2010007606
Level:
A
In how many ways can a four-person team be selected from a group of \(10\) students?
\(\frac{10!}
{4!\, 6!}\)
\(\frac{10!}
{4!}\)
\(\frac{10!}
{ 6!}\)
\(10!\)
A
2010007601
Level:
A
How many ways are there to arrange the letters in the Czech word LOKOMOTIVA?
\( \frac{10!}{3!} \)
\( \frac{10!}{3} \)
\( \frac{10!}{2!} \)
\( 10!\)
2010007410
Level:
A
Find the vector of length \(\sqrt{2}\), which is perpendicular to the \(y\)-axis.
\( \left(\sqrt{2},0\right)\)
\( (2,0)\)
\( (0,2)\)
\( \left(0,\sqrt{2}\right)\)
2010007409
Level:
A
Find the vector of length \(\sqrt{3}\), which is perpendicular to the \(x\)-axis.
\( \left(0,\sqrt{3}\right)\)
\( (3,0)\)
\( (0,3)\)
\( \left(\sqrt{3},0\right)\)
2010007408
Level:
A
Given the points \( A=[4,4]\) and \(S=[-2,2]\), find the point \(B\), such that \(S\) is the center of \(AB\).
\( B=[-8,0]\)
\( B=[1,3]\)
\( B=[10,6]\)
\( B=[-5,1]\)
2010007407
Level:
A
Given the points \( A=[3,1]\) and \(S=[-1,3]\), find the point \(B\), such that \(S\) is the center of \(AB\).
\( B=[-5,5]\)
\( B=[1,2]\)
\( B=[7,-1]\)
\( B=[-3,4]\)
2010007406
Level:
A
Find the parallel vector to the vector \(\overrightarrow{AB}\), where \(A=[-3,2]\), \(B=[1,4]\).
\( (2,1)\)
\( (-1,2)\)
\( (4,6)\)
\( (4,1)\)
2010007405
Level:
A
Find the parallel vector to the vector \(\overrightarrow{AB}\), where \(A=[1,2]\), \(B=[4,-1]\).
\( (1,-1)\)
\( (3,3)\)
\( (3,1)\)
\( (5,1)\)
2010007404
Level:
A
Find the parallel vector to the vector \((12, 4)\).
\( (6,2)\)
\( (-4,12)\)
\( (6,8)\)
\( (-6,2)\)
2010007403
Level:
A
Find the parallel vector to the vector \((1, 4)\).
\( (2,8)\)
\( (2,2)\)
\( (-1,2)\)
\( (8,-2)\)