb{R} \) is:
\( \bigcup\limits_{k\in\mathbb{Z}}\left\{\frac{\pi}3+k\pi;\frac{2\pi}3+k\pi\right\} \)
\( \bigcup\limits_{k\in\mathbb{Z}}\left\{\frac{\pi}3+2k\pi;\frac{2\pi}3+2k\pi\right\} \)
\( \bigcup\limits_{k\in\mathbb{Z}}\left\{\frac{\pi}3+k\pi\right\} \)
\( \bigcup\limits_{k\in\mathbb{Z}}\left\{\frac{2\pi}3+k\pi\right\} \)

1003086103

Level: 
C
The solution set of the equation \( 2\sin x + \mathrm{tg}\,x = 0 \), \( x\in\mathbb{R} \) is:
\( \bigcup\limits_{k\in\mathbb{Z}}\left\{k\pi;\frac{2\pi}3+2k\pi;\frac{4\pi}3+2k\pi\right\} \)
\( \bigcup\limits_{k\in\mathbb{Z}}\left\{2k\pi;\frac{2\pi}3+2k\pi;\frac{4\pi}3+2k\pi\right\} \)
\( \bigcup\limits_{k\in\mathbb{Z}}\left\{k\pi;\frac{5\pi}6+k\pi;\frac{7\pi}6+k\pi\right\} \)
\( \bigcup\limits_{k\in\mathbb{Z}}\left\{k\pi;\frac{5\pi}6+2k\pi;\frac{7\pi}6+2k\pi\right\} \)

1003158408

Level: 
C
The class consists of \( 10\,\% \) long haired boys, \( 30\,\% \) short haired boys, \( 50\,\% \) long haired girls and \( 10\,\% \) short haired girls. We choose one of the students from the class randomly. Find the probability that the student has long hair if you know he is a boy.
\( 0{.}25 \)
\( 0{.}40 \)
\( 0{.}10 \)
\( 0{.}03 \)

1003158407

Level: 
C
The long-term records of a car dealer show that a customer getting a new car buys within special equipment offers a parking assistant system (PAS) with the probability \( 50\,\% \) and that he buys a xenon flashlight with the probability \( 20\,\% \). Both items of special equipment (PAS and xenon lamps) are purchased by the customer with the probability \( 10\,\% \). What is the probability that the customer bought xenon lamps if you know he bought PAS?
\( 20\,\% \)
\( 60\,\% \)
\( 10\,\% \)
\( 80\,\% \)