2010007401
Level:
A
Find the perpendicular vector to the vector \((3; -4)\).
\( (8;6)\)
\( (-6;8)\)
\( (6;-8)\)
\( (3;4)\)
A
2010007205
Level:
A
Select the set that does not contain the measures of coterminal angles with an angle of radian measure \( \frac{\pi}4 \). (Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.)
\( \left\{\frac54\pi;\, -\frac{21}4\pi \right\} \)
\( \left\{\frac94\pi;\, -\frac74\pi \right\} \)
\( \left\{\frac{17}4\pi;\, \frac{41}4\pi \right\} \)
\( \left\{\frac{33}4\pi;\, \frac{49}4\pi \right\} \)
2010007204
Level:
A
Which of the given degree values is of the angle coterminal to the angle of \( -1500^{\circ} \)? (Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.)
\( 300^{\circ} \)
\( -300^{\circ} \)
\( 60^{\circ} \)
\( -120^{\circ} \)
2010007203
Level:
A
Select the measure of an angle that is coterminal to an angle of \( 70^{\circ} \). (Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.)
\( 430^{\circ} \)
\( 360^{\circ} \)
\( 290^{\circ} \)
\( 860^{\circ} \)
2010007202
Level:
A
Express the degree measure of an angle if its radian measure is \( \frac{8\pi}{15} \).
\( 96^{\circ} \)
\( 84^{\circ} \)
\( 264^{\circ} \)
\( 204^{\circ} \)
2010007201
Level:
A
Select such a pair of numbers that represents measures of two coterminal angles. (Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.)
\( -\frac{13}2\pi;\ 5.5\pi \)
\( \frac{17}2\pi;\ 15.5\pi \)
\( -\frac{9}2\pi;\ \frac{9}{2}\pi \)
\( -15.5\pi;-\frac{21}2\pi \)
2010007106
Level:
A
Determine the number of four-digit positive integers that can be formed using the digits \(0\), \(1\), \(2\), \(3\), \(4\). The digits can be used repeatedly.
\( 500 \)
\( 96 \)
\( 625 \)
\( 120 \)
2010007105
Level:
A
There are \(20\) girls and \(10\) boys in the class. How many ways are there to designate a president and vice-president of the class if it is required that at least one position will be held by a girl.
\(2\cdot 20\cdot 10 + 20 \cdot 19 =780\)
\(2\cdot 20\cdot 10=400\)
\(20\cdot 19 =380\)
\(20\cdot 10 =200\)
2010007104
Level:
A
There are \(5\) different roads between cities A and B. Find the number of possible ways from the city A to the city B and back, if it is required to use one road from A to B and another different one from B to A.
\( 5 \cdot 4 = 20\)
\( 5 + 4 = 9\)
\( 5 \cdot 5 = 25\)
\( 2 \cdot 5 = 10\)
2010007006
Level:
A
Find the number of possible ways how to organize a group of \(4\) boys and \(6\) girls in one ordered row, if all the boys should stand on the first four positions and the girls on remining positions.
\( 4! \cdot 6!\)
\( 10!\)
\( 4 \cdot 6\)
\(\frac{10!}
{4!\, 6!}\)