MikaStars39/nano-eval huggingface dataset:
In assessing metabolic processes we are usually more interested in the work that may be performed for the consumption of a given mass of compound than the heat it can produce (which merely keeps the body warm). What is the maximum energy that can be extracted as non-expansion work when 2.0 kg of glucose is burned under standard conditions at 25°C with the production of water vapour? The reaction is $\mathrm{C_{6} H_{1 2} O_{6} ( s )+6 O_{2} ( g ) \to6 C O_{2} ( g )+6 H_{2} O ( g ).}$

Options:
A. $$
{2. 4 \times1 0^{4} \mathrm{~ k J}}
$$
B. $$
{3. 8 \times1 0^{4} \mathrm{~ k J}}
$$
C. $$
{2. 6 \times1 0^{4} \mathrm{~ k J}}
$$
D. $$
{2. 5 \times1 0^{4} \mathrm{~ k J}}
$$
E. $$
{2. 9 \times1 0^{4} \mathrm{~ k J}}
$$
F. $$
{3. 53 \times1 0^{4} \mathrm{~ k J}}
$$
G. $$
{3. 1 \times1 0^{4} \mathrm{~ k J}}
$$
H. $$
{2. 7 \times1 0^{4} \mathrm{~ k J}}
$$
I. $$
{3. 52 \times1 0^{4} \mathrm{~ k J}}
$$
J. $$
{2. 8 \times1 0^{4} \mathrm{~ k J}}
$$
Answer: G
What is the standard enthalpy of a reaction for which the equilibrium constant is halved when the temperature is increased by 10 K at 298 K?

Options:
A. $$
{-5 5. 6 \mathrm{k J \ m o l}^{-1}}
$$
B. $$
{-5 6. 7 \mathrm{k J \ m o l}^{-1}}
$$
C. $$
{-6 0. 1 \mathrm{k J \ m o l}^{-1}}
$$
D. $$
{-5 8. 0 \mathrm{k J \ m o l}^{-1}}
$$
E. $$
{-5 1. 7 \mathrm{k J \ m o l}^{-1}}
$$
F. $$
{-4 8. 3 \mathrm{k J \ m o l}^{-1}}
$$
G. $$
{-5 3. 9 \mathrm{k J \ m o l}^{-1}}
$$
H. $$
{-5 0. 2 \mathrm{k J \ m o l}^{-1}}
$$
I. $$
{-5 4. 5 \mathrm{k J \ m o l}^{-1}}
$$
J. $$
{-5 2. 9 \mathrm{k J \ m o l}^{-1}}
$$
Answer: J
Devise a cell in which the cell reaction is $\mathrm{M n ( s )+C l_{2} ( g )}$ $\to\mathrm{M n C l}_{2} ( \mathrm{a q} )$ . Give the half-reactions for the electrodes and from the standard cell potential of +2.54 $\vee$ deduce the standard potential of the Mn$^{2+}$/Mn couple.

Options:
A. $$
{+1. 9 4 \mathrm{V}}
$$
B. $$
{+3. 0 1 \mathrm{V}}
$$
C. $$
{+0. 8 7 \mathrm{V}}
$$
D. $$
{+1. 1 9 \mathrm{V}}
$$
E. $$
{-1. 5 5 \mathrm{V}}
$$
F. $$
{+2. 3 3 \mathrm{V}}
$$
G. $$
{-2. 4 6 \mathrm{V}}
$$
H. $$
{-2. 7 8 \mathrm{V}}
$$
I. $$
{-0. 7 2 \mathrm{V}}
$$
J. $$
{-1. 1 8 \mathrm{V}}
$$
Answer: J
The atomic radii of $M g^{2+}$ and $F^{-}$ ions are 0.072 and 0.133 nm, respectively.
What is the force of attraction between these two ions at their equilibrium interionic separation (i.e., when the ions just touch one another)?

Options:
A. $$
7. 2 0 \times1 0^{-8} \, \mathrm{N}
$$
B. $$
2. 0 0 \times1 0^{-8} \, \mathrm{N}
$$
C. $$
3. 7 0 \times1 0^{-8} \, \mathrm{N}
$$
D. $$
1. 3 0 \times1 0^{-8} \, \mathrm{N}
$$
E. $$
8. 4 0 \times1 0^{-8} \, \mathrm{N}
$$
F. $$
4. 9 0 \times1 0^{-8} \, \mathrm{N}
$$
G. $$
9. 8 0 \times1 0^{-8} \, \mathrm{N}
$$
H. $$
1. 1 0 \times1 0^{-8} \, \mathrm{N}
$$
I. $$
1. 5 0 \times1 0^{-8} \, \mathrm{N}
$$
J. $$
6. 6 0 \times1 0^{-8} \, \mathrm{N}
$$
Answer: H
Titanium (Ti) has an HCP crystal structure and a density of $4.51 g/cm^{3}$. What is the volume of its unit cell in cubic meters?

Options:
A. $$
1. 0 5 8 \times1 0^{-2 8} \, \mathrm{m}^{3} / \mathrm{u n i t \, c e l l}
$$
B. $$
1 . 9 7 \times 1 0^{-2 9} \, \mathrm{m}^{3} / \mathrm{u n i t \, c e l l}
$$
C. $$
2 . 8 0 \times 1 0^{-2 7} \, \mathrm{m}^{3} / \mathrm{u n i t \, c e l l}
$$
D. $$
5 . 5 4 \times 1 0^{-2 7} \, \mathrm{m}^{3} / \mathrm{u n i t \, c e l l}
$$
E. $$
9 . 1 2 \times 1 0^{-3 0} \, \mathrm{m}^{3} / \mathrm{u n i t \, c e l l}
$$
F. $$
6 . 0 2 \times 1 0^{-2 9} \, \mathrm{m}^{3} / \mathrm{u n i t \, c e l l}
$$
G. $$
3 . 1 4 \times 1 0^{-3 0} \, \mathrm{m}^{3} / \mathrm{u n i t \, c e l l}
$$
H. $$
8 . 2 9 \times 1 0^{-2 9} \, \mathrm{m}^{3} / \mathrm{u n i t \, c e l l}
$$
I. $$
4 . 3 5 \times 1 0^{-2 8} \, \mathrm{m}^{3} / \mathrm{u n i t \, c e l l}
$$
J. $$
7 . 8 1 \times 1 0^{-2 8} \, \mathrm{m}^{3} / \mathrm{u n i t \, c e l l}
$$
Answer: A
Magnesium ($Mg$) has an $HCP$ crystal structure, a c/a ratio of 1.624, and a density of $1.74 g/cm^{3}$. The atomic radius for Mg.is().

Options:
A. $$
0. 1 3 0 \mathrm{~ n m}
$$
B. $$
0. 1 6 0 \mathrm{~ n m}
$$
C. $$
0. 1 8 0 \mathrm{~ n m}
$$
D. $$
0. 2 0 0 \mathrm{~ n m}
$$
E. $$
0. 1 4 0 \mathrm{~ n m}
$$
F. $$
0. 1 7 5 \mathrm{~ n m}
$$
G. $$
0. 1 6 5 \mathrm{~ n m}
$$
H. $$
0. 1 5 0 \mathrm{~ n m}
$$
I. $$
0. 1 9 0 \mathrm{~ n m}
$$
J. $$
0. 1 5 5 \mathrm{~ n m}
$$
Answer: B
For an ASTM grain size of $6$, approximately how many grains would there be per square inch under each of the following conditions without any magnification?

Options:
A. $$n_{1}=260,000grains/in^{2}$$
B. $$n_{1}=340,000grains/in^{2}$$
C. $$n_{1}=380,000grains/in^{2}$$
D. $$n_{1}=360,000grains/in^{2}$$
E. $$n_{1}=320,000grains/in^{2}$$
F. $$n_{1}=240,000grains/in^{2}$$
G. $$n_{1}=280,000grains/in^{2}$$
H. $$n_{1}=440,000grains/in^{2}$$
I. $$n_{1}=300,000grains/in^{2}$$
J. $$n_{1}=400,000grains/in^{2}$$
Answer: E
The activation energy for the diffusion of copper in silver is 193,000 J/mol. What is the diffusion coefficient at 100 K (927°C), given that $D$ at100 $K$ (727°C) is $1. 0 \times 1 0^{-1 4}$ $m^{2}$/s?

Options:
A. $6. 3 \, \times\, 1 0^{-1 5} \ \mathrm{m}^{2} / \mathrm{s}$
B. $5. 8 \, \times\, 1 0^{-1 4} \ \mathrm{m}^{2} / \mathrm{s}$
C. $5. 4 \, \times\, 1 0^{-1 4} \ \mathrm{m}^{2} / \mathrm{s}$
D. $2. 7 \, \times\, 1 0^{-1 2} \ \mathrm{m}^{2} / \mathrm{s}$
E. $9. 1 \, \times\, 1 0^{-1 3} \ \mathrm{m}^{2} / \mathrm{s}$
F. $1. 9 \, \times\, 1 0^{-1 6} \ \mathrm{m}^{2} / \mathrm{s}$
G. $4. 8 \, \times\, 1 0^{-1 3} \ \mathrm{m}^{2} / \mathrm{s}$
H. $3. 2 \, \times\, 1 0^{-1 2} \ \mathrm{m}^{2} / \mathrm{s}$
I. $7. 0 \, \times\, 1 0^{-1 5} \ \mathrm{m}^{2} / \mathrm{s}$
J. $8. 5 \, \times\, 1 0^{-1 3} \ \mathrm{m}^{2} / \mathrm{s}$
Answer: G
The outer suface of a steel gear is to be hardened by increasing its carbon content; the carbon is to be supplied from an external carbon-rich atmosphere maintained at an elevated temperature. A diffusion heat treatment at 600°C (873 K) for 100 min increases the carbon concentration to 0.75 wt% at a position 0.5 mm below the surface. What is the diffusion time required at 900°C (1173 K) to achieve this same concentration also at a 0.5mm position ?Assume that the surface carbon content is the same for both heat treatments, which is maintained constant.

Options:
A. $$
8. 3 7 \mathrm{~ m i n}
$$
B. $$
6. 2 5 \mathrm{~ m i n}
$$
C. $$
4. 6 1 \mathrm{~ m i n}
$$
D. $$
7. 0 0 \mathrm{~ m i n}
$$
E. $$
7. 8 2 \mathrm{~ m i n}
$$
F. $$
5. 4 9 \mathrm{~ m i n}
$$
G. $$
2. 6 4 \mathrm{~ m i n}
$$
H. $$
9. 1 3 \mathrm{~ m i n}
$$
I. $$
3. 5 0 \mathrm{~ m i n}
$$
J. $$
1. 4 9 \mathrm{~ m i n}
$$
Answer: C
A 10-mm-diameter Brinell hardness indenter produced an indentation 2.50 mm in diameter in $a$ steel alloy when a load of 1000 kg was used. The HB of this material is().

Options:
A. $$
2 0 7. 9
$$
B. $$
2 0 3. 2
$$
C. $$
2 1 0. 0
$$
D. $$
1 9 0. 5
$$
E. $$
1 9 5. 6
$$
F. $$
1 9 8. 4
$$
G. $$
2 0 9. 8
$$
H. $$
1 8 5. 3
$$
I. $$
2 0 0. 5
$$
J. $$
2 1 2. 0
$$
Answer: I
A cylindrical specimen of cold-worked steel has a Brinell hardness of 240.
If the specimen remained cylindrical during deformation and its original radius was 10 mm (0.40 in.), determine its radius after deformation.is().

Options:
A. $$
10. 0 5 \ \mathrm{m m} \ \ ( 0. 3 9 6 \ \mathrm{i n} )
$$
B. $$
8. 6 5 \ \mathrm{m m} \ \ ( 0. 3 4 0 \ \mathrm{i n} )
$$
C. $$
9. 1 1 \ \mathrm{m m} \ \ ( 0. 3 6 4 \ \mathrm{i n} )
$$
D. $$
9. 5 5 \ \mathrm{m m} \ \ ( 0. 3 7 6 \ \mathrm{i n} )
$$
E. $$
7. 9 0 \ \mathrm{m m} \ \ ( 0. 3 1 1 \ \mathrm{i n} )
$$
F. $$
10. 7 5 \ \mathrm{m m} \ \ ( 0. 4 2 3 \ \mathrm{i n} )
$$
G. $$
9. 8 5 \ \mathrm{m m} \ \ ( 0. 3 8 8 \ \mathrm{i n} )
$$
H. $$
8. 3 3 \ \mathrm{m m} \ \ ( 0. 3 2 8 \ \mathrm{i n} )
$$
I. $$
11. 0 0 \ \mathrm{m m} \ \ ( 0. 4 3 3 \ \mathrm{i n} )
$$
J. $$
10. 2 5 \ \mathrm{m m} \ \ ( 0. 4 0 4 \ \mathrm{i n} )
$$
Answer: C
Suppose that a wing component on an aircreft is fabricated from an aluminum alloy that has a plane- strain frcture oughnesof 26.0Ma $\sqrt{m}$ (23.7 ksi $\sqrt{i n}$ . t has ben ermined hat facture reustsas rs 112 MPa (16,240 psi) when the maximum internal crack length is 8.6 mm (0.34 in.). For this same component and alloy, compute the stress level at which fracture will occur for a critical internal crack length of 6.0 mm (0.24 in.).

Options:
A. $$
1 4 0 \mathrm{~ M P a ~} ( 2 0, 3 0 0 \mathrm{~ p s i )}
$$
B. $$
1 3 0 \mathrm{~ M P a ~} ( 1 8, 8 5 0 \mathrm{~ p s i )}
$$
C. $$
1 2 2 \mathrm{~ M P a ~} ( 1 7, 7 0 0 \mathrm{~ p s i )}
$$
D. $$
1 3 6 \mathrm{~ M P a ~} ( 1 9, 4 5 0 \mathrm{~ p s i )}
$$
E. $$
1 3 2 \mathrm{~ M P a ~} ( 1 9, 0 0 0 \mathrm{~ p s i )}
$$
F. $$
1 2 5 \mathrm{~ M P a ~} ( 1 8, 1 5 0 \mathrm{~ p s i )}
$$
G. $$
1 3 8 \mathrm{~ M P a ~} ( 1 9, 6 5 0 \mathrm{~ p s i )}
$$
H. $$
1 2 8 \mathrm{~ M P a ~} ( 1 8, 6 0 0 \mathrm{~ p s i )}
$$
I. $$
1 3 4 \mathrm{~ M P a ~} ( 1 9, 3 0 0 \mathrm{~ p s i )}
$$
J. $$
1 4 2 \mathrm{~ M P a ~} ( 2 0, 5 5 0 \mathrm{~ p s i )}
$$
Answer: I
Compute the volume percent of graphite, $v_{G}$ in a 2.5 wt% C cast iron, assuming that all the carbon exists as the graphite phase. Assume densities of 7.9 and 2.3 g/$cm^3$ for ferrite and graphite, respectively.

Options:
A. $$0.041or4.1vol%$$
B. $$0.131or13.1vol%$$
C. $$0.081or8.1vol%$$
D. $$0.051or5.1vol%$$
E. $$0.071or7.1vol%$$
F. $$0.091or9.1vol%$$
G. $$0.101or10.1vol%$$
H. $$0.061or6.1vol%$$
I. $$0.111or11.1vol%$$
J. $$0.121or12.1vol%$$
Answer: C
When kaolinate clay Al2(Si2O5)(OH)4 is heated to a sufficient high temperature, chemical water is driven off.
Under these circumstances, what is the composition of the remaining product (in weight percent A12O3)?

Options:
A. $$
5 0. 1 {\mathrm{~ w t}} \%
$$
B. $$
4 6. 8 {\mathrm{~ w t}} \%
$$
C. $$
4 6. 0 {\mathrm{~ w t}} \%
$$
D. $$
4 9. 4 {\mathrm{~ w t}} \%
$$
E. $$
4 4. 3 {\mathrm{~ w t}} \%
$$
F. $$
4 7. 2 {\mathrm{~ w t}} \%
$$
G. $$
4 8. 6 {\mathrm{~ w t}} \%
$$
H. $$
5 1. 7 {\mathrm{~ w t}} \%
$$
I. $$
4 3. 9 {\mathrm{~ w t}} \%
$$
J. $$
4 5. 9 {\mathrm{~ w t}} \%
$$
Answer: J
The modulus of elasticity for spinel (MgAl2O4) having 5 vol% porosity is 240 GPa $( 3 5 \times1 0^{6} p s i )$ . Compute the modulus of elasticity for 15 vol% porosity.

Options:
A. $$
1 8 8 \ \mathrm{G P a} \ \left( 2 7. 2 \ \times\ 1 0^{6} \ \mathrm{p s i} \right)
$$
B. $$
1 8 2 \ \mathrm{G P a} \ \left( 2 6. 4 \ \times\ 1 0^{6} \ \mathrm{p s i} \right)
$$
C. $$
1 8 5 \ \mathrm{G P a} \ \left( 2 6. 8 \ \times\ 1 0^{6} \ \mathrm{p s i} \right)
$$
D. $$
1 9 0 \ \mathrm{G P a} \ \left( 2 7. 6 \ \times\ 1 0^{6} \ \mathrm{p s i} \right)
$$
E. $$
2 0 5 \ \mathrm{G P a} \ \left( 2 9. 7 \ \times\ 1 0^{6} \ \mathrm{p s i} \right)
$$
F. $$
2 1 0 \ \mathrm{G P a} \ \left( 3 0. 6 \ \times\ 1 0^{6} \ \mathrm{p s i} \right)
$$
G. $$
1 9 5 \ \mathrm{G P a} \ \left( 2 8. 4 \ \times\ 1 0^{6} \ \mathrm{p s i} \right)
$$
H. $$
2 1 5 \ \mathrm{G P a} \ \left( 3 1. 2 \ \times\ 1 0^{6} \ \mathrm{p s i} \right)
$$
I. $$
1 9 9 \ \mathrm{G P a} \ \left( 2 8. 8 \ \times\ 1 0^{6} \ \mathrm{p s i} \right)
$$
J. $$
2 0 0 \ \mathrm{G P a} \ \left( 2 9. 0 \ \times\ 1 0^{6} \ \mathrm{p s i} \right)
$$
Answer: G
Soda and lime are added to a glass batch in the form of soda ash (Na $_{2}CO_{y})$ and lime-stone
$(CaCO_{3}).$ During heating, these two ingredients decompose to give off carbon dioxide (CO,the resulting productsbeingsodaaand lime. The weight of soda ash and limestone that must be added to 125 Ib $_m$ $ofquartz($Si$O_2)$ to yield a glass of composition 78 wt% Si$O_{2}$ 17 wi% Na$_{2}O,and5$ wt% CaO.is().

Options:
A. $$
\mathrm{l 4. 3} \, \mathrm{l b}_{\mathrm{m}}
$$
B. $$
\mathrm{l 2. 3} \, \mathrm{l b}_{\mathrm{m}}
$$
C. $$
\mathrm{l 8. 9} \, \mathrm{l b}_{\mathrm{m}}
$$
D. $$
\mathrm{l 7. 4} \, \mathrm{l b}_{\mathrm{m}}
$$
E. $$
\mathrm{l 9. 6} \, \mathrm{l b}_{\mathrm{m}}
$$
F. $$
\mathrm{l 6. 1} \, \mathrm{l b}_{\mathrm{m}}
$$
G. $$
\mathrm{l 5. 0} \, \mathrm{l b}_{\mathrm{m}}
$$
H. $$
\mathrm{l 1. 9} \, \mathrm{l b}_{\mathrm{m}}
$$
I. $$
\mathrm{l 3. 8} \, \mathrm{l b}_{\mathrm{m}}
$$
J. $$
\mathrm{l 2. 7} \, \mathrm{l b}_{\mathrm{m}}
$$
Answer: A
Crosslinked copolymers consisting of 35 wt% ethylene and 65 wt% propylene may have elastic properties similar to those for natural rubber. For a copolymer of this composition, determine the fraction of both repeat unit types.

Options:
A. 0.40
B. 0.45
C. 0.55
D. 0.50
E. 0.60
F. 0.75
G. 0.25
H. 0.70
I. 0.65
J. 0.35
Answer: C
For some viscoelastic polymers that are subjected to stress relaxation tests, the stress decays with time according to
$$
\sigma( t )=\sigma( 0 ) \mathrm{e x p} \! \left(-{\frac{t} {\tau}} \right)
$$
where $\sigma(t)$ and $\sigma(0)$ represent the time-dependent and initial (ie, time $= 0$ ) stresses, respectively, and t and$ $\tau$ denote elapsed time and the relaxation time, respectively; $\tau$ is a time-independent constant characteristic of the material $A$ specimen of a viscoelastic polymer whose stress relaxation obeys Equation 15.10 was suddenly pulled in tension to a measured strain of 0.5; the stress necessary to maintain this constant strain was measured as a function of time Determine $E_{r}(10)$ for this material if the initial stress level was 3.5 MPa (500 psi), which dropped to 0.5 MPa (70 psi) afer 30 s.

Options:
A. $$
4. 0 9 \ \mathrm{M P a} \ ( 5 9 3 \ \mathrm{p s i} )
$$
B. $$
2. 7 7 \ \mathrm{M P a} \ ( 4 0 2 \ \mathrm{p s i} )
$$
C. $$
3. 7 3 \ \mathrm{M P a} \ ( 5 4 0 \ \mathrm{p s i} )
$$
D. $$
3. 1 4 \ \mathrm{M P a} \ ( 4 5 5 \ \mathrm{p s i} )
$$
E. $$
3. 5 1 \ \mathrm{M P a} \ ( 5 0 9 \ \mathrm{p s i} )
$$
F. $$
3. 8 0 \ \mathrm{M P a} \ ( 5 5 1 \ \mathrm{p s i} )
$$
G. $$
2. 9 8 \ \mathrm{M P a} \ ( 4 3 2 \ \mathrm{p s i} )
$$
H. $$
4. 2 7 \ \mathrm{M P a} \ ( 6 1 9 \ \mathrm{p s i} )
$$
I. $$
3. 6 6 \ \mathrm{M P a} \ ( 5 2 2 \ \mathrm{p s i} )
$$
J. $$
2. 5 0 \ \mathrm{M P a} \ ( 3 6 3 \ \mathrm{p s i} )
$$
Answer: I
$I t$ is desired to produce an aligned carbon fiber-epoxy matrix composite having $a$ longitudinal tensile strength of 500 MPa (72,500 psi). Calculate the volume fraction of fibers necessary if (1) the average fiber diameter and length are 0.01 nm ($3. 9 \times1 0^{-1}$ in) and 0.5 mm $( 2 \times1 0^{-2}$ in.), respectively; (2) the fiber fracture strength is 4.0 GPa ( $5. 8 \times1 0^{5}$ psi); (3) the fiber-matrix bond strength is 25 MPa (3625 psi); and (4) the matrix stress at composite failwre is 7.0 MPa (1000 psi).

Options:
A. $$
0. 4 4 7
$$
B. $$
0. 5 1 0
$$
C. $$
0. 2 8 5
$$
D. $$
0. 3 3 4
$$
E. $$
0. 3 9 7
$$
F. $$
0. 4 0 5
$$
G. $$
0. 2 9 2
$$
H. $$
0. 2 6 9
$$
I. $$
0. 3 0 8
$$
J. $$
0. 4 1 2
$$
Answer: E
At room temperature the electrical conductivity of PbS is $25 \, (\Omega \cdot m)^{-1}$, whereas the electron and hole mobilites are 0.06 and $0.02 \, \text{m}^2 / \text{V} \cdot \text{s}$ respectively. The intrinsic carrierconcentration for PbS at room temperature is().

Options:
A. $$
3. 7 8 \times1 0^{1 9} \mathrm{~ m^{-3} ~}
$$
B. $$
1. 9 5 \times1 0^{2 1} \mathrm{~ m^{-3} ~}
$$
C. $$
9. 8 4 \times1 0^{1 7} \mathrm{~ m^{-3} ~}
$$
D. $$
5. 4 2 \times1 0^{2 3} \mathrm{~ m^{-3} ~}
$$
E. $$
8. 2 7 \times1 0^{2 0} \mathrm{~ m^{-3} ~}
$$
F. $$
6. 5 3 \times1 0^{2 2} \mathrm{~ m^{-3} ~}
$$
G. $$
4. 1 2 \times1 0^{2 4} \mathrm{~ m^{-3} ~}
$$
H. $$
2. 8 9 \times1 0^{1 8} \mathrm{~ m^{-3} ~}
$$
I. $$
0. 3 6 \times1 0^{2 2} \mathrm{~ m^{-3} ~}
$$
J. $$
7. 6 1 \times1 0^{2 0} \mathrm{~ m^{-3} ~}
$$
Answer: B
The room-temperature electrical conductivity of silicon that has been doped with $10^{23} \, \text{m}^{-3}$ of arsenic atoms is () .

Options:
A. $$
3 2 3 5 \ ( \Omega\mathrm{-m} )^{-1}
$$
B. $$
8 1 7 7 \ ( \Omega\mathrm{-m} )^{-1}
$$
C. $$
7 6 3 8 \ ( \Omega\mathrm{-m} )^{-1}
$$
D. $$
6 2 0 5 \ ( \Omega\mathrm{-m} )^{-1}
$$
E. $$
2 9 9 4 \ ( \Omega\mathrm{-m} )^{-1}
$$
F. $$
1 0 4 0 \ ( \Omega\mathrm{-m} )^{-1}
$$
G. $$
5 5 4 3 \ ( \Omega\mathrm{-m} )^{-1}
$$
H. $$
9 7 2 0 \ ( \Omega\mathrm{-m} )^{-1}
$$
I. $$
4 8 6 1 \ ( \Omega\mathrm{-m} )^{-1}
$$
J. $$
1 5 8 9 \ ( \Omega\mathrm{-m} )^{-1}
$$
Answer: F
At temperatures between $541^{\circ} C (813 K)$ and $727^{\circ} C (1000 K)$ , the activation energy and pre-exponential for the diffusion coefficient of $\text{Na}^{+}$ in NaCl are 173,000 , J/mol and $4.0 \times 10^{-5} \text{m}^2$, respectively. Compute the mobility for an $\text{Na}^+ \text{ ion at } 600^{\circ} \text{C (873 K).}$

Options:
A. $$
9. 0 2 \times1 0^{-1 5} \mathrm{~ m}^{2} /V\mathrm{-s}
$$
B. $$
1. 7 9 \times1 0^{-1 4} \mathrm{~ m}^{2} /V\mathrm{-s}
$$
C. $$
5. 6 7 \times1 0^{-1 6} \mathrm{~ m}^{2} /V\mathrm{-s}
$$
D. $$
7. 4 3 \times1 0^{-1 7} \mathrm{~ m}^{2} /V\mathrm{-s}
$$
E. $$
8. 9 8 \times1 0^{-1 8} \mathrm{~ m}^{2} /V\mathrm{-s}
$$
F. $$
2. 0 1 \times1 0^{-1 2} \mathrm{~ m}^{2} /V\mathrm{-s}
$$
G. $$
2. 3 4 \times1 0^{-1 3} \mathrm{~ m}^{2} /V\mathrm{-s}
$$
H. $$
3. 8 5 \times1 0^{-1 1} \mathrm{~ m}^{2} /V\mathrm{-s}
$$
I. $$
6. 1 4 \times1 0^{-1 9} \mathrm{~ m}^{2} /V\mathrm{-s}
$$
J. $$
4. 5 6 \times1 0^{-1 2} \mathrm{~ m}^{2} /V\mathrm{-s}
$$
Answer: G
Calculate the heat flux through a sheet of brass 7.5 mm (0.30 in.) thick if the temperatures at the two faces are 150°C and 50°C (302°F and 122F); assume steady-state heat flow.

Options:
A. $$
2. 1 0 \times1 0^{7} \mathrm{~ W / m}^{2}
$$
B. $$
1. 3 0 \times1 0^{7} \mathrm{~ W / m}^{2}
$$
C. $$
1. 8 0 \times1 0^{5} \mathrm{~ W / m}^{2}
$$
D. $$
2. 0 5 \times1 0^{6} \mathrm{~ W / m}^{2}
$$
E. $$
1. 9 5 \times1 0^{6} \mathrm{~ W / m}^{2}
$$
F. $$
1. 5 0 \times1 0^{5} \mathrm{~ W / m}^{2}
$$
G. $$
1. 6 0 \times1 0^{6} \mathrm{~ W / m}^{2}
$$
H. $$
1. 1 0 \times1 0^{6} \mathrm{~ W / m}^{2}
$$
I. $$
2. 2 0 \times1 0^{6} \mathrm{~ W / m}^{2}
$$
J. $$
1. 0 5 \times1 0^{6} \mathrm{~ W / m}^{2}
$$
Answer: G
Visible light having $a$ wavelength of 5 × $10^{-7}$ m appears green. Compute the frequency and energy of
a photon of this light.

Options:
A. $$
2. 7 6 \, \times\, 1 0^{-1 9} \, \mathrm{J} \ \ ( 1. 8 4 \, \mathrm{c V} )
$$
B. $$
1. 9 7 \, \times\, 1 0^{-1 9} \, \mathrm{J} \ \ ( 1. 3 6 \, \mathrm{c V} )
$$
C. $$
3. 3 4 \, \times\, 1 0^{-1 9} \, \mathrm{J} \ \ ( 2. 1 3 \, \mathrm{c V} )
$$
D. $$
2. 1 8 \, \times\, 1 0^{-1 9} \, \mathrm{J} \ \ ( 1. 5 0 \, \mathrm{c V} )
$$
E. $$
4. 6 0 \, \times\, 1 0^{-1 9} \, \mathrm{J} \ \ ( 3. 0 5 \, \mathrm{c V} )
$$
F. $$
5. 1 9 \, \times\, 1 0^{-1 9} \, \mathrm{J} \ \ ( 3. 4 5 \, \mathrm{c V} )
$$
G. $$
3. 9 8 \, \times\, 1 0^{-1 9} \, \mathrm{J} \ \ ( 2. 4 8 \, \mathrm{c V} )
$$
H. $$
4. 0 1 \, \times\, 1 0^{-1 9} \, \mathrm{J} \ \ ( 2. 6 8 \, \mathrm{c V} )
$$
I. $$
5. 7 8 \, \times\, 1 0^{-1 9} \, \mathrm{J} \ \ ( 3. 8 4 \, \mathrm{c V} )
$$
J. $$
1. 2 9 \, \times\, 1 0^{-1 9} \, \mathrm{J} \ \ ( 0. 9 8 \, \mathrm{c V} )
$$
Answer: G
Gallium arsenide (GaAs) and gallium phosphide (GaP) are compound semiconductors that have room-temperature band gap energies of 1.42 and 2.26 eV, respectively, and form solid solutions in all proportions. The band gap of the alloy increases approximately linearly with GaP additions (in mol%). Alloys of these two materials are used for light-emitting diodes (LEDs), in which light is generated by conduction band-to-valence band electron transitions. Determine the composition of a GaAs-GaP alloy that will emit red light having a wavelength of 0.68 um.

Options:
A. 27.1mol%
B. 22.3mol%
C. 72.8mol%
D. 35.4mol%
E. 44.5mol%
F. 62.1mol%
G. 15.9mol%
H. 47.6mol%
I. 49.2mol%
J. 58.7mol%
Answer: H
Let $p$ be a prime and $G=\mathrm{S L}_{2} ( \mathbb{F}_{p} )$ . What is the order of $G$?

Options:
A. $$p^3(p-1)$$
B. $$p^2(p-1)$$
C. $$p(p^2-1)$$
D. $$p^2(p+1)$$
E. $$p(p+1)$$
F. $$p^3(p^2-1)$$
G. $$p(p^2+1)$$
H. $$p^2(p^2-1)$$
I. $$p(p^3-1)$$
J. $$p(p^2-p)$$
Answer: C
Let $f \in\mathbb{C} [ x, y, z ]$ be an irreducible homogenous polynomial of degree $d > 0$ . For each integer $n \geq d$ , define
$$
P ( n )=\operatorname{d i m}_{\mathbb{C}} \mathbb{C} [ x, y, z ]_{n} / f \cdot\mathbb{C} [ x, y, z ]_{n-d},
$$
where $\mathbb{C} [ x, y, z ]_{d}$ is the subspace of homogenous polynomials of degree $n$ . So there are constants $c$ such that for $n$ sufficiently large,
$$
P ( n )=( ~~).
$$

Options:
A. $$d + n c$$
B. $$d^2n - c$$
C. $$dn - c$$
D. $$cd + n$$
E. $$cn + d$$
F. $$2nd+c$$
G. $$dn+c$$
H. $$n d - c$$
I. $$n + d c$$
J. $$d^{2} + n$$
Answer: G
The density of octane (which we take to model gasoline) is 0.703 g cm$^{-3}$ : what amount (in moles) of octane molecules do you get when you buy 1.00 dm$^{3}$ (1.00 litre) of gasoline?

Options:
A. $$
2. 8 0 \times1 0^{2 4} \mathrm{o c t a n e m o l e c u l e s}
$$
B. $$
9. 5 2 \times1 0^{2 3} \mathrm{o c t a n e m o l e c u l e s}
$$
C. $$
7. 4 3 \times1 0^{2 3} \mathrm{o c t a n e m o l e c u l e s}
$$
D. $$
3. 1 4 \times1 0^{2 4} \mathrm{o c t a n e m o l e c u l e s}
$$
E. $$
6. 1 8 \times1 0^{2 4} \mathrm{o c t a n e m o l e c u l e s}
$$
F. $$
1. 7 6 \times1 0^{2 4} \mathrm{o c t a n e m o l e c u l e s}
$$
G. $$
5. 6 4 \times1 0^{2 4} \mathrm{o c t a n e m o l e c u l e s}
$$
H. $$
4. 8 5 \times1 0^{2 4} \mathrm{o c t a n e m o l e c u l e s}
$$
I. $$
2. 3 9 \times1 0^{2 4} \mathrm{o c t a n e m o l e c u l e s}
$$
J. $$
3. 7 1 \times1 0^{2 4} \mathrm{o c t a n e m o l e c u l e s}
$$
Answer: J
What mass of carbon monoxide is needed to reduce 1.0 t of iron(lll) oxide to the metal?

Options:
A. $$
8. 2 \times1 0^{2} \mathrm{~ k g}
$$
B. $$
3. 9 \times1 0^{3} \mathrm{~ k g}
$$
C. $$
4. 8 \times1 0^{2} \mathrm{~ k g}
$$
D. $$
6. 5 \times1 0^{1} \mathrm{~ k g}
$$
E. $$
7. 0 \times1 0^{2} \mathrm{~ k g}
$$
F. $$
5. 3 \times1 0^{2} \mathrm{~ k g}
$$
G. $$
9. 0 \times1 0^{1} \mathrm{~ k g}
$$
H. $$
1. 1 \times1 0^{3} \mathrm{~ k g}
$$
I. $$
4. 2 \times1 0^{2} \mathrm{~ k g}
$$
J. $$
2. 5 \times1 0^{2} \mathrm{~ k g}
$$
Answer: F
$\mathsf{A}$ meteorological balloon had a radius of 1.5 m when released at sea level at 20'C and expanded to a radius of 3.5 m when it had risen to its maximum altitude where the temperature was -25°C. What is the pressure inside the balloon at that altitude?

Options:
A. $$
9. 0 \times1 0^{-2} \mathrm{~ a t m}
$$
B. $$
8. 1 \times1 0^{-2} \mathrm{~ a t m}
$$
C. $$
5. 7 \times1 0^{-2} \mathrm{~ a t m}
$$
D. $$
7. 9 \times1 0^{-2} \mathrm{~ a t m}
$$
E. $$
7. 5 \times1 0^{-2} \mathrm{~ a t m}
$$
F. $$
5. 9 \times1 0^{-2} \mathrm{~ a t m}
$$
G. $$
8. 5 \times1 0^{-2} \mathrm{~ a t m}
$$
H. $$
6. 2 \times1 0^{-2} \mathrm{~ a t m}
$$
I. $$
6. 7 \times1 0^{-2} \mathrm{~ a t m}
$$
J. $$
7. 2 \times1 0^{-2} \mathrm{~ a t m}
$$
Answer: I
In an experiment to determine the calorific value of a food, a sample of the food was burned in an oxygen atmosphere and the temperature rose by 2.89°C. When a current of 1.27 $\mathrm{A}$ from a 12.5 $\mathsf{V}$ source flowed through the same calorimeter for 157 s, the temperature rose by 3.88°C. What energy is released as heat by the combustion?

Options:
A. $$ {-2. 9 3 \mathrm{~ k J}} $$
B. $$ {+1. 5 0 \mathrm{~ k J}} $$
C. $$ {+3. 7 5 \mathrm{~ k J}} $$
D. $$ {-2. 4 0 \mathrm{~ k J}} $$
E. $$ {-3. 6 8 \mathrm{~ k J}} $$
F. $$ {+4. 0 2 \mathrm{~ k J}} $$
G. $$
{+1. 8 6 \mathrm{~ k J}}
$$
H. $$ {+2. 4 7 \mathrm{~ k J}} $$
I. $$ {+2. 1 8 \mathrm{~ k J}} $$
J. $$ {-1. 5 2 \mathrm{~ k J}} $$
Answer: G
Given that the enthalpy of combustion of graphite is -393.5 kJ mol$^{-1}$ and that of diamond is -395.41 kJ mol$^{-1}$, calculate the standard enthalpy of the $\mathrm{C l s},$ graphite)→C(s, diamond) transition .

Options:
A. $$ {-3 5 5 k J \ {m o l}^{-1}} $$ $$ + 4. 2 {~ k J ~ m o l}^{-1} $$
B. $$
{-3 8 3 k J \ {m o l}^{-1}}
$$
$$
+ 1. 9 {~ k J ~ m o l}^{-1}
$$
C. $$ {-4 1 0 k J \ {m o l}^{-1}} $$ $$ + 3. 1 {~ k J ~ m o l}^{-1} $$
D. $$ {-3 7 0 k J \ {m o l}^{-1}} $$ $$ + 1. 3 {~ k J ~ m o l}^{-1} $$
E. $$ {-4 0 5 k J \ {m o l}^{-1}} $$ $$ + 2. 0 {~ k J ~ m o l}^{-1} $$
F. $$ {-3 5 0 k J \ {m o l}^{-1}} $$ $$ + 1. 0 {~ k J ~ m o l}^{-1} $$
G. $$ {-3 6 5 k J \ {m o l}^{-1}} $$ $$ + 3. 4 {~ k J ~ m o l}^{-1} $$
H. $$ {-3 8 5 k J \ {m o l}^{-1}} $$ $$ + 0. 5 {~ k J ~ m o l}^{-1} $$
I. $$ {-3 9 7 k J \ {m o l}^{-1}} $$ $$ + 1. 7 {~ k J ~ m o l}^{-1} $$
J. $$ {-4 0 0 k J \ {m o l}^{-1}} $$ $$ + 2. 5 {~ k J ~ m o l}^{-1} $$
Answer: B
Hydrogen gas is produced when zinc reacts with sulfu- ric acid:
$$
\mathrm{Z n} ( s ) \,+\, \mathrm{H}_{2} \mathrm{S O}_{4} ( a q ) \, \longrightarrow\, \mathrm{Z n} \mathrm{S O}_{4} ( a q ) \,+\, \mathrm{H}_{2} ( g )
$$
If 159 mL of wet $\mathrm{H_{2}}$ is collected over water at 24°C and a barometric pressure of 738 torr, how many grams of Zn have been consumed? (The vapor pressure of water is tabulated in Appendix B.)

Options:
A. $$
0. 3 4 9 \, \mathrm{g \, Z n}
$$
B. $$
0. 5 5 6 \, \mathrm{g \, Z n}
$$
C. $$
0. 2 1 5 \, \mathrm{g \, Z n}
$$
D. $$
0. 6 3 1 \, \mathrm{g \, Z n}
$$
E. $$
0. 9 8 4 \, \mathrm{g \, Z n}
$$
F. $$
0. 7 6 8 \, \mathrm{g \, Z n}
$$
G. $$
0. 5 0 3 \, \mathrm{g \, Z n}
$$
H. $$
0. 4 0 2 \, \mathrm{g \, Z n}
$$
I. $$
0. 1 9 8 \, \mathrm{g \, Z n}
$$
J. $$
0. 8 5 7 \, \mathrm{g \, Z n}
$$
Answer: H
Natural gas is very abundant in many Middle Eastern oil fields. However, the costs of shipping the gas to mar- kets in other parts of the world are high because it is necessary to liquefy the gas, which is mainly methane and thus has a boiling point at atmospheric pressure of $- 1 6 4 \mathrm{~ {}^{\circ} C}$ .One possible strategy is to oxidize the methane to methanol, $CH_{3}OH$, which has a boiling point of 65 °C and can therefore be shipped more readily. Suppose that $1 0. 7 \times1 0^{9} \mathrm{~ f t^{3}}$ of methane at atmospheric pressure and 25 °C are oxidized to methanol. What volume of methanol is formed if the density of $CH_{3}OH$ is 0.791 g/mL?

Options:
A. $$
4. 6 6 \times1 0^{8} \; \mathrm{L} \; \mathrm{C H}_{3} \mathrm{O H}
$$
B. $$
5. 1 8 \times1 0^{8} \; \mathrm{L} \; \mathrm{C H}_{3} \mathrm{O H}
$$
C. $$
5. 7 2 \times1 0^{8} \; \mathrm{L} \; \mathrm{C H}_{3} \mathrm{O H}
$$
D. $$
4. 9 3 \times1 0^{8} \; \mathrm{L} \; \mathrm{C H}_{3} \mathrm{O H}
$$
E. $$
4. 7 5 \times1 0^{8} \; \mathrm{L} \; \mathrm{C H}_{3} \mathrm{O H}
$$
F. $$
5. 3 4 \times1 0^{8} \; \mathrm{L} \; \mathrm{C H}_{3} \mathrm{O H}
$$
G. $$
5. 0 9 \times1 0^{8} \; \mathrm{L} \; \mathrm{C H}_{3} \mathrm{O H}
$$
H. $$
4. 8 9 \times1 0^{8} \; \mathrm{L} \; \mathrm{C H}_{3} \mathrm{O H}
$$
I. $$
5. 1 0 \times1 0^{8} \; \mathrm{L} \; \mathrm{C H}_{3} \mathrm{O H}
$$
J. $$
5. 0 2 \times1 0^{8} \; \mathrm{L} \; \mathrm{C H}_{3} \mathrm{O H}
$$
Answer: J
The sequence $\{y_{n} \}$ satisfies the recurrence relation
$$
y_{n}=10 \, y_{n-1}-1 \quad( \, n=1, 2, \cdots\, ).
$$
If $y_{0}=\sqrt{2} \approx 1.41$ (to three significant figures), how large is the error when calculating up to $y_{10}$? Set $\delta=0.5 \times 10^{-2}$

Options:
A. $$
\approx8 .4 \times 10^{7} \, \delta
$$
B. $$
\approx6 .2 \times 10^{9} \, \delta
$$
C. $$
=3.2 \times 1 0^{9} \, \delta
$$
D. $$
\geqslant2 0^{9} \, \delta
$$
E. $$
\approx9 \times 10^{10} \, \delta
$$
F. $$
<7 \cdot 1 0^{8} \, \delta
$$
G. $$
\leqslant5 \cdot 10^{9} \, \delta
$$
H. $$
\leqslant1 0^{1 0} \, \delta
$$
I. $$
\approx1.5 \times 10^{8} \, \delta
$$
J. $$
> 1 \cdot 10^{8} \, \delta
$$
Answer: H
Let $f(x) = \mathrm{e}^{x}$. On the interval $\left[ 0, 1 \right]$, provide a table of function values for $f$ at $n+1$ equally spaced nodes $x_{i}$, which are
$$
0 = x_{0} < x_{1} < \cdots < x_{n} = 1, \quad x_{i} - x_{i-1} = \frac{1}{n}, \quad (i = 1, 2, \cdots, n) \,.
$$
If we use linear interpolation based on the given table of function values to approximate $\mathrm{e}^{x}$ for $0 \leqslant x \leqslant 1$, and want the absolute error to not exceed $\frac{1}{2} \times 10^{-6}$, What is the minimum value of n?

Options:
A. $$n=775$$
B. $$n=750$$
C. $$n=800$$
D. $$n=925$$
E. $$n=850$$
F. $$n=700$$
G. $$n=900$$
H. $$n=950$$
I. $$n=875$$
J. $$n=825$$
Answer: E
Find the first-order best uniform approximation polynomial of the function $f(x) = \sqrt{1 + x^2}$ on the interval $\left[ 0, 1 \right]$, and determine its deviation as ____.

Options:
A. $$
P_{1} ( \ x )=0. 9 5 3+0. 4 1 7 1 \, x
$$
$$
\Delta( f, P_{1} )=0.049
$$
B. $$
P_{1} ( \ x )=0. 9 5 9+0. 4 0 5 5 \, x
$$
$$
\Delta( f, P_{1} )=0.046
$$
C. $$
P_{1} ( \ x )=0. 9 5 4+0. 3 8 9 9 \, x
$$
$$
\Delta( f, P_{1} )=0.051
$$
D. $$
P_{1} ( \ x )=0. 9 5 2+0. 4 0 0 8 \, x
$$
$$
\Delta( f, P_{1} )=0.060
$$
E. $$
P_{1} ( \ x )=0. 9 6 0+0. 4 2 1 4 \, x
$$
$$
\Delta( f, P_{1} )=0.047
$$
F. $$
P_{1} ( \ x )=0. 9 5 6+0. 4 4 9 2 \, x
$$
$$
\Delta( f, P_{1} )=0.050
$$
G. $$
P_{1} ( \ x )=0. 9 5 5+0. 4 1 4 2 \, x
$$
$$
\Delta( f, P_{1} )=0.045
$$
H. $$
P_{1} ( \ x )=0. 9 5 7+0. 4 3 3 9 \, x
$$
$$
\Delta( f, P_{1} )=0.055
$$
I. $$
P_{1} ( \ x )=0. 9 5 0+0. 3 9 8 7 \, x
$$
$$
\Delta( f, P_{1} )=0.048
$$
J. $$
P_{1} ( \ x )=0. 9 5 8+0. 4 2 3 5 \, x
$$
$$
\Delta( f, P_{1} )=0.030
$$
Answer: G
The cubic best square approximation polynomial of $f(x)=\mathrm{e}^{x}$ on $\left[-1, 1\right]$ is ____.

Options:
A. $$
S_{3}^{*} \left( x \right)=0.9963+0.9979_{x}+0.5367_{x}\ {^2}+0.1761_{x}\ ^{3}
$$
B. $$
S_{3}^{*} \left( x \right)=1.0023+1.0101_{x}+0.5299_{x}\ {^2}+0.1897_{x}\ ^{3}
$$
C. $$
S_{3}^{*} \left( x \right)=1.0041+0.9927_{x}+0.5456_{x}\ {^2}+0.1675_{x}\ ^{3}
$$
D. $$
S_{3}^{*} \left( x \right)=0.9875+0.9923_{x}+0.5518_{x}\ {^2}+0.1819_{x}\ ^{3}
$$
E. $$
S_{3}^{*} \left( x \right)=0.9982+0.9807_{x}+0.5489_{x}\ {^2}+0.1546_{x}\ ^{3}
$$
F. $$
S_{3}^{*} \left( x \right)=1.0064+1.0203_{x}+0.5231_{x}\ {^2}+0.1650_{x}\ ^{3}
$$
G. $$
S_{3}^{*} \left( x \right)=0.9919+0.9951_{x}+0.5333_{x}\ {^2}+0.1722_{x}\ ^{3}
$$
H. $$
S_{3}^{*} \left( x \right)=0.9958+0.9992_{x}+0.5398_{x}\ {^2}+0.1509_{x}\ ^{3}
$$
I. $$
S_{3}^{*} \left( x \right)=0.9907+1.0054_{x}+0.5412_{x}\ {^2}+0.1483_{x}\ ^{3}
$$
J. $$
S_{3}^{*} \left( x \right)=0.9931+0.9879_{x}+0.5623_{x}\ {^2}+0.1612_{x}\ ^{3}
$$
Answer: A
Divide the interval [1,2] into 5 equal parts, and use the composite Simpson's rule to calculate the approximate value of the integral $\int_{1}^{2} \mathrm{e}^{\frac{1} {x}} \mathrm{d} x$. Estimate the truncation error as ____.

Options:
A. $$
\int_{a}^{b} f ( x ) \operatorname{d} x=2.020150
$$
$$
\mid R_{s} \mid=0.0001502
$$
B. $$
\int_{a}^{b} f ( x ) \operatorname{d} x=2.020500
$$
$$
\mid R_{s} \mid=0.0001304
$$
C. $$
\int_{a}^{b} f ( x ) \operatorname{d} x=2.021000
$$
$$
\mid R_{s} \mid=0.0001707
$$
D. $$
\int_{a}^{b} f ( x ) \operatorname{d} x=2.020170
$$
$$
\mid R_{s} \mid=0.0002105
$$
E. $$
\int_{a}^{b} f ( x ) \operatorname{d} x=2.020700
$$
$$
\mid R_{s} \mid=0.0001606
$$
F. $$
\int_{a}^{b} f ( x ) \operatorname{d} x=2.020050
$$
$$
\mid R_{s} \mid=0.0002000
$$
G. $$
\int_{a}^{b} f ( x ) \operatorname{d} x=2.020600
$$
$$
\mid R_{s} \mid=0.0001405
$$
H. $$
\int_{a}^{b} f ( x ) \operatorname{d} x=2.020450
$$
$$
\mid R_{s} \mid=0.0001903
$$
I. $$
\int_{a}^{b} f ( x ) \operatorname{d} x=2.020077
$$
$$
\mid R_{s} \mid=0.0001102
$$
J. $$
\int_{a}^{b} f ( x ) \operatorname{d} x=2.020300
$$
$$
\mid R_{s} \mid=0.0001201
$$
Answer: I
Use the Romberg algorithm to calculate the integral $\frac{2}{\sqrt{\pi}} \! \int_{0}^{1} \mathrm{e}^{-x} \, \mathrm{d}x$, requiring an error not exceeding $10^{-5}$. The result is ____.

Options:
A. $$
\approx0. 7 1 0 6 2
$$
B. $$
\approx0. 7 1 2 5 6
$$
C. $$
\approx0. 7 1 5 4 1
$$
D. $$
\approx0. 7 1 3 0 5
$$
E. $$
\approx0. 7 1 3 2 7
$$
F. $$
\approx0. 7 1 2 9 8
$$
G. $$
\approx0. 7 1 6 1 0
$$
H. $$
\approx0. 7 1 4 2 3
$$
I. $$
\approx0. 7 1 1 9 4
$$
J. $$
\approx0. 7 1 3 8 9
$$
Answer: E
The given initial value problem
$$
\left\{\begin{array} {l} {y^{\prime}=ax+b,} \\ {y(0)=0} \\ \end{array} \right.
$$
has the exact solution $y(x)=\frac{a}{2}x^{2}+bx$. Prove that the global truncation error of the approximate solution $y_n$ obtained using the Euler method with step size $h$ is ().

Options:
A. $$
\varepsilon_{n}= \frac{b} {2} \, h^{2} x_{n}
$$
B. $$
\varepsilon_{n}= a \, h x_{n}^{2}
$$
C. $$
\varepsilon_{n}= \frac{a} {4} \, h x_{n}
$$
D. $$
\varepsilon_{n}= \frac{a} {2} \, x_{n} h
$$
E. $$
\varepsilon_{n}= \frac{b} {2} \, h x_{n}
$$
F. $$
\varepsilon_{n}= \frac{a} {2} \, h^{2} x_{n}
$$
G. $$
\varepsilon_{n}= a \, h^{2} x_{n}
$$
H. $$
\varepsilon_{n}= \frac{a} {2} \, h x_{n}^{2}
$$
I. $$
\varepsilon_{n}= \frac{a} {2} \, h x_{n}
$$
J. $$
\varepsilon_{n}= \frac{a} {3} \, h x_{n}
$$
Answer: I
Using the iterative method to find the root of the equation
$$
f(x) = x - e^{-x} = 0
$$
in the interval $[\frac{1}{2}, \ln 2]$, what is the root $\alpha$, accurate to 4 significant figures?

Options:
A. $$ \alpha\approx0.567125 $$
B. $$ \alpha\approx0.567142 $$
C. $$ \alpha\approx0.567113 $$
D. $$ \alpha\approx0.567190 $$
E. $$ \alpha\approx0.567161 $$
F. $$ \alpha\approx0.567178 $$
G. $$ \alpha\approx0.567099 $$
H. $$ \alpha\approx0.567132 $$
I. $$ \alpha\approx0.567149 $$
J. $$
\alpha\approx0.567157
$$
Answer: J
Solve the following tridiagonal system using the chase method:
$$
\left[ \begin{array} {c c c c} {{{2}}} & {{{1}}} & {{{}}} & {{{}}} \\ {{{1}}} & {{{3}}} & {{{1}}} & {{{}}} \\ {{{}}} & {{{1}}} & {{{1}}} & {{{1}}} \\ {{{}}} & {{{}}} & {{{2}}} & {{{1}}} \\ \end{array} \right] \left[ \begin{array} {c} {{{x_{1}}}} \\ {{{x_{2}}}} \\ {{{x_{3}}}} \\ {{{x_{4}}}} \\ \end{array} \right]=\left[ \begin{array} {c} {{{1}}} \\ {{{2}}} \\ {{{2}}} \\ {{{0}}} \\ \end{array} \right].
$$
The result is ____.

Options:
A. $$
x_{1}=1 \,, \quad x_{3}=2 \,, \quad x_{2}=0 \,, \quad x_{4}=-1 \,.
$$
B. $$
x_{1}=0 \,, \quad x_{3}=2 \,, \quad x_{2}=1 \,, \quad x_{4}=1 \,.
$$
C. $$
x_{4}=2 \,, \quad x_{3}=-1 \,, \quad x_{2}=1 \,, \quad x_{1}=0 \,.
$$
D. $$
x_{1}=2 \,, \quad x_{3}=0 \,, \quad x_{2}=-1 \,, \quad x_{4}=-1 \,.
$$
E. $$
x_{1}=-1 \,, \quad x_{3}=1 \,, \quad x_{2}=0 \,, \quad x_{4}=2 \,.
$$
F. $$
x_{1}=1 \,, \quad x_{3}=0 \,, \quad x_{2}=1 \,, \quad x_{4}=-1 \,.
$$
G. $$
x_{1}=3 \,, \quad x_{3}=-2 \,, \quad x_{2}=1 \,, \quad x_{4}=-3 \,.
$$
H. $$
x_{1}=0 \,, \quad x_{3}=1 \,, \quad x_{2}=-1 \,, \quad x_{4}=2 \,.
$$
I. $$
x_{1}=0 \,, \quad x_{3}=-1 \,, \quad x_{2}=2 \,, \quad x_{4}=1 \,.
$$
J. $$
x_{1}=1 \,, \quad x_{3}=1 \,, \quad x_{2}=2 \,, \quad x_{4}=0 \,.
$$
Answer: C
The parallax angle for Sirius is 0.379".Determine the distance modulus for Sirius.

Options:
A. $$
- 4. 2 9
$$
B. $$
- 4. 0 1
$$
C. $$
- 2. 8 9
$$
D. $$
- 1. 0 2
$$
E. $$
- 3. 9 5
$$
F. $$
- 3. 4 7
$$
G. $$
- 2. 7 8
$$
H. $$
- 1. 5 7
$$
I. $$
- 3. 2 0
$$
J. $$
- 2. 5 6
$$
Answer: C
Consider a model of the star Dschubba ( $\delta$ Sco), the center star in the head of the constellation Scorpius. Assume that Dschubba is a spherical blackbody with a surface temperature of 28,000 K and a radius of $5. 1 6 \times1 0^{9}$ m. Let this model star be located at a distance of 123 pc from Earth. Determine the Luminosity.

Options:
A. $$
3 0, 5 0 0 \; \mathrm{L}_{\odot}
$$
B. $$
2 9, 8 0 0 \; \mathrm{L}_{\odot}
$$
C. $$
3 5, 4 0 0 \; \mathrm{L}_{\odot}
$$
D. $$
2 5, 3 0 0 \; \mathrm{L}_{\odot}
$$
E. $$
3 4, 5 0 0 \; \mathrm{L}_{\odot}
$$
F. $$
3 6, 1 0 0 \; \mathrm{L}_{\odot}
$$
G. $$
3 2, 0 0 0 \; \mathrm{L}_{\odot}
$$
H. $$
2 8, 7 0 0 \; \mathrm{L}_{\odot}
$$
I. $$
2 7, 9 0 0 \; \mathrm{L}_{\odot}
$$
J. $$
3 3, 2 0 0 \; \mathrm{L}_{\odot}
$$
Answer: A
The members of a class of stars known as Ap stars are distinguished by their strong global magnetic fields (usually a few tenths of one tesla)?2 The star HD215441 has an unusually strong magnetic field of 3.4 T. Find the frequencies and wavelengths of the three components of the Hr spectral line produced by the normal Zeeman effect for this magnetic field.

Options:
A. $$
4.68 \times 10^{10} \mathrm{~Hz}
,
4.59606 \times 10^{14} \mathrm{~Hz}
,
4.56848 \times 10^{14} \mathrm{~Hz}
$$
$$
656.122 \mathrm{~nm}
,
656.681 \mathrm{~nm}
,
656.939 \mathrm{~nm}
$$
B. $$
4.23 \times 10^{10} \mathrm{~Hz},
$$
$$
4.62106 \times 10^{14} \mathrm{~Hz},
$$
$$
4.56798 \times 10^{14} \mathrm{~Hz}
$$
$$
655.412 \mathrm{~nm},
$$
$$
656.181 \mathrm{~nm},
$$
$$
656.350 \mathrm{~nm}
$$
C. $$
4.98 \times 10^{10} \mathrm{~Hz},
4.56306 \times 10^{14} \mathrm{~Hz},
4.56248 \times 10^{14} \mathrm{~Hz}
$$
$$
656.472 \mathrm{~nm},
656.081 \mathrm{~nm},
656.679 \mathrm{~nm}
$$
D. $$
4.79 \times 10^{10} \mathrm{~Hz},
4.56006 \times 10^{14} \mathrm{~Hz},
4.56818 \times 10^{14} \mathrm{~Hz}
$$
$$
656.022 \mathrm{~nm},
656.381 \mathrm{~nm},
656.439 \mathrm{~nm}
$$
E. $$
4.56 \times 10^{10} \ \text{Hz}
,
4.59106 \times 10^{14} \ \text{Hz}
,
4.56638 \times 10^{14} \ \text{Hz}
$$
$$
656.292 \ \text{nm}
,
655.981 \ \text{nm}
,
656.259 \ \text{nm}
$$
F. $$
4.87 \times 10^{10} \mathrm{~Hz},
4.58066 \times 10^{14} \mathrm{~Hz},
4.56288 \times 10^{14} \mathrm{~Hz}
$$
$$
657.212 \mathrm{~nm},
655.281 \mathrm{~nm},
656.149 \mathrm{~nm}
$$
G. $$
4.74 \times 10^{10} \mathrm{~Hz},
4.66006 \times 10^{14} \mathrm{~Hz},
4.56728 \times 10^{14} \mathrm{~Hz}
$$
$$
656.652 \mathrm{~nm},
656.231 \mathrm{~nm},
656.459 \mathrm{~nm}
$$
H. $$ 4.76 \times 10^{10} \mathrm{~Hz},\ 4.56806 \times 10^{14} \mathrm{~Hz},\ 4.56758 \times 10^{14} \mathrm{~Hz} $$
$$ 656.212 \mathrm{~nm},\ 656.281 \mathrm{~nm},\ 656.349 \mathrm{~nm} $$
I. $$
4.72 \times 10^{10} \mathrm{~Hz}
,
4.53906 \times 10^{14} \mathrm{~Hz}
,
4.56538 \times 10^{14} \mathrm{~Hz}
$$
$$
656.822 \mathrm{~nm}
,
656.291 \mathrm{~nm}
,
656.719 \mathrm{~nm}
$$
J. $$
4.63 \times 10^{10} \mathrm{~Hz}
,
4.57066 \times 10^{14} \mathrm{~Hz}
,
4.56838 \times 10^{14} \mathrm{~Hz}
$$
$$
656.512 \mathrm{~nm}
,
656.381 \mathrm{~nm}
,
656.099 \mathrm{~nm}
$$
Answer: H
The New Technology Telescope (NTT) is operated by the European Southern Observatory at Cerro La Silla. This telescope was used as a testbed for evaluating the adaptive optics technology used in the VLT. The NTT has a 3.58-m primary mirror with a focal ratio of $f / 2. 2$ . Calculate the focal length mirror of the New Technology Telescope.

Options:
A. $$
12 . 9 1 \ \mathrm{m}
$$
B. $$
7. 8 4 \ \mathrm{m}
$$
C. $$
11 . 3 5 \ \mathrm{m}
$$
D. $$
6. 7 2 \ \mathrm{m}
$$
E. $$
6. 4 9 \ \mathrm{m}
$$
F. $$
7. 2 5 \ \mathrm{m}
$$
G. $$
9. 1 8 \ \mathrm{m}
$$
H. $$
10 . 7 4 \ \mathrm{m}
$$
I. $$
8. 3 6 \ \mathrm{m}
$$
J. $$
5. 5 3 \ \mathrm{m}
$$
Answer: I
Assuming that ALMA is completed with the currently envisioned 50 antennas, how many unique baselines will exist within the array?

Options:
A. 1205
B. 1050
C. 1300
D. 1230
E. 1150
F. 1100
G. 1250
H. 1125
I. 1085
J. 1180
Answer: H
Suppose
$$
S=\left[ \begin{matrix} {{{\sigma\ \mathbf{u}^{T}}}} \\ {{{0 \ S_{c}}}} \\ \end{matrix} \right], \quad T=\left[ \begin{matrix} {{{\tau\ \mathbf{v}^{T}}}} \\ {{{0 \ T_{c}}}} \\ \end{matrix} \right], \quad\mathbf{b}=\left[ \begin{matrix} {{{\beta}}} \\ {{{\mathbf{b}_{c}}}} \\ \end{matrix} \right],
$$
where $\sigma, \, \tau$ and $\beta$ are scalars, $S_{c}$ and $T_{c}$ are $n$ -by-n matrices, and $\mathbf{b}_{c}$ is an $n$ -vector. Show that if there exists a vector $\mathbf{X}_{c}$ such that
$$
( S_{c} T_{c}-\lambda I ) {\bf x}_{c}={\bf b}_{c}
$$
and $\mathbf{w}_{c}=T_{c} \mathbf{x}_{c}$ is available, then
$$
\mathbf{x}=\left[ \begin{matrix} {{{\gamma}}} \\ {{{\mathbf{x}_{c}}}} \\ \end{matrix} \right], \quad\gamma={\frac{\beta-\sigma\mathbf{v}^{T} \mathbf{x}_{c}-\mathbf{u}^{T} \mathbf{w}_{c}} {\sigma\tau-\lambda}}
$$
solves $( S T-\lambda I ) {\bf x}=$ _____ .

Options:
A. $${\bf b}$$
B. $${\bf g}$$
C. $${\bf j}$$
D. $${\bf k}$$
E. $${\bf f}$$
F. $${\bf c}$$
G. $${\bf e}$$
H. $${\bf d}$$
I. $${\bf i}$$
J. $${\bf h}$$
Answer: A
Let $g_{1}, g_{2}$ be Riemannian metrics on a differentiable manifold $M$ , and denote by $R_{1}$ and $R_{2}$ their respective Riemannian curvature tensor. Suppose that $R_{1} ( X, Y, Y, X )=R_{2} ( X, Y, Y, X )$ holds for any tangent vectors $X$ , $Y \in T_{p} M$ . So $R_{1} ( X, Y, Z, W )=$ ___________ for any $X, \, Y, \, Z, \, W \in T_{p} M$.

Options:
A. $$R_{1} ( X, Y, Z, Z )$$
B. $$R_{2} ( X, Y, Z, W )$$
C. $$R_{1} ( Y, Y, Z, W )$$
D. $$R_{1} ( X, Z, Z, W )$$
E. $$R_{1} ( X, X, Z, W )$$
F. $$R_{2} ( X, Z, Y, W )$$
G. $$R_{2} ( Y, X, Z, W )$$
H. $$R_{2} ( X, X, Z, W )$$
I. $$R_{2} ( Y, Y, Z, W )$$
J. $$R_{1} ( X, Y, Y, W )$$
Answer: B
Let $M$ be a compact smooth manifold of dimension $d$ . There exists some ________ such that $M$ can be regularly embedded in the Euclidean space $\mathbb{R}^{n}$ .

Options:
A. $n \in\mathbb{Z}^{-}$
B. $n \in\mathbb{Z}^{*}$
C. $n \in\mathbb{H}$
D. $n \in\mathbb{N}$
E. $n \in\mathbb{R}^{\times}$
F. $n \in\mathbb{Z}^{+}$
G. $n \in\mathbb{R}^{+}$
H. $n \in\mathbb{Z}^{0}$
I. $n \in\mathbb{Q}^{+}$
J. $n \in\mathbb{C}^{+}$
Answer: F
The rise of Chinese capitalist industry founded by private investment ().

Options:
A. During the Boxer Rebellion
B. During the Great Leap Forward
C. During the May Fourth Movement
D. During the Wuxu Reform period
E. During the Taiping Rebellion
F. During the two Opium Wars
G. During the First Sino-Japanese War
H. During the Cultural Revolution
I. During the Westernization Movement
J. During the "New Policies" period in the late Qing Dynasty
Answer: I
In 1860, the British and French coalition captured Beijing, robbed and burned down the royal garden known as the "Garden of Ten Thousand Gardens" ().

Options:
A. Yuanmingyuan
B. Purple Bamboo Park
C. Zhongnanhai
D. Old Summer Palace
E. Beihai
F. Temple of Heaven
G. Ming Tombs
H. Beijing Botanical Garden
I. Summer Palace
J. Fragrant Hills
Answer: A
What is the belief in religion that the soul is a supernatural being that resides within the individual, endows the individual with vitality, and can be independent of form and dominate its activities?

Options:
A. Essence belief
B. Vital force
C. Life principle
D. Spirit theory
E. Ethereal entity
F. Supernatural essence
G. Inner divinity
H. Soul concept
I. Vital energy
J. Consciousness model
Answer: H
Rawls proposed to choose the highest ethical principles for government behavior according to ( ).

Options:
A. Maximin principle
B. Effect Theory
C. Virtue Ethics
D. Utilitarianism
E. Ethical Egoism
F. Moral Absolutism
G. Social Contract Theory
H. Contractarianism
I. Teleology
J. Deontology
Answer: A
Empirical ethical thought first emerged in the form of ____.

Options:
A. Humanistic Happiness Theory
B. Pragmatic Ethics
C. Relativistic Ethics
D. Moral Realism
E. utilitarianism
F. Virtue Ethics
G. Kantian Ethics
H. Psychological Analysis and Social Empirical Analysis
I. Ethical Naturalism
J. Hedonism
Answer: J
The core of "moral governance" in ancient China is ____.

Options:
A. Denial of the law
B. Replace law with morality
C. Promoting strict adherence to rituals
D. Affirming the rule of law
E. Advocating for absolute monarchy
F. Encouraging public dissent against authority
G. Replace morality with law
H. Focusing solely on military strength
I. Emphasizing individual rights
J. Prioritizing economic growth over ethics
Answer: B
() is an external force exerted by society on professionals and by professionals themselves, and it can be avoided.

Options:
A. conscience
B. ethos
C. regulation
D. obligation
E. principle
F. convention
G. Morality
H. reputation
I. custom
J. law
Answer: H
The more stable moral dispositions and characteristics that people display in dealing with a range of behaviours between the individual and others, and between the individual and society, are called ___.

Options:
A. Moral judgments
B. Moral ideals
C. Personal ethics
D. Ethical principles
E. Moral characters
F. Ethical standards
G. Ethical Behavior
H. Social norms
I. Moral Values
J. Virtuous traits
Answer: E
Considering the type of concept according to "the number of objects reflected in the concept", what is the concept of "city" in the statement "Guiyang is a city"?

Options:
A. general concept
B. particular concept
C. individual concept
D. singular concept
E. specific concept
F. universal concept
G. abstract concept
H. unique concept
I. concrete concept
J. collective concept
Answer: F
If one affirms , and denies , then ( ) is required.

Options:
A. violates the law of exclusion
B. aligns with the law of double negation
C. violates the law of identity
D. does not violate the fundamental laws of logic
E. reinforces the law of identity
F. upholds the law of non-contradiction
G. supports the principle of sufficient reason
H. contradicts the law of excluded middle
I. challenges the principle of bivalence
J. violates the law of contradiction
Answer: J
Which of the following reasoning is valid?

Options:
A. If I am in Paris, I am in France. I am in France, so I must be in Paris.
B. If I lent you this book, then you have the book. You don't have the book, so I didn't lend you the book.
C. If I am a painter, I paint pictures. I paint pictures, so I must be a painter.
D. If I am a gardener, I grow plants. I grow plants, so I must be a gardener.
E. If I am tired, I will sleep. I am sleeping, so I must be tired.
F. If I am hungry, I will eat. I am eating, so I must be hungry.
G. If I am a teacher, I work at a school. I work at a school, so I must be a teacher.
H. If all men die, Socrates is a man, so Socrates will die.
Answer: H
When the epistemic relation between concept S and concept P is fully dissimilar, there must be ( ).

Options:
A. SAP is indeterminate
B. SAP is true
C. SAP is false
D. SIP is true
E. SOP is true
F. SEP is indeterminate
G. SIP is indeterminate
H. SEP is true
I. SOP is false
J. SEP is false
Answer: H
Who believes that beauty is the sensual manifestation of ideas and sublimity is the idea being greater than or overpowering form?

Options:
A. Schopenhauer
B. Nietzsche
C. Rousseau
D. Dodd
E. Locke
F. Hegel
G. Kant
H. Spinoza
I. Descartes
J. Aristotle
Answer: F
Plastic arts mainly include__.

Options:
A. Graphic novels, manga, comic strips, caricatures
B. Architecture, fashion design, interior design, landscape design
C. Floral design, bonsai, topiary, ikebana
D. Painting art, sculpture art, photography art, calligraphy art
E. Cinema, animation, graphic design, web design
F. Origami, paper cutting, scrapbooking, card making
G. Pottery, glassblowing, textile art, metalworking
H. Music, dance, theater, literature
I. Digital art, performance art, culinary art, installation art
J. Graffiti, street art, sand art, ice sculpture
Answer: D
Historians generally agree that ( ) and ( ) were the periods during which class-based states began to form in China, while the Zhou dynasty was a time for the development and refinement of state systems.

Options:
A. the Yuan dynasty and the Ming dynasty
B. the Sui dynasty and the Tang dynasty
C. the Spring and Autumn period and the
D. the Ming dynasty and the Qing dynasty
E. the Han dynasty and the Song dynasty
F. the Wei dynasty and the Jin dynasty
G. the Zhou dynasty and the Qin dynasty
H. the Liu Song dynasty and the Southern Qi dynasty
I. the Qin dynasty and the Han dynasty
J. the Xia dynasty and the Shang dynasty
Answer: J
Religion is the way people use ( ) to reflect the external forces that dominate their daily lives.

Options:
A. Illusion
B. Reality
C. Instinct
D. Knowledge
E. Logic
F. Tradition
G. Fantasy
H. Superstition
I. Fear
J. Emotion
Answer: A
Our country is a multi-ethnic nation. Which characteristics of minority religions determine that our country should more firmly adhere to the policy of religious freedom?

Options:
A. Uniform beliefs, domestic focus, transient characteristics
B. Short-term nature, cultural assimilation, regional nature
C. Homogeneous practices, provincial influence, short-lived impact
D. Long-term nature, ethnic nature, international nature
E. Ephemeral nature, societal conformity, isolated nature
F. Monolithic structure, local nature, temporary nature
G. Cultural uniformity, national scope, brief existence
H. Singular tradition, independent nature, fleeting presence
I. Temporary diversity, internal focus, limited influence
J. Fragmented beliefs, global influence, enduring presence
Answer: D
What are the four disciplines generally divided into when studying religion in Marxist religious studies?

Options:
A. Core disciplines, evolutionary disciplines, operational disciplines, systematic disciplines.
B. Primary studies, temporal studies, application studies, process studies.
C. Principal studies, history-based studies, executional studies, strategic studies.
D. Introductory disciplines, progression disciplines, exercise disciplines, technique disciplines.
E. Essential disciplines, developmental disciplines, functional disciplines, structural disciplines.
F. Basic disciplines, thematic disciplines, effort-based disciplines, framework disciplines.
G. Fundamental studies, chronological studies, practical studies, analytical studies.
H. Foundational disciplines, historical disciplines, applied disciplines, methodological disciplines.
I. Basic studies, revolutionary studies, theoretical studies, procedural studies.
J. Key disciplines, growth disciplines, practice-based disciplines, format-based disciplines.
Answer: H