9000136904
Level:
B
Simplify \(\left({n+1\above 0.0pt
n} \right) +\left ({n+1\above 0.0pt
1} \right)\)
for \(n\in \mathbb{N}\).
\(2(n + 1)\)
\(n + 2\)
\(\left({n+2\above 0.0pt
n} \right)\)
\(2\)
\(\left (n + 1\right )^{2}\)
Combinatorics
9000136902
Level:
B
Simplify \(\left({12\above 0.0pt
10}\right) -\left ({12\above 0.0pt
2} \right)\).
\(0\)
\(66\)
\(\left({12\above 0.0pt
8} \right)\)
\(1\)
\(\left({12\above 0.0pt
0} \right)\)
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.
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.