A

9000150307

Level: 
A
Evaluate the following integral on \(\mathbb{R}\). \[ \int 8\cdot 5^{x}\, \text{d}x \]
\(\frac{8\cdot 5^{x}} {\ln 5} + c,\ c\in \mathbb{R}\)
\(\frac{8\cdot 5^{x}} {\ln x} + c,\ c\in \mathbb{R}\)
\(8\cdot 5^{x}\cdot \ln 5 + c,\ c\in \mathbb{R}\)
\(8\cdot 5^{x}\cdot \ln x + c,\ c\in \mathbb{R}\)

9000148906

Level: 
A
Each candidate in a tender is fluent in at least one out of two required languages (English and French). There are \(20\) candidates fluent in English and \(14\) candidates fluent in French. From these amounts \(10\) candidates are fluent in both languages. How many candidates are there in the tender?
\(24\)
\(34\)
\(14\)
\(44\)

9000150101

Level: 
A
Evaluate the following integral on \(\mathbb{R}\). \[ \int \left (\cos x -\sin x\right )\, \mathrm{d}x \]
\(\sin x +\cos x + c,\ c\in \mathbb{R}\)
\(\sin x -\cos x + c,\ c\in \mathbb{R}\)
\(-\sin x +\cos x + c,\ c\in \mathbb{R}\)
\(-\sin x -\cos x + c,\ c\in \mathbb{R}\)

9000150103

Level: 
A
Evaluate the following integral on the interval \(\left(-\frac{\pi}2;\frac{\pi}2\right)\). \[ \int \left ( \frac{3} {\cos ^{2}x} - 3\mathrm{e}^{x}\right )\, \mathrm{d}x \]
\(3\mathop{\mathrm{tg}}\nolimits x - 3\mathrm{e}^{x} + c,\ c\in \mathbb{R}\)
\(- 3\mathop{\mathrm{tg}}\nolimits x - 3\mathrm{e}^{x} + c,\ c\in \mathbb{R}\)
\(- 3\mathop{\mathrm{tg}}\nolimits x + 3\mathrm{e}^{x} + c,\ c\in \mathbb{R}\)
\(3\mathop{\mathrm{tg}}\nolimits x + 3\mathrm{e}^{x} + c,\ c\in \mathbb{R}\)

9000148909

Level: 
A
There are \(24\) girls and \(8\) boys in the class. How many ways are there to designate a president and vice-president of the class if it is required that one of the position will be held by a boy and the other one by a girl?
\(24\cdot 8\cdot 2=384\)
\(24\cdot 8=192\)
\(\frac{32!} {2!\; 30!}=496\)
\(\frac{32!} {24!\; 8!}=10\:518\:300\)

9000148904

Level: 
A
Pamela needs new ski for a ski course. There are skis from six different vendors in a shop. The shop has four different ski pairs from each vendor, but two vendors have all products behind Pam's financial limit. How many pairs are at disposal for Pam?
\(4\cdot 4=16\)
\(4!=24\)
\(4\cdot 2=8\)
\(4 + 2=6\)