1003019902
Level:
A
Find the solution of the equation.
\[
\sqrt{x^2-4x+3}=\sqrt{x^2-6x+3}
\]
\(x\in\{0\}\)
\(x\in\mathbb{R}\)
\(x\in\emptyset\)
\(x\in\mathbb{R}\setminus\{0\}\)
A
1003019901
Level:
A
Find the solution of the equation.
\[
\sqrt{-3x^2+2x+5}=3
\]
\(x\in\emptyset\)
\(x\in[-2;2]\)
\(x\in\{-2;2\}\)
\(x\in\mathbb{R}\)
1003020001
Level:
A
Find the sum of the roots of the equation.
\[
4x^2+2x=0
\]
\(-\frac12\)
\(0\)
\(2\)
\(-2\)
1003019801
Level:
A
Find the domain of the expression.
\[
\frac{x^2+4x-5}{-3x^2-19x+14}
\]
\(\mathbb{R}\setminus\left\{-7;\frac23\right\}\)
\(\mathbb{R}\setminus\left\{7;-\frac23\right\}\)
\(\left(7;-\frac23\right)\)
\(\left(-7;\frac23\right)\)
9000168704
Level:
A
Given the ellipse \(9x^{2} + 4y^{2} + 36x - 24y + 36 = 0\),
find the vertex on the minor axis.
\([-4;3]\)
\([-5;3]\)
\([-2;0]\)
\([-2;1]\)
9000168705
Level:
A
Given the ellipse \(16x^{2} + 9y^{2} + 32x - 36y - 92 = 0\),
find the vertex on the major axis.
\([-1;-2]\)
\([-1;-1]\)
\([3;2]\)
\([2;2]\)
9000153804
Level:
A
Find the number of \(3\)-combinations
from the set \(\{2,3,4,5\}\).
\(4\)
\(6\)
\(24\)
\(20\)
9000153805
Level:
A
Find the number of \(3\)-combinations
with repetition from the set \(\{2,3,4,5\}\).
\(20\)
\(4\)
\(24\)
\(12\)
9000153810
Level:
A
Find the number of positive integers with three mutually different digits which can be written just
using the digits \(2\),
\(3\),
\(4\),
\(5\) and which can
be divided by \(3\).
\(12\)
\(6\)
\(9\)
\(10\)
9000153809
Level:
A
Find the number of positive integers with three mutually different digits which can be written just
using the digits \(2\),
\(3\),
\(4\),
\(5\) and which can
be divided by \(4\).
\(6\)
\(9\)
\(10\)
\(5\)