1003158304
Level:
C
If eight coins are tossed together, what is the probability of getting at least two tails? Round the result to four decimal places.
\( 0{.}9648 \)
\( 0{.}0352 \)
\( 0{.}0273 \)
\( 0{.}9727 \)
\( 0{.}8750 \)
C
1003158303
Level:
C
If you roll a dice ten times, what is the probability of getting one exactly five times? Round the result to four decimal places.
\( 0{.}0130 \)
\( 0{.}0033 \)
\( 0{.}5000 \)
\( 0{.}1984 \)
\( 0{.}0833 \)
1003158302
Level:
C
What is the probability that among \( 10 \) boys from a class born in the same year (\( 365 \) days) there are at least two having the same birthday? Round the result to four decimal places.
\( 0{.}1169 \)
\( 0{.}1619 \)
\( 0{.}1961 \)
\( 0{.}1916 \)
\( 0{.}1196 \)
\( 0{.}1691 \)
1003158301
Level:
C
A deck of playing cards contains \( 4 \) aces, \( 12 \) face cards and \( 16 \) number cards. If you draw two cards, what is the probability that exactly one of the drawn cards is an ace or exactly one of the drawn cards is a face? Round the result to four decimal places.
\( 0{.}6129 \)
\( 0{.}7097 \)
\( 0{.}3065 \)
\( 0{.}3548 \)
1003086009
Level:
C
The solution set of the equation \( \sin x + \cos x = 0 \) for \( x\in\mathbb{R} \) is:
\( \bigcup\limits_{k\in\mathbb{Z}}\left\{\frac{3\pi}4+2k\pi;\frac{7\pi}4+2k\pi\right\} \)
\( \bigcup\limits_{k\in\mathbb{Z}}\left\{\frac{3\pi}4+2k\pi\right\} \)
\( \mathbb{R} \)
\( \emptyset \)
1003086007
Level:
C
The solution set of the equation \( \sin^4x = 1 - \cos^2x \) for \( x\in\left[0^{\circ};360^{\circ}\right] \) is:
\( \left\{0^{\circ};90^{\circ};180^{\circ};270^{\circ};360^{\circ} \right\} \)
\( \left\{0^{\circ};180^{\circ};360^{\circ} \right\} \)
\( \left\{0^{\circ};90^{\circ};270^{\circ};360^{\circ} \right\} \)
\( \left\{90^{\circ};270^{\circ}\right\} \)
1003086006
Level:
C
The sum of all \( x \) that are solutions of the equation \( \sqrt3\,\mathrm{cotg}^2x - 2\,\mathrm{cotg}\,x -\sqrt3 = 0 \) on the interval \( \left[0^{\circ}; 360^{\circ}\right] \) is:
\( 660^{\circ} \)
\( 240^{\circ} \)
\( 420^{\circ} \)
\( 150^{\circ} \)
1003086005
Level:
C
The equation \( 3\mathrm{tg}^2x + 4\sqrt3\mathrm{tg}\, x + 3 = 0 \) has two solutions on the interval \( \left[0^{\circ}; 180^{\circ}\right]\). The smaller one is:
\( 120^{\circ} \)
\( 150^{\circ} \)
\( 30^{\circ} \)
\( 60^{\circ} \)
1003086004
Level:
C
The arithmetic mean of all the solutions of the equation \( \sin^2x - \cos^2x + \sin x = 0 \) on the interval \( \left[0^{\circ}; 360^{\circ}\right] \) is:
\( 150^{\circ} \)
\( 90^{\circ} \)
\( 360^{\circ} \)
\( 210^{\circ} \)
1003086003
Level:
C
The sum of all \( x\in\left[0^{\circ};360^{\circ}\right] \) satisfying the equation \( \cos 2x = \cos x \) is:
\( 720^{\circ} \)
\( 360^{\circ} \)
\( 480^{\circ} \)
\( 120^{\circ} \)