B

9000149410

Level: 
B
Find all lines passing through the point \(A = [-2;-6]\) such that the distance from the point \([0.0]\) to these lines is \(2\sqrt{2}\).
\(p_{1}\colon 7x + y + 20 = 0\), \(p_{2}\colon x - y - 4 = 0\)
\(p\colon 7x - y = 0\)
\(p\colon x + y + 2\sqrt{2} = 0\)
\(p_{1}\colon x - y + 2\sqrt{2} = 0\), \(p_{2}\colon x + y - 2\sqrt{2} = 0\)

9000146202

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

9000141501

Level: 
B
Let \(A\) be set with \(n\) mutually different elements. If \(n\) is increased by \(2\), then number of \(3\)-permutations is increased by \(384\). Find \(n\). (The term „\(k\)-permutation” stands for an ordered arrangement of \(k\) objects from a set of \(n\) objects.)
\(8\)
\(64\)
\(32\)