B

9000141502

Level: 
B
Let \(A\) be set with \(n\) mutually different elements. The number of \(5\)-permutations with repetition is \(1024\). Find \(n\). (The term „\(k\)-permutation with repetition” stands for an ordered arrangement of \(k\) objects from a set of \(n\) objects, when each object can be chosen more than once.)
\(4\)
\(5\)
\(2\)

9000146208

Level: 
B
Factor the following expression. \[ \left (2x - 1\right )^{2} -\left (x + 3\right )^{2} \]
\(\left (x - 4\right )\left (3x + 2\right )\)
\(\left (x - 4\right )\left (3x - 2\right )\)
\(\left (x + 4\right )\left (3x + 2\right )\)
\(\left (x + 4\right )\left (3x - 2\right )\)

9000146202

Level: 
B
Expand the following expression. \[ \left (a^{2} + \sqrt{3}b\right )^{3} \]
\(a^{6} + 3\sqrt{3}a^{4}b + 9a^{2}b^{2} + 3\sqrt{3}b^{3}\)
\(a^{6} + \sqrt{3}a^{4}b + 3a^{2}b^{2} + 3\sqrt{3}b^{3}\)
\(a^{5} + 3\sqrt{3}a^{4}b + 9a^{2}b^{2} + 3\sqrt{3}b^{3}\)
\(a^{5} + \sqrt{3}a^{4}b + 3a^{2}b^{2} + 3\sqrt{3}b^{3}\)