9000080909
Level:
B
Find the set difference \(B\setminus A\)
for \(A = \{x\in \mathbb{Z};x < 2\}\)
and \(B = \{x\in \mathbb{Z};x < 5\}\).
\(\{2;3;4\}\)
\(\{x\in \mathbb{Z};x < 2\}\)
\(\{3;4\}\)
\(\emptyset \)
B
9000083609
Level:
B
Assuming \(x\neq 0\),
\(x\neq \pm y\),
\(y\neq 0\),
simplify the expression.
\[
\frac{\frac{x^{2}+y^{2}}
{x} - 2y}
{\left ( \frac{1}
{y^{2}} - \frac{1}
{x^{2}} \right )\cdot \frac{xy}
{x+y}}
\]
\(y(x - y)\)
\(\frac{x-y}
{y} \)
\(x(x - y)\)
\(\frac{x-y}
{x} \)
9000081408
Level:
B
For \(x\in \mathbb{R}^{-}\) consider
expressions \(|x|\),
\(|- x|\),
\(-|x|\) and
\(- x\).
Which of these attains only negative values?
\(-|x|\)
\(|x|\)
\(|- x|\)
\(- x\)
9000084909
Level:
B
Among the following numbers, find the number so that in its factorization into primes each prime is squared.
\(36\)
\(24\)
\(120\)
\(360\)
\(512\)
9000084901
Level:
B
Which of the following numbers is a prime?
\(17\)
\(1\)
\(27\)
\(91\)
\(289\)
9000084908
Level:
B
From the following list of numbers choose the one that has in its prime factorization the highest power of a prime.
\(1\: 024\)
\(21\)
\(100\)
\(330\)
\(486\)
9000084902
Level:
B
In the following list find the set which does not contain any prime number.
\(91,\ 243\)
\(13,\ 100\)
\(2,\ 4\)
\(29,\ 81\)
\(101,\ 211\)
9000084907
Level:
B
Among the following numbers, find the one that has the greatest number of different primes in its prime factorization.
\(330\)
\(21\)
\(100\)
\(486\)
\(1\: 024\)
9000084903
Level:
B
In the following list find the set which contains only prime numbers.
\(13,\ 131\)
\(1,\ 31,\ 211\)
\(289,\ 291\)
\(17,\ 169\)
\(51,\ 97\)
9000084906
Level:
B
In the following list find the number such that the prime factorization of this
number contains exactly one cube power.
\(24\)
\(12\)
\(63\)
\(196\)
\(420\)