C

2010009904

Level: 
C
A part of the graph of the function \( f(x)=\frac{-3}x \) is shown in the picture. Identify which of the following statements is true.
The function \( g \) defined by \( g(x)=-\left|f(x)\right| \) is bounded above.
The function \( m \) defined by \( m(x)=\left|f(x)\right| \) is bounded above.
The function \( h \) defined by \( h(x)=-f(x)\) is bounded below.
The function \( f \) is bounded below.

2010009805

Level: 
C
The solution set of the inequality \( |\cos x| \leq \frac12 \) for \( x\in\mathbb{R} \) is:
\( \bigcup\limits_{k\in\mathbb{Z}}\left[\frac{\pi}3+k\pi;\frac{2\pi}3+k\pi\right] \)
\( \bigcup\limits_{k\in\mathbb{Z}}\left[-\frac{\pi}3+k\pi;\frac{\pi}3+k\pi\right] \)
\( \bigcup\limits_{k\in\mathbb{Z}}\left[\frac{\pi}3+k\pi; \infty\right) \)
\( \bigcup\limits_{k\in\mathbb{Z}}\left[\frac{\pi}3+k\pi;\frac{4\pi}3+k\pi\right] \)

2010009804

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

2010008908

Level: 
C
We are given skew lines $a$ and $b$. \begin{align*} a\colon x&= -1-2t, & b\colon x&= 1-3s, \\ y&= -2+3t, & y&=2s, \\ z&= -4+2t;\ t\in\mathbb{R}, & z&= 2-2s;\ s\in\mathbb{R}. \end{align*} Find parametric equations of a straight line $p$, that is intersecting both lines $a$ and $b$ and lying in the plane $2x+3y-z-8=0$.
$\begin{aligned} p\colon x&=-9+r, \\ y&=10+r, \\ z&=4+5r;\ r\in\mathbb{R} \end{aligned}$
$\begin{aligned} p\colon x&=-9-2r, \\ y&=10-2r, \\ z&=4+10r;\ r\in\mathbb{R} \end{aligned}$
$\begin{aligned} p\colon x&=-9-10r, \\ y&=10+9r, \\ z&=4-r;\ r\in\mathbb{R} \end{aligned}$
$\begin{aligned} p\colon x&=-9+2r, \\ y&=10+2r, \\ z&=4-2r;\ r\in\mathbb{R} \end{aligned}$