9000136904
Level:
B
Simplify \(\left({n+1\above 0.0pt
n} \right) +\left ({n+1\above 0.0pt
1} \right)\)
for \(n\in \mathbb{N}\).
\(2(n + 1)\)
\(n + 2\)
\(\left({n+2\above 0.0pt
n} \right)\)
\(2\)
\(\left (n + 1\right )^{2}\)
B
9000136905
Level:
B
For \(n\in \mathbb{N}\),
\(n\geq 2\), the difference \(\left({n\above 0.0pt
2} \right) -\left ({ n\above 0.0pt
n-2}\right)\)
equals to:
\(0\)
\(\left (n + 2\right )\left (n + 1\right )\)
\(\left({n+2\above 0.0pt
n} \right)\)
\(n^{2} - 1\)
\(\left({n\above 0.0pt
n}\right)\)
9000136902
Level:
B
Simplify \(\left({12\above 0.0pt
10}\right) -\left ({12\above 0.0pt
2} \right)\).
\(0\)
\(66\)
\(\left({12\above 0.0pt
8} \right)\)
\(1\)
\(\left({12\above 0.0pt
0} \right)\)
9000121802
Level:
B
Consider a regular polygon with the central angle of
\(20^{\circ }\). In the figure the cut of a regular polygon with unspecified number of vertices is shown. The red angle is the central angle of the polygon. Find
the number of vertices of this polygon.
\(18\)
\(9\)
\(20\)
\(15\)
9000136907
Level:
B
Solve the equation involving binomial coefficients.
\[
\left({x + 1\above 0.0pt
x} \right) -\left ({x + 1\above 0.0pt
x + 1}\right) = 21
\]
\(21\)
\(20\)
\(11\)
\(10\)
The equation has no solution.
9000121804
Level:
B
Find the number of vertices of a regular polygon with
\(27\)
diagonals.
\(9\)
\(18\)
\(6\)
\(24\)
9000136906
Level:
B
Solve the equation involving binomial coefficient.
\[
\left({x\above 0.0pt
2}\right) = 15
\]
\(6\)
\(5\)
\(4\)
\(3\)
The equation has no solution.
9000121801
Level:
B
Find the number of diagonals in the regular decagon (a regular polygon with
\(10\)
vertices).
\(35\)
\(7\)
\(10\)
\(70\)
9000136908
Level:
B
Solve the equation involving binomial coefficients.
\[
\left({x + 1\above 0.0pt
x} \right) -\left ({x + 1\above 0.0pt
1} \right) = 1
\]
The equation has no solution.
\(- 1\)
\(1\)
\(2\)
\(0\)
9000121805
Level:
B
For a regular pentagon find the interior angle. In the figure a regular pentagon with an interior angle marked in red is shown.
\(108\)
\(144\)
\(112\)
\(72\)