9000141509
Level:
B
Assuming \(x\in \mathbb{N}\),
find the solution set of the following inequality.
\[
2\cdot \left({x - 1\above 0.0pt
x - 3}\right) + x\cdot (x - 9)\leq - 8
\]
\(\{3;4;5\}\)
\(\{1;2;3;4;5\}\)
\([ 1;5] \)
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.)
\(4\)
\(5\)
\(2\)
9000141503
Level:
B
Let \(A\) be a
set with \(n\)
mutually different elements. If two elements are removed from
\(A\), the number of all
permutations of set \(A\)
decreases \(20\)-times.
Find \(n\).
\(5\)
\(4\)
\(5\) or
\(- 4\)
9000141504
Level:
B
Let \(A\) be a
set with \(n\)
mutually different elements. If we add one element to the set
\(A\), the number of
\(3\)-combinations
of a set \(A\) is
increased by \(21\).
Find \(n\).
\(7\)
\(6\)
\(43\)
9000146207
Level:
B
Factor the following expression.
\[
4a^{2} -\left (a - 1\right )^{2}
\]
\(\left (a + 1\right )\left (3a - 1\right )\)
\(\left (a - 1\right )\left (3a - 1\right )\)
\(\left (a + 1\right )\left (3a + 1\right )\)
\(\left (a - 1\right )\left (3a + 1\right )\)
9000146208
Level:
B
Factor the following expression.
\[
\left (2x - 1\right )^{2} -\left (x + 3\right )^{2}
\]
\(\left (x - 4\right )\left (3x + 2\right )\)
\(\left (x - 4\right )\left (3x - 2\right )\)
\(\left (x + 4\right )\left (3x + 2\right )\)
\(\left (x + 4\right )\left (3x - 2\right )\)
9000146201
Level:
B
Expand the following expression.
\[
\left (2x^{3} - y^{2}\right )^{3}
\]
\(8x^{9} - 12x^{6}y^{2} + 6x^{3}y^{4} - y^{6}\)
\(8x^{9} - 4x^{6}y^{2} + 2x^{3}y^{4} - y^{6}\)
\(8x^{6} - 12x^{5}y^{2} + 6x^{3}y^{4} - y^{5}\)
\(8x^{6} - 4x^{5}y^{2} + 2x^{3}y^{4} - y^{5}\)
9000140510
Level:
B
Find the solution set of the equation assuming
\(x\in \mathbb{N}\).
\[
(x + 1)! + x! = 6x + 12
\]
\(\{3\}\)
\(\{2\}\)
\(\{1\}\)
\(\{4\}\)
9000140505
Level:
B
Simplify \(\frac{72!}
{70!+71!}\).
\(71\)
\(72\)
\(\frac{72}
{141}\)
\(\frac{72!}
{141!}\)
9000138306
Level:
B
Two dice are rolled. Find the probability that we get the number \(3\) at least once.
\(\frac{11}
{36}\doteq 0{.}3056\)
\(\frac{3}
{36}\doteq 0{.}0833\)
\(\frac{10}
{36}\doteq 0{.}2778\)
\(\frac{12}
{36}\doteq 0{.}3333\)