9000140502
Level:
B
Simplify for \(n\in \mathbb{N}\).
\[
\frac{(n + 1)!}
{(n - 1)!}
\]
\(n^{2} + n\)
\((n + 1)^{2}\)
\(\frac{n+1}
{n-1}\)
\(- 1\)
B
9000140503
Level:
B
Simplify for \(n\in \mathbb{N}\).
\[
\frac{(n + 1)! + (n - 1)!}
{n!}
\]
\(\frac{n^{2}+n+1}
{n} \)
\(2\)
\(n^{2} - 1\)
\(\frac{n^{2}-n+1}
{n} \)
9000140509
Level:
B
Find the solution set of the equation assuming
\(x\in \mathbb{N}\).
\[
(x + 1)! = 6(x - 1)!
\]
\(\{2\}\)
\(\{ - 3;\ 2\}\)
\(\left \{\frac{5}
{7}\right \}\)
\(\left \{\frac{7}
{5}\right \}\)
9000140510
Level:
B
Find the solution set of the equation assuming
\(x\in \mathbb{N}\).
\[
(x + 1)! + x! = 6x + 12
\]
\(\{3\}\)
\(\{2\}\)
\(\{1\}\)
\(\{4\}\)
9000140505
Level:
B
Simplify \(\frac{72!}
{70!+71!}\).
\(71\)
\(72\)
\(\frac{72}
{141}\)
\(\frac{72!}
{141!}\)
9000138306
Level:
B
Two dice are rolled. Find the probability that we get the number \(3\) at least once.
\(\frac{11}
{36}\doteq 0{.}3056\)
\(\frac{3}
{36}\doteq 0{.}0833\)
\(\frac{10}
{36}\doteq 0{.}2778\)
\(\frac{12}
{36}\doteq 0{.}3333\)
9000138307
Level:
B
Two dice are rolled. What is the probability of getting \(10\) as the product of the two dice.
\(\frac{2}
{36}\doteq 0{.}0556\)
\(\frac{10}
{36}\doteq 0{.}2778\)
\(\frac{1}
{36}\doteq 0{.}0278\)
\(\frac{5}
{36}\doteq 0{.}1389\)
9000138309
Level:
B
Two dices are rolled. Find the probability that we get either the
same number on both dices or the sum of the numbers on both dices is
\(6\).
\(\frac{10}
{36}\doteq 0{.}2778\)
\(\frac{11}
{36}\doteq 0{.}3056\)
\(\frac{6}
{36}\doteq 0{.}1667\)
\(\frac{5}
{36}\doteq 0{.}1389\)
9000140501
Level:
B
Simplify for \(n\in \mathbb{N}\).
\[
\frac{n!}
{(n - 1)!}
\]
\(n\)
\(\frac{n}
{n-1}\)
\(\frac{n!}
{n!-1!}\)
\(- 1\)
9000140504
Level:
B
Simplify for \(n\in \mathbb{N}\),
\(n\geq 2\).
\[
\frac{n\cdot (n - 2)!}
{(n - 1)\cdot n!}
\]
\(\frac{1}
{(n-1)^{2}} \)
\(\frac{(n^{2}-2n)!}
{(n^{2}-n)!} \)
\(\frac{n+1}
{n-1}\)
\(\frac{(n-2)!}
{(n-1)!}\)