9000141506
Level:
B
Assuming \(x\in \mathbb{N}\),
find the solution set of the following equation.
\[
\left({11\above 0.0pt
4} \right) =\left ({11\above 0.0pt
x} \right)
\]
\(\{4;7\}\)
\(\{4\}\)
\(\{ - 4\}\)
B
9000142004
Level:
B
Identify a correct statement related to the function $f$ shown in the picture.
concave up on \((-\infty ;1)\),
concave down on \((1;\infty )\),
no inflection
concave up on \((-\infty ;1)\),
concave down on \((1;\infty )\),
inflection at \(x = 1\)
concave up on \((1;\infty )\),
concave down on \((-\infty ;1)\),
inflection at \(x = 1\)
concave up on \((1;\infty )\),
concave down on \((-\infty ;1)\),
no inflection
9000141507
Level:
B
Assuming \(x,y\in \mathbb{N}\),
find the solution set of the following equation.
\[
\left({x\above 0.0pt
y}\right)^{2} - 2\cdot \left({x\above 0.0pt
y}\right) - 3 = 0
\]
\(\{[3;1];[3;2]\}\)
\(\{[3;1]\}\)
\(\{[3;1];[1;3]\}\)
9000142005
Level:
B
Identify a correct statement related to the function $f$ shown in the picture.
concave up on \((-1;0)\)
and \((1;\infty )\), concave
down on \((-\infty ;-1)\)
and \((0;1)\),
inflection at \(x_{1} = -1\),
\(x_{2} = 0\) and
\(x_{3} = 1\)
concave up on \((-1;0)\cup (1;\infty )\),
concave down on \((-\infty ;-1)\cup (0;1)\),
inflection at \(x_{1} = -1\),
\(x_{2} = 0\) and
\(x_{3} = 1\)
concave up on \((-\infty ;-1)\)
and \((0;1)\), concave
down on \((-1;0)\)
and \((1;\infty )\),
inflection at \(x_{1} = -1\),
\(x_{2} = 0\) and
\(x_{3} = 1\)
concave up on \((-\infty ;-1)\cup (0;1)\),
concave down on \((-1;0)\cup (1;\infty )\),
inflection at \(x_{1} = -1\),
\(x_{2} = 0\) and
\(x_{3} = 1\)
9000141508
Level:
B
Assuming \(x\in \mathbb{N}\),
find the solution set of the following equation.
\[
\left({x\above 0.0pt
x}\right) +\left ({x + 1\above 0.0pt
x} \right) +\left ({x + 2\above 0.0pt
x} \right) +\left ({x + 3\above 0.0pt
x} \right) = \frac{x^{3} + 59}
{6}
\]
\(\{1\}\)
\(\{4\}\)
\(\{10\}\)
9000142006
Level:
B
Identify a correct statement related to the function $f$ shown in the picture.
concave up on \((-\infty ;0)\)
and \((1;\infty )\), concave
down on \((0;1)\), a unique
inflection at \(x = 0\)
concave up on \((-\infty ;0)\)
and \((1;\infty )\), concave
down on \((0;1)\),
inflection at \(x_{1} = 0\)
and \(x_{2} = 1\)
concave up on \((-\infty ;0)\cup (1;\infty )\),
concave down on \((0;1)\), a
unique inflection at \(x = 0\)
concave up on \((0;1)\),
concave down on \((-\infty ;0)\)
and \((1;\infty )\),
inflection at \(x_{1} = 0\)
and \(x_{2} = 1\)
9000141509
Level:
B
Assuming \(x\in \mathbb{N}\),
find the solution set of the following inequality.
\[
2\cdot \left({x - 1\above 0.0pt
x - 3}\right) + x\cdot (x - 9)\leq - 8
\]
\(\{3;4;5\}\)
\(\{1;2;3;4;5\}\)
\([ 1;5] \)
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 \(n\).
\(7\)
\(6\)
\(43\)