9000033801
Level:
B
Which of the numbers in the list is a period (not necessarily the smallest period) of the
function \(m\colon y =\cos x\)?
\(4\pi \)
\(\pi \)
\(5\pi \)
\(3\pi \)
B
9000033802
Level:
B
Which of the numbers in the list is a period (not necessarily the smallest period) of the
function \(n\colon y =\mathop{\mathrm{tg}}\nolimits x\)?
\(3\pi \)
\(\frac{\pi }{2}\)
\(- \frac{\pi } {2}\)
\(\frac{3\pi }
{2}\)
9000031210
Level:
B
Given complex numbers \(z_{1} = 2\sqrt{3}\left (\cos \frac{\pi }{6} + \mathrm{i}\sin \frac{\pi }{6}\right )\)
and \(z_{2} = \sqrt{3}\left (\cos \frac{4\pi }
{3} + \mathrm{i}\sin \frac{4\pi }
{3}\right )\), find the
quotient \(\frac{z_{1}}
{z_{2}} \).
\(-\sqrt{3} + \mathrm{i}\)
\(\sqrt{3} -\mathrm{i}\)
\(\sqrt{3} + \mathrm{i}\)
\(-\sqrt{3} -\mathrm{i}\)
9000031209
Level:
B
Given complex numbers \(z_{1} = 2\sqrt{2}\left (\cos \frac{\pi }{4} + \mathrm{i}\sin \frac{\pi }{4}\right )\)
and \(z_{2} = \sqrt{2}\left (\cos \frac{7\pi }
{4} + \mathrm{i}\sin \frac{7\pi }
{4}\right )\), find
the product \(z_{1}z_{2}\).
\(4\)
\(4\mathrm{i}\)
\(- 4\mathrm{i}\)
\(- 4\)
9000033701
Level:
B
Find out, how many integer solutions the following inequality has.
\[
m^{2} + 2m - 4 < 0
\]
Five integer solutions.
Less than five integer solutions.
More than five integer solutions.
9000033304
Level:
B
Find the solution set of the following inequality.
\[
\frac{x + 4}
{x + 2}\leq 0
\]
\([ - 4,-2)\)
\((-\infty ,-4] \cup [ 2,\infty )\)
\((-\infty ,-4)\cup (-2,\infty )\)
\((-4,-2] \)
9000033305
Level:
B
Find the solution set of the following inequality.
\[
\frac{2}
{x + 1}\geq 1
\]
\((-1,1] \)
\([ - 1,1)\)
\((-\infty ,-1)\cup [ 1,\infty )\)
\((-\infty ,1] \)
9000033306
Level:
B
Find the solution set of the following inequality.
\[
\frac{2}
{3} < \frac{2 + x}
{3 + x}
\]
\((-\infty ,-3)\cup (0,\infty )\)
\(\mathbb{R}\)
\((-3,\infty )\)
\((-3,0)\)
9000033307
Level:
B
Find the solution set of the following inequality.
\[
\frac{4}
{x^{2} - x - 6}\leq 0
\]
\((-2,3)\)
\(\mathbb{R}\)
\((-\infty ,-2)\cup (3,\infty )\)
\((-3,2)\)
9000033704
Level:
B
Find the values of real parameter \(p\)
which ensure that the following quadratic equation has solutions with nonzero
imaginary part.
\[
px^{2} + 4x - p + 5 = 0
\]
\(p\in \left (1,4\right )\)
\(p\in [ 1,4] \)
\(p\in \left (-\infty ,1\right )\cup \left (4,\infty \right )\)
\(p\in \left (-\infty ,1\right ] \cup \left [ 4,\infty \right )\)