MikaStars39/nano-eval huggingface dataset:
What is the velocity of a particle with rest mass $m$ and charge $q$ after passing through a potential difference $U$ ? (assuming the initial velocity is zero)

Options:
A. $$
{\sqrt{\frac{2 q U} {m} \cdot\frac{1-{\frac{q U} {2 m c^{2}}}} {\left( 1+{\frac{q^2 U} {m c^{2}}} \right)^{2}}}}
$$
B. $$
{\sqrt{\frac{2 q U} {m} \cdot\frac{1-{\frac{q U} {m c^{2}}}} {\left( 1+{\frac{q U} {2 m c^{2}}} \right)^{2}}}}
$$
C. $$
{\sqrt{\frac{2 m U} {q} \cdot\frac{1+{\frac{q U} {m c^{3}}}} {\left( 1+{\frac{q U} {2 m c^{2}}} \right)^{2}}}}
$$
D. $$
{\sqrt{\frac{2 q U} {m} \cdot\frac{1+{\frac{q U} {m c^{2}}}} {\left( 1+{\frac{q U} {2 m c^{2}}} \right)}}}
$$
E. $$
{\sqrt{\frac{2 q U} {m} \cdot\frac{1+{\frac{q U} {2 m c^{2}}}} {\left( 1+{\frac{q U} {m c^{2}}} \right)^{2}}}}
$$
F. $$
{\sqrt{\frac{q U} {2 m} \cdot\frac{1+{\frac{2q U} {m c^{2}}}} {\left( 1+{\frac{q U} {m c^{2}}} \right)^{2}}}}
$$
G. $$
{\sqrt{\frac{q U} {m} \cdot\frac{1+{\frac{q U} {m c^{2}}}} {\left( 1-{\frac{q U} {2 m c^{2}}} \right)^{2}}}}
$$
H. $$
{\sqrt{\frac{2 q U} {m} \cdot\frac{1+{\frac{q U} {2 m c^{3}}}} {\left( 1-{\frac{q U} {m c^{2}}} \right)^{2}}}}
$$
I. $$
{\sqrt{\frac{2 q U} {m} \cdot\frac{1+{\frac{q U} {m c^{2}}}} {\left( 1+{\frac{2q U} {m c^{2}}} \right)^{2}}}}
$$
J. $$
{\sqrt{\frac{2 q U} {m} \cdot\frac{1+{\frac{q^2 U} {2 m c^{2}}}} {\left( 1+{\frac{q U} {m c^{3}}} \right)^{2}}}}
$$
Answer: E
What is the ratio of the aging rate of rocks at the center of the earth to that at the surface, due to the earth's rotation and gravitational effects? What is the ratio of the aging rate of rocks at the midpoint of the radius to that at the surface? (Assume the earth's density is uniform.)

Options:
A. $$ 0+f_{.} $$ $$ (1\div f) \times (1+f/3) = 1. $$
B. $$ 1-f_{.} $$ $$ (1-f/2) \times (1+f/4) \neq 0. $$
C. $$
1+f
$$
$$
( 1+f ) / ( 1+f / 4 )
$$
D. $$ 4+f_{.} $$ $$ (1-f) \div (1-f/4) < 1. $$
E. $$ 1-f_{.} $$ $$ (1+f/2) \times (1-f/4) < 1. $$
F. $$ 2+f_{.} $$ $$ (1+f) - (1-f/4) = 0. $$
G. $$ 1-f_{.} $$ $$ (1-f) / (1-f/4) \neq 1. $$
H. $$ 1+f_{.} $$ $$ (1-f) \div (1+f/4) \leq 1. $$
I. $$ 1+f_{.} $$ $$ (1\div f) + (1-f/3) \leq 1. $$
J. $$ 3+f_{.} $$ $$ (1+f) + (1-f/2) > 2. $$
Answer: C
Find the standard form of 82798848 and 81057226635000.

Options:
A. $$
82798848=2^{8} 3^{6} 1 1^{2}
$$
$$
8 1 0 5 7 2 2 6 6 3 5 0 0 0=2^{2} \cdot3^{5} \cdot5^{4} \cdot7^{2} \cdot1 1^{3} \cdot1 9 \cdot2 6 \cdot3 4
$$
B. $$
82798848=2^{6} 3^{4} 1 2^{3}
$$
$$
8 1 0 5 7 2 2 6 6 3 5 0 0 0=2^{5} \cdot3^{2} \cdot5^{5} \cdot7^{3} \cdot1 1^{2} \cdot1 7 \cdot3 4 \cdot3 6
$$
C. $$
82798848=2^{6} 3^{6} 1 3^{3}
$$
$$
8 1 0 5 7 2 2 6 6 3 5 0 0 0=2^{4} \cdot3^{2} \cdot5^{5} \cdot7^{2} \cdot1 1^{2} \cdot1 9 \cdot2 2 \cdot3 8
$$
D. $$
82798848=2^{8} 3^{5} 1 1^{3}
$$
$$
8 1 0 5 7 2 2 6 6 3 5 0 0 0=2^{3} \cdot3^{3} \cdot5^{4} \cdot7^{3} \cdot1 1^{2} \cdot1 7 \cdot2 3 \cdot3 7
$$
E. $$
82798848=2^{8} 3^{4} 1 1^{3}
$$
$$
8 1 0 5 7 2 2 6 6 3 5 0 0 0=2^{3} \cdot3^{4} \cdot5^{3} \cdot7^{4} \cdot1 1^{3} \cdot1 8 \cdot2 1 \cdot3 6
$$
F. $$
82798848=2^{9} 3^{3} 1 3^{4}
$$
$$
8 1 0 5 7 2 2 6 6 3 5 0 0 0=2^{4} \cdot3^{5} \cdot5^{2} \cdot7^{3} \cdot1 1^{2} \cdot1 8 \cdot3 5 \cdot3 7
$$
G. $$
82798848=2^{9} 3^{3} 1 1^{2}
$$
$$
8 1 0 5 7 2 2 6 6 3 5 0 0 0=2^{5} \cdot3^{4} \cdot5^{3} \cdot7^{2} \cdot1 1^{3} \cdot2 7 \cdot3 3 \cdot4 9
$$
H. $$
82798848=2^{9} 3^{5} 1 1^{2}
$$
$$
8 1 0 5 7 2 2 6 6 3 5 0 0 0=2^{4} \cdot3^{3} \cdot5^{2} \cdot7^{4} \cdot1 1^{2} \cdot2 9 \cdot2 3 \cdot3 8
$$
I. $$
82798848=2^{7} 3^{5} 1 2^{2}
$$
$$
8 1 0 5 7 2 2 6 6 3 5 0 0 0=2^{5} \cdot3^{3} \cdot5^{4} \cdot7^{2} \cdot1 1^{2} \cdot2 7 \cdot3 2 \cdot3 9
$$
J. $$
82798848=2^{7} 3^{4} 1 2^{3}
$$
$$
8 1 0 5 7 2 2 6 6 3 5 0 0 0=2^{2} \cdot3^{5} \cdot5^{3} \cdot7^{4} \cdot1 1^{2} \cdot2 7 \cdot4 3 \cdot3 8
$$
Answer: D
The number leaves a remainder of 3 when divided by 11, a remainder of 2 when divided by 7, and a remainder of 1 when divided by 13. What is the original number?

Options:
A. 1730
B. 1287
C. 1631
D. 1592
E. 1916
F. 1579
G. 1804
H. 1429
I. 1728
J. 1453
Answer: A
Find the remainder when $1 0^{1 0} + 1 0^{( 1 0^{2} )} + 1 0^{( 1 0^{3} )} + \cdots + 1 0^{( 1 0^{1 0} )}$ is divided by $7$.

Options:
A. 2
B. 4
C. 9
D. 7
E. 6
F. 5
G. 1
H. 8
I. 3
J. 0
Answer: F
Express $\sqrt{3+2 \sqrt{2}}$ in the form of $\sqrt a \pm \sqrt b$.

Options:
A. $\sqrt3+\sqrt1$
B. $\sqrt4-\sqrt1$
C. $\sqrt1+\sqrt0$
D. $1+\sqrt3$
E. $2+\sqrt0$
F. $2+\sqrt1$
G. $2-\sqrt2$
H. $\sqrt2+\sqrt3$
I. $1+\sqrt2$
Answer: I
Find the magnitude of $\begin{aligned}\sqrt{\sqrt[3]{5}-\sqrt[3]{4}}\:\end{aligned}$ is ().

Options:
A. $\frac{1}{3}(\sqrt[3]{7}\:+\:\sqrt[3]{14}\:-\:\sqrt[3]{49}\:)$
B. $\frac{1}{3}(\sqrt[3]{2}\:+\:\sqrt[3]{20}\:-\:\sqrt[3]{25}\:)$
C. $\frac{1}{3}(\sqrt[3]{10}\:+\:\sqrt[3]{50}\:-\:\sqrt[3]{100}\:)$
D. $\frac{1}{3}(\sqrt[3]{3}\:+\:\sqrt[3]{8}\:-\:\sqrt[3]{27}\:)$
E. $\frac{1}{3}(\sqrt[3]{4}\:+\:\sqrt[3]{9}\:-\:\sqrt[3]{8}\:)$
F. $\frac{1}{3}(\sqrt[3]{5}\:+\:\sqrt[3]{16}\:-\:\sqrt[3]{4}\:)$
G. $\frac{1}{3}(\sqrt[3]{8}\:+\:\sqrt[3]{32}\:-\:\sqrt[3]{64}\:)$
H. $\frac{1}{3}(\sqrt[3]{9}\:+\:\sqrt[3]{27}\:-\:\sqrt[3]{81}\:)$
I. $\frac{1}{3}(\sqrt[3]{1}\:+\:\sqrt[3]{4}\:-\:\sqrt[3]{9}\:)$
J. $\frac{1}{3}(\sqrt[3]{6}\:+\:\sqrt[3]{18}\:-\:\sqrt[3]{36}\:)$
Answer: B
Find the first digit after the decimal point of the number $( 2+\sqrt{3} )^{1000}$.

Options:
A. 2
B. 0
C. 4
D. 5
E. 6
F. 7
G. 3
H. 9
I. 8
J. 1
Answer: H
Ten workers need to assemble the parts for 50 products. First, each product must be painted, which takes a painter 10 minutes, and then it needs 5 minutes to dry. Next, an assembler needs 20 minutes to assemble the parts for each product. How many painters and assemblers should be arranged in order to complete this task in the shortest possible time (it is not allowed for two workers to simultaneously paint or assemble the same product)?

Options:
A. 8 painters and 2 assembler should be utilized.
B. 7 painters and 2 assemblers are essential.
C. 9 painters and 4 assemblers need to work.
D. 6 painters and 3 assemblers will suffice.
E. 2 painters and 9 assemblers must be assigned.
F. 1 painter and 8 assemblers are necessary.
G. 5 painters and 4 assemblers should be employed.
H. 3 painters and 6 assemblers are needed.
I. 2 painters and 7 assemblers are required.
J. 4 painters and 5 assemblers are mandatory.
Answer: H
To ensure that the three roots of the polynomial $x^{3} + a x^{2} + b x + c$ form an arithmetic sequence, what conditions should its coefficients satisfy?

Options:
A. $$
c b^{3}-a^{2}+\frac{b}{8}=0.
$$
B. $$
a^{2}+b^{2}-c^{2}=0.
$$
C. $$
b^{3}-c a+\frac{a}{7}=0.
$$
D. $$
b^{2}-3a+\frac{c}{6}=0.
$$
E. $$
a^{2}-3b+\frac{c}{2}=0.
$$
F. $$
\frac{2} {2 7} a^{3}-\frac{a b} {3}+c=0.
$$
G. $$
3a-c b+\frac{a}{9}=0.
$$
H. $$
c^{2}-a b+\frac{a}{5}=0.
$$
I. $$
3c-a b+\frac{b}{4}=0.
$$
J. $$
a c^{3}-b^{2}+\frac{1}{2}=0.
$$
Answer: F
Solve the equation ${\frac{1+\operatorname{tan} \, x} {1-\operatorname{tan} \,x}}=1+\operatorname{sin}\ 2x$.

Options:
A. $x=\frac{\pi}{4}+k\pi$ and $x=k\pi$
B. $x=-\frac{\pi}{2}+k\pi$ and $x=k\pi$
C. $x=\frac{\pi}{6}+k\pi$ and $x=k\pi$
D. $x=-\frac{3\pi}{4}+k\pi$ and $x=k\pi$
E. $x=\pi+k\pi$ and $x=k\pi$
F. $x=\frac{\pi}{3}+k\pi$ and $x=k\pi$
G. $x=-\frac{\pi}{6}+k\pi$ and $x=k\pi$
H. $x=-\frac{\pi}{4}+k\pi$ and $x=k\pi$
I. $x=\frac{5\pi}{6}+k\pi$ and $x=k\pi$
J. $x=\frac{3\pi}{4}+k\pi$ and $x=k\pi$
Answer: H
Given the velocity distribution of the fluid as $u_{x}=1-y, u_{y}=t$, find the streamline passing through the point (0, 0) at $t=1$.

Options:
A. $$
y^{2}-2 y+x^{2}=0
$$
B. $$
y^{2}+x^{2}-2 y=0
$$
C. $$
y^{2}-2 y+2 x=0
$$
D. $$
y=2 x^{2}+x-2
$$
E. $$
y=2 x^{2}-2 x y
$$
F. $$
2 y^{2}-y+2 x=1
$$
G. $$
y^{2}+2 y-2 x=0
$$
H. $$
y^{2}+2 x-y=0
$$
I. $$
x^{2}+2 y-2 x=0
$$
J. $$
y^{2}-2 x+2 y=1
$$
Answer: C
There is a planar flow, $u_{x} = x - 4y \,, \ u_{y} = -y - 4x \,,$ find the velocity potential function $\varphi^{2}$.

Options:
A. $$
\begin{array} {l} {{\varphi=x y-\frac{1} {2} y^{2}+C_{6}}} \\ \end{array}
$$
B. $$
\begin{array} {l} {{\varphi=\frac{1} {2} x^{2}-\frac{1} {2} y^{2}-4 x y+C_{1}}} \\ \end{array}
$$
C. $$
\begin{array} {l} {{\varphi=\frac{1} {2} y^{2}+x^{2}+C_{5}}} \\ \end{array}
$$
D. $$
\begin{array} {l} {{\varphi=\frac{1} {2} x^{2}+4 x y+C_{8}}} \\ \end{array}
$$
E. $$
\begin{array} {l} {{\varphi=x-y-4 x y+C_{4}}} \\ \end{array}
$$
F. $$
\begin{array} {l} {{\varphi=x^{2}+4 y^{2}-x C_{7}}} \\ \end{array}
$$
G. $$
\begin{array} {l} {{\varphi=\frac{1} {3} x^{3}-y+C_{3}}} \\ \end{array}
$$
H. $$
\begin{array} {l} {{\varphi= y-x^{2}+ y^{2}+C_{9}}} \\ \end{array}
$$
I. $$
\begin{array} {l} {{\varphi=\frac{1} {2} x^{2}+\frac{1} {2} y^{2}+x y+C_{10}}} \\ \end{array}
$$
J. $$
\begin{array} {l} {{\varphi=x^{2}+y^{2}-2 x y+C_{2}}} \\ \end{array}
$$
Answer: B
There are three water pipes with the same diameter, with a diameter of $d=100 \, \mathrm{mm}$. Each pipe has a flow rate of $Q=0.015 \, \mathrm{m}^{3}/\mathrm{s}$, and a length of $l=1000 \, \mathrm{m}$. The equivalent roughness of each pipe is $\Delta_{1}=0.1 \, \mathrm{mm}$, $\Delta_{2}=0.4 \, \mathrm{mm}$, and $\Delta_{3}=3 \, \mathrm{mm}$. The water temperature is 20°C. Find the head loss along each pipe, $h_{\int}$.

Options:
A. $h_{\int 1} \!=\! 3 7. \, 5 ( \mathrm{m} )$ , $h_{\int 2} \!$ $= 5 9. 0 3 \left( {\mathrm{m}} \right), \; \; h_{\int 3} \!=1 0 4. \; 4 \left( {\mathrm{m}} \right)$
B. $h_{\int 1} \!=\! 3 8. \, 7 ( \mathrm{m} )$ , $h_{\int 2} \!$ $= 5 5. 8 3 \left( {\mathrm{m}} \right), \; \; h_{\int 3} \!=1 0 6. \; 1 \left( {\mathrm{m}} \right)$
C. $h_{\int 1} \!=\! 3 5. \, 4 ( \mathrm{m} )$ , $h_{\int 2} \!$ $= 5 8. 7 5 \left( {\mathrm{m}} \right), \; \; h_{\int 3} \!=1 0 8. \; 6 \left( {\mathrm{m}} \right)$
D. $h_{\int 1} \!=\! 3 9. \, 2 ( \mathrm{m} )$ , $h_{\int 2} \!$ $= 5 6. 6 1 \left( {\mathrm{m}} \right), \; \; h_{\int 3} \!=1 1 5. \; 0 \left( {\mathrm{m}} \right)$
E. $h_{\int 1} \!=\! 3 2. \, 8 ( \mathrm{m} )$ , $h_{\int 2} \!$ $= 5 7. 2 9 \left( {\mathrm{m}} \right), \; \; h_{\int 3} \!=1 1 0. \; 3 \left( {\mathrm{m}} \right)$
F. $h_{\int 1} \!=\! 3 8. \, 6 ( \mathrm{m} )$ , $h_{\int 2} \!$ $= 5 4. 8 8 \left( {\mathrm{m}} \right), \; \; h_{\int 3} \!=1 0 7. \; 9 \left( {\mathrm{m}} \right)$
G. $h_{\int 1} \!=\! 4 0. \, 5 ( \mathrm{m} )$ , $h_{\int 2} \!$ $= 5 3. 4 7 \left( {\mathrm{m}} \right), \; \; h_{\int 3} \!=1 0 2. \; 5 \left( {\mathrm{m}} \right)$
H. $h_{\int 1} \!=\! 2 8. \, 3 ( \mathrm{m} )$ , $h_{\int 2} \!$ $= 4 5. 9 3 \left( {\mathrm{m}} \right), \; \; h_{\int 3} \!=9 5. 2 \left( {\mathrm{m}} \right)$
I. $h_{\int 1} \!=\! 4 1. \, 1 ( \mathrm{m} )$ , $h_{\int 2} \!$ $= 5 2. 0 9 \left( {\mathrm{m}} \right), \; \; h_{\int 3} \!=1 1 4. \; 2 \left( {\mathrm{m}} \right)$
J. $h_{\int 1} \!=\! 4 2. \, 7 ( \mathrm{m} )$ , $h_{\int 2} \!$ $= 6 0. 1 2 \left( {\mathrm{m}} \right), \; \; h_{\int 3} \!=1 1 2. \; 8 \left( {\mathrm{m}} \right)$
Answer: B
A pipeline with a diameter of 15 cm and a length of 10 m is transporting oil at a flow rate of 0.04 m³/s. Water is now used for the experiment, with the model's pipe diameter equal to the prototype's. The kinematic viscosity of the oil in the prototype is $v=0.13$ cm²/s, and the experimental water temperature in the model is $t = 10 \circ\mathrm{C}$. What should be the flow rate in the model to achieve similarity with the prototype?

Options:
A. $0. 008\mathrm{m} ^{3}/ \mathbf{s}$
B. $0. 001\mathrm{m} ^{3}/ \mathbf{s}$
C. $0. 005\mathrm{m} ^{3}/ \mathbf{s}$
D. $0. 004\mathrm{m} ^{3}/ \mathbf{s}$
E. $0. 010\mathrm{m} ^{3}/ \mathbf{s}$
F. $0. 003\mathrm{m} ^{3}/ \mathbf{s}$
G. $0. 007\mathrm{m} ^{3}/ \mathbf{s}$
H. $0. 009\mathrm{m} ^{3}/ \mathbf{s}$
I. $0. 006\mathrm{m} ^{3}/ \mathbf{s}$
J. $0. 002\mathrm{m} ^{3}/ \mathbf{s}$
Answer: D
Given a trapezoidal channel section with a bottom width $b=1 \mathrm{m}$ and a side slope coefficient $m=1$. In the horizontal channel section, the conjugate depths of the hydraulic jump are $h_{1}=0.2 \mathrm{m}$ and $h_{2}=0.6 \mathrm{m}$. Find the flow rate $Q$ through the channel. [The depth of the centroid of a trapezoidal section $h_{c} = h \ \ ( 3b + 2mh ) \ / 6 \ / \ ( b+mh ) \ ]$

Options:
A. $0.803\mathrm{m}^{3}/$s
B. $0.849\mathrm{m}^{3}/$s
C. $0.785\mathrm{m}^{3}/$s
D. $0.763\mathrm{m}^{3}/$s
E. $0.894\mathrm{m}^{3}/$s
F. $0.915\mathrm{m}^{3}/$s
G. $0.825\mathrm{m}^{3}/$s
H. $0.832\mathrm{m}^{3}/$s
I. $0.867\mathrm{m}^{3}/$s
J. $0.877\mathrm{m}^{3}/$s
Answer: B
A three-opening flat control gate is used, with a water depth of $H = 2.5 \mathrm{m}$ in front of the gate, and all three openings are opened simultaneously. The pier thickness is $d = 0.60 \mathrm{m}$, and the width of each opening is $b = 3.4 \mathrm{m}$. The upstream channel is the same width as the gate chamber, and the elevations of the upstream and downstream channel bottoms are the same as that of the gate bottom. When the flow rate $Q = 19.6 \mathrm{m}^3/\mathrm{s}$, the water depth downstream of the gate is $h_{t} = 1.75 \mathrm{m}$, with a flow velocity coefficient of $\varphi = 0.95$. Find the opening height $e$ of the gate.

Options:
A. 0.6m
B. 0.9m
C. 1.0m
D. 0.7m
E. 1.4m
F. 0.8m
G. 1.3m
H. 1.5m
I. 1.1m
J. 1.2m
Answer: A
When analyzing and mapping the infiltration line of an underground open channel with non-uniform gradient seepage, for the case of a positive slope $i > 0$, there is ()

Options:
A. There exists a parallel water depth P---P reference line, but there is no slope-based depth S---S reference line, which can divide 3 zones.
B. There exists a channel water depth C---C reference line, but there is no uniform water depth U---U reference line, which can segment 6 areas.
C. There exists a divided water depth D---D reference line, but there is no parallel water depth P---P reference line, which can separate 5 segments.
D. There exists a gradient water depth G---G reference line, but there is no channel water depth C---C reference line, which can segment 2 areas.
E. There exists a surface water depth S---S reference line, but there is no critical water depth K---K reference line, which can split 5 areas.
F. There exists a critical water depth K---K reference line, but there is no uniform water depth U---U reference line, which can affect 3 areas.
G. There exists a slope-based depth S---S reference line, but there is no normal water depth N---N reference line, which can alter 4 areas.
H. There exists a normal water depth N---N reference line, but there is no critical water depth K---K reference line, which can be divided into 2 areas.
I. There exists an infiltration water depth I---I reference line, but there is no gradient water depth G---G reference line, which can divide 4 areas.
J. There exists a uniform water depth U---U reference line, but there is no normal water depth N---N reference line, which can define 2 boundaries.
Answer: H
A flat plate is moving uniformly on the liquid surface with a velocity of $V = 0.5 \mathrm{m/s}$, and the plate area is $A = 1200 \mathrm{cm}^2$. Below the plate, there are two layers of liquid with dynamic viscosity coefficients of $\mu_{1} = 0.142 \mathrm{N} \cdot \mathrm{s/m}^2$ and $\mu_{2} = 0.235 \mathrm{N} \cdot \mathrm{s/m}^2$, and layer thicknesses of $h_{1} = 1 \mathrm{mm}$ and $h_{2} = 1.4 \mathrm{mm}$, respectively. Determine the internal frictional force $F$ exerted on the plate.

Options:
A. $$
2. \ 4 8 5 \mathrm{N}
$$
B. $$
8. \ 1 0 0 \mathrm{N}
$$
C. $$
3. \ 7 2 0 \mathrm{N}
$$
D. $$
4. \ 6 1 5 \mathrm{N}
$$
E. $$
7. \ 2 3 0 \mathrm{N}
$$
F. $$
6. \ 0 9 5 \mathrm{N}
$$
G. $$
3. \ 5 5 5 \mathrm{N}
$$
H. $$
2. \ 1 9 0 \mathrm{N}
$$
I. $$
5. \ 8 4 0 \mathrm{N}
$$
J. $$
5. \ 9 4 5 \mathrm{N}
$$
Answer: D
Given that the water depth upstream of the curved gate is $H_{1} = 4 \mathrm{m}$ and the water depth downstream is $H_{2} = 2 \mathrm{m}$, with the center of the gate $o$ located at $H_{1} / 2$ from the ground, calculate the total hydrostatic pressure on the gate per unit width.

Options:
A. $$
7 8. 5 0 \mathrm{~ ( k N )}
$$
B. $$
3 8. 7 5 \mathrm{~ ( k N )}
$$
C. $$
6 7. 9 4 \mathrm{~ ( k N )}
$$
D. $$
6 5. 1 9 \mathrm{~ ( k N )}
$$
E. $$
4 9. 3 8 \mathrm{~ ( k N )}
$$
F. $$
8 9. 6 2 \mathrm{~ ( k N )}
$$
G. $$
5 4. 2 8 \mathrm{~ ( k N )}
$$
H. $$
7 2. 0 1 \mathrm{~ ( k N )}
$$
I. $$
5 9. 8 6 \mathrm{~ ( k N )}
$$
J. $$
4 2. 3 4 \mathrm{~ ( k N )}
$$
Answer: I
The known velocity distribution of an incompressible fluid in a plane is given by
$\begin{aligned} {{u_{x}}} & {{} {{}=1+y}} \\ {{u_{y}}} & {{} {{}=a t}} \\ \end{aligned}$
where $a$ is a constant. Find the trajectory equation of the fluid particle located at point (0, 0) at $t=0$. Determine the streamline equation passing through point (0, 0) at $t=1 \mathrm{s}$.

Options:
A. $$
y^{2} \!-\! x a \!+\! t \!=\! 0
$$
B. $$
x^{2} \!+\! y \!-\! a \!=\! 0
$$
C. $$
y \!-\! x/2 \!+\! at \!=\! 0
$$
D. $$
2y \!-\! at \!+\! x \!=\! 0
$$
E. $$
x^{2} / 2 \!+\! a y t \!=\! 0
$$
F. $$
x+y^{2} \!-\! a t y \!=\! 0
$$
G. $$
y+y^{2} / 2 \!-\! a t x \!=\! 0
$$
H. $$
a t y \!-\! x \!-\! y \!=\! 0
$$
I. $$
x y \!-\! a t \!+\! y \!=\! 0
$$
J. $$
2x \!+\! a y t \!-\! 1 \!=\! 0
$$
Answer: G
The outer diameter of a certain turbine impeller is $d_{1}=2.4 \, \mathrm{m}$, and the inner diameter is $d_{2}=1.6 \, \mathrm{m}$, with an inflow rate of $Q=0.27 \, \mathrm{m}^{3}/\mathrm{s}$. The absolute velocity of the water entering the impeller is $v_{1}=20 \, \mathrm{m/s}$, with an inflow angle of $\alpha_{1}=20^{\circ}$ (the angle between $v_{1}$ and $u_{1}$); the absolute velocity of the water leaving the impeller is $v_{2}=5 \, \mathrm{m/s}$, with an outflow angle of $\alpha_{2}=80^{\circ}$ (the angle between $v_{2}$ and $u_{2}$); the head loss within the impeller is $h_{w_{1-2}}=0.02 w_{2}^{2} / (2g)$. Find the torque $M_{flow}$ of the impeller.

Options:
A. $$
4. 2 \, \mathrm{( k N \cdot m )}
$$
B. $$
5. 0 \, \mathrm{( k N \cdot m )}
$$
C. $$
7. 4 \, \mathrm{( k N \cdot m )}
$$
D. $$
3. 6 \, \mathrm{( k N \cdot m )}
$$
E. $$
8. 5 \, \mathrm{( k N \cdot m )}
$$
F. $$
6. 8 \, \mathrm{( k N \cdot m )}
$$
G. $$
6. 3 \, \mathrm{( k N \cdot m )}
$$
H. $$
9. 1 \, \mathrm{( k N \cdot m )}
$$
I. $$
5. 9 \, \mathrm{( k N \cdot m )}
$$
J. $$
7. 9 \, \mathrm{( k N \cdot m )}
$$
Answer: I
The dynamic viscosity coefficient $\mu = 0.035 \mathrm{N} \cdot \mathrm{s / m}^{2}$, density $830 \mathrm{kg} / \mathrm{m}^{3}$ oil flows at a rate of $Q = 0.003 \mathrm{m}^{3} / \mathrm{s}$ in a pipe with a diameter $d = 0.05 \mathrm{m}$. Calculate the head loss for a pipe length of 50m.

Options:
A. $4. 0 9 \ ( \mathrm{m} )$
B. $3. 8 2 \ ( \mathrm{m} )$
C. $5. 1 8 \ ( \mathrm{m} )$
D. $5. 0 2 \ ( \mathrm{m} )$
E. $4. 2 1 \ ( \mathrm{m} )$
F. $4. 3 2 \ ( \mathrm{m} )$
G. $3. 7 5 \ ( \mathrm{m} )$
H. $4. 5 0 \ ( \mathrm{m} )$
I. $4. 6 3 \ ( \mathrm{m} )$
J. $3. 9 8 \ ( \mathrm{m} )$
Answer: E
The flow rate $Q = 0.027 \, \mathrm{m}^3/\mathrm{s}$ in a certain water pipeline has a head loss along a 1000m length of $20 \, \mathrm{m}$, with a water temperature of $t = 20^\circ \mathrm{C}$. It is a standard cast iron pipe with an equivalent roughness $\Delta = 0.3 \, \mathrm{mm}$. Determine the pipe diameter $d_{\circ}$.

Options:
A. $$
d \!=\! 0. 1 3 5 \mathrm{m}
$$
B. $$
d \!=\! 0. 1 8 5 \mathrm{m}
$$
C. $$
d \!=\! 0. 1 2 0 \mathrm{m}
$$
D. $$
d \!=\! 0. 1 4 9 \mathrm{m}
$$
E. $$
d \!=\! 0. 1 6 0 \mathrm{m}
$$
F. $$
d \!=\! 0. 1 2 5 \mathrm{m}
$$
G. $$
d \!=\! 0. 1 9 0 \mathrm{m}
$$
H. $$
d \!=\! 0. 1 5 0 \mathrm{m}
$$
I. $$
d \!=\! 0. 1 7 5 \mathrm{m}
$$
J. $$
d \!=\! 0. 1 5 5 \mathrm{m}
$$
Answer: D
There are two water pipes, pipes A and B. Pipe A has a diameter of $d = 0.2 \,, \mathrm{mm}$, and a flow rate of 0.94 L/s. Pipe B has a diameter of $d = 0.04 \, \mathrm{m}$, and a flow rate of 3.5 L/s. The water temperature in both pipes is 15°C. Find the flow velocities for pipes A and B.

Options:
A. $$
v_{A} \!=\! 0.10 \ (\mathrm{m/s}),
v_{B} \!=\! 3.000 \ (\mathrm{m/s})
$$
B. $$
v_{A} \!=\! 0.15 \ (\mathrm{m/s}),
v_{B} \!=\! 2.900 \ (\mathrm{m/s})
$$
C. $$
v_{A} \!=\! 0.11 \ (\mathrm{m/s}),
v_{B} \!=\! 2.880 \ (\mathrm{m/s})
$$
D. $$
v_{A} \!=\! 0.07 \ (\mathrm{m/s}),
v_{B} \!=\! 2.350 \ (\mathrm{m/s})
$$
E. $$
v_{A} \!=\! 0.05 \ (\mathrm{m/s}),
v_{B} \!=\! 2.000 \ (\mathrm{m/s})
$$
F. $$
v_{A} \!=\! 0.20 \ (\mathrm{m/s}),
v_{B} \!=\! 2.500 \ (\mathrm{m/s})
$$
G. $$
v_{A} \!=\! 0.03 \ (\mathrm{m/s}),
v_{B} \!=\! 2.785 \ (\mathrm{m/s})
$$
H. $$
v_{A} \!=\! 0.25 \ (\mathrm{m/s}),
v_{B} \!=\! 1.500 \ (\mathrm{m/s})
$$
I. $$
v_{A} \!=\! 0.18 \ (\mathrm{m/s}),
v_{B} \!=\! 2.100 \ (\mathrm{m/s})
$$
J. $$
v_{A} \!=\! 0.12 \ (\mathrm{m/s}),
v_{B} \!=\! 2.700 \ (\mathrm{m/s})
$$
Answer: G
Given that at a certain point in a sand layer, when the stress reaches the ultimate equilibrium, the normal stress and shear stress on the maximum shear stress plane passing through that point are 264 kPa and 132 kPa, respectively. Concerning the values of the major principal stress $\sigma_{1}$, minor principal stress $\sigma_{3}$, and the internal friction angle $\varphi$ of the sand, which of the following options is correct?

Options:
A. $$
\boldsymbol{\sigma}_{1}=3 5 0 \, \mathrm{k P a} \,, \, \, \, \boldsymbol{\sigma}_{3}=1 5 0 \, \mathrm{k P a} \,, \, \, \, \boldsymbol{\varphi}=2 8^{\circ}
$$
B. $$
\boldsymbol{\sigma}_{1}=3 8 5 \, \mathrm{k P a} \,, \, \, \, \boldsymbol{\sigma}_{3}=1 3 5 \, \mathrm{k P a} \,, \, \, \, \boldsymbol{\varphi}=3 3^{\circ}
$$
C. $$
\boldsymbol{\sigma}_{1}=3 8 0 \, \mathrm{k P a} \,, \, \, \, \boldsymbol{\sigma}_{3}=1 4 0 \, \mathrm{k P a} \,, \, \, \, \boldsymbol{\varphi}=3 2^{\circ}
$$
D. $$
\boldsymbol{\sigma}_{1}=3 6 5 \, \mathrm{k P a} \,, \, \, \, \boldsymbol{\sigma}_{3}=1 5 5 \, \mathrm{k P a} \,, \, \, \, \boldsymbol{\varphi}=2 6^{\circ}
$$
E. $$
\boldsymbol{\sigma}_{1}=4 2 0 \, \mathrm{k P a} \,, \, \, \, \boldsymbol{\sigma}_{3}=1 0 5 \, \mathrm{k P a} \,, \, \, \, \boldsymbol{\varphi}=3 8^{\circ}
$$
F. $$
\boldsymbol{\sigma}_{1}=3 9 0 \, \mathrm{k P a} \,, \, \, \, \boldsymbol{\sigma}_{3}=1 3 0 \, \mathrm{k P a} \,, \, \, \, \boldsymbol{\varphi}=2 9^{\circ}
$$
G. $$
\boldsymbol{\sigma}_{1}=3 9 6 \, \mathrm{k P a} \,, \, \, \, \boldsymbol{\sigma}_{3}=1 3 2 \, \mathrm{k P a} \,, \, \, \, \boldsymbol{\varphi}=3 0^{\circ}
$$
H. $$
\boldsymbol{\sigma}_{1}=4 0 0 \, \mathrm{k P a} \,, \, \, \, \boldsymbol{\sigma}_{3}=1 2 0 \, \mathrm{k P a} \,, \, \, \, \boldsymbol{\varphi}=3 5^{\circ}
$$
I. $$
\boldsymbol{\sigma}_{1}=4 1 0 \, \mathrm{k P a} \,, \, \, \, \boldsymbol{\sigma}_{3}=1 1 0 \, \mathrm{k P a} \,, \, \, \, \boldsymbol{\varphi}=3 7^{\circ}
$$
J. $$
\boldsymbol{\sigma}_{1}=3 7 5 \, \mathrm{k P a} \,, \, \, \, \boldsymbol{\sigma}_{3}=1 4 5 \, \mathrm{k P a} \,, \, \, \, \boldsymbol{\varphi}=2 7^{\circ}
$$
Answer: G
The natural unit weight of a certain soil sample is $\gamma=17 \mathrm{kN/m}^{3}$, the dry unit weight is $\gamma_{\mathrm{d}}=14.5 \mathrm{kN/m}^{3}$, the saturated unit weight is $\gamma_{\mathrm{sat}}=18 \mathrm{kN/m}^{3}$, the liquidity index $I_{\mathrm{L}}=0$, and the plastic limit of the soil $w_{\mathrm{p}}$ is ( ).

Options:
A. 14.9%
B. 16.7%
C. 22.5%
D. 19.5%
E. 15.3%
F. 20.1%
G. 13.8%
H. 17.2%
I. 18.4%
J. 21.0%
Answer: H
A certain precast square pile has a cross-sectional side length of $0.4 \, \text{m}$ and a pile length of $12 \, \text{m}$. It uses C25 concrete, and the surrounding soil of the pile is plastic silty clay. The proportional coefficient of its horizontal resistance coefficient is $m=16 \, \text{MN/m}^{4}$. The reinforcement ratio of the pile body is 0.8%. If the allowable horizontal displacement at the pile top $\chi_{0_{\text{a}}} = 10 \, \text{mm}$, then the characteristic value of its single pile horizontal bearing capacity is () kN.

Options:
A. 78.9kN
B. 60.5kN
C. 72.4kN
D. 67.8kN
E. 85.4kN
F. 75.2kN
G. 95.7kN
H. 92.3kN
I. 82.6kN
J. 89.1kN
Answer: I
The foundation of a certain highway project is composed of clay, with an ultimate bearing capacity of 380 kPa under dynamic loads and 370 kPa under static loads. The safety factor under dynamic loads is 1.6, and under static loads, it is 2.0,The allowable seismic bearing capacity enhancement factor for this soil layer is ().

Options:
A. 2.0
B. 1.6
C. 1.3
D. 1.4
E. 1.2
F. 1.8
G. 2.1
H. 1.1
I. 1.7
J. 1.5
Answer: C
Male, 75 years old. Underwent emergency surgery for an incarcerated inguinal hernia for 2 days. During the operation, a large mass of small intestine was found in the hernia sac, which was still viable, along with a small amount of pale yellow exudate. The hernia ring was loosened, the small intestine was returned to the abdominal cavity, and a hernia repair was performed. On the second day post-operation, the patient experienced increased abdominal pain compared to before, with a temperature of 38.8°C, abdominal tenderness, rebound tenderness, muscle rigidity, and $WBC 18 \times 10^9 / L$. The most likely cause is ().

Options:
A. Missed perforated appendix during surgery
B. Retained foreign object from hernia operation
C. Overlooked cholecystitis causing complications
D. Acute appendicitis unrelated to hernia repair
E. Omitted necrotic intestinal segment in the abdomen
F. Newly developed gastric ulcer perforation
G. Undiagnosed paralytic ileus post-operation
H. Pre-existing chronic indigestion worsened
I. Misdiagnosed urinary tract infection symptoms
J. Post-surgical bacterial infection of the incision
Answer: E
A steel ball weighing 10 N falls vertically onto someone's head. Assume the compressive strength of the skull is $1.7 \times 10^{8} \mathrm{Pa}$. The contact time between the steel ball and the skull is $1 \times 10^{-3} \mathrm{s}$, and the contact area is $0.4 \mathrm{cm}^{2}$. If this person's height is 1.80 m, from what minimum height above the ground must the ball fall to fracture the person's skull?

Options:
A. 4.72m
B. 3.78m
C. 4.25m
D. 3.92m
E. 4.58m
F. 4.11m
G. 5.04m
H. 3.65m
I. 4.89m
J. 4.36m
Answer: F
Water flows steadily through a horizontal pipe with varying cross-sections. The cross-sectional area at the outlet is three times that of the narrowest part of the pipe. If the flow speed at the outlet is $2 \mathrm{m} / \mathrm{s}$, what is the pressure at the narrowest part?

Options:
A. $$
7. 5 \times1 0^{6} \mathrm{P a}
$$
B. $$
2. 6 \times1 0^{3} \mathrm{P a}
$$
C. $$
3. 3 \times1 0^{5} \mathrm{P a}
$$
D. $$
1. 9 \times1 0^{4} \mathrm{P a}
$$
E. $$
4. 0 \times1 0^{4} \mathrm{P a}
$$
F. $$
8. 5 \times1 0^{4} \mathrm{P a}
$$
G. $$
6. 3 \times1 0^{4} \mathrm{P a}
$$
H. $$
7. 2 \times1 0^{5} \mathrm{P a}
$$
I. $$
5. 8 \times1 0^{6} \mathrm{P a}
$$
J. $$
9. 1 \times1 0^{3} \mathrm{P a}
$$
Answer: F
A train A is traveling forward at a speed of $u_{1}=20 \mathrm{m/s}$. If the driver of train A hears the frequency of train A's whistle as $\nu=120 \mathrm{Hz}$, another train B is traveling at a speed of $u_{2}=25 \mathrm{m/s}$. The speed of sound in air is $340 \mathrm{m/s}$. Calculate:
If at this time there is a wind blowing from train A towards train B at a speed of $15 \mathrm{m/s}$, when trains A and B are moving towards each other, what frequency $\nu^{\prime}$ does the driver of train B hear from train A's whistle?

Options:
A. $$
\approx139 \, \mathrm{Hz}
$$
B. $$
\approx140 \, \mathrm{Hz}
$$
C. $$
\approx130 \, \mathrm{Hz}
$$
D. $$
\approx142 \, \mathrm{Hz}
$$
E. $$
\approx128 \, \mathrm{Hz}
$$
F. $$
\approx132 \, \mathrm{Hz}
$$
G. $$
\approx138 \, \mathrm{Hz}
$$
H. $$
\approx134 \, \mathrm{Hz}
$$
I. $$
\approx1 3 6 \, \mathrm{H z}
$$
J. $$
\approx145 \, \mathrm{Hz}
$$
Answer: I
Simple harmonic alternating current $\begin{array} {r l} {{i}} & {{} {{( t )}}} & {{{} {=} I_{\mathrm{m}} \mathrm{c o s} \, ( \omega t+{\frac{\pi} {6}} ) \, \mathrm{A}}} \\ \end{array}$, at $t=0$, $i=0.866 \mathrm{A}$. Find the maximum value of the current in the circuit. What is the reading on an AC ammeter?

Options:
A. $$
2. 5 \mathrm{A},0.75A
$$
B. $$ 2.3 \mathrm{A},0.77A $$
C. $$ 2.0 \mathrm{A},0.78A $$
D. $$ 1.5 \mathrm{A},0.85A $$
E. $$
1.2 \mathrm{A},0.80A
$$
F. $$ 1.8 \mathrm{A},0.76A $$
G. $$ 1.3 \mathrm{A},0.83A $$
H. $$
1. 0 \mathrm{A},0.71A
$$
I. $$ 1.1 \mathrm{A},0.74A $$
J. $$ 0.9 \mathrm{A},0.73A $$
Answer: H
Determine the highest and lowest frequencies of the Balmer series in the hydrogen atomic spectrum.

Options:
A. $$
2.10 \times1 0^{-6} \mathrm{m}
$$
$$1.95 \times1 0^{1 4} \mathrm{H z}$$
B. $$
1.90 \times1 0^{-5} \mathrm{m}
$$
$$2.00 \times1 0^{1 4} \mathrm{H z}$$
C. $$
2.50 \times1 0^{-6} \mathrm{m}
$$
$$2.30 \times1 0^{1 4} \mathrm{H z}$$
D. $$
1.99 \times1 0^{-5} \mathrm{m}
$$
$$1.90 \times1 0^{1 4} \mathrm{H z}$$
E. $$
1.50 \times1 0^{-5} \mathrm{m}
$$
$$3.10 \times1 0^{1 4} \mathrm{H z}$$
F. $$
1.10 \times1 0^{-5} \mathrm{m}
$$
$$2.80 \times1 0^{1 4} \mathrm{H z}$$
G. $$
1. 4 6 \times1 0^{-6} \mathrm{m}
$$
$$2.05 \times1 0^{1 4} \mathrm{H z}$$
H. $$
1.85 \times1 0^{-6} \mathrm{m}
$$
$$2.50 \times1 0^{1 4} \mathrm{H z}$$
I. $$
2.00 \times1 0^{-6} \mathrm{m}
$$
$$2.20 \times1 0^{1 4} \mathrm{H z}$$
J. $$
1.20 \times1 0^{-5} \mathrm{m}
$$
$$2.70 \times1 0^{1 4} \mathrm{H z}$$
Answer: G
Determine the ionization energy of the hydrogen atom.

Options:
A. $$
1. 9 6 \times1 0^{-1 9} \mathrm{J}
$$
B. $$
2. 0 9 \times1 0^{-1 8} \mathrm{J}
$$
C. $$
2. 2 5 \times1 0^{-1 8} \mathrm{J}
$$
D. $$
2. 3 2 \times1 0^{-1 8} \mathrm{J}
$$
E. $$
3. 0 0 \times1 0^{-1 9} \mathrm{J}
$$
F. $$
2. 5 4 \times1 0^{-1 8} \mathrm{J}
$$
G. $$
1. 6 5 \times1 0^{-1 8} \mathrm{J}
$$
H. $$
1. 7 7 \times1 0^{-1 9} \mathrm{J}
$$
I. $$
2. 1 7 \times1 0^{-1 8} \mathrm{J}
$$
J. $$
1. 8 8 \times1 0^{-1 8} \mathrm{J}
$$
Answer: I
The diameter of a human red blood cell is $8 \mu\mathrm{m}$, with a thickness of $2 \sim 3 \mu\mathrm{m}$, and a mass of $10^{-13} \mathbf{kg}$. Assuming the uncertainty in measuring the position of the red blood cell is $0.1 \mu\mathrm{m}$, calculate the uncertainty in its velocity.

Options:
A. $$
1. 1 \times1 0^{-1 5} \mathrm{m / s}
$$
B. $$
6. 0 \times1 0^{-1 2} \mathrm{m / s}
$$
C. $$
9. 8 \times1 0^{-1 2} \mathrm{m / s}
$$
D. $$
8. 7 \times1 0^{-1 3} \mathrm{m / s}
$$
E. $$
6. 6 \times1 0^{-1 4} \mathrm{m / s}
$$
F. $$
2. 3 \times1 0^{-1 3} \mathrm{m / s}
$$
G. $$
4. 9 \times1 0^{-1 3} \mathrm{m / s}
$$
H. $$
3. 5 \times1 0^{-1 2} \mathrm{m / s}
$$
I. $$
5. 4 \times1 0^{-1 5} \mathrm{m / s}
$$
J. $$
7. 2 \times1 0^{-1 4} \mathrm{m / s}
$$
Answer: E
A certain hospital has a $^{60}{C o}$ therapy machine, equipped with a $^{60}{Co}$ source with an activity of $1200 \mathrm{Ci}$. It is scheduled to replace the $^{60}{Co}$ source when the activity decays to $300 \mathrm{Ci}$. How many years can this $^{60}{Co}$ source be used? The half-life of $^{60}{Co}$ is 5.27 years.

Options:
A. 5.90 years
B. 7.42 years
C. 10.54 years
D. 13.16 years
E. 6.87 years
F. 9.53 years
G. 8.31 years
H. 7.88 years
I. 11.05 years
J. 12.49 years
Answer: C
The linear absorption coefficient of X-rays with a certain wavelength passing through water is $0.77 \mathrm{cm}^{-1}$, and the linear absorption coefficient through a certain human tissue is $1.02 \mathrm{cm}^{-1}$. Given that the $k$ value is 1000 and the CT value of water is zero, find the CT value of this human tissue.

Options:
A. $$315H$$
B. $$355H$$
C. $$305H$$
D. $$325H$$
E. $$288H$$
F. $$380H$$
G. $$290H$$
H. $$345H$$
I. $$267H$$
J. $$342H$$
Answer: D
A disc-shaped flywheel with a mass of $M$, a radius of $R$, and uniform density distribution. During the process of spinning with angular velocity $\omega$, a fragment with a mass of $m$ detaches and flies off from the edge of the flywheel, assuming that the speed of the fragment at the time it detaches from the flywheel is exactly directed vertically upward. The angular momentum and rotational kinetic energy of the remaining part of the flywheel are ______.

Options:
A. $$2\omega$$
$$
\frac{1} {4} ( M-2 m ) R^{2} \omega
$$
$$
\frac{1} {4} ( M-3 m ) R^{2} \omega^{2}
$$
B. $$\omega^{3}$$
$$
\frac{1} {2} ( M-2 m ) R^{2} \omega
$$
$$
\frac{3} {8} ( M-m ) R^{2} \omega^{2}
$$
C. $$\omega$$
$$
\frac{1} {3} ( M-3 m ) R^{2} \omega
$$
$$
\frac{1} {8} ( M-2 m ) R^{2} \omega^{2}
$$
D. $$\omega$$
$$
\frac{1} {2} ( M-2 m ) R^{2} \omega
$$
$$
\frac{1} {4} ( M-2 m ) R^{2} \omega^{2}
$$
E. $$\omega$$
$$
\frac{3} {4} ( M-2 m ) R^{2} \omega
$$
$$
\frac{1} {2} ( M-m ) R^{2} \omega^{2}
$$
F. $$\frac{\omega}{2}$$
$$
\frac{1} {2} ( M-m ) R^{2} \omega
$$
$$
\frac{1} {8} ( M-2 m ) R^{2} \omega^{2}
$$
G. $$\omega$$
$$
\frac{2} {3} ( M-m ) R^{2} \omega
$$
$$
\frac{1} {3} ( M-m ) R^{2} \omega^{2}
$$
H. $$\frac{\omega}{3}$$
$$
\frac{3} {4} ( M-2 m ) R^{2} \omega
$$
$$
\frac{1} {2} ( M-2 m ) R^{2} \omega^{2}
$$
I. $$\omega$$
$$
\frac{1} {2} ( M-3 m ) R^{2} \omega
$$
$$
\frac{1} {4} ( M-2 m ) R^{2} \omega
$$
J. $$\omega^{2}$$
$$
\frac{1} {3} ( M-m ) R^{2} \omega
$$
$$
\frac{1} {3} ( M-2 m ) R^{2} \omega^{2}
$$
Answer: D
In a biogas digester, at a location $1m$ below the liquid surface, bubbles with a radius of $2.0 \times 10^{-3} \mathrm{~m}$ are formed. What is the actual pressure inside the bubble?
$$
( \ \sigma_{\mathrm{water}}=0.0712 \ \mathrm{N} \cdot \mathrm{m}^{-1} \ )
$$

Options:
A. $1.08\times10^{5} Pa$
B. $1.30\times10^{5} Pa$
C. $1.00\times10^{5} Pa$
D. $9.50\times10^{4} Pa$
E. $1.05\times10^{5} Pa$
F. $1.25\times10^{5} Pa$
G. $1.20\times10^{5} Pa$
H. $1.11\times10^{5} Pa$
I. $9.80\times10^{4} Pa$
J. $1.15\times10^{5} Pa$
Answer: H
A particle performs a harmonic oscillation along the $X$ axis with an amplitude of $A$ and a period of $2s$. The oscillation is expressed using a cosine function. Use the rotating vector method to determine the initial phase and the time it first passes through the equilibrium position under the following condition. (At $t=0$, the particle is at position $x=-A$).

Options:
A. $\pi/2,1s$
B. $0,0.5s$
C. $3\pi/2,0.5s$
D. $0,1s$
E. $2\pi,0.5s$
F. $\pi,1s$
G. $\pi,1.5s$
H. $2\pi,1.5s$
I. $\pi,0.5s$
Answer: I
A plane harmonic wave propagates along the negative direction of the x-axis at a speed of $2.0 \, \mathrm{m} \cdot \mathrm{s}^{-1}$. If the position of the wave source is at $x=0$, and the vibration equation for the particle at $x=-0.5 \, \mathrm{m}$ is $y=0.10 \cos \left( \pi t + \frac{\pi}{12} \right)$ (m), find the vibration equation of the wave source.

Options:
A. $$
y= 0. 2 0 \mathrm{s i n} \left( \pi t+{\frac{\pi} {2}} \right) ( \mathrm{m} )
$$
B. $$
y= 0. 0 8 \mathrm{c o s} \left( \pi t+{\frac{\pi} {5}} \right) ( \mathrm{m} )
$$
C. $$
y= 0. 1 2 \mathrm{c o s} \left( \pi t+{\frac{\pi} {10}} \right) ( \mathrm{m} )
$$
D. $$
y= 0. 1 0 \mathrm{c o s} \left( 2\pi t+{\frac{\pi} {4}} \right) ( \mathrm{m} )
$$
E. $$
y= 0. 0 5 \mathrm{s i n} \left( 2\pi t+{\frac{\pi} {3}} \right) ( \mathrm{m} )
$$
F. $$
y= 0. 1 5 \mathrm{c o s} \left( \pi t+{\frac{\pi} {6}} \right) ( \mathrm{m} )
$$
G. $$
y= 0. 1 0 \mathrm{c o s} \left( \pi t+{\frac{\pi} {3}} \right) ( \mathrm{m} )
$$
H. $$
y= 0. 1 0 \mathrm{s i n} \left( \pi t+{\frac{3\pi} {8}} \right) ( \mathrm{m} )
$$
I. $$
y= 0. 1 0 \mathrm{s i n} \left( \pi t+{\frac{\pi} {8}} \right) ( \mathrm{m} )
$$
J. $$
y= 0. 0 9 \mathrm{c o s} \left( \pi t+{\frac{\pi} {7}} \right) ( \mathrm{m} )
$$
Answer: G
In a uniform magnetic field of $B$ with the proton and electron flying vertically at the same velocity, the ratio of the proton orbital radius $R_{1}$to the electron orbital radius $R_{2}$ is ____.

Options:
A. $$
\frac{m_{\mathrm{e}}} {m_{\mathrm{p}}}
$$
B. $$
\frac{r_{\mathrm{e}}} {r_{\mathrm{p}}}
$$
C. $$
\frac{q_{\mathrm{e}}} {q_{\mathrm{p}}}
$$
D. $$
\frac{m_{\mathrm{p}}} {m_{\mathrm{c}}}
$$
E. $$
\frac{m_{\mathrm{p}}^2} {m_{\mathrm{e}}}
$$
F. $$
\frac{q_{\mathrm{p}}} {q_{\mathrm{e}}}
$$
G. $$
\frac{v_{\mathrm{p}}} {v_{\mathrm{e}}}
$$
H. $$
\frac{m_{\mathrm{p}}} {m_{\mathrm{e}}^2}
$$
I. $$
\frac{1} {m_{\mathrm{p}}}
$$
J. $$
\frac{v_{\mathrm{e}}} {v_{\mathrm{p}}}
$$
Answer: D
The interface between a certain liquid ($n=1.3$) and glass ($m=1.5$) is spherical. An object in the liquid is placed on the axis of the spherical surface at a distance of 39 cm from the surface, forming a virtual image 30 cm in front of the surface. What is the radius of curvature of the spherical surface?

Options:
A. -25cm
B. -14cm
C. -20cm
D. -12cm
E. -16cm
F. -15cm
G. -18cm
H. -19cm
I. -13cm
J. -9cm
Answer: D
Nylon 66 is synthesized from the molar reaction of adipic acid and hexamethylenediamine. Given that the equilibrium constant for the polymerization reaction is $K \!=\! 4 3 2$, calculate how much water content should be controlled in the reaction system to synthesize a polycondensate with a degree of polymerization of 200.

Options:
A. $$
0. 0 5 1 8 \mathrm{m o l} / \mathrm{L}
$$
B. $$
0. 0 8 1 5 \mathrm{m o l} / \mathrm{L}
$$
C. $$
0. 0 3 1 6 \mathrm{m o l} / \mathrm{L}
$$
D. $$
0. 0 9 1 9 \mathrm{m o l} / \mathrm{L}
$$
E. $$
0. 0 2 0 7 \mathrm{m o l} / \mathrm{L}
$$
F. $$
0. 6 0 5 1 \mathrm{m o l} / \mathrm{L}
$$
G. $$
0. 0 4 1 1 \mathrm{m o l} / \mathrm{L}
$$
H. $$
0. 0 7 2 5 \mathrm{m o l} / \mathrm{L}
$$
I. $$
0. 0 1 0 8 \mathrm{m o l} / \mathrm{L}
$$
J. $$
0. 1 5 0 9 \mathrm{m o l} / \mathrm{L}
$$
Answer: I
Styrene $(M_{1})$ and butadiene $(\mathbf{M}_{2})$ undergo free radical copolymerization at 5°C, with $r_{1}=0.64$ and $r_{2}=1.38$. It is known that the chain propagation rate constants for the homopolymerization of styrene and butadiene are 49 L/(mol·s) and 251 L/(mol·s), respectively. Try to determine the reaction rate constant for copolymerization.

Options:
A. $$
k_{1 2} \!=\! 6 4. 6 9 \mathrm{L / ( m o l ~ \cdot~ s )} \,, \, \, k_{2 1} \!=\! 1 8 3. \, 5 1 \mathrm{L / ( m o l ~ \cdot~ s )}
$$
B. $$
k_{1 2} \!=\! 8 3. 1 8 \mathrm{L / ( m o l ~ \cdot~ s )} \,, \, \, k_{2 1} \!=\! 1 6 5. \, 6 7 \mathrm{L / ( m o l ~ \cdot~ s )}
$$
C. $$
k_{1 2} \!=\! 5 9. 7 2 \mathrm{L / ( m o l ~ \cdot~ s )} \,, \, \, k_{2 1} \!=\! 1 7 2. \, 4 4 \mathrm{L / ( m o l ~ \cdot~ s )}
$$
D. $$
k_{1 2} \!=\! 9 1. 5 4 \mathrm{L / ( m o l ~ \cdot~ s )} \,, \, \, k_{2 1} \!=\! 1 7 4. \, 6 8 \mathrm{L / ( m o l ~ \cdot~ s )}
$$
E. $$
k_{1 2} \!=\! 7 0. 3 5 \mathrm{L / ( m o l ~ \cdot~ s )} \,, \, \, k_{2 1} \!=\! 1 8 7. \, 9 4 \mathrm{L / ( m o l ~ \cdot~ s )}
$$
F. $$
k_{1 2} \!=\! 7 2. 4 7 \mathrm{L / ( m o l ~ \cdot~ s )} \,, \, \, k_{2 1} \!=\! 1 7 9. \, 3 2 \mathrm{L / ( m o l ~ \cdot~ s )}
$$
G. $$
k_{1 2} \!=\! 7 6. 5 6 \mathrm{L / ( m o l ~ \cdot~ s )} \,, \, \, k_{2 1} \!=\! 1 8 1. \, 8 8 \mathrm{L / ( m o l ~ \cdot~ s )}
$$
H. $$
k_{1 2} \!=\! 9 8. 2 6 \mathrm{L / ( m o l ~ \cdot~ s )} \,, \, \, k_{2 1} \!=\! 1 5 9. \, 7 3 \mathrm{L / ( m o l ~ \cdot~ s )}
$$
I. $$
k_{1 2} \!=\! 6 8. 4 2 \mathrm{L / ( m o l ~ \cdot~ s )} \,, \, \, k_{2 1} \!=\! 1 9 5. \, 3 9 \mathrm{L / ( m o l ~ \cdot~ s )}
$$
J. $$
k_{1 2} \!=\! 7 5. 3 8 \mathrm{L / ( m o l ~ \cdot~ s )} \,, \, \, k_{2 1} \!=\! 1 6 1. \, 4 9 \mathrm{L / ( m o l ~ \cdot~ s )}
$$
Answer: G
It is known that the equilibrium melting point of polypropylene is 176°C and the melting heat of its molar repeating unit is 8.36 kJ/mol. Try to calculate the melting point of the copolymer when the second monomer that does not enter the crystal lattice is copolymerized with it and the second monomer accounts for 10% of the mole fraction.

Options:
A. $$
4 4 3. 3 \mathrm{K} ( 1 7 0. 1 \mathrm{^{°} C} )
$$
B. $$
4 3 5. 5 \mathrm{K} ( 1 6 2. 3 \mathrm{^{°} C} )
$$
C. $$
4 5 5. 5 \mathrm{K} ( 1 8 2. 0 \mathrm{^{°} C} )
$$
D. $$
4 3 0. 0 \mathrm{K} ( 1 6 5. 8 \mathrm{^{°} C} )
$$
E. $$
4 2 8. 8 \mathrm{K} ( 1 5 5. 8 \mathrm{^{°} C} )
$$
F. $$
4 4 0. 0 \mathrm{K} ( 1 6 9. 8 \mathrm{^{°} C} )
$$
G. $$
4 0 0. 0 \mathrm{K} ( 1 2 6. 8 \mathrm{^{°} C} )
$$
H. $$
4 1 5. 5 \mathrm{K} ( 1 4 8. 4 \mathrm{^{°} C} )
$$
I. $$
4 5 0. 0 \mathrm{K} ( 1 7 6. 8 \mathrm{^{°} C} )
$$
J. $$
4 6 0. 0 \mathrm{K} ( 1 8 7. 0 \mathrm{^{°} C} )
$$
Answer: E
Given that the flow activation energies of polyethylene and polymethyl methacrylate are 42 kJ/mol and 193 kJ/mol respectively, the viscosity of polyethylene at 200°C is 91 Pa·s, and the viscosity of polymethyl methacrylate at 240°C is 200 Pa·s. Calculate the viscosity of polyethylene at 210°C and 190°C.

Options:
A. $$
\eta_{4 8 3}=6 8 {\mathrm{P a ~ \cdot~ s}}
$$
$$
\eta_{4 6 3}=1 2 5 \mathrm{P a \cdot s}
$$
B. $$
\eta_{4 8 3}=7 3 {\mathrm{P a ~ \cdot~ s}}
$$
$$
\eta_{4 6 3}=1 1 5 \mathrm{P a \cdot s}
$$
C. $$
\eta_{4 8 3}=6 5 {\mathrm{P a ~ \cdot~ s}}
$$
$$
\eta_{4 6 3}=1 3 5 \mathrm{P a \cdot s}
$$
D. $$
\eta_{4 8 3}=7 8 {\mathrm{P a ~ \cdot~ s}}
$$
$$
\eta_{4 6 3}=1 0 5 \mathrm{P a \cdot s}
$$
E. $$
\eta_{4 8 3}=8 5 {\mathrm{P a ~ \cdot~ s}}
$$
$$
\eta_{4 6 3}=1 3 0 \mathrm{P a \cdot s}
$$
F. $$
\eta_{4 8 3}=9 0 {\mathrm{P a ~ \cdot~ s}}
$$
$$
\eta_{4 6 3}=1 0 0 \mathrm{P a \cdot s}
$$
G. $$
\eta_{4 8 3}=8 3 {\mathrm{P a ~ \cdot~ s}}
$$
$$
\eta_{4 6 3}=1 1 2 \mathrm{P a \cdot s}
$$
H. $$
\eta_{4 8 3}=8 0 {\mathrm{P a ~ \cdot~ s}}
$$
$$
\eta_{4 6 3}=1 2 0 \mathrm{P a \cdot s}
$$
I. $$
\eta_{4 8 3}=7 0 {\mathrm{P a ~ \cdot~ s}}
$$
$$
\eta_{4 6 3}=1 0 5 \mathrm{P a \cdot s}
$$
J. $$
\eta_{4 8 3}=7 7 {\mathrm{P a ~ \cdot~ s}}
$$
$$
\eta_{4 6 3}=1 1 0 \mathrm{P a \cdot s}
$$
Answer: B
Styrene undergoes solution polymerization at 60°C with di-tert-butyl peroxide as the initiator and benzene as the solvent. When the concentration of the styrene monomer $c ( \mathbf{M} )=1 \mathrm{mol} / \mathbf{L}$ and the initiator concentration $c \left( {\bf I} \right) ~=0.01 \mathrm{mol} / {\bf L}$, the initial rates of initiation and polymerization are $4 \times 10^{-11} \mathrm{mol} / ( \mathrm{L} \cdot \mathrm{s} )$ and $1.5 \times 10^{-7} \mathrm{mol} / ( \mathrm{L} \cdot \mathrm{s} )$, respectively. Try to determine the main termination mode of the chain under low conversion in the above polymerization reaction, and the ratio of true termination to chain transfer termination, based on calculations is(). Known data: at 60°C, $C_{\mathrm{M}}=8.0 \times 10^{-5}$, $C_{\mathrm{I}}=3.2 \times 10^{-4}$, $C_{\mathrm{S}}=2.3 \times 10^{-6}$, the density of styrene is 0.887 g/mL, and the density of benzene is 0.839 g/mL. Assume the styrene-benzene system is an ideal solution.

Options:
A. Coincidence Termination
44%
B. Radical Disproportionation
29%
C. Fragmented Chain Debonding
58%
D. Alternative End Formation
48%
E. Crossover Polymers Formation
56%
F. Ionic Chain Cutting
36%
G. Random Chain Scission
22%
H. Crosslinked Network Growth
50%
I. Spontaneous Deactivation
33%
J. Cyclization Side Reaction
41%
Answer: A
An equimolar amount of diol and dicarboxylic acid is polycondensed to form polyester, with an additional 1.5 mol% acetic acid (based on the total number of monomers) as a functional group blocker. When $P \!=\! 0.995$, what is the average degree of polymerization $\overline{{{X}}}_{n}$ of the polyester?

Options:
A. 0.950
B. 1.025
C. 1.002
D. 0.988
E. 1.030
F. 1.015
G. 0.947
H. 0.971
I. 0.960
J. 0.933
Answer: H
With benzoyl peroxide as initiator and ethyl acetate as solvent, methyl methacrylate undergoes polymerization at 60°C. Assume that the total volume of polymer in the reactor is 1 L, the density is $0.878 \mathrm{~g \cdot mL}^{-1}$, the mass of the monomer is 300 g, the initiator dose is 0.6 $\gamma_{\mathrm{6}}$ of the monomer dose, $k_{\mathrm{d}} = 2.0 \times 10^{-6} \, \mathrm{s}^{-1}$, $k_{\mathrm{p}} = 367 \, \mathrm{~L} \cdot \mathrm{mol}^{-1} \cdot \mathrm{s}^{-1}$, $k_{\mathrm{t}} = 0.93 \times 10^{7} \, \mathrm{~L} \cdot \mathrm{mol}^{-1} \cdot \mathrm{s}^{-1}$, $f = 0.8$, $C_{\mathrm{I}} = 0.02$, $C_{\mathrm{M}} = 0.18 \times 10^{-4}$, $C_{\mathrm{S}} = 0.46 \times 10^{-6}$, kinetic chain termination is mainly through disproportionation, about 85%. Calculate the number average degree of polymerization of the product when the reaction is stopped at low conversion?

Options:
A. $$
\overline{{{X_{\mathrm{n}}}}} \!=\! 5. 9 7 \! \times\! 1 0^{3}
$$
B. $$
\overline{{{X_{\mathrm{n}}}}} \!=\! 3. 5 9 \! \times\! 1 0^{5}
$$
C. $$
\overline{{{X_{\mathrm{n}}}}} \!=\! 7. 4 1 \! \times\! 1 0^{2}
$$
D. $$
\overline{{{X_{\mathrm{n}}}}} \!=\! 2. 8 7 \! \times\! 1 0^{3}
$$
E. $$
\overline{{{X_{\mathrm{n}}}}} \!=\! 6. 8 1 \! \times\! 1 0^{1}
$$
F. $$
\overline{{{X_{\mathrm{n}}}}} \!=\! 1. 5 0 \! \times\! 1 0^{2}
$$
G. $$
\overline{{{X_{\mathrm{n}}}}} \!=\! 8. 3 3 \! \times\! 1 0^{6}
$$
H. $$
\overline{{{X_{\mathrm{n}}}}} \!=\! 4. 2 3 \! \times\! 1 0^{4}
$$
I. $$
\overline{{{X_{\mathrm{n}}}}} \!=\! 4. 6 5 \! \times\! 1 0^{7}
$$
J. $$
\overline{{{X_{\mathrm{n}}}}} \!=\! 9. 2 0 \! \times\! 1 0^{4}
$$
Answer: D
1 g of PMMA is dissolved in 50 mL of benzene at 20°C. The density of PMMA is $1.18\ g\mathrm{cm}^{-3}$, the density of benzene is $0.879 \ \mathrm{g \cdot cm}^{-3}$, and the relative molecular mass is $1 \times 10^{5}$. What is the entropy change?

Options:
A. $$
0. 0 3 9 \ ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
B. $$
0. 0 4 5 \ ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
C. $$
0. 0 7 7 \ ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
D. $$
0. 0 5 2 \ ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
E. $$
0. 0 9 3 \ ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
F. $$
0. 0 6 4 \ ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
G. $$
0. 1 1 5 \ ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
H. $$
0. 0 8 8 \ ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
I. $$
0. 1 0 2 \ ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
J. $$
0. 0 7 1 \ ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
Answer: C
The number average molecular weight of a sample of polyisobutylene is 428,000. The second virial coefficient measured in chlorobenzene solution at 25 °C is $\varGamma_{2} \!=\! 94.5 \ \mathrm{cm}^{3} \cdot \mathrm{g}^{-1}$. Given that the density of chlorobenzene at 25 °C is 1.119 $\mathrm{g \cdot cm^{-3}}$, calculate the osmotic pressure of the $7.0 \times 10^{-6} \ \mathrm{mol \cdot dm^{-3}}$ chlorobenzene solution of this polymer?

Options:
A. 17.9 Pa
B. 15.8 Pa
C. 25.4 Pa
D. 22.7 Pa
E. 21.8 Pa
F. 20.1 Pa
G. 24.3 Pa
H. 19.5 Pa
I. 18.2 Pa
J. 23.6 Pa
Answer: D
Suppose a certain polymer has a glass transition temperature $T_{g}=320 \, \mathrm{K}$ and a density $\rho_{0}=1 \times 10^{3} \, \mathrm{kg \cdot m^{-3}}$. Its viscosity at 400 K is measured to be $10^{5} \, \mathrm{Pa \cdot s}$. Now, if a sufficient amount of propylene glycol $(T_{\mathrm{g}} = 160 \, \mathrm{K}, \rho_{\mathrm{l}} = 1 \times 10^{3} \, \mathrm{kg \cdot m^{-3}})$ is used to fully swell the polymer such that the polymer's volume fraction makes up 0.70 of the swollen mixture, what is the viscosity of this plasticized polymer at the same temperature $(400 \,\mathrm{K})$? Assume linear additivity of free volumes for the polymer and the plasticizer.

Options:
A. $$
8 6. 7 4 \mathrm{~ P a ~ \cdot~ s ~}
$$
B. $$
9 9. 7 2 \mathrm{~ P a ~ \cdot~ s ~}
$$
C. $$
1 0 3. 9 0 \mathrm{~ P a ~ \cdot~ s ~}
$$
D. $$
8 1. 0 5 \mathrm{~ P a ~ \cdot~ s ~}
$$
E. $$
1 1 7. 0 8 \mathrm{~ P a ~ \cdot~ s ~}
$$
F. $$
5 9. 2 8 \mathrm{~ P a ~ \cdot~ s ~}
$$
G. $$
7 4. 8 3 \mathrm{~ P a ~ \cdot~ s ~}
$$
H. $$
1 2 1. 5 6 \mathrm{~ P a ~ \cdot~ s ~}
$$
I. $$
6 7. 4 9 \mathrm{~ P a ~ \cdot~ s ~}
$$
J. $$
9 4. 3 1 \mathrm{~ P a ~ \cdot~ s ~}
$$
Answer: A
Given that a certain photoresistor has a resistance of 2.5 kΩ under 100 lx of illumination, and it is known that within the $90 \sim 120\, \mathrm{lx}$ range, $\gamma = 0.9$, the resistance of the photoresistor under 110 lx of illumination is ().

Options:
A. 2.6kΩ
B. 1.5kΩ
C. 2.7kΩ
D. 2.1kΩ
E. 1.8kΩ
F. 2.8kΩ
G. 2.3kΩ
H. 2.0kΩ
I. 2.4kΩ
J. 3.0kΩ
Answer: G
At what temperature are the spontaneous emission rate and the stimulated emission rate equal when $\lambda=0.5 \mu\mathrm{m}$? At $T=300\mathrm{K}$, at what wavelength are the spontaneous emission rates equal?

Options:
A. $7. 4 1 \times1 0^{2 9} \, K$,$7. 6 0 8 \times1 0^{1} M$
B. $4. 2 3 \times1 0^{1 8} \, K$,$3. 6 8 1 \times1 0^{4} M$
C. $1. 8 3 \times1 0^{2 2} \, K$,$2. 5 9 3 \times1 0^{5} M$
D. $2. 6 5 \times1 0^{2 7} \, K$,$8. 9 9 0 \times1 0^{3} M$
E. $3. 7 2 \times1 0^{3 0} \, K$,$9. 7 0 5 \times1 0^{2} M$
F. $8. 0 9 \times1 0^{2 4} \, K$,$5. 1 4 7 \times1 0^{4} M$
G. $7. 1 9 \times1 0^{3 3} \, K$,$1. 4 4 2 \times1 0^{4} M$
H. $6. 5 4 \times1 0^{2 6} \, K$,$4. 2 7 9 \times1 0^{6} M$
I. $5. 9 8 \times1 0^{2 1} \, K$,$1. 2 3 7 \times1 0^{4} M$
J. $9. 3 2 \times1 0^{2 3} \, K$,$6. 5 0 2 \times1 0^{7} M$
Answer: G
PIN photodiode, illuminated by $6 \times 10^{12}$ photons with a wavelength of $1.55 \mu m$, produces $2 \times 10^{12}$ photons at the output. What are the quantum efficiency and responsivity?

Options:
A. 0.54,$6. 0 2 1 \times1 0^{5} V/W$
B. 0.45,$8. 9 2 7 \times1 0^{5} V/W$
C. 0.49,$4. 1 8 6 \times1 0^{6} V/W$
D. 0.16,$1. 1 3 7 \times1 0^{6} V/W$
E. 0.21,$7. 9 4 0 \times1 0^{6} V/W$
F. 0.28,$2. 6 3 5 \times1 0^{6} V/W$
G. 0.37,$2. 5 7 8 \times1 0^{5} V/W$
H. 0.33,$1. 0 4 2 \times1 0^{6} V/W$
I. 0.39,$3. 4 8 1 \times1 0^{6} V/W$
J. 0.25,$5. 9 3 2 \times1 0^{5} V/W$
Answer: H