MikaStars39/nano-eval huggingface dataset:
What are the J2000.0 Galactic coordinates of Sgr $\mathrm{A}^{\star}?$

Options:
A. $$
0. 8 2 9^{\circ}
$$
$$
+0. 0 5 0 9^{\circ}
$$
B. $$
1. 0 5 5^{\circ}
$$
$$
-0. 2 1 4 3^{\circ}
$$
C. $$
0. 9 5 0^{\circ}
$$
$$
-0. 0 8 2 6^{\circ}
$$
D. $$
0. 7 3 1^{\circ}
$$
$$
+0. 1 4 9 5^{\circ}
$$
E. $$
0. 9 4 4^{\circ}
$$
$$
-0. 0 4 6 1^{\circ}
$$
F. $$
0. 8 4 8^{\circ}
$$
$$
+0. 1 0 3 7^{\circ}
$$
G. $$
0. 6 9 7^{\circ}
$$
$$
+0. 0 3 8 7^{\circ}
$$
H. $$
1. 1 0 2^{\circ}
$$
$$
-0. 0 7 3 4^{\circ}
$$
I. $$
1. 0 2 0^{\circ}
$$
$$
-0. 0 9 6 2^{\circ}
$$
J. $$
0. 7 8 3^{\circ}
$$
$$
+0. 0 2 5 8^{\circ}
$$
Answer: E
Estimate the Eddington luminosity of a black hole with the mass of Sgr $\mathrm{A}^{\star}$ . What is the ratio of the upper limit of the bolometric luminosity of Sgr $\mathrm{A}^{\star}$ to its Eddington luminosity?

Options:
A. $$
0. 1 5 \ \mathrm{m}^{2} \ \mathrm{k g}^{-1}
$$
$$
1 \times1 0^{5} \, \mathrm{L}_{\odot}
$$
B. $$
0. 0 6 \ \mathrm{m}^{2} \ \mathrm{k g}^{-1}
$$
$$
1 \times1 0^{3} \, \mathrm{L}_{\odot}
$$
C. $$
0. 0 5 \ \mathrm{m}^{2} \ \mathrm{k g}^{-1}
$$
$$
2 \times1 0^{6} \, \mathrm{L}_{\odot}
$$
D. $$
0. 0 8 \ \mathrm{m}^{2} \ \mathrm{k g}^{-1}
$$
$$
7 \times1 0^{4} \, \mathrm{L}_{\odot}
$$
E. $$
0. 0 3 \ \mathrm{m}^{2} \ \mathrm{k g}^{-1}
$$
$$
5 \times1 0^{3} \, \mathrm{L}_{\odot}
$$
F. $$
0. 0 1 \ \mathrm{m}^{2} \ \mathrm{k g}^{-1}
$$
$$
6 \times1 0^{5} \, \mathrm{L}_{\odot}
$$
G. $$
0. 0 4 \ \mathrm{m}^{2} \ \mathrm{k g}^{-1}
$$
$$
9 \times1 0^{4} \, \mathrm{L}_{\odot}
$$
H. $$
0. 0 7 \ \mathrm{m}^{2} \ \mathrm{k g}^{-1}
$$
$$
4 \times1 0^{3} \, \mathrm{L}_{\odot}
$$
I. $$
0. 0 2 \ \mathrm{m}^{2} \ \mathrm{k g}^{-1}
$$
$$
3 \times1 0^{4} \, \mathrm{L}_{\odot}
$$
J. $$
0. 1 2 \ \mathrm{m}^{2} \ \mathrm{k g}^{-1}
$$
$$
8 \times1 0^{2} \, \mathrm{L}_{\odot}
$$
Answer: I
Suppose that an intruder star (a main-sequence M star) travels perpendicularly through the Galactic disk. What are the odds of the intruder colliding with another star during its passage through the disk? Take the thickness of the disk to be approximately 1 kpc.

Options:
A. $$
\approx3. 7 \times1 0^{-1 2}
$$
B. $$
\approx4. 2 \times1 0^{-1 1}
$$
C. $$
\approx1. 2 \times1 0^{-1 6}
$$
D. $$
\approx9. 1 \times1 0^{-1 4}
$$
E. $$
\approx1. 0 \times1 0^{-1 5}
$$
F. $$
\approx7. 8 \times1 0^{-1 7}
$$
G. $$
\approx2. 5 \times1 0^{-1 3}
$$
H. $$
\approx5. 0 \times1 0^{-1 8}
$$
I. $$
\approx6. 3 \times1 0^{-1 4}
$$
J. $$
\approx8. 5 \times1 0^{-1 2}
$$
Answer: G
If $[X]_{complement}=1.1101010$, then $[X]_{original}=$().

Options:
A. 1.0110010
B. 1.0101100
C. 1.1100110
D. 1.1100010
E. 1.1110101
F. 1.0001110
G. 1.1001101
H. 1.1011000
I. 1.0100111
J. 1.0010110
Answer: J
Assume that the machine word length is $8$ bits (including 1 sign bit), $A=15$, $B=24$. What the results of $[ A+B ]_{complement}$ and $[ A-B ]_{complement}$ is().

Options:
A. +37, -1
B. +36, -6
C. +38, -10
D. +35, -2
E. +30, -7
F. +33, -4
G. +31, -3
H. +32, -8
I. +34, -5
J. +39, -9
Answer: J
Given $A=-1 0 0 1$ and $B=-0 1 0 1$, find $[ A+B ]_{complement}=$ ().

Options:
A. $$10001$$
B. $$01100$$
C. $$10010$$
D. $$10101$$
E. $$11000$$
F. $$01111$$
G. $$01010$$
H. $$00111$$
I. $$00101$$
J. $$11011$$
Answer: C
In a two-level storage system composed of Cache and main memory, both are accessed simultaneously. The access time of the Cache is 100ns, while the access time of the main memory is 1000ns. If both the Cache and main memory are accessed at the same time, and the desired effective (average) access time must not exceed 115% of the Cache access time, then the Cache hit rate must be at least ().

Options:
A. 89%
B. 59%
C. 91%
D. 69%
E. 98%
F. 95%
G. 93%
H. 99%
I. 97%
J. 79%
Answer: H
Assuming several $16K\times8$ memory chips are used to form a $64K\times8$ memory, and each chip unit adopts an interleaved addressing method, the minimum address of the chip where the address BFFH is located is ().

Options:
A. $$1000H$$
B. $$2500H$$
C. $$0C00H$$
D. $$2000H$$
E. $$3000H$$
F. $$0400H$$
G. $$0800H$$
H. $$0003H$$
I. $$1A00H$$
J. $$0FFFH$$
Answer: H
A particular hard disk has a total of 4 recording surfaces, with a storage area inner radius of 10 cm and an outer radius of 15.5 cm. The track density is 60 tracks/cm, the outer layer bit density is 600 bits/cm, and the rotational speed is 6000 revolutions per minute. Assuming each sector has a capacity of 512B, each track has 12 sectors, and the average seek time is 10.5 ms, calculate the average disk access time as _____.

Options:
A. 18.27ms
B. 21.35ms
C. 16.33ms
D. 22.50ms
E. 19.46ms
F. 20.58ms
G. 17.74ms
H. 14.89ms
I. 23.62ms
J. 25.47ms
Answer: C
A processor contains a total of 32 registers and uses a 16-bit immediate number. Its instruction system structure comprises 142 instructions in total. In a given program, 20% of the instructions have one input register and one output register; 30% of the instructions have two input registers and one output register; 25% of the instructions have one input register, one output register, and one immediate number register; the remaining 25% of the instructions have one immediate number input register and one output register. How many bits are required for any one of the above four types of instructions? Assume that the instruction system structure requires all instructions to be multiples of 8 in length.

Options:
A. 56
B. 24
C. 16
D. 48
E. 32
F. 88
G. 40
H. 64
I. 80
J. 72
Answer: G
There is a four-stage pipeline, which completes the four steps of fetching instructions, decoding instructions and retrieving data, executing the operation, and writing back. Assume the time to complete each step is 100ns, 100ns, 80ns, and 50ns, respectively. Inquire: if improvements are made in the hardware design, how much delay is required at a minimum?

Options:
A. 70ns
B. 140ns
C. 90ns
D. 110ns
E. 100ns
F. 130ns
G. 150ns
H. 160ns
I. 80ns
J. 120ns
Answer: E
Assuming a computer's CPU has a clock speed of 80 MHz, a CPI of 4, and each instruction accesses memory 1.5 times on average. The block size exchanged between the main memory and the Cache is 16B, with a Cache hit rate of 99%. The memory bus bandwidth is 32 bits. To improve performance, the main memory adopts a Quad-Leve low-order interleaved storage mode, with one leve activated every 1/4 memory cycle during operation. If the memory cycle of each bank is 50 ns, what is the maximum bandwidth that this main memory can provide?

Options:
A. $$
3 3 0 \mathrm{M B} / \mathrm{s}
$$
B. $$
3 5 0 \mathrm{M B} / \mathrm{s}
$$
C. $$
3 2 0 \mathrm{M B} / \mathrm{s}
$$
D. $$
2 5 0 \mathrm{M B} / \mathrm{s}
$$
E. $$
3 6 0 \mathrm{M B} / \mathrm{s}
$$
F. $$
2 9 0 \mathrm{M B} / \mathrm{s}
$$
G. $$
2 8 0 \mathrm{M B} / \mathrm{s}
$$
H. $$
3 8 0 \mathrm{M B} / \mathrm{s}
$$
I. $$
4 0 0 \mathrm{M B} / \mathrm{s}
$$
J. $$
4 5 0 \mathrm{M B} / \mathrm{s}
$$
Answer: C
In the following situations, the total time required to transmit a 1000KB file is ______, which is the time from the beginning of the transmission until the last bit of the file reaches the destination. Assuming the round-trip time (RTT) is 100ms, a packet is 1KB (i.e., 1024B) of data, and the initial handshake process before starting the transmission of the entire file data requires 2RTT of time. Assume the bandwidth is infinitely large, meaning we take the transmission time as 0, and can send up to 20 packets after each RTT.

Options:
A. 5.35s
B. 5.50s
C. 5.20s
D. 5.15s
E. 5.05s
F. 5.10s
G. 4.95s
H. 5.25s
I. 5.30s
J. 5.45s
Answer: D
If the channel's maximum data transmission rate in a noise-free situation is not less than the maximum data transmission rate under a signal-to-noise ratio of 30dB, then the number of signal states is at least ().

Options:
A. 48
B. 16
C. 12
D. 32
E. 20
F. 10
G. 256
H. 8
I. 64
J. 128
Answer: D
The Data Link Layer employs the Go-Back-N (GBN) protocol. If the size of the sending window is 32, at least () bits of sequence number are needed to ensure the protocol functions correctly.

Options:
A. 10
B. 5
C. 8
D. 14
E. 7
F. 11
G. 6
H. 13
I. 9
J. 12
Answer: G
The host A transmits data to host B via a 128kb/s satellite link using the sliding window protocol. The one-way propagation delay of the link is 250ms, and the frame size is 1000 bytes. Without considering the overhead of acknowledgment frames, to ensure that the link utilization is not less than 80%, the number of bits for the frame sequence number must be at least ().

Options:
A. 1
B. 9
C. 2
D. 5
E. 8
F. 10
G. 3
H. 7
I. 6
J. 4
Answer: J
In a network using the CSMA/CD protocol, the transmission medium is a single cable with a transmission rate of 1 Gb/s, and the signal propagation speed in the cable is 200,000 km/s. If the minimum data frame length is reduced by 800 bits, the distance between the two farthest stations needs to be at least ().

Options:
A. Shorten 240m
B. Contract 120m
C. Expand 60m
D. Shorten 200m
E. Reduce 80m
F. Increase 160m
G. Extend 180m
H. Expand 200m
I. Increase 220m
J. Expand 140m
Answer: E
If constructing a CSMA/CD bus network with a rate of 100 Mb/s, where the signal propagation speed in the cable is $2×10^{-5} \, km/s$, and the minimum data frame length is 125 bytes, the maximum length of the bus cable is______. (Assume there are no repeaters in the bus cable.)

Options:
A. 1500m
B. 800m
C. 2000m
D. 500m
E. 1000m
F. 1800m
G. 2500m
H. 1200m
I. 3000m
J. 2200m
Answer: E
If a network uses a half-duplex switch with 24 10Mb/s ports as the connecting device, the average bandwidth obtained by each connection point is (). The total capacity of the switch is ().

Options:
A. $$0.313 \mathrm{M b} / \mathrm{s}$$ $$3.13 \mathrm{M b} / \mathrm{s}$$
B. $$1.250 \mathrm{M b} / \mathrm{s}$$ $$12.5 \mathrm{M b} / \mathrm{s}$$
C. $$0.208 \mathrm{M b} / \mathrm{s}$$ $$2.08 \mathrm{M b} / \mathrm{s}$$
D. $$0.952 \mathrm{M b} / \mathrm{s}$$ $$9.52 \mathrm{M b} / \mathrm{s}$$
E. $$0.625 \mathrm{M b} / \mathrm{s}$$ $$6.25 \mathrm{M b} / \mathrm{s}$$
F. $$1.042 \mathrm{M b} / \mathrm{s}$$ $$10.4 \mathrm{M b} / \mathrm{s}$$
G. $$0.833 \mathrm{M b} / \mathrm{s}$$ $$8.33 \mathrm{M b} / \mathrm{s}$$
H. $$1.667 \mathrm{M b} / \mathrm{s}$$ $$16.7 \mathrm{M b} / \mathrm{s}$$
I. $$2.083 \mathrm{M b} / \mathrm{s}$$ $$20.8 \mathrm{M b} / \mathrm{s}$$
J. $$
0.417 \mathrm{M b} / \mathrm{s}
$$
$$
4.17 \mathrm{M b} / \mathrm{s}
$$
Answer: J
Every host accessing the Internet needs to be assigned an ${IP}$ address (assuming the default subnet mask is used). Which of the following can be assigned as an ${IP}$ address for the host?

Options:
A. $$
1 2 7. 0 0 1. 6 3
$$
B. $$
1 1 0. 4 7. 1 0. 0
$$
C. $$
1 2 8. 2 0 0. 6 5
$$
D. $$
2 5 5. 1 0 0. 0 8
$$
E. $$
1 6 9. 2 5 4. 0 5
$$
F. $$
1 7 3. 4 5. 9 9. 6
$$
G. $$
1 2 6. 2 5 5. 0 0
$$
H. $$
1 7 2. 3 1. 2 5 6
$$
I. $$
1 9 2. 0 0 2. 1 6
$$
J. $$
2 2 4. 1 6 9. 3 0
$$
Answer: B
When storing tea leaves, attention should be paid to temperature control. For every 10°C increase in temperature, the rate of browning for tea leaves will increase () times.

Options:
A. 2-4
B. 7-9
C. 4-6
D. 12-14
E. 5-7
F. 3-5
G. 1-2
H. 0-1
I. 9-11
J. 6-8
Answer: F
A heavy symmetric top with a fixed point precesses around a vertical axis at a constant angular velocity $\varOmega$, with a constant nutation angle $\theta_{0}$. The mass of the top is $m$, and the distance from the center of mass to the fixed point is $h$. The spin angular velocity is ().

Options:
A. $$
\frac{( I_{1}-I_{3} ) \varOmega^{2} \operatorname{c o s} \theta_{0}+g h} {\varOmega I_{3}}
$$
B. $$
\frac{( I_{1}-I_{3} ) \varOmega^{2} \operatorname{c o s} \theta_{0}+m g h} {\varOmega I_{3}}
$$
C. $$
\frac{( I_{1}+I_{3} ) \varOmega^{2} \operatorname{c o s} \theta_{0}-m g h} {\varOmega I_{3}}
$$
D. $$
\frac{( I_{3}-I_{1} ) \varOmega \operatorname{c o s} \theta_{0}+m g h} {\varOmega I_{3}}
$$
E. $$
\frac{( I_{1}-I_{3} ) \varOmega \operatorname{c o s} \theta_{0}+m g h} {\varOmega I_{3}}
$$
F. $$
\frac{( I_{3}-I_{1} ) \varOmega^{2} \operatorname{c o s} \theta_{0}-m g h} {\varOmega I_{1}}
$$
G. $$
\frac{( I_{3}-I_{1} ) \varOmega^{2} \operatorname{c o s} \theta_{0}+m g h} {I_{3}}
$$
H. $$
\frac{( I_{1}-I_{3} ) \varOmega^{2} \sin \theta_{0}+m g h} {\varOmega I_{3}}
$$
I. $$
\frac{( I_{1}+I_{3} ) \varOmega^{2} \operatorname{c o s} \theta_{0}+m g h} {\varOmega I_{3}}
$$
J. $$
\frac{( I_{1}-I_{3} ) \varOmega^{2} + m g h \operatorname{c o s} \theta_{0}} {\varOmega I_{3}}
$$
Answer: B
A uniform heavy sphere with radius $r$ can roll within a fixed inner surface that has a horizontal axis and a radius of $R$. What is the equation of motion and the period of small oscillations of the sphere around the equilibrium position?

Options:
A. $$
\frac{7} {5} m ( R-r )^{3} \ddot{\theta}+m g ( R-r ) \operatorname{s i n} \theta=0
$$
$$
T=2 \pi\sqrt{\frac{7 ( R-r )} {5 g}}
$$
B. $$
\frac{7} {5} m ( R+r )^{2} \ddot{\theta}+m g ( R-r ) \operatorname{s i n} \theta=0
$$
$$
T=2 \pi\sqrt{\frac{7 ( R+r )} {5 g}}
$$
C. $$
\frac{7} {8} m ( R+r )^{2} \ddot{\theta}+m g ( R-r ) \operatorname{s i n} \theta=0
$$
$$
T=2 \pi\sqrt{\frac{7 ( R+r )} {8 g}}
$$
D. $$
\frac{7} {5} m ( R-r )^{2} \ddot{\theta}+m g ( R+r ) \operatorname{s i n} \theta=0
$$
$$
T=2 \pi\sqrt{\frac{7 ( R+r )} {5 g}}
$$
E. $$
\frac{9} {5} m ( R+r )^{2} \ddot{\theta}+m g ( R-r ) \operatorname{c o s} \theta=0
$$
$$
T=2 \pi\sqrt{\frac{9 ( R+r )} {5 g}}
$$
F. $$
\frac{7} {3} m ( R-r )^{2} \ddot{\theta}-m g ( R-r ) \operatorname{s i n} \theta=0
$$
$$
T=2 \pi\sqrt{\frac{7 ( R-r )} {3 g}}
$$
G. $$
\frac{5} {9} m ( R-r )^{2} \ddot{\theta}+m g ( R-r ) \operatorname{s i n} \theta=0
$$
$$
T=2 \pi\sqrt{\frac{5 ( R-r )} {9 g}}
$$
H. $$
\frac{5} {7} m ( R-r )^{2} \ddot{\theta}+m g ( r-R ) \operatorname{s i n} \theta=0
$$
$$
T=2 \pi\sqrt{\frac{5 ( r-R )} {7 g}}
$$
I. $$
\frac{7} {5} m ( R-r )^{2} \ddot{\theta}+2 m g ( R-r ) \operatorname{s i n} \theta=0
$$
$$
T=2 \pi\sqrt{\frac{7 ( R-r )} {5 g}} + 1
$$
J. $$
\frac{7} {5} m ( R-r )^{2} \ddot{\theta}+m g ( R-r ) \operatorname{s i n} \theta=0
$$
$$
T=2 \pi\sqrt{\frac{7 ( R-r )} {5 g}}
$$
Answer: J
An $\alpha$ particle (mass $0.67 \times 10^{-26} \, \mathrm{kg}$) enters a concrete protective wall at a speed of 0.8c ($c$ is the speed of light in a vacuum). The wall is 0.35m thick, and the speed of the particle decreases to $5c/13$ when it exits from the other side of the wall.
How long does it take for the particle to pass through the wall?

Options:
A. $$
12ns
$$
B. $$
5ns
$$
C. $$
4ns
$$
D. $$
3ns
$$
E. $$
15ns
$$
F. $$
10ns
$$
G. $$
9ns
$$
H. $$
6ns
$$
I. $$
2ns
$$
J. $$
7ns
$$
Answer: I
A small air bubble with a radius $r=0.10 \times 10^{-2} \mathrm{m}$ rises in a viscous liquid. The viscosity coefficient of the liquid is $\eta=0.11 \mathrm{Pa} \cdot \mathrm{s}$, and its density is $0.72 \times 10^{3} \, \mathrm{kg} \, / \, \mathrm{m}^{3}$. What is the terminal velocity of its ascent?

Options:
A. $$
3. 2 \! \times\! 1 0^{-2} \mathrm{m / s}
$$
B. $$
2. 5 \! \times\! 1 0^{-2} \mathrm{m / s}
$$
C. $$
4. 8 \! \times\! 1 0^{-2} \mathrm{m / s}
$$
D. $$
1. 3 \! \times\! 1 0^{-2} \mathrm{m / s}
$$
E. $$
6. 6 \! \times\! 1 0^{-2} \mathrm{m / s}
$$
F. $$
1. 4 \! \times\! 1 0^{-2} \mathrm{m / s}
$$
G. $$
8. 1 \! \times\! 1 0^{-2} \mathrm{m / s}
$$
H. $$
1. 9 \! \times\! 1 0^{-2} \mathrm{m / s}
$$
I. $$
7. 4 \! \times\! 1 0^{-2} \mathrm{m / s}
$$
J. $$
9. 7 \! \times\! 1 0^{-2} \mathrm{m / s}
$$
Answer: F
Let $\{f_{j} ( x ) \}$ be a sequence of functions defined on $R^{n}$. Try using the sets
$$
\{x : f_{j} ( x ) \geq\frac{1} {k} \}, ( j, k=1, 2, \cdots)
$$
to represent the set
$$
\left\{x : \varlimsup_{j \to\infty} f_{j} ( x ) > 0 \right\}
$$.

Options:
A. $$
\bigcap_{n=1}^{\infty} \bigcup_{k=1}^{\infty} \bigcup_{j=n}^{\infty} \left\{x : f_{j} ( x ) \geq\frac{1} {k} \right\}
$$
B. $$
\bigcup_{n=1}^{\infty} \bigcap_{k=1}^{\infty} \bigcap_{j=n}^{\infty} \left\{x : f_{j} ( x ) < \frac{1} {k} \right\}
$$
C. $$
\bigcap_{j=1}^{\infty} \bigcap_{k=1}^{\infty} \bigcup_{n=j}^{\infty} \left\{x : f_{j} ( x ) < \frac{1} {k} \right\}
$$
D. $$
\bigcup_{k=1}^{\infty} \bigcap_{n=1}^{\infty} \bigcup_{j=n}^{\infty} \left\{x : f_{j} ( x ) \geq\frac{1} {k} \right\}
$$
E. $$
\bigcap_{k=1}^{\infty} \bigcup_{j=1}^{\infty} \bigcup_{n=j}^{\infty} \left\{x : f_{j} ( x ) > \frac{1} {k} \right\}
$$
F. $$
\bigcup_{j=1}^{\infty} \bigcap_{k=1}^{\infty} \bigcap_{n=j}^{\infty} \left\{x : f_{j} ( x ) < \frac{1} {k} \right\}
$$
G. $$
\bigcap_{k=1}^{\infty} \bigcap_{n=1}^{\infty} \bigcup_{j=n}^{\infty} \left\{x : f_{j} ( x ) > \frac{1} {k} \right\}
$$
H. $$
\bigcap_{n=1}^{\infty} \bigcup_{k=1}^{\infty} \bigcap_{j=n}^{\infty} \left\{x : f_{j} ( x ) \leq\frac{1} {k} \right\}
$$
I. $$
\bigcup_{j=1}^{\infty} \bigcap_{k=1}^{\infty} \bigcup_{n=j}^{\infty} \left\{x : f_{j} ( x ) > \frac{1} {k} \right\}
$$
J. $$
\bigcap_{k=1}^{\infty} \bigcup_{n=1}^{\infty} \bigcap_{j=n}^{\infty} \left\{x : f_{j} ( x ) < \frac{1} {k} \right\}
$$
Answer: D
Find
$$
E_{n}=\left( 0, 1 / n \right) \left( n \in\mathbb{N} \right).
$$
the limit superior and limit inferior of the sequence of sets.

Options:
A. $$
\overline{\lim }_{n \rightarrow \infty} E_{n}=\{0\}.
$$
B. $$
\overline{\lim }_{n \rightarrow \infty} E_{n}=-\mathbb{N}.
$$
C. $$
\overline{\lim }_{n \rightarrow \infty} E_{n}=\varnothing .
$$
D. $$
\overline{\lim }_{n \rightarrow \infty} E_{n}=\emptyset .
$$
E. $$
\overline{\lim }_{n \rightarrow \infty} E_{n}=[0,1].
$$
F. $$
\overline{\lim }_{n \rightarrow \infty} E_{n}=\mathbb{R}^+.
$$
G. $$
\overline{\lim }_{n \rightarrow \infty} E_{n}=(0,1).
$$
H. $$
\overline{\lim }_{n \rightarrow \infty} E_{n}=\mathbb{Q}.
$$
I. $$
\overline{\lim }_{n \rightarrow \infty} E_{n}=(-1,0).
$$
J. $$
\overline{\lim }_{n \rightarrow \infty} E_{n}=(-\infty,0).
$$
Answer: C
For points in the interval (0,1) represented using decimal expansion, let $E$ be the set of all points with no more than 9 digits in their representation. Find $m ( E )$.

Options:
A. $$
m ( E )=0
$$
B. $$
m ( E )=1
$$
C. $$
m ( E )=10
$$
D. $$
m ( E )=0.9
$$
E. $$
m ( E )=0.001
$$
F. $$
m ( E )=0.5
$$
G. $$
m ( E )=\infty
$$
H. $$
m ( E )=\pi
$$
I. $$
m ( E )=0.01
$$
J. $$
m ( E )=0.1
$$
Answer: A
Find the value of the integral
$$
I=\int_{0}^{1} \frac{\operatorname{ln} (1-x)}{x} \mathrm{d} x.
$$.

Options:
A. $$
\pi / 4
$$
B. $$
-1 / 2
$$
C. $$
\pi^{2} / 8
$$
D. $$
- \pi^{2} / 6
$$
E. $$
- \ln(3/2)
$$
F. $$
0
$$
G. $$
e^{-\pi}/2
$$
H. $$
\ln 2
$$
I. $$
\sqrt{2} / 3
$$
J. $$
1 - \ln \pi
$$
Answer: D
Let $f {\in} L ( \mathbf{R}^{1} )$, and for any interval $I$, denote
$$
f_{I}=\frac{1} {| I |} \int_{I} f ( x ) \, \mathrm{d} x, \; \; \; E_{I}=\{x \in I \, \mid \, f ( x ) > f_{I} \},
$$
find the value of
$$
\int_{I} \bigl| f ( x )=f_{I} \bigr| \, \mathrm{d} x
$$.

Options:
A. $$
2 \! \! \int_{E_{l}} [ f ( x )-f_{l} ] \mathrm{d} x.
$$
B. $$
0.5 \! \int_{E_{I}} \{ h ( x ) + f_{I} \} \mathrm{d} x.
$$
C. $$
\int_{I} \langle f ( x ) > f_{I} \rangle \, \mathrm{d} x.
$$
D. $$
5 \! \! \int_{G_{I}} [ t ( x )-t_{I} ] \mathrm{d} x.
$$
E. $$
4 \! \! \int_{F_{l}} | f ( x )-f_{l} | \mathrm{d} x.
$$
F. $$
6 \! \! \int_{H_{l}} [ u ( x )-u_{l} ] \mathrm{d} x.
$$
G. $$
3 \! \! \int_{F_{I}} [ g ( y )-g_{I} ] \mathrm{d} y.
$$
H. $$
\int_{J} \langle s ( z )=s_{J} \rangle \, \mathrm{d} z.
$$
I. $$
\int_{I} | f ( x ) | \, \mathrm{d} x + E_{I}.
$$
J. $$
\frac{1}{3} \! \int_{h_{I}} [ f ( x )-f_{h} ] \mathrm{d} x.
$$
Answer: A
Let $f {\in} L ( [ 0, \infty) ), a > 0$. What is the value of $\int_{0}^{+\infty} \sin(ax) \, \mathrm{d}x \int_{0}^{+\infty} f(y) \mathrm{e}^{-xy} \, \mathrm{d}y$?

Options:
A. $$
\int_{0}^{+\infty} \frac{f ( y ) \mathrm{d} y} {y^{2}+a^{2}}
$$
B. $$
2a \! \int_{0}^{+\infty} \frac{f ( y ) \mathrm{d} y} {a^{2}+y^{3}}
$$
C. $$
a \! \int_{0}^{+\infty} \frac{f ( y ) \mathrm{d} y} {a^{2}+y^{2}}
$$
D. $$
a \! \int_{0}^{1} \frac{f ( y ) \mathrm{d} y} {a^{2}+y^{2}}
$$
E. $$
a^{2} \! \int_{0}^{+\infty} \frac{f ( y ) \mathrm{d} y} {1+a^{2}}
$$
F. $$
a \! \int_{0}^{+\infty} \frac{f ( y ) \mathrm{d} y} {1+y^{2}}
$$
G. $$
\frac{a}{2} \! \int_{0}^{+\infty} \frac{f ( y ) \mathrm{d} y} {y^{2}+x}
$$
H. $$
a^{3} \! \int_{0}^{+\infty} \frac{f ( y ) \mathrm{d} y} {a^{2}+y}
$$
I. $$
\int_{0}^{+\infty} \frac{f ( y ) \mathrm{d} y} {x^{2}+a}
$$
J. $$
a \! \int_{1}^{+\infty} \frac{f ( y ) \mathrm{d} y} {a^{3}+y^{2}}
$$
Answer: C
What is the value of $\bigvee_{0}^{4 \pi} \left( \operatorname{cos} x \right)$?

Options:
A. 10
B. 20
C. 14
D. 16
E. 4
F. 12
G. 6
H. 18
I. 2
J. 8
Answer: J
Let $f(x)$ be a strictly increasing continuous function on $\left[a, b\right]$. What is the necessary and sufficient condition for $f(x)$ to be absolutely continuous on $\left[a, b\right]$ given that $E=\{x \in [a, b] \mid f^{\prime}(x)=\infty\}$?

Options:
A. $$
m ( f ( x ) )=a+b
$$
B. $$
f ( E ) \text{ is convex }
$$
C. $$
m ( f ( E ) )=0
$$
D. $$
f^{\prime}(x) \text{ is constant }
$$
E. $$
f ( x ) \text{ is differentiable }
$$
F. $$
E \text{ is a compact set }
$$
G. $$
m ( E )=f ( a )+b
$$
H. $$
f^{\prime}(x) \text{ is bounded }
$$
I. $$
E \text{ is countable }
$$
J. $$
E \subsetneq \left [ a , b \right ]
$$
Answer: C
Let $f \! \in\! L ( [ a, b ] )$, and define $g ( x ) = f ( x ) \! \int_{a}^{x} \! f ( t ) \mathrm{d} t$. What is the value of $I$?

Options:
A. $$
\int_{a}^{b} f ( x ) \cdot x \bigg( \int_{a}^{x} f ( t ) \mathrm{d} t \bigg) \mathrm{d} x
$$
B. $$
\bigg(\int_{a}^{b} x \bigg( f ( x ) \bigg) \mathrm{d} x \bigg)^{2}
$$
C. $$
\frac{1} {3} \bigg( \int_{a}^{b} f ( x ) \mathrm{d} x \bigg)^{3}
$$
D. $$
\int_{a}^{b} \bigg( f ( x ) \bigg)^{2} \mathrm{d} x
$$
E. $$
\int_{a}^{b} \bigg( f ( x ) \int_{a}^{b} f ( t ) \mathrm{d} t \bigg) \mathrm{d} x
$$
F. $$
\frac{1} {2} \bigg( \int_{a}^{b} f ( x ) \mathrm{d} x \bigg)^{2}
$$
G. $$
\frac{1} {4} \bigg( \int_{a}^{b} f ( x ) \int_{a}^{x} f ( t ) \mathrm{d} t \bigg)
$$
H. $$
\int_{a}^{b} f ( x ) \bigg( \int_{a}^{x} f ( t ) \mathrm{d} t \bigg) \mathrm{d} x
$$
I. $$
\frac{1} {2} \bigg( \int_{a}^{b} \big( x \cdot f ( x ) \big) \mathrm{d} x \bigg)
$$
J. $$
\bigg(\int_{a}^{b} \bigg( f ( x ) \int_{a}^{x} f ( t ) \mathrm{d} t \bigg) \mathrm{d} x \bigg)
$$
Answer: F
Direct current motor, given $\mathrm{P}_{\mathrm{N}}=90 \mathrm{kW}$, $\mathrm{U}_{\mathrm{N}}=230 \mathrm{V}$, $\mathrm{n}_{\mathrm{N}}=1450 \mathrm{r}/\mathrm{min}$, and $\eta=0.89$. Find the rated current $\mathbf{I}_{N}$ is ().

Options:
A. 391A
B. 405A
C. 387A
D. 412A
E. 378A
F. 394A
G. 399A
H. 370A
I. 401A
J. 415A
Answer: A
A coil with 1000 turns and an iron core is connected to an AC power source of $110 \mathrm{V}, 50 \mathrm{Hz}$. According to the readings of the ammeter and wattmeter, $\mathrm{I}_{1} = 0.5 \mathrm{A}$ and $\mathrm{P}_{1} = 10 \mathrm{w}$. When the iron core is removed, the current and power change to 100 A and 1000 w, respectively. Assuming negligible magnetic leakage, determine the equivalent circuits for both scenarios is ().

Options:
A. 2000.0Ω,0.50Ω
B. 2210.0Ω,0.45Ω
C. 2275.0Ω,0.52Ω
D. 2199.6Ω,0.46Ω
E. 2200.0Ω,0.49Ω
F. 2300.0Ω,0.55Ω
G. 2150.0Ω,0.47Ω
H. 2180.0Ω,0.48Ω
I. 2250.0Ω,0.60Ω
J. 2100.0Ω,0.40Ω
Answer: D
A three-phase, 4-pole wound-rotor induction motor operates at a supply frequency $\mathrm{f}_{1} = 50 \, \mathrm{Hz}$. The per-phase rotor resistance is $\mathrm{R_r} = 0.02 \, \Omega$, and the rated speed is $\mathrm{n_N} = 1485 \, \mathrm{r/min}$. The load torque remains constant at the rated value. To reduce the speed to $1050 \, \mathrm{r/min}$, what additional resistance needs to be connected in series with each rotor phase?

Options:
A. 0.50Ω
B. 0.49Ω
C. 0.58Ω
D. 0.65Ω
E. 0.36Ω
F. 0.75Ω
G. 0.72Ω
H. 0.81Ω
I. 0.67Ω
J. 0.45Ω
Answer: C
The relationship between the saturated vapor pressure of n-heptane and temperature can be expressed by the following formula:
$$
\operatorname{l g} p^{0}=6. 9 2 6-\frac{1 2 8 4} {t+2 1 9}
$$
where $p^{0}$ is the saturated vapor pressure in mmHg, and $t$ is the temperature in $^\circ C$. Try to convert the above formula into an expression using SI units.

Options:
A. $$
= 4. 3 2 9-{\frac{1 5 7 2} {T-6 2}}
$$
B. $$
= 5. 9 8 8-{\frac{1 5 2 0} {T+9 7}}
$$
C. $$
= 8. 6 0 3-{\frac{2 1 1 0} {T-4 9}}
$$
D. $$
= 6. 8 1 7-{\frac{1 2 8 4} {T+7 4}}
$$
E. $$
= 9. 0 5 1-{\frac{1 2 8 4} {T-5 4}}
$$
F. $$
= 7. 9 3 2-{\frac{2 1 0 3} {T-7 0}}
$$
G. $$
= 5. 7 4 5-{\frac{1 3 4 9} {T+8 2}}
$$
H. $$
= 6. 1 5 0-{\frac{1 6 7 4} {T+5 5}}
$$
I. $$
= 7. 2 4 5-{\frac{1 3 3 6} {T-4 8}}
$$
J. $$
= 8. 1 9 8-{\frac{1 8 9 0} {T+3 1}}
$$
Answer: E
The glycerin at a temperature of 20°C flows through a rectangular duct with a width of 1m and a height of 0.1m at a mass flow rate of $10 \mathrm{kg/s}$. The flow is fully developed. Determine the velocity of the glycerin at the center of the duct and the velocity at a point 25mm away from the center.

Options:
A. $$
= 0. 0 8 9 2 \, {\mathrm{m / s}}
$$
B. $$
= 0. 0 6 7 2 \, {\mathrm{m / s}}
$$
C. $$
= 0. 0 7 1 8 \, {\mathrm{m / s}}
$$
D. $$
= 0. 0 9 2 1 \, {\mathrm{m / s}}
$$
E. $$
= 0. 0 4 8 5 \, {\mathrm{m / s}}
$$
F. $$
= 0. 0 5 9 7 \, {\mathrm{m / s}}
$$
G. $$
= 0. 0 6 5 3 \, {\mathrm{m / s}}
$$
H. $$
= 0. 1 5 2 4 \, {\mathrm{m / s}}
$$
I. $$
= 0. 1 2 3 4 \, {\mathrm{m / s}}
$$
J. $$
= 0. 0 9 8 1 \, {\mathrm{m / s}}
$$
Answer: A
Under normal pressure, air at a temperature of 45°C flows through the annular space of a horizontal casing at a volumetric flow rate of $10 \mathrm{m}^{3} / \mathrm{h}$. The outer diameter of the inner pipe is 50mm, and the inner diameter of the outer pipe is 100mm. Find the radial distance at the location of the maximum air velocity.

Options:
A. $$
= 0. 0 9 5 3 \mathrm{m}
$$
B. $$
= 0. 0 8 8 1 \mathrm{m}
$$
C. $$
= 0. 0 5 4 8 \mathrm{m}
$$
D. $$
= 0. 0 6 5 0 \mathrm{m}
$$
E. $$
= 0. 0 5 1 4 \mathrm{m}
$$
F. $$
= 0. 0 2 8 9 \mathrm{m}
$$
G. $$
= 0. 0 7 3 2 \mathrm{m}
$$
H. $$
= 0. 0 4 2 5 \mathrm{m}
$$
I. $$
= 0. 0 1 2 4 \mathrm{m}
$$
J. $$
= 0. 0 3 6 8 \mathrm{m}
$$
Answer: J
Air flows between two parallel smooth plates 25 mm apart at a speed of 0.15 m/s at 20°C. Determine how far from the entrance the boundary layers on the two plates merge. The properties of air at 20°C are $\rho = 1.205 \, \mathrm{kg/m}^{3}, \, \mu = 1.81 \times 10^{-5} \, \mathrm{Pa} \cdot \mathrm{s}$.

Options:
A. $$
= 0. 0 5 8 2 \mathrm{m}
$$
B. $$
= 0. 1 2 5 0 \mathrm{m}
$$
C. $$
= 0. 1 5 4 6 \mathrm{m}
$$
D. $$
= 0. 0 9 9 9 \mathrm{m}
$$
E. $$
= 0. 1 0 0 0 \mathrm{m}
$$
F. $$
= 0. 0 4 5 3 \mathrm{m}
$$
G. $$
= 0. 0 3 1 2 \mathrm{m}
$$
H. $$
= 0. 0 6 2 4 \mathrm{m}
$$
I. $$
= 0. 1 1 1 1 \mathrm{m}
$$
J. $$
= 0. 0 7 8 9 \mathrm{m}
$$
Answer: H
A certain viscous fluid flows steadily past a flat plate surface at a velocity of $u_{0}$, forming a laminar boundary layer. It is known that within the boundary layer, the velocity distribution of the fluid is described as: $u_{x}=a+b \operatorname{sinc} y$. Use the boundary layer integral momentum equation to derive the calculation formulas for the boundary layer thickness and the plate drag coefficient.

Options:
A. $$
= 0. 6 5 6 R e_{x}^{-1 / 2}
$$
B. $$
= 1. 2 3 7 R e_{x}^{-1 / 5}
$$
C. $$
= 2. 0 0 1 R e_{x}^{-1 / 6}
$$
D. $$
= 0. 8 9 1 R e_{x}^{-1 / 4}
$$
E. $$
= 0. 5 8 8 R e_{x}^{-2 / 3}
$$
F. $$
= 0. 4 7 9 R e_{x}^{-2 / 5}
$$
G. $$
= 1. 5 0 2 R e_{x}^{-1 / 3}
$$
H. $$
= 0. 9 9 0 R e_{x}^{-1 / 7}
$$
I. $$
= 0. 7 4 3 R e_{x}^{-3 / 5}
$$
J. $$
= 0. 3 0 4 R e_{x}^{-3 / 4}
$$
Answer: A
Water at 20°C flows turbulently inside a straight pipe with an internal diameter of 2 meters. The velocity distribution is measured as $u_{x} = 10 + 0.8 \ln y$, with the shear stress at 1/3 meter from the pipe wall being $103 \, \mathrm{Pa}$. Try to calculate the eddy viscosity and mixing length at that point. It is known that the density of water at 20°C is $998.2 \, \mathrm{kg/m}^{3}$ and the dynamic viscosity is $1.005 \times 10^{-3} \, \mathrm{Pa \cdot s}$.

Options:
A. $$
= 0. 1 5 2 4 \mathrm{m}
$$
B. $$
= 0. 2 5 7 6 \mathrm{m}
$$
C. $$
= 0. 1 6 9 2 \mathrm{m}
$$
D. $$
= 0. 2 6 0 5 \mathrm{m}
$$
E. $$
= 0. 1 7 8 1 \mathrm{m}
$$
F. $$
= 0. 3 0 2 1 \mathrm{m}
$$
G. $$
= 0. 1 9 0 7 \mathrm{m}
$$
H. $$
= 0. 3 4 1 9 \mathrm{m}
$$
I. $$
= 0. 2 8 4 3 \mathrm{m}
$$
J. $$
= 0. 1 3 3 8 \mathrm{m}
$$
Answer: J
An incompressible fluid flows steadily along a flat plate wall, forming a turbulent boundary layer on the plate surface where the flow is two-dimensional. If the velocity distribution in the $x$ direction satisfies the $1/7$ power law, try to derive the expression for the velocity component in the $y$ direction using the continuity equation.

Options:
A. $$
= 0. 0 3 4 6 u_{0}^{6 / 5} ( x \nu)^{2 / 3} \biggl( \frac{y} {\delta} \biggr)^{1 / 7}
$$
B. $$
= 0. 0 4 5 6 u_{0}^{3 / 5} ( x \nu)^{2 / 5} \biggl( \frac{y} {\delta} \biggr)^{6 / 7}
$$
C. $$
= 0. 0 3 7 6 u_{0}^{4 / 5} ( x \nu)^{1 / 5} \biggl( \frac{y} {\delta} \biggr)^{8 / 7}
$$
D. $$
= 0. 0 3 7 0 u_{0}^{2 / 3} ( x \nu)^{1 / 4} \biggl( \frac{y} {\delta} \biggr)^{6 / 8}
$$
E. $$
= 0. 0 3 8 6 u_{0}^{3 / 2} ( x \nu)^{1 / 7} \biggl( \frac{y} {\delta} \biggr)^{3 / 7}
$$
F. $$
= 0. 0 3 6 6 u_{0}^{2 / 7} ( x \nu)^{5 / 5} \biggl( \frac{y} {\delta} \biggr)^{2 / 7}
$$
G. $$
= 0. 0 3 2 6 u_{0}^{4 / 6} ( x \nu)^{3 / 4} \biggl( \frac{y} {\delta} \biggr)^{7 / 9}
$$
H. $$
= 0. 0 2 7 6 u_{0}^{1 / 5} ( x \nu)^{1 / 5} \biggl( \frac{y} {\delta} \biggr)^{4 / 7}
$$
I. $$
= 0. 0 3 3 6 u_{0}^{5 / 5} ( x \nu)^{3 / 5} \biggl( \frac{y} {\delta} \biggr)^{7 / 7}
$$
J. $$
= 0. 0 3 9 6 u_{0}^{2 / 5} ( x \nu)^{4 / 5} \biggl( \frac{y} {\delta} \biggr)^{5 / 7}
$$
Answer: C
Food not only provides the nutrients necessary for the human body but primarily generates energy to maintain the required body temperature and perform work against the environment. Consider a person who consumes 2100 kcal per day, of which 2000 kcal is converted to thermal energy and 100 kcal is used to perform work against the environment. The person is in an environment at 20 °C, with a convective heat transfer coefficient between the person's skin and the environment of $3 \setminus \mathrm{W} / (\mathrm{m}^{2} \cdot \mathrm{K})$. At this temperature, the person essentially does not sweat. What is the average temperature of the person's skin approximately ?

Options:
A. $$
3 7 {\sim} 3 9°C
$$
B. $$
3 0 {\sim} 3 2°C
$$
C. $$
3 4 {\sim} 3 6°C
$$
D. $$
26 °C
$$
E. $$
3 3 {\sim} 3 5°C
$$
F. $$
3 6 {\sim} 3 8°C
$$
G. $$
2 8 {\sim} 3 0°C
$$
H. $$
4 0 {\sim} 4 3°C
$$
I. $$
2 6 {\sim} 2 8°C
$$
J. $$
3 1 {\sim} 3 3°C
$$
Answer: D
A steel sphere with a radius of 25 mm has a thermal conductivity of $433 \mathrm{~W / (m \cdot K)}$, a density of $7849 \ \mathrm{kg} / \mathrm{m}^{3}$, and a specific heat capacity of $0.4609 \mathrm{~kJ / (kg \cdot K)}$. The initial temperature of the steel sphere is uniform at 700 K. This sphere is then placed in an environment with a temperature of 400 K, where the convective heat transfer coefficient between the sphere's surface and the environment is $11.36 \, \mathrm{W} / (\mathrm{m}^{2} \cdot \mathrm{K})$. Determine the temperature of the steel sphere after 1 $\mathbf{h}$

Options:
A. $$
= 4 3 0. 5 \mathrm{~ K}
$$
B. $$
= 4 4 4. 6 \mathrm{~ K}
$$
C. $$
= 3 2 5. 7 \mathrm{~ K}
$$
D. $$
= 5 4 2. 1 \mathrm{~ K}
$$
E. $$
= 6 0 0. 4 \mathrm{~ K}
$$
F. $$
= 5 0 0. 0 \mathrm{~ K}
$$
G. $$
= 4 0 1. 3 \mathrm{~ K}
$$
H. $$
= 4 8 9. 2 \mathrm{~ K}
$$
I. $$
= 4 7 5. 9 \mathrm{~ K}
$$
J. $$
= 4 6 8. 8 \mathrm{~ K}
$$
Answer: I
An aluminum cylinder with a diameter of 12 cm and a length of 12 cm is initially heated to 200 °C and then immersed in a large tank containing liquid at a temperature of 90 °C. As the liquid in the tank is continuously replaced, the temperature of the liquid in the tank can remain constant. The measured convection heat transfer coefficient between the surface of the cylinder and the liquid is $h = 570 \, \mathrm{W} / (\mathrm{m}^{2} \cdot \mathrm{K})$, and the average thermal diffusivity and thermal conductivity of the object are $\alpha = 9.45 \times 10^{-5} \, \mathrm{m}^{2} / \mathrm{s}$ and $k = 208 \, \mathrm{W} / (\mathrm{m} \cdot \mathrm{K})$, respectively. Find the temperature at the center of the cylinder after 1 minute.

Options:
A. $$
t=1 3 5. 2 \mathrm{~} \mathrm{C}
$$
B. $$
t=1 4 7. 5 \mathrm{~} \mathrm{C}
$$
C. $$
t=1 3 9. 5 \mathrm{~} \mathrm{C}
$$
D. $$
t=1 5 0. 0 \mathrm{~} \mathrm{C}
$$
E. $$
t=1 4 2. 0 \mathrm{~} \mathrm{C}
$$
F. $$
t=1 4 9. 0 \mathrm{~} \mathrm{C}
$$
G. $$
t=1 4 5. 3 \mathrm{~} \mathrm{C}
$$
H. $$
t=1 4 1. 5 \mathrm{~} \mathrm{C}
$$
I. $$
t=1 3 7. 7 \mathrm{~} \mathrm{C}
$$
J. $$
t=1 4 3. 8 \mathrm{~} \mathrm{C}
$$
Answer: H
Hot water at a temperature of 333 K flows at a uniform speed of 2 m/s over a cold flat plate surface with a constant wall temperature of 293 $\mathrm{K}$. Calculate the velocity boundary layer thickness and temperature boundary layer thickness at a point 2 m from the leading edge of the plate. Also, determine the total heat transfer rate when the water flows over a flat plate surface with a length of 2 m and a width of 1 m, and indicate the percentage of the heat transfer rate in the turbulent boundary layer relative to the total heat transfer rate.

Options:
A. $$
= 7 6. 1 \%$$
B. $$
= 9 1. 6 \%$$
C. $$
= 6 7. 9 \%$$
D. $$
= 5 9. 3 \%$$
E. $$
= 8 3. 2 \%$$
F. $$
= 8 0. 8 \%$$
G. $$
= 7 2. 5 \%$$
H. $$
= 5 5. 4 \%$$
I. $$
= 9 4. 7 \%
$$
J. $$
= 6 8. 4 \%$$
Answer: I
The cohesive energy $U$ of a solid and the Debye characteristic temperature $\theta_{\mathrm{D}}$ are both functions of volume $\mathbf{V}$. Using the natural logarithm of the partition function, determine the equation of state for a solid under low and high temperature conditions. Let the symbol $\gamma$ represent
$$
\gamma=-\frac{\partial \ln \theta_{\mathrm{D}}}{\partial \ln \mathrm{V}}
$$
Under conditions of high and low temperatures, the equation of state for a solid can be expressed as____.

Options:
A. $$
\mathrm{p=-\frac{\partial U }{\partial V}-\gamma\frac{U_{0}}{V}}
$$
B. $$
\mathrm{p=\frac{d \ U}{d \ V}+\gamma\frac{\ln U}{V}}
$$
C. $$
\mathrm{p=\frac{\partial U}{\partial V}-\gamma\frac{U}{V}}
$$
D. $$
\mathrm{p=-\gamma\frac{U-U_{0}} {V}+\frac{d \ U_{0}} {d \ V}}
$$
E. $$
\mathrm{p=-\frac{d \ V}{d \ U}+\gamma\frac{U_{0}}{V}}
$$
F. $$
\mathrm{p=\gamma\frac{d \ V}{d \ U}-\frac{U}{V}}
$$
G. $$
\mathrm{p=-\frac{d \ U_{0}} {d \ V}+\gamma\frac{U-U_{0}} {V}}
$$
H. $$
\mathrm{p=\gamma\frac{\partial U}{\partial U_{0}}-\frac{V}{U}}
$$
I. $$
\mathrm{p=\gamma \frac{d \ U}{d \ V}-\frac{U_{0}}{V}}
$$
J. $$
\mathrm{p=-\frac{d \ U_{0}} {d \ V}+\gamma\frac{\ln V}{U}}
$$
Answer: G
At $25^\circ \mathrm{C}$, under pressures ranging from 0 to 1000 atm, the experimental data for water is measured as follows:
$$
\left( \frac{\partial \mathrm{V}}{\partial \mathrm{T}} \right)_{p} = (4.5 \times 10^{-3} + 1.4 \times 10^{-6} \mathrm{p}) \, \mathrm{cm}^{3} \cdot \mathrm{mol}^{-1} \cdot \mathrm{K}^{-1}
$$
If the pressure on water is increased from 1 atm to 1000 atm under constant temperature at 25°C, determine the increase in entropy and the amount of heat absorbed from the surroundings. Answer is ______.

Options:
A. $$
- 0. 4 3 2 \, \mathrm{J} \cdot\mathrm{m o l}^{-1} \cdot\mathrm{K}^{-1}
$$
$$
- 1 3 8 \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
B. $$
- 0. 7 1 8 \, \mathrm{J} \cdot\mathrm{m o l}^{-1} \cdot\mathrm{K}^{-1}
$$
$$
- 1 9 3 \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
C. $$
- 0. 3 8 2 \, \mathrm{J} \cdot\mathrm{m o l}^{-1} \cdot\mathrm{K}^{-1}
$$
$$
- 1 2 5 \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
D. $$
- 0. 5 5 9 \, \mathrm{J} \cdot\mathrm{m o l}^{-1} \cdot\mathrm{K}^{-1}
$$
$$
- 1 6 4 \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
E. $$
- 0. 5 2 7 \, \mathrm{J} \cdot\mathrm{m o l}^{-1} \cdot\mathrm{K}^{-1}
$$
$$
- 1 5 7 \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
F. $$
- 0. 5 4 6 \, \mathrm{J} \cdot\mathrm{m o l}^{-1} \cdot\mathrm{K}^{-1}
$$
$$
- 1 4 2 \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
G. $$
- 0. 6 2 4 \, \mathrm{J} \cdot\mathrm{m o l}^{-1} \cdot\mathrm{K}^{-1}
$$
$$
- 1 7 9 \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
H. $$
- 0. 5 1 3 \, \mathrm{J} \cdot\mathrm{m o l}^{-1} \cdot\mathrm{K}^{-1}
$$
$$
- 1 7 8 \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
I. $$
- 0. 4 9 7 \, \mathrm{J} \cdot\mathrm{m o l}^{-1} \cdot\mathrm{K}^{-1}
$$
$$
- 1 6 1 \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
J. $$
- 0. 6 4 5 \, \mathrm{J} \cdot\mathrm{m o l}^{-1} \cdot\mathrm{K}^{-1}
$$
$$
- 2 0 4 \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
Answer: E
A current of 10A (Amperes) passes through a 25Ω (Ohm) resistor for a duration of $1 \mathrm{S}$. The increase in entropy of the resistor if it is encased in an adiabatic shell is (). Its initial temperature is $27^{\circ} \mathrm{C}$, the mass of the resistor is 10g, and its specific heat capacity is $\mathbf{C_{p}}=0.20 \mathbf{cal} \cdot\mathbf{g}^{-1} \mathrm{K}^{-1}$.

Options:
A. $$
1. 8 5 2 Card/Close
$$
B. $$
1. 5 4 9 Card/Open
$$
C. $$
1. 2 7 4 Card/Close
$$
D. $$
1. 4 1 5 Card/Open
$$
E. $$
1. 9 1 8 Card/Open
$$
F. $$
1. 6 2 5 Card/Close
$$
G. $$
1. 3 6 0 Card/Close
$$
H. $$
1. 0 9 1 Card/Open
$$
I. $$
1. 3 8 6 Card/Open
$$
J. $$
1. 7 9 3 Card/Close
$$
Answer: I
Let $z=x+iy$, find
$$
( 1 ) \mid\mathrm{e}^{i-2 z} \mid; \quad( 2 ) \mid\mathrm{e}^{z^{2}} \mid; \quad( 3 ) \mathrm{Re} ( \mathrm{e}^{\frac{1} {z}} )
$$.

Options:
A. $$
\mathrm{e}^{x-i y}
$$
$$
e^{y-x^{2}}
$$
$$
{\frac{xy} {{{ey}^{2}}+{x}}} \operatorname{s i n} {\frac{y} {x^{2}+y^{2}}}
$$
B. $$
\mathrm{e}^{x-2}
$$
$$
e^{y^{2}-x}
$$
$$
{\frac{x^{2}} {{{ex}}+{y^{2}}}} \operatorname{c o s} {\frac{x} {x^{2}+y^{2}}}
$$
C. $$
-\mathrm{e}^{2 x}
$$
$$
e^{x y - y^{2}}
$$
$$
{\frac{y^{2}} {{{ex}^{2}}+{y}}} \operatorname{s i n} {\frac{y} {x^{2}+y^{2}}}
$$
D. $$
e^{x}
$$
$$
\mathrm{e}^{y^{2} - y}
$$
$$
{\frac{x} {{{ex}}+{y^{2}}}} \operatorname{s i n} {\frac{y} {x^{2}+y^{2}}}
$$
E. $$
\mathrm{e}^{-2 y}
$$
$$
e^{y^{2}-x^{2}}
$$
$$
{\frac{y} {{{e y}^{2}}+{x^{2}}}} \operatorname{c o s} {\frac{x} {x^{2}+y^{2}}}
$$
F. $$
\mathrm{e}^{2 x + 1}
$$
$$
e^{2 x-y}
$$
$$
{\frac{yx} {{{ex}^{2}}+{y}}} \operatorname{c o s} {\frac{x} {y^{2}+x^{2}}}
$$
G. $$
\mathrm{e}^{y+i}
$$
$$
e^{x y - x}
$$
$$
{\frac{1} {{{ex}}+{x^{2}}}} \operatorname{c o s} {\frac{y} {y^{2}+x^{2}}}
$$
H. $$
\mathrm{e}^{2 i x}
$$
$$
e^{x^{2}+y}
$$
$$
{\frac{y} {{{ex}^{2}}+{x^{2}}}} \operatorname{s i n} {\frac{x} {x^{2}+y^{2}}}
$$
I. $$
-\mathrm{e}^{x+y}
$$
$$
e^{x-y^{2}}
$$
$$
{\frac{1} {{{ex}^{2}}+{y^{2}}}} \operatorname{c o s} {\frac{y} {y^{2}+x}}
$$
J. $$
\mathrm{e}^{-2 x}
$$
$$
e^{x^{2}-y^{2}}
$$
$$
{\frac{x} {{{ex}^{2}}+{y^{2}}}} \operatorname{c o s} {\frac{y} {x^{2}+y^{2}}}
$$
Answer: J
Calculate the integral $\int_{-1}^{1} \mid z \mid \mathrm{d} z$, with the integration path as: (1) a straight line segment; (2) the semicircle of the unit circle on the upper half; (3) the semicircle of the unit circle on the lower half.

Options:
A. $$0$$
$$1$$
$$2$$
B. $$2$$
$$1$$
$$2$$
C. $$2$$
$$2$$
$$0$$
D. $$2$$
$$1$$
$$1$$
E. $$0$$
$$2$$
$$1$$
F. $$1$$
$$2$$
$$0$$
G. $$1$$
$$2$$
$$2$$
H. $$1$$
$$1$$
$$2$$
I. $$0$$
$$2$$
$$2$$
J. $$2$$
$$2$$
$$1$$
Answer: G
Given $u+v=( x-y ) ( x^{2}+4 x y+y^{2} )-2 ( x+y )$, try to determine the analytic function $f ( z )=u + \mathrm{i} v$.

Options:
A. $$
z^{2}+2 z+k
$$
, where k can be any arbitrary constant
B. $$
z^{3}+z+k
$$
, where k can be any arbitrary constant
C. $$
z^{6}-3 z+k
$$
, where k can be any arbitrary constant
D. $$
z^{3}-2 z+k
$$
, where k can be any arbitrary constant
E. $$
z^{5}+z+k
$$
, where k can be any arbitrary constant
F. $$
z^{4}-2 z+k
$$
, where k can be any arbitrary constant
G. $$
z^{3}+3 z+k
$$
, where k can be any arbitrary constant
H. $$
z^{4}-z+k
$$
, where k can be any arbitrary constant
I. $$
z^{3}-3 z+k
$$
, where k can be any arbitrary constant
J. $$
z^{5}-z+k
$$
, where k can be any arbitrary constant
Answer: D
Expand the function $f(z) = \frac{1}{(z-a)(z-b)}$ into a series in the neighborhood of $z=0$ (where $0 < |a| < |b|$).

Options:
A. $$
\frac{a+b} {a-b} \sum_{n=0}^{\infty} \frac{b^{n+1}-a^{n+1}} {b^{n+1} \cdot a^{n}} z^{''}
$$
B. $$
\frac{1} {a-b} \sum_{n=1}^{\infty} \frac{a^{n-1}-b^{n-1}} {a^{n} \cdot b^{n}} z^{''}
$$
C. $$
\frac{1} {a-b} \sum_{n=0}^{\infty} \frac{b^{n+1}-a^{n+1}} {b^{n+1} \cdot a^{n+1}} z^{''}
$$
D. $$
\frac{1} {a-b} \sum_{n=0}^{\infty} \frac{b^{n}-a^{n}} {a^{n+1} \cdot b^{n+1}} z^{''}
$$
E. $$
\frac{1} {b-a} \sum_{n=0}^{\infty} \frac{b^{n+2}-a^{n+2}} {b^{n+1} \cdot a^{n}} z^{''}
$$
F. $$
\frac{1} {b-a} \sum_{n=1}^{\infty} \frac{a^{n+1}-b^{n+1}} {a^{n} \cdot b^{n}} z^{''}
$$
G. $$
\frac{1} {a+b} \sum_{n=0}^{\infty} \frac{b^{n+1}-a^{n+1}} {a^{n} \cdot b^{n+1}} z^{''}
$$
H. $$
\frac{1} {a-b} \sum_{n=0}^{\infty} \frac{a^{n+1}-b^{n+1}} {a^{n+1} \cdot b^{n+1}} z^{''}
$$
I. $$
\frac{b-a} {a+b} \sum_{n=0}^{\infty} \frac{a^{n}-b^{n}} {b^{n} \cdot a^{n+1}} z^{''}
$$
J. $$
\frac{1} {a+b} \sum_{n=1}^{\infty} \frac{b^{n}-a^{n}} {b^{n} \cdot a^{n}} z^{''}
$$
Answer: H
Calculation of real number integral
$$
I = \int_{0}^{2 \pi} \sin^{2n} x \, \mathrm{d}x \, (n \text{ is a natural number})
$$

Options:
A. $$
\frac{2 \pi (n!) n (n + 2)}{2^{2n - 1}}
$$
B. $$
\frac{\pi (2n + 1)!}{2^{2n + 1} (n!)^2}
$$
C. $$
\frac{4 \pi n! (n - 1)!}{2^{2n + 2}}
$$
D. $$
\frac{2 \pi\cdot2 n ( n-1 ) \cdots( n+1 )} {2^{2 n} n!}
$$
E. $$
\frac{4 \pi (2n)!}{(n!) 2^{2n + 1}}
$$
F. $$
\frac{2 \pi n! (n - 1) (2n)}{2^{2n} (n!)}
$$
G. $$
\frac{\pi (2n - 1)!}{2^{2n} (n + 1)(n!)^2}
$$
H. $$
\frac{2 \pi (n - 1)! n (n + 3)}{2^{n}}
$$
I. $$
\frac{\pi n (n - 1) (n + 1)}{2^{n} (n!)^2}
$$
J. $$
\frac{\pi n (n + 1) (n - 1)!}{2^{2n - 2}}
$$
Answer: D
Calculate the following products:
$$
( 2 ) \ {\frac{1} {2 \pi\mathrm{i}}} \int_{| z |=2} {\frac{\mathrm{e}^{\mathrm{z i}}} {1+z^{2}}} \mathrm{d} z
$$

Options:
A. $$
\frac{\mathrm{e}^{-\mathrm{i} \pi}+\mathrm{e}^{\mathrm{i}}} {4 \mathrm{i}},
$$
B. $$
\frac{\mathrm{e}^{\mathrm{i}}+\mathrm{e}^{\mathrm{i} \pi}} {4 \pi},
$$
C. $$
\frac{\mathrm{e}^{\mathrm{i}}-\mathrm{e}^{\mathrm{z}}} {2 \mathrm{i}},
$$
D. $$
\frac{\mathrm{e}^{\mathrm{i}}-\mathrm{e}^{2 \mathrm{i}}} {\pi},
$$
E. $$
\frac{\mathrm{e}^{-\mathrm{z}}+\mathrm{e}^{\mathrm{z i}}} {\pi \mathrm{i}},
$$
F. $$
\frac{\mathrm{e}^{2 \mathrm{i}}-\mathrm{e}} {3 \mathrm{i}},
$$
G. $$
\frac{\mathrm{e}^{-\mathrm{i}}+\mathrm{e}^{\mathrm{i} \pi}} {3 \mathrm{i}},
$$
H. $$
\frac{\mathrm{e}^{-\mathrm{i}}-\mathrm{e}} {2 \mathrm{i}},
$$
I. $$
\frac{\mathrm{e}+\mathrm{e}^{-\mathrm{i} \pi}} {2 \pi},
$$
J. $$
\frac{\mathrm{e}^{1+\mathrm{i}}-\mathrm{e}^{-\mathrm{i}}} {2 \mathrm{e}},
$$
Answer: H
Calculate the integral
$$
\int_{0}^{+\infty} \frac{x \sin(m x)}{x^{4} + a^{4}} \, \mathrm{d}x \quad \text{where} \begin{cases} m > 0 \\ a > 0 \end{cases}
$$

Options:
A. $$
\frac{\pi} {2 a^{2}} \mathrm{e}^{\frac{ma} {\sqrt{2}}} \cdot\operatorname{c o s} \frac{m a} {\sqrt{2}}
$$
B. $$
\frac{\pi} {2 a^{2}} \mathrm{e}^{\frac{ma} {\sqrt{2}}} \cdot\operatorname{s i n} \frac{m a} {\sqrt{2}}
$$
C. $$
\frac{\pi} {a^{3}} \mathrm{e}^{\frac{ma} {\sqrt{2}}} \cdot\operatorname{s i n} \frac{m a} {\sqrt{2}}
$$
D. $$
\frac{\pi} {2 a} \mathrm{e}^{\frac{ma} {\sqrt{2}}} \cdot\operatorname{s i n} \frac{m a} {\sqrt{2}}
$$
E. $$
\frac{\pi} {2 a^{2}} \mathrm{e}^{\frac{ma} {\sqrt{2}}} \cdot\operatorname{s i n} \frac{2m a} {\sqrt{2}}
$$
F. $$
\frac{\pi} {2 a^{2}} \mathrm{e}^{-\frac{ma} {\sqrt{2}}} \cdot\operatorname{s i n} \frac{m a} {\sqrt{2}}
$$
G. $$
\frac{\pi} {2 a^{2}} \mathrm{e}^{\frac{-ma} {\sqrt{2}}} \cdot\operatorname{s i n} \frac{m a} {2\sqrt{2}}
$$
H. $$
\frac{\pi} {2 a^{3}} \mathrm{e}^{\frac{ma} {\sqrt{2}}} \cdot\operatorname{s i n} \frac{m a} {\sqrt{2}}
$$
I. $$
\frac{\pi} {2 a^{2}} \mathrm{e}^{\frac{ma} {\sqrt{3}}} \cdot\operatorname{s i n} \frac{m a} {\sqrt{2}}
$$
J. $$
\frac{\pi} {a^{2}} \mathrm{e}^{\frac{ma} {\sqrt{2}}} \cdot\operatorname{s i n} \frac{m a} {2\sqrt{2}}
$$
Answer: B
Attempt to calculate the integral $\int_{0}^{\infty} \frac{x \cdot \sin \beta r}{(x^2 + b^2)} \mathrm{d}x, \beta > 0, b > 0$.

Options:
A. $$
\frac{\pi}{\beta + b^2}
$$
B. $$
\pi b \sin(\beta b)
$$
C. $$
\frac{\pi b}{\beta + 1}
$$
D. $$
\frac{\pi \mathrm{e}^{-\beta b}}{2}
$$
E. $$
\pi e^{-\beta b^2}
$$
F. $$
\frac{\pi \beta}{b + 1}
$$
G. $$
\beta \pi \cos(\beta b)
$$
H. $$
\pi \mathrm{e}^{-\frac{\beta}{b}}
$$
I. $$
\pi\mathrm{e}^{-\beta b}
$$
J. $$
\frac{\pi}{2}\mathrm{e}^{-\beta b}
$$
Answer: I
Separately find the fractional linear transformation $w = L(z)$ that conformally maps the upper half-plane $z$ ($\operatorname{Im} z > 0$) to the unit disk ($|w| < 1$), satisfying the conditions:
$$
L(\mathrm{i}) = 0, \operatorname{arg} L^{\prime}(\mathrm{i}) = \frac{\pi}{2}.
$$

Options:
A. $$
{\frac{1+z\mathrm{i}}{\mathrm{i}z-1}}
$$
B. $$
{\frac{z+\mathrm{i}}{\mathrm{i}-z}}
$$
C. $$
{\frac{\mathrm{i}-z} {\mathrm{i}+z}}
$$
D. $$
{\frac{\mathrm{i}-z\mathrm{i}}{z-\mathrm{i}}}
$$
E. $$
{\frac{\mathrm{i}z+1}{z+\mathrm{i}}}
$$
F. $$
{\frac{z-\mathrm{i}}{z+\mathrm{i}}}
$$
G. $$
{\frac{1-z\mathrm{i}}{z+\mathrm{i}}}
$$
H. $$
{\frac{z-\mathrm{i}}{\mathrm{i}+z}}
$$
I. $$
{\frac{\mathrm{i}+z}{\mathrm{i}-z}}
$$
J. $$
{\frac{\mathrm{i}z-1}{\mathrm{i}+z}}
$$
Answer: C
Try to derive the equation of the image $\varGamma$ of the line $C: \mathrm{Im} \; z = 0$ (the real axis) under the linear transformation
$$
w = \frac{z - i}{(2 - i)z - 1},
$$
and determine the point symmetric to $w_0 = 2$ with respect to $\varGamma$.

Options:
A. $$
\frac{5+3\mathrm{i}}{4}
$$
B. $$
\frac{3+\mathrm{i}} {2}
$$
C. $$
1-\frac{\mathrm{i}}{3}
$$
D. $$
\frac{2-\mathrm{i}}{3}
$$
E. $$
\frac{3+2\mathrm{i}}{5}
$$
F. $$
-\frac{2}{3+\mathrm{i}}
$$
G. $$
2+3\mathrm{i}
$$
H. $$
-\frac{3+\mathrm{i}}{2}
$$
I. $$
\frac{1+2\mathrm{i}}{3}
$$
J. $$
\frac{3-\mathrm{i}}{2}
$$
Answer: B
Parameters of the two-degree-of-freedom car model are as follows:
Total mass $\mathrm{m}=1818.2 \, \mathrm{kg}$
Moment of inertia around axis $o_{z}$ $I_{z}=3885 \, \mathrm{kg} \cdot \mathrm{m}^{2}$
Wheelbase $L=3.048 \, \mathrm{m}$
Distance from the center of mass to the front axle $a=1.463 \, \mathrm{m}$
Distance from the center of mass to the rear axle $b=1.585 \, \mathrm{m}$
Total lateral stiffness of the front wheels $k_{1}=62618 \, \mathrm{N} / \mathrm{rad}$
Total lateral stiffness of the rear wheels $k_{2}=-110185 \, \mathrm{N} / \mathrm{rad}$
Overall steering gear ratio $i=20$
To find:
The peak reaction time $\mathcal{E}$ for the transient response of yaw rate fluctuation at a vehicle speed of $\mathbf{u}=30.56 \, \mathrm{m/s}$.

Options:
A. $$
\varepsilon=\frac{arctg \Phi - \frac{\omega} {\xi\omega_{0}}} {\omega}
$$
B. $$
\varepsilon=\frac{arctg \omega \Phi - \frac{\xi} {\omega_{0}}} {\xi}
$$
C. $$
\varepsilon=\frac{\xi arctg - \Phi\frac{\omega} {\omega_{0}}} {\omega}
$$
D. $$
\varepsilon=\frac{\Phi\frac{\xi\omega}{arctg} - \omega_{0}} {\omega}
$$
E. $$
\varepsilon=\frac{\omega arctg \frac{\Phi} {\xi\omega_{0}}} {\omega}
$$
F. $$
\varepsilon=\frac{a r c t g \frac{\omega} {\xi\omega_{0}}-\Phi} {\omega}
$$
G. $$
\varepsilon=\frac{\xi arctg \Phi + \frac{\omega} {\omega_{0}}} {\omega}
$$
H. $$
\varepsilon=\frac{\omega_{0}\Phi - arctg \frac{\omega} {\xi}} {\omega}
$$
I. $$
\varepsilon=\frac{\omega\Phi - arctg \frac{\xi\omega_{0}}{\omega}} {\xi}
$$
J. $$
\varepsilon=\frac{\Phi arctg + \frac{\omega} {\xi\omega_{0}}} {\omega_{0}}
$$
Answer: F
Land tax is a fee paid by landowners to the state, characterized by being compulsory, gratuitous, and exceeding economic attributes, and it falls under the category of ().

Options:
A. Assets
B. Subsidies
C. Donations
D. Dividends
E. Interest
F. Mortgages
G. Utilities
H. Finance
I. Investments
J. Fees
Answer: H
Acidic ponds should ______ adjust the pH value.

Options:
A. Pouring Olive Oil
B. Using Liquid Detergent
C. Sprinkling Sand Particles
D. Sprinkling Baking Soda
E. Adding Sugar Crystals
F. Adding Ground Pepper
G. Mixing Salt Granules
H. Spreading Quicklime
I. Adding Vinegar Drops
J. Spreading Coffee Powder
Answer: H
The rocket accelerates from a state of rest to $v=\sqrt{0.9999c}$. Suppose the acceleration of the rocket in its instantaneous proper inertial frame is $| \dot{v} |=20 \ \mathrm{m} \cdot\mathrm{s}^{-2}$. How much time is required to accelerate the rocket according to the clock at rest and the clock inside the rocket?

Options:
A. $$
3. 2 0 \ a
$$
$$
5 0. 8 \ a
$$
B. $$
2. 5 2 \ a
$$
$$
4 7. 5 \ a
$$
C. $$
2. 9 5 \ a
$$
$$
4 6. 1 \ a
$$
D. $$
4. 0 0 \ a
$$
$$
5 7. 3 \ a
$$
E. $$
3. 6 4 \ a
$$
$$
5 9. 2 \ a
$$
F. $$
2. 7 1 \ a
$$
$$
4 8. 6 \ a
$$
G. $$
1. 7 5 \ a
$$
$$
3 4. 9 \ a
$$
H. $$
2. 3 8 \ a
$$
$$
4 5. 5 \ a
$$
I. $$
3. 9 5 \ a
$$
$$
5 8. 0 \ a
$$
J. $$
1. 8 9 \ a
$$
$$
3 5. 7 \ a
$$
Answer: B