9000168703
Level:
A
Given the ellipse \(25x^{2} + 9y^{2} - 150x + 18y + 9 = 0\),
find the vertex on the major axis.
\([3;4]\)
\([3;2]\)
\([8;-1]\)
\([6;-1]\)
A
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 \(4\).
\(6\)
\(9\)
\(10\)
\(5\)
9000153801
Level:
A
Find the number of mutually different triangles such that each side of each triangle
is either \(2\),
\(3\),
\(4\) or
\(5\).
\(17\)
\(14\)
\(20\)
\(16\)
9000375401
Level:
A
Find a set of the values of the real parameter
\(a\) which
ensure that the following equation has a unique solution.
\[
a^{3}x + 4a - 1 = a^{2}x + 3
\]
\(\mathbb{R}\setminus \{0;1\}\)
\(\mathbb{R}\setminus \{ - 1;1\}\)
\(\mathbb{R}\setminus \{0\}\)
\(\mathbb{R}\setminus \{ - 1;0\}\)
9000153802
Level:
A
Find the number of mutually different isosceles triangles (at least
two sides are equal) such that each side of each triangle is either
\(2\),
\(3\),
\(4\) or
\(5\).
\(14\)
\(16\)
\(17\)
\(24\)