| 1 Correct units: $kg/(m \cdot s)$. | 0.10 |
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1
The following expression is obtained: $$ L^3 T^{-1} = L^{a} (M L^{-2} T^{-2})^{b} (M L^{-1} T^{-1})^{c}. $$ |
0.20 |
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2
The correct system of equations is obtained: $$\begin{cases} b + c = 0\\ -1 = -2b - c \\ 3 = a - 2b - c. \end{cases}$$ |
0.10 |
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| 3 The values are found correctly: $$ a=4,~b=1,~c=-1.$$ | 3 × 0.20 |
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1
Correct expression for the pressure force: $$F_p = \Delta P \cdot \pi r^2.$$ |
0.20 |
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1
It is indicated that for a stationary flow, the sum of the lengthwise forces acting on the cylindrical element in question is zero: $$ F_p - F_{fr} = 0. $$ |
0.20 |
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2
The expression for the friction force on the lateral surface of a thin layer is obtained: $$ F_{fr} = \eta\,\frac{-\Delta v}{\Delta r}\cdot 2\pi r L. $$ |
0.30 |
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3
Correct expression for $g$: $$ \frac{-\Delta v}{\Delta r} = -g(r) = \frac{\Delta P}{2\eta L}\, r. $$ |
0.20 |
|
| 4 Correct graph of the dependence $g(r)$ is sketched. | 0.15 |
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| 1 The idea that the change in velocity is proportional to the area under the graph of $g(r)$ was used. | 0.20 |
|
| 2 It is obtained that $v \propto (R^2-r^2)$ | 0.20 |
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3
Correct expression for $v(r)$: $$ v(r)=\frac{k}{2}(R^2-r^2)=\frac{\Delta P}{4\eta L}(R^2-r^2). $$ |
0.20 |
|
| 1 Correct expression for the maximal velocity: $$v_{\max} = v(0) = \frac{\Delta P}{4\eta L}\,R^2.$$ | 0.20 |
|
| 1 Correct graph of $v(r^2)$ is sketched. | 0.15 |
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1
The area under the graph is computed: $$ \text{Area} = \frac{v_{\max}\,R^2}{2}. $$ |
0.10 |
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2
The total volumetric flow rate is obtained: $$ Q = \frac{\pi \Delta P R^4}{8\eta L}. $$ |
0.30 |
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1
The expression for the hydrodynamic resistance is obtained: $$Z_{\text{г}} = \frac{8 \eta L}{\pi R^4}.$$ |
0.10 |
|
|
1
The fluid flow rate in one of the narrow tubes is obtained: $$Q_1 = \frac{Q}{N}.$$ |
0.20 |
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1
Correct ratio is obtained: $$\frac{\Delta P_1}{\Delta P_2} = \frac{\alpha^4N}{\beta}.$$ |
0.20 |
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| 1 The units for hydrodynamic resistances in the table are correct. | 0.10 |
|
| 2 Correct values of $Z$ for each level. | 4 × 0.20 |
|
| 3 The values of $Z$ are given with an excessive number of significant digits. | 4 × -0.10 |
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| 1 Correct values of $\Delta P$ for each level. | 4 × 0.20 |
|
| 2 Values of $\Delta P$ are given with an excessive number of significant digits. | 4 × -0.10 |
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| 1 It was computed that the resistance of the arterioles decreased by $1.2^4$ times. | 0.20 |
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| 1 The new total circuit resistance is computed: $Z_{\rm tot,new} \approx 8.78\times10^7$ Pa$\cdot$s/m${}^3$ | 0.20 |
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| 2 The old total circuit resistance is computed: $Z_{\rm tot,old} \approx 16.6\times10^7$ Pa$\cdot$s/m${}^3$ | 0.20 |
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| 3 The following expression is obtained: $$\frac{\Delta P_{\rm new}}{\Delta P_0}=4\frac{Z_{\rm tot,new}}{Z_{\rm tot,old}}$$ | 0.20 |
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|
4
The correct ratio is computed: $$\frac{\Delta P_{\rm new}}{\Delta P_0} \approx 2.12.$$ |
0.20 |
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1
The formula for calculating the mechanical power $N$ is written: $$N = Q \Delta P.$$ |
0.30 |
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2
The correct ratio is obtained: $$\frac{N_{\rm new}}{N_0} \approx 8.5.$$ |
0.10 |
|
The figure below schematically depicts the circulatory systems of the following vertebrates:
Match the numbers 1-3 in the list with the letters A-C in the diagram. Each letter can be used only once.
| 1 3 matches with the answer 1C, 2A, 3B. | 0.20 |
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| 2 1 match with the answer 1C, 2A, 3B. | 0.10 |
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| 1 The number of matches with the answer 1C, 2E, 3A, 4B, 5D (if there are at least two repeated letters, no points are given). | 5 × 0.06 |
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| 1 Five matches with the answer A, C, D, F, H (the order may be different), the incorrect letters (B, E, G) are not written out. | 0.30 |
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| 2 At least four correct letters and no more than one incorrect letter. | 0.20 |
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| 3 At least three correct letters and no more than two incorrect letters. | 0.10 |
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| 4 Less than three correct letters or three incorrect letters. | 0.00 |
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| Chemical nature | ||
| 2 The number of hormones for which only one cell is marked (in the "Nature" section), and this cell is correct. | 6 × 0.05 |
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| Organ | ||
| 4 The number of hormones for which only one cell is marked (in the "Organ" section), and this cell is correct. | 6 × 0.05 |
|
| Increase of the blood pressure | ||
| 6 $\text{max}(\text{The number of correct answers} - \text{the number of incorrect answers}; 0)$ | 3 × 0.10 |
|
Estimate the effective surface area of the lungs $S$.
Use $D = 10^{-11}$ m${}^2$/s, $d = 1$ μm.
|
1
$W = Q\dfrac{\Delta \nu}{\Delta t}.$ |
0.10 |
|
| 2 $\Delta p = \Delta n kT.$ | 0.10 |
|
| 3 $S\approx 70~\text{m}^2.$ | 0.10 |
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| 1 Correct equation that allows to determine the concentration of $[H^+]$ in solution A, for example: $K_{a_1} = \dfrac{x^2}{0.15 - x}$. | 0.20 |
|
| 2 $\text{pH}_A~2.20.$ | 0.10 |
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| 3 Correct equation that allows to determine the concentration of $[\text{H}^+]$ in solution B, for example: $K_{a_1} \approx\dfrac{[\text{H}^+]C_{salt}}{C_{acid}}$. | 0.20 |
|
| 4 $\text{pH}_B~3.57.$ | 0.10 |
|
| 1 The dilution of solution A is taken into account. | 0.10 |
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| 2 Correct equation that allows to determine the concentration of $[\text{H}^+]$ in solution A, for example: $K_{a_1} = \dfrac{x(0.017 + x)}{0.125 - x} $. | 0.10 |
|
| 3 $\text{pH}_A~1.73$ or $1.78$ in assumption $[\text{H}^+] \ll [\text{H}_2\text{CO}_3]$. | 0.20 |
|
| 4 $\Delta \text{pH}_A = -0.47.$ | 0.05 |
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| 5 The reaction $\text{NaHCO}_3 + \text{HCl} \rightarrow \text{H}_2\text{CO}_3 + \text{NaCl}$ is taking into account. | 0.10 |
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| 6 Recalculation of the weak acid concentration: $0.142~\text{M}$. | 0.10 |
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| 7 Recalculation of the salt concentration: $0.108~\text{M}$. | 0.10 |
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| 8 Correct equation that allows to determine the concentration of $[H^+]$ in solution B, for example: $[\text{H}^+] \approx \dfrac{K_{a_1} C_{acid}}{C_{salt}}$. | 0.10 |
|
| 9 $\text{pH}_B~3.45$. | 0.10 |
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| 10 $\Delta \text{pH}_B = -0.12.$ | 0.05 |
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| 1 $[\text{CO}_2] = kp(\text{CO}_2)$. | 0.10 |
|
| 2 $[\text{CO}_2] = 1.22\cdot10^{-3}~\text{M}$. | 0.10 |
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| 1 $ [\text{H}_2\text{CO}_3]= K_h[\text{CO}_2]$. | 0.10 |
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| 2 $ [\text{H}_2\text{CO}_3] = 3.66\cdot10^{-6}~\text{M}$ | 0.10 |
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| 3 $[\text{HCO}_3^-] = \dfrac{K_{a_1}[\text{H}_2\text{CO}_3]}{[\text{H}^+]} $. | 0.10 |
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| 4 $[\text{HCO}_3^-] = 0.025~\text{M}$. | 0.10 |
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| 1 $ s = [\text{CO}_2] + [\text{H}_2\text{CO}_3] + [\text{HCO}_3^-] $, or $s \approx [\text{HCO}_3^-]$ and it is noted that concentrations of other forms can be ignored. | 0.10 |
|
| 2 $s \approx 0.026~\text{M}$ or $s \approx 0.025~\text{M}$ | 0.10 |
|
| 1 $\alpha = \dfrac{[\text{HbO}_2\text{H}]}{[\text{HbO}_2\text{H}] + [\text{HbO}_2^-]}.$ | 0.05 |
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| 2 $[\text{HbO}_2^-] = \dfrac{K_a}{[\text{H}^+]} [\text{HbO}_2\text{H}]$ | 0.05 |
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| 3 $\alpha = 0.86.$ | 0.10 |
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| 4 $\beta = \dfrac{[\text{Hb}\text{H}]}{[\text{Hb}\text{H}] + [\text{Hb}^-]}.$ | 0.05 |
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| 5 $[\text{Hb}^-] = \dfrac{K_a}{[\text{H}^+]} [\text{Hb}\text{H}]$ | 0.05 |
|
| 6 $\beta = 0.14$. | 0.10 |
|
| 1 Correct expression that allows to determine $a, b, c, d$ is written. | 0.10 |
|
| 2 $a = 34$. | 0.05 |
|
| 3 $b = 32$. | 0.05 |
|
| 4 $c = 4$. | 0.05 |
|
| 5 $d = 4$. | 0.05 |
|
Below is a list of chemical bonds that appear in the structures mentioned above. Write down the letters representing the chemical bonds in the appropriate cells of the table below. Note that the same letters may be used in different cells.
A. Disulfid bridges (–S–S–).
B. Ionic bonds.
C. Hydrogen bonds within a molecule.
D. Hydrophobic interactions.
E. Peptide bonds.
F. Intermolecular hydrogen bonds.
| 1 Only the letter E is indicated for the primary structure. | 0.05 |
|
| 2 Only the letter C is indicated for the secondary structure. | 0.05 |
|
| The tertiary structure | ||
| 4 Only the correct letters A, B, C, D are written. | 0.10 |
|
| 5 There are at least three correct letters and no more than one incorrect letter (E or F). | 0.05 |
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| 6 There are less than three correct letters or 2 incorrect letters (E and F). | 0.00 |
|
| The quaternary structure | ||
| 8 Only the correct letters A, B, D, F are written. | 0.10 |
|
| 9 There are at least three correct letters and no more than one incorrect letter (C or E). | 0.05 |
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| 10 There are less than three correct letters or 2 incorrect letters (C and E). | 0.00 |
|
| 1 The number of correct answers. | 7 × 0.05 |
|
| 1 $K_a = \dfrac{[\text{PL}]}{[\text{P}][\text{L}]}$ | 0.05 |
|
| 2 $\theta = \dfrac{[\text{L}]}{[\text{L}] + 1/K_a}.$ | 0.05 |
|
| 3 $K_a = 1 / [\text{L}]_{0.5}$. | 0.10 |
|
| 1 Both graphs pass through (0,0). | 0.05 |
|
| 2 Both graphs have the form of a hyperbola. | 0.05 |
|
| 3 Both graphs have a horizontal asymptote of $\theta = 1$. | 0.05 |
|
| 4 For carbon monoxide, the graph has plateaued faster than the graph for oxygen. | 0.10 |
|
| 1 The numerical values of $1/T$ are calculated. | 5 × 0.02 |
|
| 2 The axes are labeled and numbered. | 0.10 |
|
| 3 The points are correctly plotted on the graph. | 5 × 0.03 |
|
| 4 An approximating line was drawn. | 0.10 |
|
| 5 The numerical values of $\ln K_a$ were calculated. | 5 × 0.02 |
|
| 6 The slope $\alpha$ of the graph $\ln K_a(1/T)$ is determined: $\alpha \approx 6600$ K. | 0.20 |
|
| 7 The numerical value of $\Delta H$ is computed: $\Delta H \approx -55$ kJ/mol. | 0.15 |
|
| 1 $\theta = \dfrac{[\text{L}]^n}{[\text{L}]^n + 1/K_a} .$ | 0.10 |
|
| 2 $\log_{10} \left(\dfrac{\theta}{1 - \theta}\right) = n\log_{10}[\text{L}] + \log_{10} K_a$. | 0.10 |
|
| 1 $n_H \in [2.4, 3.0]$. | 0.10 |
|
| 2 $(n_H)_{max} = 4$. | 0.10 |
|
Give the reason why myoglobin cannot be used as an effective oxygen carrier (efective binding and release of oxygen molecules) from the lungs to the tissues.
A. The myoglobin molecule has a hyperbolic oxygen saturation curve.
B. The concentration of myoglobin in the blood is significantly lower than the concentration of hemoglobin.
C. The myoglobin molecule is lighter, which makes it too mobile.
D. The myoglobin molecule is too small, which can cause it to enter other tissues.
| 1 The answer А. | 0.10 |
|
Choose the correct statement:
| 1 The answer 2. | 0.20 |
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Which curve corresponds to hemoglobin in the lungs, and which corresponds to hemoglobin in tissues (mark with an "X" in the table in the answer sheets).
| 1 The table is filled in correctly. | 0.10 |
|
| 2 Filling in the table differs from the correct one. | 0.00 |
|
In certain conditions, increased level of myoglobin in blood could be a result of:
A. State of alcohol intoxication.
B. Myocardial infarction.
C. Use of sleeping pills.
D. Alzheimer's disease.
| 1 The answer B. | 0.10 |
|