Test 11
1.
\(\beta(a,b)=2a+3b-ab\)
\(\beta(1,x)=\beta(x,1)\)
\(\Rightarrow x=?\)
A) \(1\)B) \(2\)C) \(3\)D) \(4\)E) \(5\)
2.
\(\beta(x,y)=\samefrac{1}{x}+\samefrac{1}{y}\)
\(\beta\left(\samefrac{1}{2},\samefrac{1}{7}\right)=\beta\left(\samefrac{1}{a},\samefrac{2}{a}\right)\)
\(\Rightarrow a=?\)
A) \(1\)B) \(2\)C) \(3\)D) \(6\)E) \(9\)
3.
\(\beta(x,y)=|x|+2y-2\)
\(\beta(-2,3)=\beta(5,a)\)
\(\Rightarrow a=?\)
A) \(1\)B) \(\samefrac{3}{2}\)C) \(\samefrac{5}{2}\)D) \(4\)E) \(5\)
4.
\(\beta\left(\samefrac{1}{x},y\right)=x+\samefrac{1}{y}\)
\(\beta\left(\samefrac{1}{3},\samefrac{1}{2}\right)=\beta\left(\samefrac{3}{a},3\right)\)
\(\Rightarrow a=?\)
A) \(20\)B) \(18\)C) \(15\)D) \(14\)E) \(6\)
5.
\(\beta(a,b)=a^2-2a+b,\)
\(\beta(2,x)=\beta(x,-4)\)
\(\Rightarrow \{x_1,x_2\}=?\)
A) \(\{1,-1\}\)B) \(\{1,4\}\)C) \(\{-1,4\}\)D) \(\{4,-4\}\)E) \(\{0,4\}\)
6.
\(\beta(a,b)=\begin{cases}2a+b&a\ge b\\a^2+b&a<b\end{cases}\)
\(\beta(4,2)=\beta(1,x)\)
\(\Rightarrow x=?\)
A) \(-1\)B) \(1\)C) \(2\)D) \(6\)E) \(9\)
7.
\(\beta(a,b)=\begin{cases}2a-b,&a\le b\\a+b,&a>b\end{cases}\)
\(\beta(2,3)=\beta(3,x)\)
\(x<5\)
\(\Rightarrow x=?\)
A) \(-2\)B) \(-1\)C) \(0\)D) \(1\)E) \(2\)
8.
\(\beta=\{(x,y)\in\mathbb{Z}^+\times\mathbb{Z}^+\mid x\cdot y=12\}\)
\(\Rightarrow n(\beta)=?\)
A) \(2\)B) \(3\)C) \(4\)D) \(6\)E) \(12\)