B

1003027305

Level: 
B
Choose an incorrect evaluation of the following indefinite integral on \( (0;\infty) \). \[ \int\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\,\mathrm{d}x \]
\( x^2-2x+c\text{, }c\in\mathbb{R} \)
\( \frac{x^2}2-x+c\text{, }c\in\mathbb{R} \)
\( \frac{x^2-2x}2+c\text{, }c\in\mathbb{R} \)
\( \frac{x^4-4x^2}{2x(x+2)}+c\text{, }c\in\mathbb{R} \)

1003027302

Level: 
B
Evaluate the following indefinite integral on \( \left(-\frac{\pi}2;\frac{\pi}2 \right) \). \[ \int \left(\frac1{\cos x}-\sin x\cdot\mathrm{tg}\,x\right)\,\mathrm{d}x \]
\( \sin x+c\text{, }c\in\mathbb{R} \)
\( \cos x+c\text{, }c\in\mathbb{R} \)
\( -\sin x+c\text{, }c\in\mathbb{R} \)
\( -\cos x+c\text{, }c\in\mathbb{R} \)

1003027301

Level: 
B
Evaluate the following indefinite integral on \( \left(0;\frac{\pi}2 \right) \). \[ \int\frac{(\sin x+\cos x)^2-1}{\sin x\cos x}\,\mathrm{d}x \]
\( 2x+c\text{, }c\in\mathbb{R} \)
\( x+c\text{, }c\in\mathbb{R} \)
\( \mathrm{tg}\,x+c\text{, }c\in\mathbb{R} \)
\( c\text{, }c\in\mathbb{R} \)

1003029305

Level: 
B
The production process of a particular component consists of three independent phases. Through long-term monitoring of production quality were found success rates of individual phases \( 90\% \), \( 80\% \) and \( 85\% \). If all three phases of the process are successful, the component is of good quality. What is the probability of producing a good quality component?
\( 0{.}612 \)
\( 0{.}003 \)
\( 0{.}388 \)
\( 0{.}997 \)

1003029302

Level: 
B
The quality inspection found that \( 85\% \) of the items are without defect, exactly one defect has \( 10\% \) of the items, and the other items have more than one defect. We pick one item randomly. What is the probability that this item has at least one defect?
\( 0{.}15 \)
\( 0{.}10 \)
\( 0{.}95 \)
\( 0{.}01 \)