C

2000017604

Level: 
C
Which of the given matrices \(A\), \(B\), \(C\) and \(D\) has a different determinant than the others? \[ A=\left (\array{ 6 & 11 \cr 2 & 2\cr } \right ) \] \[ B=\left (\array{ 1 & 3 \cr 5 & 2\cr } \right ) \] \[ C=\left (\array{ 5 & -2 \cr 10 & -6\cr } \right ) \] \[ D=\left (\array{ 10 & 0 \cr -7 & -1\cr } \right ) \]
\( B\)
\( D\)
All given matrices have the same determinant.
Each matrix has a different determinant.

2010017305

Level: 
C
The picture shows parts of the graphs of the functions \[ \text{$f(x)= \frac{k_{1}} {x} $ and $g(x) = \frac{k_{2}} {x} $.} \] Find the relationship between \(k_{1}\) and \(k_{2}\)?
\( k_1 < k_2\)
\( k_1 \geq k_2\)
\( k_1 = k_2\)
The relationship between \(k_1\) and \(k_2\) cannot be determined from the picture.

2010017304

Level: 
C
Consider the functions \[ \text{$f(x)= -\frac{2} {3x}$ and $g(x) = \frac{k} {x}$.} \] Identify the value of the coefficient \(k\) which ensures that the graphs of both functions are symmetric about \(y\)-axis.
\( k=\frac23\)
\( k=\frac32\)
\( k=-\frac23\)
\( k=-\frac32\)

2010017302

Level: 
C
Find the interval where the function \(f(x) = -\left |2+\frac{1} {x}\right |\) is a decreasing function. The function \(f\) is graphed in the picture.
\(\left[ -\frac12; 0\right)\)
\((-\infty ;0)\)
\(\left[ -\frac12; \infty\right)\)
\(\left(-\infty ; -\frac12\right)\)