9000136909
Level:
B
Solve the equation involving binomial coefficients.
\[
\left({x + 1\above 0.0pt
x} \right) +\left ({x + 2\above 0.0pt
x + 1}\right) = 19
\]
\(8\)
\(10\)
\(12\)
\(19\)
The equation has no solution.
B
9000121806
Level:
B
The measure of the interior angle in a regular polygon is \(160^{\circ}\). Find the number of vertices of this polygon. In the figure the interior angle (marked in red) of a regular hexagon is shown.
\(18\)
\(16\)
\(32\)
\(9\)
9000136910
Level:
B
Solve the equation involving binomial coefficients.
\[
\left({x\above 0.0pt
0}\right) +\left ({x\above 0.0pt
1}\right) +\left ({x + 1\above 0.0pt
x} \right) = 25
\]
The equation has no solution.
\(9\)
\(1\)
\(5\)
\(7\)
9000121808
Level:
B
The number of diagonals in a polygon is three times bigger than the number of sides
of this polygon. Find the number of vertices of this polygon.
\(9\)
\(12\)
\(6\)
\(15\)
9000128807
Level:
B
The base \(ABCD\) of a square
pyramid \(ABCDV \) has side
\(6\, \mathrm{cm}\). The height of the
pyramid is \(4\, \mathrm{cm}\). Find the
angle between the planes \(DCV \)
and \(ABC\).
Round to two decimal places.
\(53.13^{\circ }\)
\(59.04^{\circ }\)
\(43.31^{\circ }\)
9000138301
Level:
B
Two dices are rolled. Find the probability that the sum of the numbers on both dices does not
exceed the number \(6\).
\(\frac{15}
{36}\doteq 0{.}4167\)
\(\frac{10}
{36}\doteq 0{.}2778\)
\(\frac{18}
{36}=0{.}5\)
\(\frac{12}
{36}\doteq 0{.}3333\)
9000128808
Level:
B
The base \(ABCD\) of a square
pyramid \(ABCDV \) has side
\(6\, \mathrm{cm}\). The height of the
pyramid is \(4\, \mathrm{cm}\). Find the
angle between the planes \(ADV \)
and \(BCV \).
Round to two decimal places.
\(73.74^{\circ }\)
\(36.87^{\circ }\)
\(61.93^{\circ }\)
9000138302
Level:
B
Two dices are rolled. Find the probability that we get either at least one number
\(6\) or the sum of the
numbers on both dices is \(8\).
\(\frac{14}
{36}\doteq 0{.}3889\)
\(\frac{16}
{36}\doteq 0{.}4444\)
\(\frac{11}
{36}\doteq 0{.}3056\)
\(\frac{5}
{36}\doteq 0{.}1389\)
9000128802
Level:
B
The base \(ABCD\) of a square
pyramid \(ABCDV \) has side
\(6\, \mathrm{cm}\). The height of the
pyramid is \(4\, \mathrm{cm}\). The point
\(M\) is the middle of the
side \(CV \). Find the distance
between the point \(M\)
and the line \(BC\).
\(\frac{5}
{2}\, \mathrm{cm}\)
\(\frac{\sqrt{34}}
{2} \, \mathrm{cm}\)
\(\frac{\sqrt{7}}
{2} \, \mathrm{cm}\)
9000138304
Level:
B
Two different dice (a white die and a black die) are rolled. Find the probability that we get the number
\(3\) on the black die and a
number different from \(3\)
on the white die.
\(\frac{5}
{36}\doteq 0{.}1389\)
\(\frac{3}
{36}\doteq 0{.}0833\)
\(\frac{6}
{36}\doteq 0{.}1667\)
\(\frac{1}
{36}\doteq 0{.}0278\)