MikaStars39/nano-eval huggingface dataset:
Using series-connected continuously stirred tank reactors (CSTRs) for a first-order irreversible reaction, assuming that the volume and operating temperature of each reactor are identical, the rate constant at this temperature is known to be $k \!=\! 0.92 \, \, \, \mathrm{h}^{-1}$. The feed rate of the raw material is $\upsilon_{0} = 10 \, \mathrm{m^{3} / h}$, and the required final conversion rate is 0.90. When the number of reactors in series $N$ is 100, what is the total reactor volume?

Options:
A. $$
24.6m^{3}
$$
B. $$
18.9m^{3}
$$
C. $$
15.6m^{3}
$$
D. $$
20.8m^{3}
$$
E. $$
30.5m^{3}
$$
F. $$
29.1m^{3}
$$
G. $$
28.3m^{3}
$$
H. $$
22.4m^{3}
$$
I. $$
25.3m^{3}
$$
J. $$
35.7m^{3}
$$
Answer: I
A first-order series reaction $\mathrm{A} \stackrel{1}{\longrightarrow} \mathrm{P} \stackrel{2}{\longrightarrow} \mathrm{S}$ is given. Determine the optimal reaction time $\tau_{\mathrm{o p t}}$ and the maximum yield of product $\mathbf{P}$ is ().

Options:
A. $$
\tau_{\mathrm{o p t}}={\frac{2} {k_{2}}}
$$
$$
\phi_{\operatorname* {m a x}}={\frac{c_{p, \operatorname* {m a x}}} {c_{\operatorname* {A0}}}}={\frac{\sqrt{k_{1}}} {\left(k_{1} + k_{2}\right)^{2}}}
$$
B. $$
\tau_{\mathrm{o p t}}={\sqrt{\frac{1} {k_{1} + k_{1} k_{2}}}}
$$
$$
\phi_{\operatorname* {m a x}}={\frac{c_{p, \operatorname* {m a x}}} {c_{\operatorname* {A0}}}}={\frac{1} {k_{1} + \sqrt{k_{2}}}}
$$
C. $$
\tau_{\mathrm{o p t}}={\frac{1} {k_{1} - k_{2}}}
$$
$$
\phi_{\operatorname* {m a x}}={\frac{c_{p, \operatorname* {m a x}}} {c_{\operatorname* {A0}}}}={\frac{k_{1} k_{2}} {k_{1} + k_{2}}}
$$
D. $$
\tau_{\mathrm{o p t}}={\frac{\ln 2} {k_{1} k_{2}}}
$$
$$
\phi_{\operatorname* {m a x}}={\frac{c_{p, \operatorname* {m a x}}} {c_{\operatorname* {A0}}}}={\left[ \frac{k_{2}} {k_{1}} \right]^{1 / 2}}
$$
E. $$
\tau_{\mathrm{o p t}}={\frac{1} {k_{1}+k_{2}}}
$$
$$
\phi_{\operatorname* {m a x}}={\frac{c_{p, \operatorname* {m a x}}} {c_{\operatorname* {A0}}}}={\frac{1} {\left[ 1+\left( {\frac{k_{1}} {k_{2}}} \right)^{3 / 2} \right]}}
$$
F. $$
\tau_{\mathrm{o p t}}={\frac{\ln k_{2}} {k_{1}}}
$$
$$
\phi_{\operatorname* {m a x}}={\frac{c_{p, \operatorname* {m a x}}} {c_{\operatorname* {A0}}}}={\frac{1} {\left[1+\left(k_{2}/k_{1}^{1/3}\right)\right]^{2}}}
$$
G. $$
\tau_{\mathrm{o p t}}={\frac{\ln 2} {k_{1}}}
$$
$$
\phi_{\operatorname* {m a x}}={\frac{c_{p, \operatorname* {m a x}}} {c_{\operatorname* {A0}}}}={\frac{k_{1}} {k_{1} + k_{2}}}
$$
H. $$
\tau_{\mathrm{o p t}}={\frac{1} {\sqrt{k_{1} k_{2}}}}
$$
$$
\phi_{\operatorname* {m a x}}={\frac{c_{p, \operatorname* {m a x}}} {c_{\operatorname* {A0}}}}={\frac{1} {\left[ 1+\left( {\frac{k_{2}} {k_{1}}} \right)^{1 / 2} \right]^{2}}}
$$
I. $$
\tau_{\mathrm{o p t}}={\frac{k_{2}} {k_{1}^{2}}}
$$
$$
\phi_{\operatorname* {m a x}}={\frac{c_{p, \operatorname* {m a x}}} {c_{\operatorname* {A0}}}}={\frac{\left(k_{1} + k_{2}\right)} {k_{1}^{2}}}
$$
J. $$
\tau_{\mathrm{o p t}}={\sqrt{\frac{k_{2}} {k_{1}}}}
$$
$$
\phi_{\operatorname* {m a x}}={\frac{c_{p, \operatorname* {m a x}}} {c_{\operatorname* {A0}}}}={\frac{\left[k_{2}\right]} {1+k_{1}^{1 / 2}}}
$$
Answer: H
The available reactors consist of one CSTR and one PFR, each with a volume of $4 \mathbf{m}^{3}$. The following liquid-phase reactions are carried out under isothermal conditions:
$$
\begin{array} {l l}
\mathrm{A + B \to P,} & r_{\mathrm{P}} = 1.6 c_{\mathrm{A}} \ \mathrm{mol} / (\mathrm{m}^{3} \cdot \mathrm{h}) \\
\mathrm{2A \to R,} & r_{\mathrm{R}} = 8.2 c_{\mathrm{A}}^{2} \ \mathrm{mol} / (\mathrm{m}^{3} \cdot \mathrm{h}) \\
\end{array}
$$
The mixture of A and B is processed at a rate of $8 \mathrm{m}^{3} / \mathrm{h}$, where the initial concentration of component $\mathrm{A}$ is $c_{\mathrm{A 0}} = 2 \mathrm{kmol} / \mathrm{m}^{3}$. If the desired product is $\mathbf{P}$, what is the yield of the desired product $\mathbf{P}$ when using the CSTR?

Options:
A. 0.1392
B. 0.1943
C. 0.1764
D. 0.1475
E. 0.1582
F. 0.1638
G. 0.1845
H. 0.1254
I. 0.1721
J. 0.1347
Answer: E
The system is described by the following state-space equations:
$$
{\left[ \begin{array} {l} {{{\dot{x}_{1}}}} \\ {{{\dot{x}_{2}}}} \\ {{{\dot{x}_{3}}}} \\ \end{array} \right]}={\left[ \begin{array} {l l l} {{-1}} & {{1}} & {{0}} \\ {{0}} & {{-1}} & {{1}} \\ {{0}} & {{0}} & {{-2}} \\ \end{array} \right]} {\left[ \begin{array} {l} {{x_{1}}} \\ {{x_{2}}} \\ {{x_{3}}} \\ \end{array} \right]}+{\left[ \begin{array} {l} {{0}} \\ {{0}} \\ {{1}} \\ \end{array} \right]} u
$$
$$
y=[ 1 \quad0 \quad0 ] {\left[ \begin{matrix} {{x_{1}}} \\ {{x_{2}}} \\ {{x_{3}}} \\ \end{matrix} \right]}
$$
What is the transfer function of this system?

Options:
A. $$
G(s)=\frac{1} {s^{3} \,+\, 4 s^{2} \,+\, 5 s \,+\, 2}
$$
B. $$
G(s)=\frac{1} {s^{3} \,+\, 3 s^{2} \,+\, 4 s \,+\, 2}
$$
C. $$
G(s)=\frac{1} {s^{3} \,+\, 5 s^{2} \,+\, 7 s \,+\, 4}
$$
D. $$
G(s)=\frac{1} {s^{3} \,+\, 3 s^{2} \,+\, 4 s \,+\, 3}
$$
E. $$
G(s)=\frac{1} {s^{3} \,+\, 2 s^{2} \,+\, 5 s \,+\, 3}
$$
F. $$
G(s)=\frac{1} {s^{3} \,+\, 6 s^{2} \,+\, 8 s \,+\, 4}
$$
G. $$
G(s)=\frac{1} {s^{3} \,+\, 4 s^{2} \,+\, 6 s \,+\, 3}
$$
H. $$
G(s)=\frac{1} {s^{3} \,+\, 5 s^{2} \,+\, 6 s \,+\, 4}
$$
I. $$
G(s)=\frac{1} {s^{3} \,+\, 4 s^{2} \,+\, 6 s \,+\, 2}
$$
J. $$
G(s)=\frac{1} {s^{3} \,+\, 3 s^{2} \,+\, 5 s \,+\, 1}
$$
Answer: A
What is the transfer matrix of the system described by the following state-space equations?
$$
\left[ \begin{array} {r} {{{\dot{x}_{1}}}} \\ {{{\dot{x}_{2}}}} \\ {{{\dot{x}_{3}}}} \\ \end{array} \right]=\left[ \begin{array} {r r r} {{{0}}} & {{{1}}} & {{{0}}} \\ {{{0}}} & {{{0}}} & {{{1}}} \\ {{{-2}}} & {{{-4}}} & {{{-6}}} \\ \end{array} \right] \left[ \begin{array} {r} {{{x_{1}}}} \\ {{{x_{2}}}} \\ {{{x_{3}}}} \\ \end{array} \right]+\left[ \begin{array} {r r} {{{0}}} & {{{0}}} \\ {{{0}}} & {{{1}}} \\ {{{1}}} & {{{0}}} \\ \end{array} \right] \left[ \begin{array} {r} {{{u_{1}}}} \\ {{{u_{2}}}} \\ \end{array} \right]
$$
$$
\left[ \begin{matrix} {{{y_{1}}}} \\ {{{y_{2}}}} \\ \end{matrix} \right]=\left[ \begin{matrix} {{{1}}} & {{{0}}} & {{{0}}} \\ {{{0}}} & {{{1}}} & {{{0}}} \\ \end{matrix} \right] \left[ \begin{matrix} {{{x_{1}}}} \\ {{{x_{2}}}} \\ {{{x_{3}}}} \\ \end{matrix} \right]
$$

Options:
A. $$
G(s)=\left[ \begin{array} {c c} {{{{\frac{1+s} {s^{2}+6 s^{2}+4 s+2}}}}} & {{{{\frac{5} {s^{3}+4 s+2}}}}} \\ {{{{\frac{s} {s^{3}+4+2}}}}} & {{{{\frac{6+s^{2}} {s^{3}+6 s^{2}+4+2}}}}} \\ \end{array} \right]
$$
B. $$
G(s)=\left[ \begin{array} {c c} {{{{\frac{1} {s^{2}+6 s^{2}+4 s+2}}}}} & {{{{\frac{s} {s^{3}+6 s^{2}+4 s+2}}}}} \\ {{{{\frac{s^{2}} {s^{3}+4 s+2}}}}} & {{{{\frac{s+6} {s^{2}+6 s^{2}+4s+2}}}}} \\ \end{array} \right]
$$
C. $$
G(s)=\left[ \begin{array} {c c} {{{{\frac{1} {s^{3}+6 s^{2}+4 s+2}}}}} & {{{{\frac{s+6} {s^{3}+6 s^{2}+4 s+2}}}}} \\ {{{{\frac{s} {s^{2}+6 s^{2}+4 s+2}}}}} & {{{{\frac{s^{2}+6 s} {s^{2}+6 s^{2}+4s+2}}}}} \\ \end{array} \right]
$$
D. $$
G(s)=\left[ \begin{array} {c c} {{{{\frac{s} {s^{3}+6 s^{2}+4 s+2}}}}} & {{{{\frac{1+6} {s^{2}+6 s^{2}+4+2}}}}} \\ {{{{\frac{s} {s^{2}+4 s^{2}+2}}}}} & {{{{\frac{s^{2}+4 s} {s^{3}+6 s^{2}+4s+2}}}}} \\ \end{array} \right]
$$
E. $$
G(s)=\left[ \begin{array} {c c} {{{{\frac{1} {s^{3}+6 s^{2}+2}}}}} & {{{{\frac{5} {s^{2}+4 s+2}}}}} \\ {{{{\frac{s+6} {s^{2}+6 s^{2}+4 s+2}}}}} & {{{{\frac{s} {s^{3}+6+4+2}}}}} \\ \end{array} \right]
$$
F. $$
G(s)=\left[ \begin{array} {c c} {{{{\frac{1} {s^{3}+4 s+2}}}}} & {{{{\frac{s+6} {s^{2}+6 s^{2}+4 s+2}}}}} \\ {{{{\frac{1+s} {s^{3}+4 s+2}}}}} & {{{{\frac{s^{3}} {s^{2}+4+2}}}}} \\ \end{array} \right]
$$
G. $$
G(s)=\left[ \begin{array} {c c} {{{{\frac{1} {s^{2}+4+2}}}}} & {{{{\frac{6} {s^{3}+6 s^{2}+4 s+2}}}}} \\ {{{{\frac{s^{2}} {s^{2}+6 s^{2}+4 s+2}}}}} & {{{{\frac{4+s} {s^{3}+6+2}}}}} \\ \end{array} \right]
$$
H. $$
G(s)=\left[ \begin{array} {c c} {{{{\frac{1} {s^{2}+6 s^{2}+4 s+2}}}}} & {{{{\frac{5+s} {s^{2}+6+4+2}}}}} \\ {{{{\frac{s+1} {s^{3}+6 s^{2}+4+2}}}}} & {{{{\frac{s^{2}} {s^{3}+4+2}}}}} \\ \end{array} \right]
$$
I. $$
G(s)=\left[ \begin{array} {c c} {{{{\frac{s} {s^{3}+6 s^{2}+4 s}}}}} & {{{{\frac{s+6} {s^{3}+4 s+2}}}}} \\ {{{{\frac{s+1} {s^{2}+6 s^{2}+4 s+2}}}}} & {{{{\frac{s^{2}+4} {s^{3}+6 s^{2}+2}}}}} \\ \end{array} \right]
$$
J. $$
G(s)=\left[ \begin{array} {c c} {{{{\frac{1} {s^{2}+6 s+2}}}}} & {{{{\frac{s+6} {s^{3}+4+2}}}}} \\ {{{{\frac{s^{2}} {s^{2}+6+4+2}}}}} & {{{{\frac{4+s} {s^{3}+6 s+2}}}}} \\ \end{array} \right]
$$
Answer: C
Given a cubic polynomial:
$$
a_{0} s^{3} \,+\, a_{1} s^{2} \,+\, a_{2} s \,+\, a_{3}=0
$$
where all coefficients are positive numbers. What is the application of the Routh-Hurwitz stability criterion to this equation?

Options:
A. $$
a_{0} a_{2} = a_{1} a_{3}
$$
B. $$
a_{0} a_{1} > a_{2} a_{3}
$$
C. $$
a_{1} a_{2} > a_{0} a_{3}
$$
D. $$
a_{1} a_{2} < a_{0} a_{3}
$$
E. $$
a_{2} a_{3} > a_{0} a_{1}
$$
F. $$
a_{0} a_{2} > a_{1} a_{3}
$$
G. $$
a_{1} a_{3} > a_{0} a_{2}
$$
H. $$
a_{1}^{2} > a_{0} a_{3}
$$
I. $$
a_{3} a_{1} > a_{0} a_{2}
$$
J. $$
a_{0}^{2} > a_{1} a_{2}
$$
Answer: C
For a given closed-loop system:
$$
\frac{C(s)}{R(s)} = \frac{36}{s^2 + 2s + 36}
$$
What is the rise time of this system in response to a unit step input through analysis and calculation?

Options:
A. $$
0. 2 9 9 5 \ s e c
$$
B. $$
0. 3 3 0 5 \ s e c
$$
C. $$
0. 3 1 4 2 \ s e c
$$
D. $$
0. 2 8 5 0 \ s e c
$$
E. $$
0. 3 0 0 0 \ s e c
$$
F. $$
0. 2 9 3 8 \ s e c
$$
G. $$
0. 2 8 0 2 \ s e c
$$
H. $$
0. 3 0 4 8 \ s e c
$$
I. $$
0. 2 7 6 0 \ s e c
$$
J. $$
0. 3 2 7 0 \ s e c
$$
Answer: F
Consider a unity feedback control system with the forward transfer function
$$
G(s) = \frac{K}{s(s^2 + 4s + 8)}
$$
If the gain is set as $K = 2$, what is the position of the closed-loop poles?

Options:
A. $$
s=-1. 8 8 8 8
$$
B. $$
s=-0. 2 8 8 7
$$
C. $$
s=-2. 2 2 2 2
$$
D. $$
s=-1. 2 3 4 4
$$
E. $$
s=-0. 9 9 8 7
$$
F. $$
s=-1. 5 0 0 0
$$
G. $$
s=-0. 7 7 7 8
$$
H. $$
s=-3. 1 0 0 2
$$
I. $$
s=-0. 5 4 3 2
$$
J. $$
s=-0. 3 0 5 6
$$
Answer: B
Given that the open-loop transfer function of the unit feedback system is
$$
G(s) = \frac{10}{s+1}
$$
what is the steady-state output of the system when subjected to the following input signal?
$$
r(t) = \sin\left(t + 30^{\circ}\right) - 2\cos\left(2t - 45^{\circ}\right)
$$

Options:
A. $$
C_{ss} ( t )=0. 9 1 0 sin( t+2 2. 0^{\circ} )-1. 8 2 \, cos( 2 t-3 6. 5^{\circ} )
$$
B. $$
C_{ss} ( t )=0. 9 0 5 sin( t+2 5. 0^{\circ} )-1. 6 0 \, cos( 2 t-3 8. 0^{\circ} )
$$
C. $$
C_{ss} ( t )=0. 9 0 5 sin( t+2 4. 2^{\circ} )-1. 8 0 \, cos( 2 t-3 4. 5^{\circ} )
$$
D. $$
C_{ss} ( t )=0. 8 9 5 sin( t+2 7. 0^{\circ} )-1. 7 8 \, cos( 2 t-3 4. 9^{\circ} )
$$
E. $$
C_{ss} ( t )=0. 9 0 5 sin( t+2 4. 8^{\circ} )-1. 7 9 \, cos( 2 t-5 5. 3^{\circ} )
$$
F. $$
C_{ss} ( t )=1. 0 1 5 sin( t+2 3. 5^{\circ} )-1. 8 3 \, cos( 2 t-3 6. 0^{\circ} )
$$
G. $$
C_{ss} ( t )=0. 9 9 5 sin( t+3 0. 0^{\circ} )-1. 7 0 \, cos( 2 t-3 7. 2^{\circ} )
$$
H. $$
C_{ss} ( t )=0. 8 5 0 sin( t+2 6. 0^{\circ} )-1. 6 5 \, cos( 2 t-3 4. 0^{\circ} )
$$
I. $$
C_{ss} ( t )=1. 0 0 0 sin( t+2 8. 5^{\circ} )-1. 7 5 \, cos( 2 t-3 5. 8^{\circ} )
$$
J. $$
C_{ss} ( t )=0. 8 7 0 sin( t+2 6. 5^{\circ} )-1. 7 2 \, cos( 2 t-3 3. 9^{\circ} )
$$
Answer: E
Consider a unit feedback control system with an open-loop transfer function given as
$$
G(s) = \frac{K}{s(s^2 + s + 4)}
$$
What is the value of the gain $K$ required to achieve a phase margin of 50°?

Options:
A. 2.85
B. 3.20
C. 2.50
D. 3.98
E. 3.46
F. 5.12
G. 4.00
H. 2.90
I. 4.25
J. 3.60
Answer: E
System
$$
\left[ \begin{array} {r} {{{\dot{x}_{1}}}} \\ {{{\dot{x}_{2}}}} \\ \end{array} \right]=\left[ \begin{array} {r r} {{0}} & {{1}} \\ {{-2}} & {{-3}} \\ \end{array} \right] \left[ \begin{array} {r} {{x_{1}}} \\ {{x_{2}}} \\ \end{array} \right]
$$
What is the inverse of the state transition matrix $\mathbf{\Phi}^{-1} ( t )$?

Options:
A. $$
\left[ \begin{matrix} {{{\mathbf{e}^{-t} \,-\, \mathbf{e}^{-2 t}}}} & {{{\mathbf{e}^{-t} \,+\, \mathbf{e}^{-2 t}}}} \\ {{{-2 \mathbf{e}^{-t} \,+\, \mathbf{e}^{-2 t}}}} & {{{-\mathbf{e}^{-t} \,+\, 2 \mathbf{e}^{-2 t}}}} \\ \end{matrix} \right]
$$
B. $$
\left[ \begin{matrix} {{{2 \mathbf{e}^{-t} \,+\, \mathbf{e}^{-2 t}}}} & {{{-\mathbf{e}^{-t} \,+\, 2 \mathbf{e}^{-2 t}}}} \\ {{{\mathbf{e}^{-t} \,-\, \mathbf{e}^{-2 t}}}} & {{{\mathbf{e}^{-t} \,-\, \mathbf{e}^{-2 t}}}} \\ \end{matrix} \right]
$$
C. $$
\left[ \begin{matrix} {{{-\mathbf{e}^{-t} \,+\, \mathbf{e}^{-2 t}}}} & {{{\mathbf{e}^{-t} \,-\, 2 \mathbf{e}^{-2 t}}}} \\ {{{2 \mathbf{e}^{-t} \,-\, \mathbf{e}^{-2 t}}}} & {{{2 \mathbf{e}^{-t} \,+\, \mathbf{e}^{-2 t}}}} \\ \end{matrix} \right]
$$
D. $$
\left[ \begin{matrix} {{{\mathbf{e}^{-t} \,-\, \mathbf{e}^{-2 t}}}} & {{{2 \mathbf{e}^{-t} \,-\, 2 \mathbf{e}^{-2 t}}}} \\ {{{-\mathbf{e}^{-t} \,+\, \mathbf{e}^{-2 t}}}} & {{{\mathbf{e}^{-t} \,-\, 2 \mathbf{e}^{-2 t}}}} \\ \end{matrix} \right]
$$
E. $$
\left[ \begin{matrix} {{{2 \mathbf{e}^{-t} \,-\, \mathbf{e}^{-2 t}}}} & {{{\mathbf{e}^{-t} \,-\, \mathbf{e}^{-2 t}}}} \\ {{{-2 \mathbf{e}^{-t} \,+\, 2 \mathbf{e}^{-2 t}}}} & {{{-\mathbf{e}^{-t} \,+\, 2 \mathbf{e}^{-2 t}}}} \\ \end{matrix} \right]
$$
F. $$
\left[ \begin{matrix} {{{\mathbf{e}^{-t} \,-\, \mathbf{e}^{-2 t}}}} & {{{\mathbf{e}^{-t} \,-\, 2 \mathbf{e}^{-2 t}}}} \\ {{{-2 \mathbf{e}^{-t} \,+\, 2 \mathbf{e}^{-2 t}}}} & {{{\mathbf{e}^{-t} \,+\, \mathbf{e}^{-2 t}}}} \\ \end{matrix} \right]
$$
G. $$
\left[ \begin{matrix} {{{2 \mathbf{e}^{-t} \,-\, \mathbf{e}^{-2 t}}}} & {{{-\mathbf{e}^{-t} \,+\, \mathbf{e}^{-2 t}}}} \\ {{{\mathbf{e}^{-t} \,-\, \mathbf{e}^{-2 t}}}} & {{{-\mathbf{e}^{-t} \,+\, 2 \mathbf{e}^{-2 t}}}} \\ \end{matrix} \right]
$$
H. $$
\left[ \begin{matrix} {{{2 \mathbf{e}^{-t} \,-\, \mathbf{e}^{-2 t}}}} & {{{\mathbf{e}^{-t} \,+\, \mathbf{e}^{-2 t}}}} \\ {{{-\mathbf{e}^{-t} \,+\, \mathbf{e}^{-2 t}}}} & {{{\mathbf{e}^{-t} \,-\, 2 \mathbf{e}^{-2 t}}}} \\ \end{matrix} \right]
$$
I. $$
\left[ \begin{matrix} {{{\mathbf{e}^{-t} \,+\, 2 \mathbf{e}^{-2 t}}}} & {{{2 \mathbf{e}^{-t} \,-\, \mathbf{e}^{-2 t}}}} \\ {{{2 \mathbf{e}^{-t} \,-\, \mathbf{e}^{-2 t}}}} & {{{-\mathbf{e}^{-t} \,+\, \mathbf{e}^{-2 t}}}} \\ \end{matrix} \right]
$$
J. $$
\left[ \begin{matrix} {{{\mathbf{e}^{-t} \,+\, 2 \mathbf{e}^{-2 t}}}} & {{{\mathbf{e}^{-t} \,-\, \mathbf{e}^{-2 t}}}} \\ {{{-2 \mathbf{e}^{-t} \,+\, 2 \mathbf{e}^{-2 t}}}} & {{{\mathbf{e}^{-t} \,-\, 2 \mathbf{e}^{-2 t}}}} \\ \end{matrix} \right]
$$
Answer: E
Consider the system defined by the following equation:
$$
\dot{\mathbf{x}} \,=\, \mathbf{A} \mathbf{x} \,+\, \mathbf{B} u
$$
with
$$
y = \mathbf{C} \mathbf{x}
$$
where
$$
{\bf A}=\left[ \begin{array} {r r r} {{-1}} & {{0}} & {{1}} \\ {{1}} & {{-2}} & {{0}} \\ {{0}} & {{0}} & {{-3}} \\ \end{array} \right], \quad{\bf B}=\left[ \begin{array} {r r} {{0}} \\ {{0}} \\ {{1}} \\ \end{array} \right], \quad{\bf C}=\left[ \begin{array} {r r r} {{1}} & {{1}} & {{0}} \\ \end{array} \right]
$$
What is the transfer function $Y ( s ) / U ( s )$?

Options:
A. $$
\frac{s+4} {s^{3}+3s^{2}+2s+7}
$$
B. $$
\frac{s+5} {s^{2}+2s^{2}+12s+4}
$$
C. $$
\frac{s+2} {s^{3}+5s^{2}+4s+6}
$$
D. $$
\frac{s+9} {s^{2}+7s^{2}+13s+2}
$$
E. $$
\frac{s+10} {s^{3}+9s^{2}+5s+1}
$$
F. $$
\frac{s+1} {s^{2}+4s^{2}+9s+5}
$$
G. $$
\frac{s+6} {s^{3}+7s^{2}+8s+3}
$$
H. $$
\frac{s+7} {s^{2}+8s^{2}+10s+9}
$$
I. $$
\frac{s+8} {s^{3}+6s^{2}+11s+8}
$$
J. $$
\frac{s+3} {s^{2}+6 s^{2}+1 1s+6}
$$
Answer: J
What is the transfer function expression of the following system?
$$
\left[ \begin{array} {r} {{{\dot{x}_{1}}}} \\ {{{\dot{x}_{2}}}} \\ {{{\dot{x}_{3}}}} \\ \end{array} \right]=\left[ \begin{array} {r r r} {{0}} & {{1}} & {{0}} \\ {{-1}} & {{-1}} & {{0}} \\ {{1}} & {{0}} & {{0}} \\ \end{array} \right] \left[ \begin{array} {r} {{x_{1}}} \\ {{x_{2}}} \\ {{x_{3}}} \\ \end{array} \right]+\left[ \begin{array} {r} {{0}} \\ {{1}} \\ {{0}} \\ \end{array} \right] u
$$
$$
y=[ 0 \quad0 \quad1 ] {\left[ \begin{matrix} {{x_{1}}} \\ {{x_{2}}} \\ {{x_{3}}} \\ \end{matrix} \right]}
$$

Options:
A. $$
\frac{Y ( s )} {U ( s )}=\frac{s} {s^{3}+s^{2}+1}
$$
B. $$
\frac{Y ( s )} {U ( s )}=\frac{1} {s^{3}+s^{2}+s}
$$
C. $$
\frac{Y ( s )} {U ( s )}=\frac{s+1} {s^{3}+s^{2}+s+1}
$$
D. $$
\frac{Y ( s )} {U ( s )}=\frac{1} {s^{3}+2s^{2}+s}
$$
E. $$
\frac{Y ( s )} {U ( s )}=\frac{s^{2}} {s^{3}+s^{2}+s}
$$
F. $$
\frac{Y ( s )} {U ( s )}=\frac{s^{2}+1} {s^{3}+s^{2}+s}
$$
G. $$
\frac{Y ( s )} {U ( s )}=\frac{1} {s^{3}+s+1}
$$
H. $$
\frac{Y ( s )} {U ( s )}=\frac{1} {s^{2}+s+1}
$$
I. $$
\frac{Y ( s )} {U ( s )}=\frac{s+2} {s^{3}+s^{2}+s-1}
$$
J. $$
\frac{Y ( s )} {U ( s )}=\frac{1} {s^{3}-s^{2}+s}
$$
Answer: B
If a system has $n$ processes, the maximum number of processes in the ready queue is (), and the maximum number of processes in the blocked queue is ().

Options:
A. $$
n
$$
$$n-2$$
B. $$
n-2
$$
$$n$$
C. $$
n+1
$$
$$n-1$$
D. $$
n-1
$$
$$n+1$$
E. $$
n+1
$$
$$n+2$$
F. $$
n-2
$$
$$n+1$$
G. $$
n
$$
$$n+1$$
H. $$
n
$$
$$n-1$$
I. $$
n+1
$$
$$n$$
J. $$
n-1
$$
$$n$$
Answer: J
If there are $n \ (n \geq 2)$ processes in the system, and each process requires 2 instances of a certain critical resource, then the minimum total number of such resources needed to prevent deadlock is ().

Options:
A. $$
n-1
$$
B. $$
n+1
$$
C. $$
n+2
$$
D. $$
n^2+1
$$
E. $$
n^2
$$
F. $$
\frac{n}{2}
$$
G. $$
n/3
$$
H. $$
2n-1
$$
I. $$
2n+1
$$
J. $$
3n+1
$$
Answer: B
A certain system uses the LRU page replacement algorithm and a local replacement strategy. If the system pre-allocates 4 page frames for process $\mathbf{P}$, and the sequence of page numbers accessed by process $P$ is $0, 1, 2, 7, 0, 5, 3, 5, 0, 2, 7, 6$, then the total number of page replacements occurring during the process's access of the above pages is ( ).

Options:
A. $$3$$
B. $$11$$
C. $$6$$
D. $$10$$
E. $$2$$
F. $$4$$
G. $$5$$
H. $$9$$
I. $$7$$
J. $$8$$
Answer: G
There is a matrix `int A[100][100]` stored in a row-major order. The computer uses a virtual memory system, and the physical memory consists of three pages, one of which is used to store the program, while the other two are used to store data. Assume that the program occupies one page in memory, leaving the other two pages free. If each page can hold 200 integers, how many page faults occur during the execution of Program 1 and Program 2? What about when each page can hold only 100 integers?
Program 1:
$$
\begin{array}{c}
\text{for (i = 0; i < 100; i++)} \\
\text{\ \ \ for (j = 0; j < 100; j++)} \\
\text{\ \ \ \ \ \ A[i, j] = 0;}
\end{array}
$$
Program 2:
$$
\begin{array}{c}
\text{for (j = 0; j < 100; j++)} \\
\text{\ \ \ for (i = 0; i < 100; i++)} \\
\text{\ \ \ \ \ \ A[i, j] = 0;}
\end{array}
$$

Options:
A. $$40,
80$$
$$80,4000$$
B. $$100,
50$$
$$10000,100$$
C. $$25,
50$$
$$50,2500$$
D. $$10,
20$$
$$20,1000$$
E. $$60,
120$$
$$120,6000$$
F. $$75,
150$$
$$150,7500$$
G. $$30,
60$$
$$60,3000$$
H. $$200,
400$$
$$400,20000$$
I. $$90,
180$$
$$180,9000$$
J. $$50, 5000$$
$$100, 10000$$
Answer: J
In a certain file system, for each file, users are divided into four categories: security administrators, file owners, file owners' partners, and other users. Access permissions are categorized into five types: full control, execute, modify, read, and write. If file permissions are represented by binary bit strings in the file control block, to represent the access permissions of different categories of users for a file, the minimum number of bits required to describe the file permissions is ().

Options:
A. $$
2 8
$$
B. $$
1 8
$$
C. $$
1 2
$$
D. $$
2 0
$$
E. $$
3 0
$$
F. $$
2 2
$$
G. $$
1 6
$$
H. $$
1 4
$$
I. $$
2 5
$$
J. $$
2 4
$$
Answer: D
A certain file system uses index nodes to store the attributes and address information of files, with a cluster size of 4KB. Each file index node occupies 64B and contains 11 address entries, including 8 direct address entries and one single-level indirect, double-level indirect, and triple-level indirect address entry each. The length of each address entry is 4B.
The file system uses 1M ($1 \mathbf{M}=2^{20}$) clusters to store file index nodes and 512M clusters to store file data. If the size of an image file is 5600B, how many such image files can this file system store at most?

Options:
A. $$
5 9 0 0 \mathrm{B}
$$
B. $$
5 5 5 5 \mathrm{B}
$$
C. $$
4 8 0 0 \mathrm{B}
$$
D. $$
5 0 4 0 \mathrm{B}
$$
E. $$
6 0 0 0 \mathrm{B}
$$
F. $$
4 3 2 1 \mathrm{B}
$$
G. $$
4 7 2 0 \mathrm{B}
$$
H. $$
7 2 0 0 \mathrm{B}
$$
I. $$
6 4 \mathrm{M}
$$
J. $$
6 8 0 0 \mathrm{B}
$$
Answer: I
The head formation methods of the leaf balls in the cabbage heading variants include ____, ____ and ____.

Options:
A. Curling type, Sheathing type, Binding type
B. Embracing type, Overlapping type, Twisting type
C. Expanding type, Bending type, Protruding type
D. Wrapping type, Spiral type, Folding type
E. Shearing type, Relaxing type, Splaying type
F. Stacking type, Stretching type, Folding type
G. Spiral type, Exploding type, Tight type
H. Converging type, Binding type, Flattening type
I. Layering type, Compacting type, Wrapping type
J. Interlocking type, Compact type, Rolling type
Answer: B
According to the different humidity requirements of various types of vegetables, they are categorized into five groups, including cold-resistant perennial vegetables, ______, and others.

Options:
A. High-altitude vegetables, semi-arid vegetables, jungle-friendly vegetables, and dry-resistant vegetables
B. Salt-resistant vegetables, semi-saline vegetables, arid-loving vegetables, and wet-tolerant vegetables
C. Summer-flourishing vegetables, semi-summer vegetables, winter-sensitive vegetables, and cool-resistant vegetables
D. Frost-loving vegetables, semi-moist vegetables, swamp-tolerant vegetables, and shade-tolerant vegetables
E. Tropical vegetables, semi-tropical vegetables, alpine vegetables, and desert-resilient vegetables
F. River-side vegetables, semi-wetland vegetables, prairie-adapted vegetables, and coastal-tolerant vegetables
G. Harsh-climate vegetables, semi-sustainable vegetables, light-sensitive vegetables, and drought-prone vegetables
H. Cold-hardy vegetables, semi-cold-hardy vegetables, warm-loving vegetables, and heat-tolerant vegetables
I. Humid-tolerant vegetables, semi-humid vegetables, frost-sensitive vegetables, and drought-tolerant vegetables
J. Rain-fed vegetables, semi-dryland vegetables, mountain crops, and high-soil-moisture vegetables
Answer: H
Vegetables are related to human health ____ and are ____ sources of vitamins the body needs.

Options:
A. Close, minor
B. Related, limited
C. Connected, supplemental
D. Distant, key
E. Related, negligible
F. Linked, poor
G. Associated, insignificant
H. Distant, essential
I. Close, main
J. Limited, primary
Answer: I
The Burgundian School is also known as ________.

Options:
A. The Renaissance Madrigal School
B. The Classical Period School
C. The Neoclassical Music School
D. The Second Viennese School
E. The Baroque Style School
F. The Romanesque Music School
G. The Ars Subtilior School
H. The Galant Style School
I. The Franco-Flemish School
J. The First Netherlandish School
Answer: J
Tycho Brahe's observations of the stars and planets were accurate to about 1 arc/minute. To what distance does this angle correspond at the distance of the Moon?

Options:
A. $$
0. 0 1 3 2^{\circ} {\times} {\frac{\mathrm{d i s t a n c e}} {5 9. 2^{\circ}}}
$$
B. $$
0. 0 2 2 4^{\circ} {\times} {\frac{\mathrm{d i s t a n c e}} {5 4. 7^{\circ}}}
$$
C. $$
0. 0 1 6 7^{\circ} {\times} {\frac{\mathrm{d i s t a n c e}} {5 7. 3^{\circ}}}
$$
D. $$
0. 0 2 1 1^{\circ} {\times} {\frac{\mathrm{d i s t a n c e}} {5 6. 8^{\circ}}}
$$
E. $$
0. 0 2 0 8^{\circ} {\times} {\frac{\mathrm{d i s t a n c e}} {5 3. 9^{\circ}}}
$$
F. $$
0. 0 1 5 9^{\circ} {\times} {\frac{\mathrm{d i s t a n c e}} {5 5. 5^{\circ}}}
$$
G. $$
0. 0 2 3 4^{\circ} {\times} {\frac{\mathrm{d i s t a n c e}} {6 0^{\circ}}}
$$
H. $$
0. 0 1 8 3^{\circ} {\times} {\frac{\mathrm{d i s t a n c e}} {6 1. 3^{\circ}}}
$$
I. $$
0. 0 1 9 8^{\circ} {\times} {\frac{\mathrm{d i s t a n c e}} {5 8. 1^{\circ}}}
$$
J. $$
0. 0 1 4 6^{\circ} {\times} {\frac{\mathrm{d i s t a n c e}} {5 6. 0^{\circ}}}
$$
Answer: C
An interstellar cloud fragment 0.2 light-year in diameter is rotating at a rate of one revolution per million years. It now begins to collapse. Assuming that the mass remains constant,
estimate the cloud's rotation period is_____. when it has shrunk to the size of Earth's orbit, 2 AU across.

Options:
A. $$
0. 0 3 5 \ \mathrm{y e a r s}
$$
B. $$
0. 2 0 0 \ \mathrm{y e a r s}
$$
C. $$
0. 7 5 0 \ \mathrm{y e a r s}
$$
D. $$
0. 0 4 0 \ \mathrm{y e a r s}
$$
E. $$
0. 0 2 5 \ \mathrm{y e a r s}
$$
F. $$
0. 0 1 8 \ \mathrm{y e a r s}
$$
G. $$
0. 1 0 0 \ \mathrm{y e a r s}
$$
H. $$
0. 5 0 0 \ \mathrm{y e a r s}
$$
I. $$
0. 0 9 0 \ \mathrm{y e a r s}
$$
J. $$
0. 0 5 0 \ \mathrm{y e a r s}
$$
Answer: E
Calculate the proper motion (in arc seconds per year) of gd a globular cluster with a transverse velocity (relative to the Sun) of 200 km/s and a distance of 3 kpc. How long does it take to measure this motion?

Options:
A. $$
\mathrm{r a b o u t} \ 9 \ \mathrm{y e a r s}
$$
B. $$
\mathrm{r a b o u t} \ 8 \ \mathrm{y e a r s}
$$
C. $$
\mathrm{r a b o u t} \ 3 0 \ \mathrm{y e a r s}
$$
D. $$
\mathrm{r a b o u t} \ 1 0 \ \mathrm{y e a r s}
$$
E. $$
\mathrm{r a b o u t} \ 2 5 \ \mathrm{y e a r s}
$$
F. $$
\mathrm{r a b o u t} \ 1 2 \ \mathrm{y e a r s}
$$
G. $$
\mathrm{r a b o u t} \ 5 \ \mathrm{y e a r s}
$$
H. $$
\mathrm{r a b o u t} \ 2 0 \ \mathrm{y e a r s}
$$
I. $$
\mathrm{r a b o u t} \ 1 5 \ \mathrm{y e a r s}
$$
J. $$
\mathrm{r a b o u t} \ 1 8 \ \mathrm{y e a r s}
$$
Answer: D
A quasar consumes l solar mass of material per year converting 15 percent of it directly into energy. What is the quasar's luminosity, in solar units?

Options:
A. $$
1. 5 {\times} 1 0^{1 2} L_{\odot}
$$
B. $$
1. 8 {\times} 1 0^{1 2} L_{\odot}
$$
C. $$
3. 0 {\times} 1 0^{1 2} L_{\odot}
$$
D. $$
1. 2 {\times} 1 0^{1 2} L_{\odot}
$$
E. $$
3. 4 {\times} 1 0^{1 1} L_{\odot}
$$
F. $$
4. 0 {\times} 1 0^{1 1} L_{\odot}
$$
G. $$
2. 0 {\times} 1 0^{1 3} L_{\odot}
$$
H. $$
2. 5 {\times} 1 0^{1 1} L_{\odot}
$$
I. $$
2. 1 {\times} 1 0^{1 3} L_{\odot}
$$
J. $$
2. 2 {\times} 1 0^{1 2} L_{\odot}
$$
Answer: J
Eight galaxies are located at the corners of a cube. The present distance from each galaxy to its nearest neighbor is 10 Mpc, and the entire cube is expanding according to Hubble's law, 20 gW with $H_{0}=7 0$ km/s/Mpc. Calculate the recession velocity of onecorner of the cube relative to the opposite corner.

Options:
A. $$
1 2 5 0 \ \mathrm{k m / s}
$$
B. $$
1 0 5 0 \ \mathrm{k m / s}
$$
C. $$
1 3 0 0 \ \mathrm{k m / s}
$$
D. $$
1 1 8 0 \ \mathrm{k m / s}
$$
E. $$
1 3 5 0 \ \mathrm{k m / s}
$$
F. $$
1 4 0 0 \ \mathrm{k m / s}
$$
G. $$
1 1 5 0 \ \mathrm{k m / s}
$$
H. $$
1 1 0 0 \ \mathrm{k m / s}
$$
I. $$
1 2 0 0 \ \mathrm{k m / s}
$$
J. $$
1 2 2 0 \ \mathrm{k m / s}
$$
Answer: I
At what wavelength did the background radiation peak at the start of the epoch of nudeosynthesis?

Options:
A. $$
2 \times 1 0^{-6} \mathrm{m m}
$$
B. $$
5 \times 1 0^{-5} \mathrm{m m}
$$
C. $$
6 \times 1 0^{-7} \mathrm{m m}
$$
D. $$
1 \times 1 0^{-4} \mathrm{m m}
$$
E. $$
3 \times1 0^{-9} \mathrm{m m}
$$
F. $$
8 \times 1 0^{-10} \mathrm{m m}
$$
G. $$
9 \times 1 0^{-3} \mathrm{m m}
$$
H. $$
2 \times 1 0^{-9} \mathrm{m m}
$$
I. $$
7 \times 1 0^{-11} \mathrm{m m}
$$
J. $$
4 \times 1 0^{-8} \mathrm{m m}
$$
Answer: E
A chemist finds that 30.82 $\mathrm{g}$ of nitrogen will react with 17.60 $g,$ 35.20 $g,$ 70.40 $g,$ or 88.00 $g$ of oxygen to form four different compounds.

Options:
A. 1.0, 2.0, 4.0, 5.0
B. 1.1, 2.2, 4.4, 5.5
C. 1.0, 2.5, 4.0, 6.0
D. 0.8, 2.5, 4.2, 5.2
E. 0.5, 1.5, 3.0, 4.5
F. 1.0, 3.0, 6.0, 7.0
G. 1.2, 2.4, 4.8, 5.6
H. 0.9, 2.0, 4.2, 5.1
I. 1.1, 2.3, 4.5, 5.3
J. 0.7, 1.8, 3.6, 4.8
Answer: A
How many of the indicated atoms are represented by each chemical formula: (a) carbon atoms in $C_2H_5COOCH_3$, (b) oxygen atoms in $\mathrm{C a ( C l O_{4} )_{2}}$ , (c) hydrogen atoms in $(NH_4)_2HPO_4$?

Options:
A. 4, 6, 7
B. 4, 8, 9
C. 5, 6, 10
D. 4, 8, 10
E. 5, 7, 9
F. 3, 8, 8
G. 3, 7, 8
H. 4, 7, 10
I. 3, 9, 11
J. 5, 8, 9
Answer: B
It is common in mass spectrometry to assume that the mass of a cation is the same as that of its parent atom. What percentage of the mass of an H atom does the electron represent?

Options:
A. 0.05444%
B. 0.05044%
C. 0.00055%
D. 0.05450%
E. 0.05544%
F. 0.05404%
G. 0.05445%
H. 0.05400%
I. 0.00544%
J. 0.04544%
Answer: A
When benzene (C,H) reacts with bromine (Br2), bro-mobenzene (C,H5Br) is obtained:
$$
\mathrm{C_{6} H_{6}+B r_{2} \longrightarrow C_{6} H_{5} B r+H B r}
$$
What is the theoretical yield of bromobenzene in this reaction when 30.0 $\mathbf{g}$ of benzene reacts with 65.0 $\mathbf{g}$ of bromine?

Options:
A. $$
6 2. 9 \, \mathrm{g \, C_{6} H_{5} B r}
$$
B. $$
6 0. 0 \, \mathrm{g \, C_{6} H_{6} B r}
$$
C. $$
7 1. 2 \, \mathrm{g \, C_{6} H_{5} B r}
$$
D. $$
6 1. 7 \, \mathrm{g \, C_{6} H_{5} B r}
$$
E. $$
7 0. 8 \, \mathrm{g \, C_{6} H_{5} B r}
$$
F. $$
5 7. 5 \, \mathrm{g \, C_{6} H_{5} B r}
$$
G. $$
5 9. 2 \, \mathrm{g \, C_{6} H_{4} B r}
$$
H. $$
5 8. 4 \, \mathrm{g \, C_{6} H_{5} B r}
$$
I. $$
6 0. 3 \, \mathrm{g \, C_{6} H_{5}}
$$
J. $$
6 3. 5 \, \mathrm{g \, C_{6} H_{5} B}
$$
Answer: I
An oxybromate compound, KBrO$_{x}$, where $x$ is unknown, is analyzed and found to contain 52.92% Br What is the value of $x?$

Options:
A. $$
2. 2 1
$$
B. $$
3. 5 6
$$
C. $$
1. 6 3
$$
D. $$
1. 9 3
$$
E. $$
1. 8 7
$$
F. $$
2. 7 4
$$
G. $$
2. 5 2
$$
H. $$
3. 0 0
$$
I. $$
2. 0 5
$$
J. $$
2. 0 0
$$
Answer: J
Copper is an excellent electrical conductor widely used in making electric circuits. In producing a printed circuit board for the electronics industry, a layer of copper is laminated on a plastic board. A circuit pattern is then printed on the board using a chemically resistant polymer. The board is then exposed to a chemical bath that reacts with the exposed copper, leaving the desired copper circuit, which has been protected by the overlaying polymer. Finally, a solvent removes the polymer. One reaction used to remove the exposed copper from the circuit board is
$$
\mathrm{C u} ( s )+\mathrm{C u} ( \mathrm{N H}_{3} )_{4} \mathrm{C l}_{2} ( a q )+4 \mathrm{N H}_{3} ( a q ) \longrightarrow\atop2 \mathrm{C u} ( \mathrm{N H}_{3} )_{4} \mathrm{C l} ( a q )
$$
$\mathbf{A}$ plant needs to produce 5000 circuit boards, each with a surface area measuring 2.0 in. $\times3. 0$ in. The boards are covered with a 0.65-mm layer of copper. In subsequent processing, 85% of the copper is removed. Copper has a density of 8.96 $\mathrm{g / c m^{3}}$ .Calculate the masses of Cu(NH3)4 Cl2 and NH3 needed to produce the circuit boards is(), assuming that the reaction used gives a 97% yield.

Options:
A. $$
3. 6 \times1 0^{2} \mathrm{~ k g ~ C u ( N H_{3} )_4 C l_2}
$$
$$
0. 8 \times1 0^{2} \mathrm{~ k g ~ N H_{3} ~}
$$
B. $$
3. 3 \times1 0^{2} \mathrm{~ k g ~ C u ( N H_{3} )_4 C l_2}
$$
$$
1. 3 \times1 0^{2} \mathrm{~ k g ~ N H_{3} ~}
$$
C. $$
2. 5 \times1 0^{2} \mathrm{~ k g ~ C u ( N H_{3} )_4 C l_2}
$$
$$
1. 5 \times1 0^{2} \mathrm{~ k g ~ N H_{3} ~}
$$
D. $$
2. 7 \times1 0^{2} \mathrm{~ k g ~ C u ( N H_{3} )_4 C l_2}
$$
$$
1. 6 \times1 0^{2} \mathrm{~ k g ~ N H_{3} ~}
$$
E. $$
3. 0 \times1 0^{2} \mathrm{~ k g ~ C u ( N H_{3} )_4 C l_2}
$$
$$
1. 0 \times1 0^{2} \mathrm{~ k g ~ N H_{3} ~}
$$
F. $$
3. 4 \times1 0^{2} \mathrm{~ k g ~ C u ( N H_{3} )_4 C l_2}
$$
$$
1. 0 \times1 0^{2} \mathrm{~ k g ~ N H_{3} ~}
$$
G. $$
3. 1 \times1 0^{2} \mathrm{~ k g ~ C u ( N H_{3} )_4 C l_2}
$$
$$
1. 1 \times1 0^{2} \mathrm{~ k g ~ N H_{3} ~}
$$
H. $$
3. 2 \times1 0^{2} \mathrm{~ k g ~ C u ( N H_{3} )_4 C l_2}
$$
$$
1. 2 \times1 0^{2} \mathrm{~ k g ~ N H_{3} ~}
$$
I. $$
2. 8 \times1 0^{2} \mathrm{~ k g ~ C u ( N H_{3} )_4 C l_2}
$$
$$
1. 4 \times1 0^{2} \mathrm{~ k g ~ N H_{3} ~}
$$
J. $$
2. 9 \times1 0^{2} \mathrm{~ k g ~ C u ( N H_{3} )_4 C l_2}
$$
$$
1. 2 \times1 0^{2} \mathrm{~ k g ~ N H_{3} ~}
$$
Answer: G
The "Wu Songs of Jiangnan" and the "Western Melodies of Jingchu" both belong to _____.

Options:
A. "Tangzhou Folk Music"
B. "Ancient Zhou Rhapsodies"
C. "Min River Serenades"
D. "Spring River Songs"
E. "Melodies of Yunxi"
F. "Shifan of the South"
G. "Han Dynasty Hymns"
H. "Northern Ritual Zither"
I. "Jianghu Temple Tunes"
J. "Qing Shang Xi"
Answer: J
Which is the earliest dance notation in world history?

Options:
A. "The Steps Manuscript of Persia"
B. "The Rhythms of Old Mesopotamia"
C. "The Choreography of Ancient Greece"
D. "The Carvings of Prehistoric Rituals"
E. "The Temple Dances of Babylon"
F. "The Movements of Byzantine Artistry"
G. "The Dance Manual of Deshou Palace"
H. "The Dance Codex of Early India"
I. "The Ritual Patterns of Shang Dynasty"
J. "The Footsteps Scrolls of Egypt"
Answer: G
Due to a "misidentification," which work was considered by Mr. Cao Yu to be "comparable to Shakespeare's plays"?

Options:
A. "Rickshaw Boy"
B. "The Red Lantern"
C. "The Wilderness"
D. "Teahouse"
E. "Sunrise"
F. "The Family"
G. "The True Peach Blossom Fan"
H. "The Thunderstorm"
I. "The Savage Land"
J. "Three Drops of Blood"
Answer: J
What is the title of the opera and vocal music work written by Shen Chongsui during the late Ming dynasty?

Options:
A. "Echoes of the Celestial Court"
B. "Guidelines for Composing Melodies"
C. "Balance Within the Palace Walls"
D. "Scripts of the Moonlit River"
E. "Songs of Eternal Harmony"
F. "Concord in the Winter Garden"
G. "Melodies from the Rising Phoenix"
H. "Rhythms of the Red Pavilion"
I. "Hymns to the Jade Emperor"
J. "Ballads of the Southern Kingdom"
Answer: B
The decomposition of $CaCO_3 (s)$ reaches equilibrium, $CaCO_3 (s) ⇌ CaO (s) + CO_2 (g)$. What are the number of components and degrees of freedom?

Options:
A. $$
S=3, \ R=1, \ R^{\prime}=0, \ \Phi=3, \ \ K=2, \ \ f=1.
$$
B. $$
S=4, \ R=1, \ R^{\prime}=0, \ \Phi=2, \ \ K=2, \ \ f=1.
$$
C. $$
S=3, \ R=1, \ R^{\prime}=0, \ \Phi=3, \ \ K=1, \ \ f=3.
$$
D. $$
S=2, \ R=1, \ R^{\prime}=1, \ \Phi=3, \ \ K=2, \ \ f=1.
$$
E. $$
S=3, \ R=1, \ R^{\prime}=0, \ \Phi=4, \ \ K=2, \ \ f=1.
$$
F. $$
S=4, \ R=1, \ R^{\prime}=0, \ \Phi=3, \ \ K=2, \ \ f=0.
$$
G. $$
S=3, \ R=1, \ R^{\prime}=1, \ \Phi=3, \ \ K=3, \ \ f=1.
$$
H. $$
S=3, \ R=2, \ R^{\prime}=0, \ \Phi=3, \ \ K=1, \ \ f=2.
$$
I. $$
S=2, \ R=1, \ R^{\prime}=0, \ \Phi=3, \ \ K=2, \ \ f=2.
$$
J. $$
S=3, \ R=2, \ R^{\prime}=0, \ \Phi=3, \ \ K=2, \ \ f=1.
$$
Answer: A
Under the conditions of $298 \, \mathrm{K}, p^{\Theta}$, the density of liquid benzene is $\rho = 0.875 \, \mathrm{g \cdot cm}^{-3}$. What is the $pV$ value of 1 mol of liquid benzene?

Options:
A. $$
2. 7 7 \, \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
B. $$
1. 9 4 \, \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
C. $$
2. 8 1 \, \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
D. $$
3. 1 7 \, \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
E. $$
2. 4 0 \, \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
F. $$
2. 6 5 \, \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
G. $$
2. 5 6 \, \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
H. $$
2. 3 3 \, \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
I. $$
9.03 \, \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
J. $$
3. 0 2 \, \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
Answer: I
At 298K, 98.69kPa, and $1m^3$ air, the partial pressure of water vapor is 2.928kPa If this air is cooled to 288K under equal pressure, some water vapor will condense, and the partial pressure of water vapor in the condensed air will be 1.6921 kPa What is the volume of air after cooling?

Options:
A. 890dm³
B. 910dm³
C. 945dm³
D. 860dm³
E. 980dm³
F. 1000dm³
G. 954dm³
H. 965dm³
I. 927dm³
J. 972dm³
Answer: G
It is known that $N_{2}(g)$ at 298 K has $\omega = 2354.999{cm}^{-1}$. When the vibrational ground state is taken as the zero energy point, what is the temperature of the system when $q_{v} - 10$?

Options:
A. 36000K
B. 29000K
C. 28000K
D. 31500K
E. 31000K
F. 35000K
G. 32150K
H. 34000K
I. 30000K
J. 33000K
Answer: G
$T=300 K$, $H_{2} (g) + Br_{2} (g) = 2 HBr (g)$, with the reactor volume held constant at $V=0.25 \mathrm{~dm}^{3}$. During the experiment, it was measured that after $0.01 \mathrm{~s}$ of reaction, the amount of $\mathrm{Br_{2}} (g)$ decreased by $0.001 \mathrm{~mol}$. What are the rates of reaction $r (\mathrm{H}_{2})$, $r (\mathrm{Br}_{2})$, $r (\mathrm{HBr})$, and their relationships with $r$?

Options:
A. $$
2 r=r \left( \mathrm{H}_{2} \right)=r \left( \mathrm{B r}_{2} \right), \ r=2 r \left( \mathrm{H B r} \right)
$$
B. $$
2 r=r \left( \mathrm{H}_{2} \right)=r \left( \mathrm{B r}_{2} \right), \ r=r \left( \mathrm{H B r} \right)
$$
C. $$
r=r \left( \mathrm{H}_{2} \right)=2 r \left( \mathrm{B r}_{2} \right), \ r=r \left( \mathrm{H B r} \right)
$$
D. $$
r=r \left( \mathrm{H}_{2} \right)=r \left( \mathrm{B r}_{2} \right), \ 2 r=r \left( \mathrm{H B r} \right)
$$
E. $$
r=r \left( \mathrm{B r}_{2} \right), \ r \left( \mathrm{H}_{2} \right)=2 r=r \left( \mathrm{H B r} \right)
$$
F. $$
r=r \left( \mathrm{H}_{2} \right)=r \left( \mathrm{B r}_{2} \right), \ r=2 r \left( \mathrm{H B r} \right)
$$
G. $$
r=r \left( \mathrm{H}_{2} \right)=r \left( \mathrm{B r}_{2} \right), \ r=r \left( \mathrm{H B r} \right)
$$
H. $$
r=r \left( \mathrm{H}_{2} \right) \neq r \left( \mathrm{B r}_{2} \right), \ r=r \left( \mathrm{H B r} \right)
$$
I. $$
r=2 r \left( \mathrm{H}_{2} \right)=r \left( \mathrm{B r}_{2} \right), \ r=r \left( \mathrm{H B r} \right)
$$
Answer: D
At 298 K, the standard state chemical potential of $Hg_2 Cl_2(s)$ is $-210.66 kJ \cdot mol^{-1}$. Given that the concentration of $Cl^-$ in aqueous solution is $0.1 mol \cdot kg^{-1} (\gamma_{\pm} = 0.778)$, and its chemical potential is $-137.50 kJ \cdot mol^{-1}$, what is the standard electrode potential of the electrode $Cl^- (a) \mid Hg_2\mathrm{Cl}_2(s) \mid Hg(l)$?

Options:
A. 0.2523V
B. 0.2450V
C. 0.2634V
D. 0.2761V
E. 0.2984V
F. 0.3152V
G. 0.2828V
H. 0.2678V
I. 0.2897V
J. 0.3010V
Answer: H
At 293K and 101.3 kPa, a water droplet with a radius of 1 cm is dispersed into smaller droplets with a radius of $1 \times 10^{-7} m$. Given that the surface tension of water at 293K is $7.28 \times 10^{-2} N \cdot m^{-1}$. If it is an adiabatic process, calculate the temperature change. Known $\rho( H_{2}O, l, 293K )=0.998 g \cdot cm^{-3}$, and $C_{V} (H_{2}O, l) = 4 J \cdot K^{-1} \cdot g^{-1}$. Attempt to determine the increase in Gibbs surface free energy of the system after this process, which can be reversibly completed under isothermal and isobaric conditions, and requires at least the work done by the environment.

Options:
A. 9.14K
B. 9.141J
C. 80.14J
D. 8.14J
E. 90.14J
F. 9J
G. 9.34J
H. 9.04J
I. 9.14J
J. 9.44J
Answer: I
Consider a circular cylinder in a hypersonic flow, with its axis perpendicular to the flow. Let $\phi$ be the angle measured between radii drawn to the leading edge (the stagnation point) and to any arbitrary point on the cylinder. The pressure coefficient distribution along the cylindrical surface is given by $C_{p}=2 \operatorname{c o s}^{2} \phi$ for $0 \leq\phi\leq\pi/ 2$ and $3 \pi/ 2 \leq\phi\leq2 \pi$ and $C_{p}=0$ for $\pi/ 2 \leq\phi\leq3 \pi/ 2$ . Calculate the drag coefficient for the cylinder, based on projected frontal area of the cylinder.

Options:
A. $$
{c_{\mathrm{d}}=5 / 3}
$$
B. $$
{c_{\mathrm{d}}=1 / 2}
$$
C. $$
{c_{\mathrm{d}}=3 / 2}
$$
D. $$
{c_{\mathrm{d}}=2 / 3}
$$
E. $$
{c_{\mathrm{d}}=5 / 4}
$$
F. $$
{c_{\mathrm{d}}=\pi / 2}
$$
G. $$
{c_{\mathrm{d}}=\pi / 3}
$$
H. $$
{c_{\mathrm{d}}=4 / 3}
$$
I. $$
{c_{\mathrm{d}}=1}
$$
J. $$
{c_{\mathrm{d}}=7 / 4}
$$
Answer: H
Consider a low-speed open-circuit subsonic wind tunnel with an inlet-to-throat area ratio of 12. The tunnel is turned on, and the pressure difference between the inlet (the settling chamber) and the test section is read as a height difference of 10 cm on a U-tube mercury manometer. (The density of liquid mercury is $1. 3 6 \times1 0^{4} \mathrm{~ k g / m}^{3}$ .) Calculate the velocity of the air in the test section.

Options:
A. $$
{1 6 0 \, \mathrm{m / s e c}}
$$
B. $$
{1 3 8 \, \mathrm{m / s e c}}
$$
C. $$
{1 4 2 \, \mathrm{m / s e c}}
$$
D. $$
{1 5 2 \, \mathrm{m / s e c}}
$$
E. $$
{1 4 7 \, \mathrm{m / s e c}}
$$
F. $$
{1 6 5 \, \mathrm{m / s e c}}
$$
G. $$
{1 5 8 \, \mathrm{m / s e c}}
$$
H. $$
{1 3 2 \, \mathrm{m / s e c}}
$$
I. $$
{1 3 5 \, \mathrm{m / s e c}}
$$
J. $$
{1 4 4 \, \mathrm{m / s e c}}
$$
Answer: E
For the NACA 2412 airfoil, the lift coefficient and moment coefficient about the quarter-chord at $- 6^{\circ}$ angle of attack are $- 0. 3 9$ and $- 0. 0 4 5$ -
respectively. At $4^{\circ}$ angle of attack, these coefficients are 0.65 and -0.037, respectively. Calculate the location of the aerodynamic center.

Options:
A. $$
{0. 2 4 5}
$$
B. $$
{0. 2 3 3}
$$
C. $$
{0. 2 5 8}
$$
D. $$
{0. 2 2 5}
$$
E. $$
{0. 2 4 8}
$$
F. $$
{0. 2 4 2}
$$
G. $$
{0. 2 6 1}
$$
H. $$
{0. 2 5 2}
$$
I. $$
{0. 2 3 9}
$$
J. $$
{0. 2 3 7}
$$
Answer: F
Just upstream of a shock wave, the air temperature and pressure are 288 K and 1 atm, respectively; just downstream of the wave, the air temperature and pressure are 690 K and 8.656 atm, respectively. Calculate the changes in enthalpy, internal energy, and entropy across the wave.

Options:
A. $$
3. 9 6 4 \times1 0^{5} \ {\frac{\mathrm{j o u l e}} {\mathrm{k g}}}
$$
$$
2. 7 8 4 \times1 0^{5} \ {\frac{\mathrm{j o u l e}} {\mathrm{k g}}}
$$
$$
2 3 8. 5 {\frac{\mathrm{j o u l e}} {\mathrm{k g} \ \circ\mathrm{K}}}
$$
B. $$
3. 8 3 9 \times1 0^{5} \ {\frac{\mathrm{j o u l e}} {\mathrm{k g}}}
$$
$$
2. 9 8 1 \times1 0^{5} \ {\frac{\mathrm{j o u l e}} {\mathrm{k g}}}
$$
$$
2 5 9. 5 {\frac{\mathrm{j o u l e}} {\mathrm{k g} \ \circ\mathrm{K}}}
$$
C. $$
3. 7 5 2 \times1 0^{5} \ {\frac{\mathrm{j o u l e}} {\mathrm{k g}}}
$$
$$
2. 7 3 9 \times1 0^{5} \ {\frac{\mathrm{j o u l e}} {\mathrm{k g}}}
$$
$$
2 5 8. 9 {\frac{\mathrm{j o u l e}} {\mathrm{k g} \ \circ\mathrm{K}}}
$$
D. $$
4. 0 7 7 \times1 0^{5} \ {\frac{\mathrm{j o u l e}} {\mathrm{k g}}}
$$
$$
2. 8 1 4 \times1 0^{5} \ {\frac{\mathrm{j o u l e}} {\mathrm{k g}}}
$$
$$
2 5 7. 7 {\frac{\mathrm{j o u l e}} {\mathrm{k g} \ \circ\mathrm{K}}}
$$
E. $$
4. 2 3 1 \times1 0^{5} \ {\frac{\mathrm{j o u l e}} {\mathrm{k g}}}
$$
$$
3. 0 9 4 \times1 0^{5} \ {\frac{\mathrm{j o u l e}} {\mathrm{k g}}}
$$
$$
2 6 0. 4 {\frac{\mathrm{j o u l e}} {\mathrm{k g} \ \circ\mathrm{K}}}
$$
F. $$
4. 0 3 8 \times1 0^{5} \ {\frac{\mathrm{j o u l e}} {\mathrm{k g}}}
$$
$$
2. 8 8 4 \times1 0^{5} \ {\frac{\mathrm{j o u l e}} {\mathrm{k g}}}
$$
$$
2 5 8. 2 {\frac{\mathrm{j o u l e}} {\mathrm{k g} \ \circ\mathrm{K}}}
$$
G. $$
4. 1 5 3 \times1 0^{5} \ {\frac{\mathrm{j o u l e}} {\mathrm{k g}}}
$$
$$
2. 8 0 5 \times1 0^{5} \ {\frac{\mathrm{j o u l e}} {\mathrm{k g}}}
$$
$$
2 6 0. 2 {\frac{\mathrm{j o u l e}} {\mathrm{k g} \ \circ\mathrm{K}}}
$$
H. $$
3. 8 4 8 \times1 0^{5} \ {\frac{\mathrm{j o u l e}} {\mathrm{k g}}}
$$
$$
3. 0 1 2 \times1 0^{5} \ {\frac{\mathrm{j o u l e}} {\mathrm{k g}}}
$$
$$
2 5 6. 4 {\frac{\mathrm{j o u l e}} {\mathrm{k g} \ \circ\mathrm{K}}}
$$
I. $$
4. 1 2 8 \times1 0^{5} \ {\frac{\mathrm{j o u l e}} {\mathrm{k g}}}
$$
$$
3. 0 5 4 \times1 0^{5} \ {\frac{\mathrm{j o u l e}} {\mathrm{k g}}}
$$
$$
2 5 8. 3 {\frac{\mathrm{j o u l e}} {\mathrm{k g} \ \circ\mathrm{K}}}
$$
J. $$
4. 0 8 8 \times1 0^{5} \ {\frac{\mathrm{j o u l e}} {\mathrm{k g}}}
$$
$$
2. 8 2 6 \times1 0^{5} \ {\frac{\mathrm{j o u l e}} {\mathrm{k g}}}
$$
$$
2 6 1. 3 {\frac{\mathrm{j o u l e}} {\mathrm{k g} \ \circ\mathrm{K}}}
$$
Answer: F
An airfoil is in a freestream where $p_{\infty}=0. 6 1$ atm, $\rho_{\infty}=0. 8 1 9 \; \mathrm{k g / m}^{3}$ . and $V_{\infty}=3 0 0$ m/s. At a point on the airfoil surface, the pressure is 0.5 atm. Assuming isentropic flow, calculate the velocity at that point.

Options:
A. $$
3 4 5 \ \mathrm{m / s e c}
$$
B. $$
3 8 0 \ \mathrm{m / s e c}
$$
C. $$
3 2 0 \ \mathrm{m / s e c}
$$
D. $$
3 3 0 \ \mathrm{m / s e c}
$$
E. $$
3 6 0 \ \mathrm{m / s e c}
$$
F. $$
3 2 5 \ \mathrm{m / s e c}
$$
G. $$
3 5 5 \ \mathrm{m / s e c}
$$
H. $$
3 4 0 \ \mathrm{m / s e c}
$$
I. $$
3 7 0 \ \mathrm{m / s e c}
$$
J. $$
3 9 0 \ \mathrm{m / s e c}
$$
Answer: A
Consider the isentropic flow through a supersonic nozzle. If the test-section conditions are given by $p=1$ atm, $T=2 3 0 \mathrm{~ K}$ ,and $M=2$ , calculate the reservoir pressure and temperature.

Options:
A. $$
\begin{array} {l} {{{\mathrm{p_{o}=7. 4 5 5 ~ a t m}}}} \\ {{{\mathrm{T_{o}=4 1 2 ~^{o} K}}}} \\ \end{array}
$$
B. $$
\begin{array} {l} {{{\mathrm{p_{o}=7. 6 4 1 ~ a t m}}}} \\ {{{\mathrm{T_{o}=4 1 9 ~^{o} K}}}} \\ \end{array}
$$
C. $$
\begin{array} {l} {{{\mathrm{p_{o}=7. 9 3 0 ~ a t m}}}} \\ {{{\mathrm{T_{o}=4 2 2 ~^{o} K}}}} \\ \end{array}
$$
D. $$
\begin{array} {l} {{{\mathrm{p_{o}=7. 2 9 8 ~ a t m}}}} \\ {{{\mathrm{T_{o}=4 0 1 ~^{o} K}}}} \\ \end{array}
$$
E. $$
\begin{array} {l} {{{\mathrm{p_{o}=7. 8 2 4 ~ a t m}}}} \\ {{{\mathrm{T_{o}=4 1 4 ~^{o} K}}}} \\ \end{array}
$$
F. $$
\begin{array} {l} {{{\mathrm{p_{o}=6. 8 2 4 ~ a t m}}}} \\ {{{\mathrm{T_{o}=4 0 7 ~^{o} K}}}} \\ \end{array}
$$
G. $$
\begin{array} {l} {{{\mathrm{p_{o}=8. 1 2 6 ~ a t m}}}} \\ {{{\mathrm{T_{o}=4 2 5 ~^{o} K}}}} \\ \end{array}
$$
H. $$
\begin{array} {l} {{{\mathrm{p_{o}=8. 0 1 5 ~ a t m}}}} \\ {{{\mathrm{T_{o}=4 2 7 ~^{o} K}}}} \\ \end{array}
$$
I. $$
\begin{array} {l} {{{\mathrm{p_{o}=8. 3 5 7 ~ a t m}}}} \\ {{{\mathrm{T_{o}=4 3 0 ~^{o} K}}}} \\ \end{array}
$$
J. $$
\begin{array} {l} {{{\mathrm{p_{o}=6. 5 3 2 ~ a t m}}}} \\ {{{\mathrm{T_{o}=3 8 9 ~^{o} K}}}} \\ \end{array}
$$
Answer: E
Consider a circular cylinder (oriented with its axis perpendicular to the flow) and a symmetric diamond-wedge airfoil with a half-angle of $5^{\circ}$ at zero angle of attack; both bodies are in the same Mach 5 freestream. The thickness of the airfoil and the diameter of the cylinder are the same. The drag coefficient (based on projected frontal area) of the cylinder is $4 / 3$ . Calculate the ratio of the cylinder drag to the diamond airfoil drag. What does this say about the aerodynamic performance of a blunt body
compared to a sharp-nosed slender body in supersonic flow?

Options:
A. $$
{2 7. 8}
$$
B. $$
{1 9. 3}
$$
C. $$
{3 2. 5}
$$
D. $$
{2 8. 6}
$$
E. $$
{1 5. 2}
$$
F. $$
{2 6. 7}
$$
G. $$
{1 7. 9}
$$
H. $$
{3 1. 4}
$$
I. $$
{3 0. 9}
$$
J. $$
{1 8. 4}
$$
Answer: G
Consider a flat plate at $\alpha=2 0^{\circ}$ in a Mach 20 freestream. Using straight newtonian theory, calculate the lift- and wave-drag coefficients is ().

Options:
A. $$
{0. 2 2 5}
$$
$$
{0.08}
$$
B. $$
{0. 1 9 0}
$$
$$
{0.05}
$$
C. $$
{0. 2 0 0}
$$
$$
{0.07}
$$
D. $$
{0. 2 5 0}
$$
$$
{0.09}
$$
E. $$
{0. 2 4 0}
$$
$$
{0.09}
$$
F. $$
{0. 2 1 0}
$$
$$
{0.07}
$$
G. $$
{0. 2 2 0}
$$
$$
{0.08}
$$
H. $$
{0. 1 7 5}
$$
$$
{0.06}
$$
I. $$
{0. 1 8 5}
$$
$$
{0.06}
$$
J. $$
{0. 2 3 0}
$$
$$
{0.10}
$$
Answer: G
A body has a weight of 400 $\mathbf{N}$ at standard earth's gravity of 9.806 $\mathrm{m / s^{2}}$ . When a force of 800 $\mathbf{N}$ is applied to the body, what is the value of the acceleration (i) on earth and (ii) on moon where the gravity is 1.6 $\mathrm{m / s^{2}}?$

Options:
A. $$
2 7. 9 6 1 \ \mathrm{m / s}^{2}
$$
B. $$
8 . 2 5 7 \ \mathrm{m / s}^{2}
$$
C. $$
15. 7 2 3 \ \mathrm{m / s}^{2}
$$
D. $$
20. 4 8 5 \ \mathrm{m / s}^{2}
$$
E. $$
5 . 4 9 2 \ \mathrm{m / s}^{2}
$$
F. $$
1 7. 6 8 9 \ \mathrm{m / s}^{2}
$$
G. $$
2 3. 3 4 7 \ \mathrm{m / s}^{2}
$$
H. $$
1 9. 6 1 2 \ \mathrm{m / s}^{2}
$$
I. $$
1 3. 0 9 4 \ \mathrm{m / s}^{2}
$$
J. $$
11. 8 0 3 \ \mathrm{m / s}^{2}
$$
Answer: H
Assuming that the interstices in a clay are of size equal to one tenth the mean diameter of the grain, estimate the height to which water will rise in a clay soil of average grain diameter 0.05 mm. Assume surface tension at air-water interface as 0.073 N/m.

Options:
A. $$
5. 1 9 \ \mathrm{m}
$$
B. $$
7. 4 8 \ \mathrm{m}
$$
C. $$
3. 8 1 \ \mathrm{m}
$$
D. $$
4. 6 2 \ \mathrm{m}
$$
E. $$
7. 0 4 \ \mathrm{m}
$$
F. $$
4. 3 3 \ \mathrm{m}
$$
G. $$
3. 9 7 \ \mathrm{m}
$$
H. $$
5. 9 5 \ \mathrm{m}
$$
I. $$
6. 8 2 \ \mathrm{m}
$$
J. $$
6. 2 7 \ \mathrm{m}
$$
Answer: H
Find the pressure represented by a column of
5 cm of oil of relative density 0.75.

Options:
A. $$
2 3 4. 5 6 \, \mathrm{N / m}^{2}
$$
B. $$
3 6 7. 1 3 \, \mathrm{N / m}^{2}
$$
C. $$
4 1 2. 0 0 \, \mathrm{N / m}^{2}
$$
D. $$
4 4 7. 8 9 \, \mathrm{N / m}^{2}
$$
E. $$
5 6 7. 1 3 \, \mathrm{N / m}^{2}
$$
F. $$
3 7 5. 0 5 \, \mathrm{N / m}^{2}
$$
G. $$
4 5 0. 0 5 \, \mathrm{N / m}^{2}
$$
H. $$
3 9 9. 9 8 \, \mathrm{N / m}^{2}
$$
I. $$
3 8 0. 0 0 \, \mathrm{N / m}^{2}
$$
J. $$
2 5 0. 1 5 \, \mathrm{N / m}^{2}
$$
Answer: B
A cubical tank has sides of 1.5 m. It contains water in the lower 0.6 m depth. The upper remaining part is filled with oil of relative density O.9. Calculate for one vertical side of the tank the pressure force is___.

Options:
A. $$
1 4. 7 7 7 ~ \mathrm{k N}
$$
B. $$
1 5. 1 3 3 ~ \mathrm{k N}
$$
C. $$
1 2. 9 7 6 ~ \mathrm{k N}
$$
D. $$
1 4. 9 9 9 ~ \mathrm{k N}
$$
E. $$
1 5. 2 1 0 ~ \mathrm{k N}
$$
F. $$
1 6. 0 2 5 ~ \mathrm{k N}
$$
G. $$
1 3. 4 4 4 ~ \mathrm{k N}
$$
H. $$
1 5. 3 0 5 ~ \mathrm{k N}
$$
I. $$
1 5. 8 0 0 ~ \mathrm{k N}
$$
J. $$
1 4. 5 8 9 ~ \mathrm{k N}
$$
Answer: B