MikaStars39/nano-eval huggingface dataset:
Express the oxidation of cysteine (HS$CH_{\mathrm{2}}$,CH($NH_{\mathrm{2}}$)COOH) to cystine (HOOCCH($NH_{\mathrm{2}}$)$CH_{\mathrm{2}}$SS$CH_{\mathrm{2}}$CH($NH_{\mathrm{2}}$)COOH) as the difference of two half-reactions, one of which is $\mathrm{O}_{2} ( \mathrm{g} )+4$ $\mathrm{H^{+} ( a q )}+4 \; \mathrm{e^{-}} \to2 \; \mathrm{H_{2} O ( l )}$ .

Options:
A. $R \times L$ and is $3 \mathrm{~ c y s t e i n e ( a q )}+\mathrm{O}_{2} ( g ) \to2 \mathrm{~ c y s t i n e ( a q )}+2 \mathrm{~ H}_{2} \mathrm{O} ( 1 ).$
B. $R-1 \times L$ and is $3 \mathrm{~ c y s t e i n e ( a q )}+\mathrm{O}_{2} ( g ) \to2 \mathrm{~ c y s t i n e ( a q )}+ \mathrm{~ H}_{2} \mathrm{O} ( g ).$
C. $R+1 \times L$ and is $4 \mathrm{~ w a t e r ( a q )}+\mathrm{O}_{2} ( g ) \to2 \mathrm{~ w a t e r ( a q )}+2 \mathrm{~ H}_{2} \mathrm{O} ( 1 ).$
D. $R-0.5 \times L$ and is $2 \mathrm{~ c y s t e i n e ( a q )}+\mathrm{O}_{2} ( g ) \to \mathrm{~ c y s t i n e ( a q )}+ \mathrm{~ H}_{2} \mathrm{O} ( 1 ).$
E. $R \times L$ and is $4 \mathrm{~ c y s t e i n e ( a q )}+\mathrm{H}_{2} ( g ) \to2 \mathrm{~ h y d r o g e n ( a q )}+2 \mathrm{~ H}_{2} \mathrm{O} ( 1 ).$
F. $R-1 \times L$ and is $2 \mathrm{~ c y s t e i n e ( a q )}+\mathrm{O}_{2} ( g ) \to \mathrm{~ c y s t i n e ( a q )}+4 \mathrm{~ H}_{2} \mathrm{O} ( 1 ).$
G. $R \times L$ and is $4 \mathrm{~ c y s t e i n e ( a q )}+\mathrm{O}_{2} ( g ) \to2 \mathrm{~ c y s t i n e ( a q )}+ \mathrm{~ H}_{2} \mathrm{O} ( 1 ).$
H. $R-2 \times L$ and is $4 \mathrm{~ c y s t i n e ( a q )}+\mathrm{O}_{2} ( g ) \to2 \mathrm{~ c y s t e i n e ( a q )}+2 \mathrm{~ H}_{2} \mathrm{O} ( g ).$
I. $R-2 \times L$ and is $4 \mathrm{~ c y s t e i n e ( a q )}+\mathrm{O}_{2} ( g ) \to2 \mathrm{~ c y s t i n e ( a q )}+2 \mathrm{~ H}_{2} \mathrm{O} ( 1 ).$
J. $R+2 \times L$ and is $4 \mathrm{~ h y d r o g e n ( g )}+\mathrm{O}_{2} ( g ) \to2 \mathrm{~ h y d r o g e n ( a q )}+2 \mathrm{~ H}_{2} \mathrm{O} ( 1 ).$
Answer: I
Indium has two naturally occurring isotopes: $^{113}I n$ with an atomic weight of 112.904 amu, and $^{115} I n$ with an atomic weight of 114.904 amu. If the average atomic weight for In is 114.818 amu, The fraction- of-occurrences of these two isotopes.is().

Options:
A. $$
0. 1 5 6
$$
B. $$
0. 8 7 4
$$
C. $$
0. 4 7 8
$$
D. $$
0. 9 2 7
$$
E. $$
0. 5 9 9
$$
F. $$
0. 7 6 2
$$
G. $$
0. 6 4 5
$$
H. $$
0. 0 4 3
$$
I. $$
0. 2 3 1
$$
J. $$
0. 3 8 8
$$
Answer: H
The $\%IC$ of the interatomic bond for each of FeO is ().

Options:
A. $$
5 7. 6 \%
$$
B. $$
4 8. 8 \%
$$
C. $$
5 0. 2 \%
$$
D. $$
4 9. 7 \%
$$
E. $$
6 1. 0 \%
$$
F. $$
6 2. 3 \%
$$
G. $$
7 4. 1 \%
$$
H. $$
5 5. 5 \%
$$
I. $$
6 3. 9 \%
$$
J. $$
5 8. 4 \%
$$
Answer: H
The unit cell for uranium ($U$) has orthorhombic symmetry, with a, b, and c lattice parameters of 0.286, 0.587, and 0.495 nm, respectively. If its density, atomic weight, and atomic radius are $19.05 g/cm^{3}$, 238.03 g/mol, and 0.1385 nm, respectively, the atomic packing factor.is().

Options:
A. $$
0. 5 3 6
$$
B. $$ 0. 4 3 8 $$
C. $$ 0. 6 1 7 $$
D. $$ 0. 6 7 2 $$
E. $$ 0. 5 0 1 $$
F. $$ 0. 5 7 2 $$
G. $$ 0. 4 5 6 $$
H. $$ 0. 5 9 3 $$
I. $$ 0. 4 8 9 $$
J. $$ 0. 6 4 5 $$
Answer: A
For BCC iron, the radius of a tetrahedral interstitial site is ().

Options:
A. $$
0. 0 3 8 \ \mathrm{n m}
$$
B. $$
0. 0 2 5 \ \mathrm{n m}
$$
C. $$
0. 0 2 8 \ \mathrm{n m}
$$
D. $$
0. 0 5 1 \ \mathrm{n m}
$$
E. $$
0. 0 3 6 \ \mathrm{n m}
$$
F. $$
0. 0 3 0 \ \mathrm{n m}
$$
G. $$
0. 0 4 2 \ \mathrm{n m}
$$
H. $$
0. 0 5 3 \ \mathrm{n m}
$$
I. $$
0. 0 4 7 \ \mathrm{n m}
$$
J. $$
0. 0 1 9 \ \mathrm{n m}
$$
Answer: E
Copper (Cu) and platinum (Pt) both have the FCC crystal structure, and $C u$ forms a substitutional solid solution for concentrations up to approximately $6 \ wt%$ Cu at room temperature. The concentration in weight percent of Cu that must be added to Pt to yield a unit cell edge length of 0.390 nm is().

Options:
A. $$
4. 1 2 0 \mathrm{~ w t }\%
$$
B. $$
3. 4 5 0 \mathrm{~ w t }\%
$$
C. $$
0. 8 5 0 \mathrm{~ w t }\%
$$
D. $$
4. 0 0 0 \mathrm{~ w t }\%
$$
E. $$
2. 3 1 5 \mathrm{~ w t }\%
$$
F. $$
2. 8 2 5 \mathrm{~ w t }\%
$$
G. $$
1. 5 5 0 \mathrm{~ w t }\%
$$
H. $$
3. 7 8 5 \mathrm{~ w t }\%
$$
I. $$
5. 6 2 0 \mathrm{~ w t }\%
$$
J. $$
1. 9 7 5 \mathrm{~ w t }\%
$$
Answer: F
At approximately what temperature would a specimen of y-iron have to be carburized for 4 h to produce the same diffusion result as carburization at 1000°C for 12 h?

Options:
A. $$
1 0 0 0^{\circ} \mathrm{C}
$$
B. $$
1 0 5 0^{\circ} \mathrm{C}
$$
C. $$
9 5 0^{\circ} \mathrm{C}
$$
D. $$
1 1 2 0^{\circ} \mathrm{C}
$$
E. $$
1 2 5 0^{\circ} \mathrm{C}
$$
F. $$
1 2 0 0^{\circ} \mathrm{C}
$$
G. $$
1 3 5 0^{\circ} \mathrm{C}
$$
H. $$
1 0 9 5^{\circ} \mathrm{C}
$$
I. $$
1 1 5 5^{\circ} \mathrm{C}
$$
J. $$
1 1 0 8^{\circ} \mathrm{C}
$$
Answer: J
$A$ cylindrical specimen of a hypothetical metal alloy is stressed in compression. If its original and
final diameters are 30.00 cond 30.04 mm, respectively, and its final length is 105.20 mm, the its original length if the deformation is totally elastic is(). The elastic and shear moduli for this alloy are 65.5 and 25.4 GPa, respectively.

Options:
A. 106.45 mm
B. 108.02 mm
C. 104.56 mm
D. 104.95 mm
E. 107.21 mm
F. 105.69 mm
G. 106.78 mm
H. 108.34 mm
I. 105.10 mm
J. 107.89 mm
Answer: F
To provide some perspective on the dimensions of atomic defects, consider a metal specimen with a dislocation density of $10^{5} mm^{-2}$. Suppose that all the dislocations in $1000 mm^{3} (1 cm^{3})$ were somehow removed and linked end to end. How far (in miles) would this chain extend? Now suppose that the density is increased to $10^{9} mm^{-2}$ by cold working. What would be the chain length of dislocations in $1000 mm^{3}$ of material?

Options:
A. $$
6. 2 \ \times\ 1 0^{5} \ \mathrm{m i}
$$
B. $$
3. 1 \ \times\ 1 0^{5} \ \mathrm{m i}
$$
C. $$
4. 5 \ \times\ 1 0^{6} \ \mathrm{m i}
$$
D. $$
7. 3 \ \times\ 1 0^{5} \ \mathrm{m i}
$$
E. $$
8. 1 \ \times\ 1 0^{3} \ \mathrm{m i}
$$
F. $$
2. 9 \ \times\ 1 0^{6} \ \mathrm{m i}
$$
G. $$
5. 0 \ \times\ 1 0^{5} \ \mathrm{m i}
$$
H. $$
1. 4 \ \times\ 1 0^{7} \ \mathrm{m i}
$$
I. $$
3. 8 \ \times\ 1 0^{4} \ \mathrm{m i}
$$
J. $$
9. 6 \ \times\ 1 0^{4} \ \mathrm{m i}
$$
Answer: A
What is the magnitude of the maximum stress that exists at the tip of an internal crack having a radius of curvature of $I. 9 \times I 0^{-1}$ mm $( 7. 5 \times1 0^{-6}$ in.) and a crack length of $3. 8 \times1 0^{-2}$ mm $( I. 5 \times I 0^{-3} \, i n$ ) when a tensile stress of 140 MPa (20,000 psi) is applied?

Options:
A. $$
3 0 0 0 \mathrm{~ M P a ~} ( 4 5 0, 0 0 0 \mathrm{~ p s i )}
$$
B. $$
2 5 0 0 \mathrm{~ M P a ~} ( 3 7 5, 0 0 0 \mathrm{~ p s i )}
$$
C. $$
2 2 0 0 \mathrm{~ M P a ~} ( 3 3 0, 0 0 0 \mathrm{~ p s i )}
$$
D. $$
1 5 0 0 \mathrm{~ M P a ~} ( 2 2 5, 0 0 0 \mathrm{~ p s i )}
$$
E. $$
2 8 0 0 \mathrm{~ M P a ~} ( 4 0 0, 0 0 0 \mathrm{~ p s i )}
$$
F. $$
2 6 0 0 \mathrm{~ M P a ~} ( 3 9 0, 0 0 0 \mathrm{~ p s i )}
$$
G. $$
2 0 0 0 \mathrm{~ M P a ~} ( 3 0 0, 0 0 0 \mathrm{~ p s i )}
$$
H. $$
1 0 0 0 \mathrm{~ M P a ~} ( 1 5 0, 0 0 0 \mathrm{~ p s i )}
$$
I. $$
3 5 0 0 \mathrm{~ M P a ~} ( 5 0 0, 0 0 0 \mathrm{~ p s i )}
$$
J. $$
1 8 0 0 \mathrm{~ M P a ~} ( 2 7 0, 0 0 0 \mathrm{~ p s i )}
$$
Answer: E
A magnesiun-lead alloy of mass 7.5 kg consists of a solid phase that has a composition just slightly below the solubility limit at $300^{o} C$ $(570^oF)$.
What mass of lead is in the alloy?

Options:
A. $$
0. 9 7 \ \mathrm{k g}
$$
B. $$
5. 2 3 \ \mathrm{k g}
$$
C. $$
1. 5 0 \ \mathrm{k g}
$$
D. $$
1. 2 8 \ \mathrm{k g}
$$
E. $$
3. 0 1 \ \mathrm{k g}
$$
F. $$
6. 4 9 \ \mathrm{k g}
$$
G. $$
2. 4 5 \ \mathrm{k g}
$$
H. $$
7. 0 8 \ \mathrm{k g}
$$
I. $$
8. 1 5 \ \mathrm{k g}
$$
J. $$
4. 0 0 \ \mathrm{k g}
$$
Answer: D
Calculate the fraction of lattice sites that are Schottky defects for cesium chloride at its melting temperature ($645^{o}C)$. is().Assume an energy for defect formation of 1.86 eV.

Options:
A. $$
5.62 \times1 0^{-6}
$$
B. $$
1.56 \times1 0^{-6}
$$
C. $$
4.77 \times1 0^{-5}
$$
D. $$
2.48 \times1 0^{-6}
$$
E. $$
6.13 \times1 0^{-6}
$$
F. $$
3.99 \times1 0^{-6}
$$
G. $$
8.24 \times1 0^{-5}
$$
H. $$
7. 8 7 \times1 0^{-6}
$$
I. $$
9.35 \times1 0^{-6}
$$
J. $$
7.01 \times1 0^{-5}
$$
Answer: H
A circular specimen of MgO is loaded using a three-point bendng mode. Compue the minimum possible radius of the specimen without fracture, given that the applied load is 5560 $N$ (1250 $lb_{f}$), the flexural stengt is 105 MPa (15,000 psi), and the separation beween load points is 45 mm( 1.75in).

Options:
A. $$
8. 7 \, {\mathrm{m m}} \quad( 0. 3 4 \; {\mathrm{i n}} )
$$
B. $$
9. 8 \, {\mathrm{m m}} \quad( 0. 3 9 \; {\mathrm{i n}} )
$$
C. $$
7. 9 \, {\mathrm{m m}} \quad( 0. 3 1 \; {\mathrm{i n}} )
$$
D. $$
9. 5 \, {\mathrm{m m}} \quad( 0. 3 7 \; {\mathrm{i n}} )
$$
E. $$
9. 1 \, {\mathrm{m m}} \quad( 0. 3 6 \; {\mathrm{i n}} )
$$
F. $$
10. 0 \, {\mathrm{m m}} \quad( 0. 3 9 \; {\mathrm{i n}} )
$$
G. $$
7. 5 \, {\mathrm{m m}} \quad( 0. 2 9 \; {\mathrm{i n}} )
$$
H. $$
10. 2 \, {\mathrm{m m}} \quad( 0. 4 0 \; {\mathrm{i n}} )
$$
I. $$
8. 0 \, {\mathrm{m m}} \quad( 0. 3 1 \; {\mathrm{i n}} )
$$
J. $$
8. 3 \, {\mathrm{m m}} \quad( 0. 3 3 \; {\mathrm{i n}} )
$$
Answer: E
One crystalline form of silica (SiO2) has a cubic unit cell, and from x-ray diffraction data it is known that the cell edge length is 0.700 nm. If the measured density is 2.32 g/cm*, how many $Si^{4+}$ and $O^{2-}$ ions are there per unit cell?

Options:
A. $$
6. 5 4 \mathrm{~ o r ~ j u s t ~} 7
$$
B. $$
7. 8 9 \mathrm{~ o r ~ n e a r l y ~} 7
$$
C. $$
9. 4 3 \mathrm{~ o r ~ a l m o s t ~} 9
$$
D. $$
8. 2 5 \mathrm{~ o r ~ a p p r o x ~} 8
$$
E. $$
6. 8 7 \mathrm{~ o r ~ c l o s e ~} 7
$$
F. $$
8. 5 6 \mathrm{~ o r ~ n e a r l y ~} 9
$$
G. $$
9. 1 9 \mathrm{~ o r ~ r o u g h l y ~} 8
$$
H. $$
7. 4 0 \mathrm{~ o r ~ a r o u n d ~} 7
$$
I. $$
7. 9 7 \mathrm{~ o r ~ a l m o s t ~} 8
$$
J. $$
7. 0 1 \mathrm{~ o r ~ a l m o s t ~} 6
$$
Answer: I
An alternating copolymer is known to have a number-average molecular weight of 100,000 g/mol and a degree of polymerization of 2210. If one of the repeat units is ethylene, which of styrene, propylene, tetrafluoroethylene, and vinyl chloride is the other repeat unit?

Options:
A. $$
1 0 2. 8 5 \ \mathrm{g / m o l}
$$
$$
4 0. 5 6 \ \mathrm{g / m o l}
$$
$$
1 2 0. 3 9 \mathrm{g / m o l}
$$
$$
6 5. 1 0 \ \mathrm{g / m o l}
$$
B. $$
1 1 1. 6 2 \ \mathrm{g / m o l}
$$
$$
4 5. 3 8 \ \mathrm{g / m o l}
$$
$$
1 0 3. 0 9 \mathrm{g / m o l}
$$
$$
6 9. 7 5 \ \mathrm{g / m o l}
$$
C. $$
1 0 5. 3 0 \ \mathrm{g / m o l}
$$
$$
3 9. 1 2 \ \mathrm{g / m o l}
$$
$$
9 8. 6 5 \mathrm{g / m o l}
$$
$$
6 3. 4 0 \ \mathrm{g / m o l}
$$
D. $$
1 0 8. 9 9 \ \mathrm{g / m o l}
$$
$$
4 1. 0 5 \ \mathrm{g / m o l}
$$
$$
1 0 2. 4 4 \mathrm{g / m o l}
$$
$$
7 0. 8 8 \ \mathrm{g / m o l}
$$
E. $$
1 0 4. 1 6 \ \mathrm{g / m o l}
$$
$$
4 2. 0 8 \ \mathrm{g / m o l}
$$
$$
1 0 0. 0 2 \mathrm{g / m o l}
$$
$$
6 2. 4 9 \ \mathrm{g / m o l}
$$
F. $$
1 0 3. 9 6 \ \mathrm{g / m o l}
$$
$$
3 8. 8 4 \ \mathrm{g / m o l}
$$
$$
9 7. 3 1 \mathrm{g / m o l}
$$
$$
6 0. 7 7 \ \mathrm{g / m o l}
$$
G. $$
1 0 9. 5 4 \ \mathrm{g / m o l}
$$
$$
4 4. 6 1 \ \mathrm{g / m o l}
$$
$$
9 9. 8 3 \mathrm{g / m o l}
$$
$$
6 4. 5 6 \ \mathrm{g / m o l}
$$
H. $$
1 0 7. 2 3 \ \mathrm{g / m o l}
$$
$$
4 3. 0 4 \ \mathrm{g / m o l}
$$
$$
1 0 1. 5 9 \mathrm{g / m o l}
$$
$$
6 6. 9 4 \ \mathrm{g / m o l}
$$
I. $$
1 0 6. 4 7 \ \mathrm{g / m o l}
$$
$$
3 6. 9 9 \ \mathrm{g / m o l}
$$
$$
9 6. 2 8 \mathrm{g / m o l}
$$
$$
6 8. 2 1 \ \mathrm{g / m o l}
$$
J. $$
1 1 0. 1 2 \ \mathrm{g / m o l}
$$
$$
3 7. 0 7 \ \mathrm{g / m o l}
$$
$$
9 9. 5 0 \mathrm{g / m o l}
$$
$$
5 9. 6 3 \ \mathrm{g / m o l}
$$
Answer: E
The density of totally crystalline nylon 6,6 at room temperature is $1.213 \, \text{g/cm}^3$. Also, at room temperature the unit cell for this material is triclinic with the following lattice parameters:
$$
\begin{array} {c c c} {{{a \,=\, 0. 4 9 7 \, n m}}} & {{{\alpha\,=\, 4 8. 4^{\circ}}}} \\ {{{b \,=\, 0. 5 4 7 \, n m}}} & {{{\beta\,=\, 7 6. 6^{\circ}}}} \\ {{{c \,=\, 1. 7 2 9 \, n m}}} & {{{\gamma\,=\, 6 2. 5^{\circ}}}} \\ \end{array}
$$
lf the volume of a triclinic unit cell, is a function of these lattice parameters as
$$
V_{\mathrm{t r i}}=a b c {\sqrt{1-\operatorname{c o s}^{2} \alpha-\operatorname{c o s}^{2} \beta-\operatorname{c o s}^{2} \gamma+2 \operatorname{c o s} \alpha\operatorname{c o s} \beta\operatorname{c o s} \gamma}}
$$
determine the number of repeat units per unit cell.

Options:
A. $5$ repeat units/unit cell
B. $4$ repeat units/unit cell
C. $6$ repeat units/unit cell
D. $8$ repeat units/unit cell
E. $9$ repeat units/unit cell
F. $2$ repeat units/unit cell
G. $7$ repeat units/unit cell
H. $3$ repeat units/unit cell
I. $10$ repeat units/unit cell
J. $1$ repeat unit/unit cell
Answer: J
For a continuous and oriented fiber-reinforced composite, the moduli of elasticity in the longiudinal and transverse directions are 33. 1 and 366 GPa ($4.8 \times1 0^{6}$ and $5. 3 \times1 0^{5}$ psi), respectvel. lf the volume fraction of fibers is 0.30, determine the moduli of elasticity of fiber and matrix phases.

Options:
A. $$
E_{m}=2. 8 \; \mathrm{G P a} \; \; ( 3. 8 2 \, \times\, 1 0^{5} \mathrm{~ p s i )}
$$
$$
E_{f}=1 0 2 \mathrm{~ G P a ~} ( 1 4 \times1 0^{6} \mathrm{~ p s i )}
$$
B. $$
E_{m}=2. 4 \; \mathrm{G P a} \; \; ( 3. 6 0 \, \times\, 1 0^{5} \mathrm{~ p s i )}
$$
$$
E_{f}=1 0 6 \mathrm{~ G P a ~} ( 1 6 \times1 0^{6} \mathrm{~ p s i )}
$$
C. $$
E_{m}=2. 5 \; \mathrm{G P a} \; \; ( 3. 6 5 \, \times\, 1 0^{5} \mathrm{~ p s i )}
$$
$$
E_{f}=1 1 0 \mathrm{~ G P a ~} ( 1 6 \times1 0^{6} \mathrm{~ p s i )}
$$
D. $$
E_{m}=2. 2 \; \mathrm{G P a} \; \; ( 3. 5 0 \, \times\, 1 0^{5} \mathrm{~ p s i )}
$$
$$
E_{f}=1 0 8 \mathrm{~ G P a ~} ( 1 6 \times1 0^{6} \mathrm{~ p s i )}
$$
E. $$
E_{m}=2. 3 \; \mathrm{G P a} \; \; ( 3. 5 5 \, \times\, 1 0^{5} \mathrm{~ p s i )}
$$
$$
E_{f}=1 1 5 \mathrm{~ G P a ~} ( 1 7 \times1 0^{6} \mathrm{~ p s i )}
$$
F. $$
E_{m}=3. 1 \; \mathrm{G P a} \; \; ( 4. 1 0 \, \times\, 1 0^{5} \mathrm{~ p s i )}
$$
$$
E_{f}=9 8 \mathrm{~ G P a ~} ( 1 4 \times1 0^{6} \mathrm{~ p s i )}
$$
G. $$
E_{m}=2. 6 \; \mathrm{G P a} \; \; ( 3. 7 7 \, \times\, 1 0^{5} \mathrm{~ p s i )}
$$
$$
E_{f}=1 0 4 \mathrm{~ G P a ~} ( 1 5 \times1 0^{6} \mathrm{~ p s i )}
$$
H. $$
E_{m}=2. 7 \; \mathrm{G P a} \; \; ( 3. 9 0 \, \times\, 1 0^{5} \mathrm{~ p s i )}
$$
$$
E_{f}=1 0 5 \mathrm{~ G P a ~} ( 1 5 \times1 0^{6} \mathrm{~ p s i )}
$$
I. $$
E_{m}=3. 0 \; \mathrm{G P a} \; \; ( 4. 0 0 \, \times\, 1 0^{5} \mathrm{~ p s i )}
$$
$$
E_{f}=1 0 0 \mathrm{~ G P a ~} ( 1 4 \times1 0^{6} \mathrm{~ p s i )}
$$
J. $$
E_{m}=2. 9 \; \mathrm{G P a} \; \; ( 3. 8 5 \, \times\, 1 0^{5} \mathrm{~ p s i )}
$$
$$
E_{f}=1 0 1 \mathrm{~ G P a ~} ( 1 3 \times1 0^{6} \mathrm{~ p s i )}
$$
Answer: G
The electrical conductivity of a cylindrical silicon specimen 7.0 mm (0.28 in.) diameter and 57 mm (2.25 in.) in length in which a current of 0.25 A passes in an axial direction. A voltage of 24 V is measured across two probes that are separated by 45 mm (1.75 in.) is().

Options:
A. $$
3. 9 \ ( \Omega\! \! \!-\! \! {\bf m} )^{-1}
$$
B. $$
8. 4 \ ( \Omega\! \! \!-\! \! {\bf m} )^{-1}
$$
C. $$
4. 2 \ ( \Omega\! \! \!-\! \! {\bf m} )^{-1}
$$
D. $$
7. 7 \ ( \Omega\! \! \!-\! \! {\bf m} )^{-1}
$$
E. $$
5. 3 \ ( \Omega\! \! \!-\! \! {\bf m} )^{-1}
$$
F. $$
1 2. 2 \ ( \Omega\! \! \!-\! \! {\bf m} )^{-1}
$$
G. $$
2 0. 5 \ ( \Omega\! \! \!-\! \! {\bf m} )^{-1}
$$
H. $$
6. 1 \ ( \Omega\! \! \!-\! \! {\bf m} )^{-1}
$$
I. $$
1 5 . 3 \ ( \Omega\! \! \!-\! \! {\bf m} )^{-1}
$$
J. $$
9. 8 \ ( \Omega\! \! \!-\! \! {\bf m} )^{-1}
$$
Answer: F
Germanium to which $10^{24} m^{-3}$ As atons have been added is an extrinsic semiconductor at room temperature, and virtually all the As atoms may be thought of as being ionized (ie., one charge carrier exists for each As atom)The electrical conductivity of this material, assuming electron and hole mobilities of 0. 1 and 0.05 $m^{2}/V \cdot s$, respectivey is().

Options:
A. $$
3. 5 4 \, \times\, 1 0^{4} \, \, ( \Omega\mathrm{-m} )^{-1}
$$
B. $$
1. 6 0 \, \times\, 1 0^{4} \, \, ( \Omega\mathrm{-m} )^{-1}
$$
C. $$
1. 4 5 \, \times\, 1 0^{5} \, \, ( \Omega\mathrm{-m} )^{-1}
$$
D. $$
1. 0 8 \, \times\, 1 0^{3} \, \, ( \Omega\mathrm{-m} )^{-1}
$$
E. $$
4. 1 9 \, \times\, 1 0^{3} \, \, ( \Omega\mathrm{-m} )^{-1}
$$
F. $$
2. 4 0 \, \times\, 1 0^{3} \, \, ( \Omega\mathrm{-m} )^{-1}
$$
G. $$
2. 0 3 \, \times\, 1 0^{4} \, \, ( \Omega\mathrm{-m} )^{-1}
$$
H. $$
3. 0 7 \, \times\, 1 0^{4} \, \, ( \Omega\mathrm{-m} )^{-1}
$$
I. $$
2. 7 8 \, \times\, 1 0^{5} \, \, ( \Omega\mathrm{-m} )^{-1}
$$
J. $$
2. 1 5 \, \times\, 1 0^{5} \, \, ( \Omega\mathrm{-m} )^{-1}
$$
Answer: B
Estimate the electrical conductivity at 135°C of silicon that has been doped with $1 0^{2 4} \; m^{-3}$ 0f aluminum atoms.

Options:
A. $$
1 3 0 0 \ ( \Omega\! \!-\! \mathrm{m} )^{-1}
$$
B. $$
1 0 0 5 \ ( \Omega\! \!-\! \mathrm{m} )^{-1}
$$
C. $$
1 2 3 0 \ ( \Omega\! \!-\! \mathrm{m} )^{-1}
$$
D. $$
9 8 7 0 \ ( \Omega\! \!-\! \mathrm{m} )^{-1}
$$
E. $$
1 0 5 0 \ ( \Omega\! \!-\! \mathrm{m} )^{-1}
$$
F. $$
1 1 2 0 \ ( \Omega\! \!-\! \mathrm{m} )^{-1}
$$
G. $$
1 2 1 0 \ ( \Omega\! \!-\! \mathrm{m} )^{-1}
$$
H. $$
1 1 1 5 \ ( \Omega\! \!-\! \mathrm{m} )^{-1}
$$
I. $$
1 1 0 0 \ ( \Omega\! \!-\! \mathrm{m} )^{-1}
$$
J. $$
1 1 8 0 \ ( \Omega\! \!-\! \mathrm{m} )^{-1}
$$
Answer: F
For copper, the heat capacity at constant volume $C_{v}$ at 20 $K$ is 0.38 J/mol-K and the Debye
temperature is 340 K. The specific heat at 40 K is ():

Options:
A. $$
4 9. 1 \mathrm{J / k g-K}
$$
B. $$
3 5. 0 \mathrm{J / k g-K}
$$
C. $$
5 4. 4 \mathrm{J / k g-K}
$$
D. $$
4 0. 3 \mathrm{J / k g-K}
$$
E. $$
5 6. 7 \mathrm{J / k g-K}
$$
F. $$
3 8. 5 \mathrm{J / k g-K}
$$
G. $$
5 2. 3 \mathrm{J / k g-K}
$$
H. $$
4 7. 8 \mathrm{J / k g-K}
$$
I. $$
6 0. 2 \mathrm{J / k g-K}
$$
J. $$
4 1. 9 \mathrm{J / k g-K}
$$
Answer: H
The formula for samarium iron garnet ($\text{Sm}_{3}\text{Fe}_{5}\text{O}_{12}$) may be written in the form $\mathrm{S m}_{3}^{c} \mathrm{F c}_{2}^{a} \mathrm{F c}_{3}^{d} \mathrm{O}_{1 2}$, where the superscripts $a$ $c$ and $d$ represent diferent sites on which the $S m^{3+}$ and $F e^{3+}$ ions are located. The spin magnetic moments for the $S m^{3+}$ and $F e^{3+}$ ions positioned in $a$ and $c$ sites are oriented parallel to one another and antiparallel to the $F e^{3 +}$ ions in $d$ sites. Compute the number of Bohr magnetons associated with each $S m^{3+}$ ion, given the following information: (1) each unit cell consists of eight formula $( S m_{3} F e_{5} O_{1 2} )$ unis; (2) the unit cell is cubic with an edge length of 1.2529 nm; (3) the saturation magnetization for this material is $1. 3 5 \times1 0^{5} A / m$ ; and (4) there are 5 Bohr magnetons associated with each $F e^{3+}$ ion.

Options:
A. $$
2. 6 7 \, \mathrm{B M}
$$
B. $$
3. 3 8 \, \mathrm{B M}
$$
C. $$
2. 8 6 \, \mathrm{B M}
$$
D. $$
2. 8 0 \, \mathrm{B M}
$$
E. $$
3. 0 9 \, \mathrm{B M}
$$
F. $$
3. 1 2 \, \mathrm{B M}
$$
G. $$
2. 5 9 \, \mathrm{B M}
$$
H. $$
3. 0 4 \, \mathrm{B M}
$$
I. $$
2. 9 5 \, \mathrm{B M}
$$
J. $$
2. 7 1 \, \mathrm{B M}
$$
Answer: C
The fraction of nonreflected radiation that is transmitted through a 5-mm thickness of a transparent material is 0.95. If he thickness is increased to 12mm, what fraction of light will be transmitted?

Options:
A. $$
0. 5 8 9
$$
B. $$
0. 8 8 4
$$
C. $$
0. 9 1 7
$$
D. $$
0. 6 8 2
$$
E. $$
0. 7 9 8
$$
F. $$
0. 9 6 3
$$
G. $$
0. 7 5 4
$$
H. $$
0. 7 2 9
$$
I. $$
0. 5 3 1
$$
J. $$
0. 6 4 5
$$
Answer: B
Let $V$ be a finite dimensional vector space over complex field $\mathbb{C}$ with a nondegenerate symmetric bilinear form $( *, * )$ . Let
$$
O ( V )=\{g \in\operatorname{G L} ( V ) \mid( g u, g v )=( u, v ), \ \forall u, v \in V \}
$$
be the orthogonal group. So fixed point subspace $( V \otimes_{\mathbb{C}} V )^{O ( n )}$ is ( ) -dimensional.

Options:
A. 6
B. 0
C. 5
D. 7
E. 2
F. 9
G. 4
H. 8
I. 1
J. 3
Answer: I
Let $A$ be an $n \times n$ skew symmetric real matrix.Find condition on an orthogonal $B$ such that $B=e^{A}$ is solvable for some skew symmetric and real matrix $A$ .

Options:
A. $$
A=\left( \begin{matrix} {{0}} & {{-\theta}} \\ {{\theta}} & {{0}} \\ \end{matrix} \right)
$$
B. $$
A=\left( \begin{matrix} {{0}} & {{0}} \\ {{0}} & {{0}} \\ \end{matrix} \right)
$$
C. $$
A=\left( \begin{matrix} {{\theta}} & {{1}} \\ {{-1}} & {{\theta}} \\ \end{matrix} \right)
$$
D. $$
A=\left( \begin{matrix} {{0}} & {{2\theta}} \\ {{-2\theta}} & {{0}} \\ \end{matrix} \right)
$$
E. $$
A=\left( \begin{matrix} {{0}} & {{\theta}} \\ {{-\theta}} & {{0}} \\ \end{matrix} \right)
$$
F. $$
A=\left( \begin{matrix} {{0}} & {{1}} \\ {{-1}} & {{0}} \\ \end{matrix} \right)
$$
G. $$
A=\left( \begin{matrix} {{\theta}} & {{\theta}} \\ {{-\theta}} & {{-\theta}} \\ \end{matrix} \right)
$$
H. $$
A=\left( \begin{matrix} {{0}} & {{i\theta}} \\ {{-i\theta}} & {{0}} \\ \end{matrix} \right)
$$
I. $$
A=\left( \begin{matrix} {{1}} & {{\theta}} \\ {{\theta}} & {{1}} \\ \end{matrix} \right)
$$
J. $$
A=\left( \begin{matrix} {{\theta}} & {{0}} \\ {{0}} & {{-\theta}} \\ \end{matrix} \right)
$$
Answer: E
Let $f$ be a two-dimensional (complex) representation of a finite group $G$ such that $1$ is an eigenvalue of $f ( \sigma)$ for every $\sigma\in G$ . What is $\langle1_{G}, \chi\rangle$?

Options:
A. $$
\frac{1} {| G |} \left( 1+\sum_{1 \neq x \in G} \mid \chi( x ) \mid^2 \right)
$$
B. $$
\frac{1} {| G |} \left( 0+\sum_{1 \neq x \in G} \operatorname{R e} ( \chi( x^2 ) ) \right)
$$
C. $$
\frac{1} {| G |} \left( 2+\sum_{1 \neq x \in G} \operatorname{I m} ( \overline{\chi( x )} ) \right)
$$
D. $$
\frac{1} {| G |} \left( 4+\sum_{1 \neq x \in G} \operatorname{R e} ( \chi^2( x ) ) \right)
$$
E. $$
\frac{1} {| G |} \left( 3+\sum_{1 \neq x \in G} \operatorname{I m} ( \chi( x ) ) \right)
$$
F. $$
\frac{1} {| G |} \left( 1+\sum_{1 \neq x \in G} \mid \chi( x ) \mid \right)
$$
G. $$
\frac{1} {| G |} \left( 5+\sum_{1 \neq x \in G} \operatorname{R e} ( \chi( x )^2 ) \right)
$$
H. $$
\frac{1} {| G |} \left( 2+\sum_{1 \neq x \in G} \operatorname{R e} ( \chi( x ) ) \right)
$$
I. $$
\frac{1} {| G |} \left( 3+\sum_{1 \neq x \in G} \operatorname{I m} ( \chi( x )^2 ) \right)
$$
J. $$
\frac{1} {| G |} \left( 0+\sum_{1 \neq x \in G} \operatorname{R e} ( \overline{\chi( x )} ) \right)
$$
Answer: H
Calculate the mole fractions of the molecules of a mixture that contains 56 g of benzene and 120 g of methyl-benzene (toluene).

Options:
A. $$
{0. 2 5}
$$
$$
{0. 7 5}
$$
B. $$
{0. 4 5}
$$
$$
{0. 5 5}
$$
C. $$
{0. 4 9}
$$
$$
{0. 5 1}
$$
D. $$
{0. 3 0}
$$
$$
{0. 7 0}
$$
E. $$
{0. 2 8}
$$
$$
{0. 7 2}
$$
F. $$
{0. 5 0}
$$
$$
{0. 5 0}
$$
G. $$
{0. 2 2}
$$
$$
{0. 7 8}
$$
H. $$
{0. 4 0}
$$
$$
{0. 6 0}
$$
I. $$
{0. 3 6}
$$
$$
{0. 6 4}
$$
J. $$
{0. 3 8}
$$
$$
{0. 6 2}
$$
Answer: I
Balloons were used to obtain much of the early information about the atmosphere and continue to be used today to obtain weather information. In 1782, Jacques Charles used a hydrogen-filled balloon to fly from Paris 25 km into the French countryside. What is the mass density of hydrogen relative to air at the same temperature and pressure? What mass of payload can be lifted by 10 kg of hydrogen, neglecting-in the mass of the balloon?

Options:
A. $$
{0. 0 6 0}
$$
$$
{1 3 8 k g}
$$
B. $$
{0. 0 5 8}
$$
$$
{1 4 0 k g}
$$
C. $$
{0. 0 7 0}
$$
$$
{1 3 0 k g}
$$
D. $$
{0. 0 4 5}
$$
$$
{1 4 2 k g}
$$
E. $$
{0. 1 0 2}
$$
$$
{1 2 8 k g}
$$
F. $$
{0. 0 7 2}
$$
$$
{1 3 2 k g}
$$
G. $$
{0. 0 5 5}
$$
$$
{1 4 8 k g}
$$
H. $$
{0. 0 6 9}
$$
$$
{1 3 5 k g}
$$
I. $$
{0. 0 6 7}
$$
$$
{1 3 3 k g}
$$
J. $$
{0. 0 4 9}
$$
$$
{1 4 5 k g}
$$
Answer: H
At what pressure does the mean free path of argon at 25°C become comparable to the diameter of a spherical vessel of volume 1.0 dm$^{3}$ that contains it? Take $\sigma=0. 3 6 \mathrm{~ n m}^{2}$ .

Options:
A. $$
8. 0 1 1 \mathrm{~ P a}
$$
B. $$
2. 8 3 7 \mathrm{~ P a}
$$
C. $$
0. 0 6 5 \mathrm{~ P a}
$$
D. $$
4. 1 8 9 \mathrm{~ P a}
$$
E. $$
7. 8 9 0 \mathrm{~ P a}
$$
F. $$
6. 7 5 4 \mathrm{~ P a}
$$
G. $$
3. 6 5 0 \mathrm{~ P a}
$$
H. $$
5. 4 2 3 \mathrm{~ P a}
$$
I. $$
9. 9 9 5 \mathrm{~ P a}
$$
J. $$
1. 2 4 0 \mathrm{~ P a}
$$
Answer: C
Derivation 2.2 showed how to calculate the work of reversible, isothermal expansion of a perfect gas. Suppose that the expansion is reversible but not isothermal and that the temperature decreases as the expansion proceeds. Find an expression for the work when $T=T_{i}-c ( V-V_{i} ),$ with $c$ a positive constant.

Options:
A. $$
nR\left((T_i + cV_i)\ln\frac{V_f}{V_i}- c(V_f - V_i)\right)\
$$
B. $$ nR\left((T_f + cV_i)\ln\frac{V_i}{V_f}- c(V_f - V_i)\right) $$
C. $$ nR\left((T_f + cV_f)\ln\frac{V_f}{V_i}- c(V_i - V_f)\right) $$
D. $$ nR\left((T_i + cV_i)\ln\frac{V_f}{V_i}+ c(V_i - V_f)\right) $$
E. $$ nR\left((T_f - cV_f)\ln\frac{V_i}{V_f}+ c(V_i - V_f)\right) $$
F. $$ nR\left((T_i + cV_f)\ln\frac{V_f}{V_i}- c(V_i - V_f)\right) $$
G. $$ nR\left((T_f - cV_i)\ln\frac{V_i}{V_f}- c(V_f - V_i)\right) $$
H. $$ nR\left((T_f + cV_f)\ln\frac{V_i}{V_f}+ c(V_i - V_f)\right) $$
I. $$ nR\left((T_i - cV_i)\ln\frac{V_f}{V_i}+ c(V_f - V_i)\right) $$
J. $$ nR\left((T_i - cV_f)\ln\frac{V_f}{V_i}+ c(V_f - V_i)\right) $$
Answer: A
Calculate the change in molar entropy when a sample of argon is compressed from 2.0 dm$^{3}$ to 500 cm$^{3}$ and simultaneously heated from 300 K to 400 K is(). Take $C_{V, \mathrm{m}}={\frac{3} {2}} R$.

Options:
A. $$
- 8. 5 \mathrm{~ J ~ K^{-1} ~ m o l^{-1} ~}
$$
B. $$
- 6. 8 \mathrm{~ J ~ K^{-1} ~ m o l^{-1} ~}
$$
C. $$
- 7. 9 \mathrm{~ J ~ K^{-1} ~ m o l^{-1} ~}
$$
D. $$
- 9. 0 \mathrm{~ J ~ K^{-1} ~ m o l^{-1} ~}
$$
E. $$
- 9. 2 \mathrm{~ J ~ K^{-1} ~ m o l^{-1} ~}
$$
F. $$
- 6. 7 \mathrm{~ J ~ K^{-1} ~ m o l^{-1} ~}
$$
G. $$
- 7. 4 \mathrm{~ J ~ K^{-1} ~ m o l^{-1} ~}
$$
H. $$
- 7. 1 \mathrm{~ J ~ K^{-1} ~ m o l^{-1} ~}
$$
I. $$
- 8. 1 \mathrm{~ J ~ K^{-1} ~ m o l^{-1} ~}
$$
J. $$
- 5. 3 \mathrm{~ J ~ K^{-1} ~ m o l^{-1} ~}
$$
Answer: C
An herbicide is found to contain only C, H, N, and $\mathrm{C l}$. The complete combustion of a 100.0-mg sample of the herbicide in excess oxygen produces 83.16 mL of $CO_{2}$ and 73.30 mL of $H_{2}O$ vapor at STP. A separate analysis shows that the sample also contains 16.44 mg of Cl. The percent composition of the substance is____.

Options:
A. 15.34%Xe
B. 14.25%Cl
C. 22.39%H
D. 20.22%K
E. 19.87%S
F. 28.77%F
G. 26.14%P
H. 18.50%O
I. 33.45%C
J. 32.38%N
Answer: J
Let $Y_{0}=28$, according to the recurrence formula
$$
Y_{n} = Y_{n-1} - \frac{1}{100} \sqrt{783} \ \ \ (n = 1, 2, \cdots)
$$
calculate up to $Y_{100}$. If $\sqrt{783} \approx 27.982$ (to five significant figures), how much error will there be in the calculation of $Y_{100}$?

Options:
A. $$
Y_{1 0 0} \leqslant\frac{1} {8} \times1 0^{-3}
$$
B. $$
Y_{1 0 0} \leqslant\frac{1} {2} \times1 0^{-3}
$$
C. $$
Y_{1 0 0} \leqslant\frac{1} {6} \times1 0^{-2}
$$
D. $$
Y_{1 0 0} \leqslant\frac{1} {9} \times1 0^{-1}
$$
E. $$
Y_{1 0 0} \leqslant\frac{1} {3} \times1 0^{-2}
$$
F. $$
Y_{1 0 0} \leqslant\frac{1} {1} \times1 0^{-4}
$$
G. $$
Y_{1 0 0} \leqslant\frac{1} {4} \times1 0^{-4}
$$
H. $$
Y_{1 0 0} \leqslant\frac{1} {0} \times1 0^{-7}
$$
I. $$
Y_{1 0 0} \leqslant\frac{1} {7} \times1 0^{-6}
$$
J. $$
Y_{1 0 0} \leqslant\frac{1} {5} \times1 0^{-5}
$$
Answer: B
Given that the relative error limit of the approximate number $x^{*}$ is $0.3\%$, how many significant figures does $x^{*}$ have at least?

Options:
A. 0
B. 9
C. 5
D. 7
E. 3
F. 2
G. 8
H. 4
I. 1
J. 6
Answer: F
The function table for $\operatorname{cos} x, 0^{\circ} \leq x \leq 90^{\circ}$ is given, with a step size $h=1^{\prime}=\left( 1 / 60 \right)^{\circ}$. If the function table has 5 significant figures, study the total error bound for approximating $\operatorname{cos} x$ using linear interpolation as ______.

Options:
A. $$
3. 8 9 5 0 \times1 0^{-6}
$$
B. $$
5. 9 4 1 3 \times1 0^{-6}
$$
C. $$
2. 7 6 3 5 \times1 0^{-6}
$$
D. $$
7. 2 4 5 8 \times1 0^{-6}
$$
E. $$
4. 9 8 2 7 \times1 0^{-6}
$$
F. $$
3. 0 2 3 4 \times1 0^{-6}
$$
G. $$
8. 1 0 2 4 \times1 0^{-6}
$$
H. $$
5. 0 1 0 6 \times1 0^{-6}
$$
I. $$
6. 1 5 0 9 \times1 0^{-6}
$$
J. $$
9. 3 6 7 1 \times1 0^{-6}
$$
Answer: H
Given $P(x) = 1 - x + x^2 - x^3 + x^4$ over the interval $0 \leq x \leq 1$, try to reduce the degree of $P(x)$ with an allowable error of 0.008. The result is ______.

Options:
A. $$
P ( x )=
\frac{1 2 7} {1 4 0}-\frac{4} {4} \, x-\frac{1} {5} \, x^{2}+\, x^{3} \,, \quad x \in[ \, 0 \,, 1 \, ]
$$
B. $$
P ( x )=
\frac{1 2 8} {1 2 9}-\frac{3} {4} \, x-\frac{1} {1} \, x^{2}+\, x^{4} \,, \quad x \in[ \, 0 \,, 1 \, ]
$$
C. $$
P ( x )=
\frac{1 2 7} {1 2 8}-\frac{3} {4} \, x-\frac{1} {4} \, x^{2}+\, x^{3} \,, \quad x \in[ \, 0 \,, 1 \, ]
$$
D. $$
P ( x )=
\frac{1 2 7} {1 3 0}-\frac{3} {3} \, x-\frac{1} {6} \, x^{2}+\, x^{3} \,, \quad x \in[ \, 0 \,, 1 \, ]
$$
E. $$
P ( x )=
\frac{1 2 7} {1 2 8}-\frac{0} {4} \, x-\frac{5} {4} \, x^{2}+\, x^{3} \,, \quad x \in[ \, 0 \,, 1 \, ]
$$
F. $$
P ( x )=
\frac{1 2 9} {1 2 8}-\frac{5} {4} \, x-\frac{0} {4} \, x^{2}+\, x^{2} \,, \quad x \in[ \, 0 \,, 1 \, ]
$$
G. $$
P ( x )=
\frac{1 2 7} {1 1 7}-\frac{3} {4} \, x-\frac{1} {4} \, x^{1}+\, x^{3} \,, \quad x \in[ \, 0 \,, 1 \, ]
$$
H. $$
P ( x )=
\frac{1 3 5} {1 4 0}-\frac{2} {4} \, x-\frac{2} {4} \, x^{2}+\, x^{3} \,, \quad x \in[ \, 0 \,, 1 \, ]
$$
I. $$
P ( x )=
\frac{1 2 6} {1 2 9}-\frac{3} {4} \, x-\frac{2} {4} \, x^{3}+\, x^{4} \,, \quad x \in[ \, 0 \,, 1 \, ]
$$
J. $$
P ( x )=
\frac{1 1 7} {1 2 8}-\frac{3} {1} \, x-\frac{1} {3} \, x^{2}+\, x^{3} \,, \quad x \in[ \, 0 \,, 1 \, ]
$$
Answer: C
Find the best first-degree approximating polynomial for $f(x) = \sin x$ on the interval $\left[ 0, \frac{\pi}{2} \right]$, and estimate the error as _____.

Options:
A. $$
P_{1} ( x )=$2/pi$+1.105256594 x
$$
$$
P_{1} ( x )\approx0. 0 7 8 9 5 2 3 1 6
$$
B. $$
P_{1} ( x )=i_{0}+i_{1} x
$$
$$
P_{1} ( x )\approx0. 7 5 8 4 8 9 0 5 8
$$
C. $$
P_{1} ( x )=$1/pi$+0.105256594 x
$$
$$
P_{1} ( x )\approx0. 2 1 1 4 3 5 7 8 8
$$
D. $$
P_{1} ( x )=g_{0}+g_{1} x
$$
$$
P_{1} ( x )\approx0. 5 4 1 7 6 2 9 3 0
$$
E. $$
P_{1} ( x )=j_{0}+j_{1} x
$$
$$
P_{1} ( x )\approx0. 8 2 0 6 7 1 4 3 2
$$
F. $$
P_{1} ( x )=e_{0}+e_{1} x
$$
$$
P_{1} ( x )\approx0. 4 8 0 8 3 4 6 2 9
$$
G. $$
P_{1} ( x )=h_{0}+h_{1} x
$$
$$
P_{1} ( x )\approx0. 9 6 4 2 1 5 3 7 5
$$
H. $$
P_{1} ( x )=c_{0}+c_{1} x
$$
$$
P_{1} ( x )\approx0. 3 6 2 7 0 7 5 4 2
$$
I. $$
P_{1} ( x )=$2/pi$+0.105256594 x
$$
$$
P_{1} ( x )\approx0. 1 0 5 2 5 6 5 9 4
$$
J. $$
P_{1} ( x )=f_{0}+f_{1} x
$$
$$
P_{1} ( x )\approx0. 6 3 9 1 9 8 5 0 1
$$
Answer: I
Calculate the integral $I=\int_{0}^{1} {\frac{1} {1+x}} \mathrm{d} x$ using the composite Simpson's rule with $n=5$ and estimate the truncation error to be ____.

Options:
A. $$
S_{5}=0.69315
$$
$$
\mid R_{n} ( f ) \mid= 1. 3 3 3 3 \times1 0^{-5}
$$
B. $$
S_{5}=0.69305
$$
$$
\mid R_{n} ( f ) \mid= 2. 1 3 3 3 \times1 0^{-5}
$$
C. $$
S_{5}=0.69300
$$
$$
\mid R_{n} ( f ) \mid= 1. 4 3 3 3 \times1 0^{-5}
$$
D. $$
S_{5}=0.69320
$$
$$
\mid R_{n} ( f ) \mid= 2. 3 3 3 3 \times1 0^{-5}
$$
E. $$
S_{5}=0.69330
$$
$$
\mid R_{n} ( f ) \mid= 1. 6 3 3 3 \times1 0^{-5}
$$
F. $$
S_{5}=0.69295
$$
$$
\mid R_{n} ( f ) \mid= 2. 3 3 3 3 \times1 0^{-5}
$$
G. $$
S_{5}=0.69340
$$
$$
\mid R_{n} ( f ) \mid= 1. 3 3 3 3 \times1 0^{-5}
$$
H. $$
S_{5}=0.69310
$$
$$
\mid R_{n} ( f ) \mid= 1. 5 3 3 3 \times1 0^{-5}
$$
I. $$
S_{5}=0.69325
$$
$$
\mid R_{n} ( f ) \mid= 3. 3 3 3 3 \times1 0^{-5}
$$
J. $$
S_{5}=0.69335
$$
$$
\mid R_{n} ( f ) \mid= 1. 8 3 3 3 \times1 0^{-5}
$$
Answer: A
Calculate the integral using the trapezoidal rule
$$
y=\int_{0}^{x} \mathrm{e}^{-t^{2}} \, \mathrm{d} t
$$
to the approximate values at $x = 0.5, 0.75,$ and $1$ is____.

Options:
A. $$
\begin{array} {c} {{{y ( 0, 2 5 ) =0, 2 1 2 4 2 7 \,,}}} \\ {{{y ( 0, 5 0 ) =0, 4 8 4 2 0 4 \,,}}} \\ {{{y ( 0, 7 5 ) =0, 6 2 9 7 7 7 \,,}}} \\ {{{y ( 1, 0 0 ) =0. 7 6 2 9 8 5 \,}}} \\ \end{array}
$$
B. $$
\begin{array} {c} {{{y ( 0, 2 5 ) =0, 2 3 2 4 2 7 \,,}}} \\ {{{y ( 0, 5 0 ) =0, 4 5 9 2 0 4 \,,}}} \\ {{{y ( 0, 7 5 ) =0, 6 2 4 7 7 7 \,,}}} \\ {{{y ( 1, 0 0 ) =0. 7 4 7 9 8 5 \,}}} \\ \end{array}
$$
C. $$
\begin{array} {c} {{{y ( 0, 2 5 ) =0, 2 4 2 4 2 7 \,,}}} \\ {{{y ( 0, 5 0 ) =0, 4 5 7 2 0 4 \,,}}} \\ {{{y ( 0, 7 5 ) =0, 6 2 5 7 7 7 \,,}}} \\ {{{y ( 1, 0 0 ) =0. 7 4 2 9 8 5 \,}}} \\ \end{array}
$$
D. $$
\begin{array} {c} {{{y ( 0, 2 5 ) =0, 2 8 2 4 2 7 \,,}}} \\ {{{y ( 0, 5 0 ) =0, 4 7 2 3 0 4 \,,}}} \\ {{{y ( 0, 7 5 ) =0, 6 5 5 7 7 7 \,,}}} \\ {{{y ( 1, 0 0 ) =0. 7 1 8 9 8 5 \,}}} \\ \end{array}
$$
E. $$
\begin{array} {c} {{{y ( 0, 2 5 ) =0, 3 2 4 4 2 7 \,,}}} \\ {{{y ( 0, 5 0 ) =0, 4 4 2 2 0 4 \,,}}} \\ {{{y ( 0, 7 5 ) =0, 6 3 4 7 7 7 \,,}}} \\ {{{y ( 1, 0 0 ) =0. 7 5 3 9 8 5 \,}}} \\ \end{array}
$$
F. $$
\begin{array} {c} {{{y ( 0, 2 5 ) =0, 2 4 3 4 2 7 \,,}}} \\ {{{y ( 0, 5 0 ) =0, 4 6 2 2 0 4 \,,}}} \\ {{{y ( 0, 7 5 ) =0, 6 4 5 7 7 7 \,,}}} \\ {{{y ( 1, 0 0 ) =0. 7 5 1 9 8 5 \,}}} \\ \end{array}
$$
G. $$
\begin{array} {c} {{{y ( 0, 2 5 ) =0, 2 9 2 4 2 7 \,,}}} \\ {{{y ( 0, 5 0 ) =0, 4 2 2 2 0 4 \,,}}} \\ {{{y ( 0, 7 5 ) =0, 6 3 8 7 7 7 \,,}}} \\ {{{y ( 1, 0 0 ) =0. 7 4 5 8 8 5 \,}}} \\ \end{array}
$$
H. $$
\begin{array} {c} {{{y ( 0, 2 5 ) =0, 2 4 1 4 2 7 \,,}}} \\ {{{y ( 0, 5 0 ) =0, 4 7 2 2 0 4 \,,}}} \\ {{{y ( 0, 7 5 ) =0, 6 1 5 7 7 7 \,,}}} \\ {{{y ( 1, 0 0 ) =0. 7 3 9 8 8 5 \,}}} \\ \end{array}
$$
I. $$
\begin{array} {c} {{{y ( 0, 2 5 ) =0, 2 5 1 4 2 7 \,,}}} \\ {{{y ( 0, 5 0 ) =0, 4 3 7 2 0 4 \,,}}} \\ {{{y ( 0, 7 5 ) =0, 6 3 5 7 7 7 \,,}}} \\ {{{y ( 1, 0 0 ) =0. 7 5 2 9 8 5 \,}}} \\ \end{array}
$$
J. $$
\begin{array} {c} {{{y ( 0, 2 5 ) =0, 2 2 4 4 2 7 \,,}}} \\ {{{y ( 0, 5 0 ) =0, 4 8 2 2 0 4 \,,}}} \\ {{{y ( 0, 7 5 ) =0, 6 1 7 7 7 7 \,,}}} \\ {{{y ( 1, 0 0 ) =0. 7 4 6 9 8 5 \,}}} \\ \end{array}
$$
Answer: C
Using the bisection method to find the root of the equation
$$
f(x) = x^{3} + x^{2} - 3x - 3 = 0
$$
The interval $[1, 2]$ is(), where the absolute error must not exceed $10^{-2}$.

Options:
A. $$
x_{7}=1. 7 0 4 8 5
$$
B. $$
x_{7}=1. 7 2 6 5 6
$$
C. $$
x_{7}=1. 8 0 2 1 3
$$
D. $$
x_{7}=1. 8 9 2 3 4
$$
E. $$
x_{7}=1. 6 4 3 2 8
$$
F. $$
x_{7}=1. 7 1 3 5 3
$$
G. $$
x_{7}=1. 7 3 5 9 8
$$
H. $$
x_{7}=1. 7 8 4 5 1
$$
I. $$
x_{7}=1. 6 9 5 3 7
$$
J. $$
x_{7}=1. 8 5 7 4 9
$$
Answer: B
What is the root of the equation \( x = 1.6 + 0.98 \cos x \)?

Options:
A. 1.585547
B. 1.475893
C. 1.692013
D. 1.689762
E. 1.624578
F. 1.602134
G. 1.793412
H. 1.477682
I. 1.524879
J. 1.558723
Answer: A
$\mathrm{A 1. 2} \times1 0^{4}$ kg spacecraft is launched from Earth and is to be accelerated radially away from the Sun using a circular solar sail. The initial acceleration of the spacecraft is to be $1 g$. Assuming a flat sail, determine the radius of the sail if it is
shiny, so it reflects the Sun's light. (Hint: The spacecraft, like Earth, is orbiting the Sun. )

Options:
A. $$
5 5 \ \mathrm{k m}
$$
B. $$
6 4 \ \mathrm{k m}
$$
C. $$
8 8 \ \mathrm{k m}
$$
D. $$
7 5 \ \mathrm{k m}
$$
E. $$
6 0 \ \mathrm{k m}
$$
F. $$
7 0 \ \mathrm{k m}
$$
G. $$
8 3 \ \mathrm{k m}
$$
H. $$
5 9 \ \mathrm{k m}
$$
I. $$
9 7 \ \mathrm{k m}
$$
J. $$
9 1 \ \mathrm{k m}
$$
Answer: B
over all wavelengths to obtain an expression for the total luminosity of a blackbody model star. Hint:
$$
\int_{0}^{\infty} \frac{u^{3} \, d u} {e^{u}-1}=\frac{\pi^{4}} {1 5}.
$$

Options:
A. $$
\frac{8 \pi^{3} R^{2} k^{4} T^{4}} {1 5 c^{4} h^{3}}
$$
B. $$
\frac{9 \pi^{5} R^{2} k^{3} T^{4}} {2 0 c^{2} h^{2}}
$$
C. $$
\frac{6 \pi^{6} R^{2} k^{2} T^{4}} {1 9 c^{2} h^{3}}
$$
D. $$
\frac{2 \pi^{6} R^{2} k^{4} T^{5}} {1 8 c^{2} h^{3}}
$$
E. $$
\frac{4 \pi^{5} R^{3} k^{2} T^{3}} {1 6 c^{3} h^{4}}
$$
F. $$
\frac{5 \pi^{4} R^{2} k^{5} T^{4}} {1 0 c^{2} h^{3}}
$$
G. $$
\frac{1 0 \pi^{6} R^{2} k^{3} T^{3}} {1 5 c^{2} h^{3}}
$$
H. $$
\frac{7 \pi^{4} R^{2} k^{4} T^{2}} {1 5 c^{3} h^{3}}
$$
I. $$
\frac{3 \pi^{5} R^{2} k^{4} T^{4}} {1 1 c^{2} h^{3}}
$$
J. $$
\frac{8 \pi^{6} R^{2} k^{4} T^{4}} {1 5 c^{2} h^{3}}
$$
Answer: J
Using the Rayleigh criterion, estimate the angular resolution limit of the human eye at 550 nm. Assume that the diameter of the pupil is 5 mm.

Options:
A. $$
1. 4 2 \times1 0^{-4}
$$
$$
3 1^{\prime\prime}
$$
B. $$
1. 3 4 \times1 0^{-4}
$$
$$
2 8^{\prime\prime}
$$
C. $$
1. 3 5 \times1 0^{-4}
$$
$$
3 2^{\prime\prime}
$$
D. $$
1. 3 0 \times1 0^{-4}
$$
$$
2 6^{\prime\prime}
$$
E. $$
1. 2 8 \times1 0^{-4}
$$
$$
2 2^{\prime\prime}
$$
F. $$
1. 1 5 \times1 0^{-4}
$$
$$
3 5^{\prime\prime}
$$
G. $$
1. 2 5 \times1 0^{-4}
$$
$$
2 5^{\prime\prime}
$$
H. $$
1. 4 0 \times1 0^{-4}
$$
$$
2 7^{\prime\prime}
$$
I. $$
1. 3 9 \times1 0^{-4}
$$
$$
2 4^{\prime\prime}
$$
J. $$
1. 5 0 \times1 0^{-4}
$$
$$
3 0^{\prime\prime}
$$
Answer: B
Suppose that a radio telescope receiver has a bandwidth of 50 MHz centered at 1.430 GHz $( 1 \mathrm{~ G H z}=1 0 0 0 \mathrm{~ M H z} )$. Assume that, rather than being a perfect detector over the entire bandwidth, the receiver's frequency dependence is triangular, meaning that the sensitivity of the detector is 0% at the edges of the band and 100% at its center. This filter function can be expressed as
$$
f_{\nu}=\left\{\begin{array} {c l} {{{{\frac{\nu} {v_{m}-v_{\ell}}-{\frac{\nu_{\ell}} {v_{m}-v_{\ell}}}}}}} & {{{{\mathrm{i f ~} v_{\ell} \leq v \leq v_{m}}}}} \\ {{{{-\frac{\nu} {v_{u}-v_{m}}+\frac{v_{u}} {v_{u}-v_{m}}}}}} & {{{{\mathrm{i f ~} v_{m} \leq v \leq v_{u}}}}} \\ {{{{0}}}} & {{{{\mathrm{e l s e w h e r e}}.}}} \\ \end{array} \right.
$$
Assume that the radio dish is a 100% efficient reflector over the receiver's bandwidth and has a diameter of 100 m. Assume also that the source NGC 2558 (a spiral galaxy with an apparent visual magnitude of 13.8) has a constant spectral flux density of $S=2. 5$ mJy over the detector bandwidth. Calculate the total power measured at the receiver.

Options:
A. $$
5. 0 4 \times1 0^{-1 8} \mathrm{~ W}
$$
B. $$
9. 0 2 \times1 0^{-1 9} \mathrm{~ W}
$$
C. $$
8. 3 9 \times1 0^{-1 8} \mathrm{~ W}
$$
D. $$
6. 7 2 \times1 0^{-1 9} \mathrm{~ W}
$$
E. $$
4. 9 1 \times1 0^{-1 8} \mathrm{~ W}
$$
F. $$
9. 5 6 \times1 0^{-1 9} \mathrm{~ W}
$$
G. $$
1. 4 7 \times1 0^{-1 7} \mathrm{~ W}
$$
H. $$
7. 5 1 \times1 0^{-1 7} \mathrm{~ W}
$$
I. $$
2. 3 5 \times1 0^{-1 8} \mathrm{~ W}
$$
J. $$
3. 8 6 \times1 0^{-1 6} \mathrm{~ W}
$$
Answer: E
Below is the fuzzy matrix
$$
R=\left[ \begin{matrix} {{1. 0}} & {{0. 3}} & {{0. 5}} & {{0. 9}} \\ {{0. 3}} & {{1. 0}} & {{0. 6}} & {{0. 2}} \\ {{0. 5}} & {{0. 6}} & {{1. 0}} & {{0. 4}} \\ {{0. 9}} & {{0. 2}} & {{0. 4}} & {{1. 0}} \\ \end{matrix} \right]
$$
What is the transitive closure $t(R)$?

Options:
A. $$ t(R)=\left[ \begin{matrix} {{1. 0}} & {{0. 3}} & {{0. 5}} & {{0. 9}} \\ {{0. 3}} & {{1. 0}} & {{0. 6}} & {{0. 4}} \\ {{0. 5}} & {{0. 6}} & {{1. 0}} & {{0. 5}} \\ {{0. 9}} & {{0. 4}} & {{0. 5}} & {{1. 0}} \\ \end{matrix} \right] $$
B. $$ t(R)=\left[ \begin{matrix} {{1. 0}} & {{0. 5}} & {{0. 7}} & {{0. 9}} \\ {{0. 5}} & {{1. 0}} & {{0. 6}} & {{0. 5}} \\ {{0. 7}} & {{0. 6}} & {{1. 0}} & {{0. 7}} \\ {{0. 9}} & {{0. 5}} & {{0. 7}} & {{1. 0}} \\ \end{matrix} \right] $$
C. $$
t(R)=\left[ \begin{matrix} {{1. 0}} & {{0. 5}} & {{0. 5}} & {{0. 9}} \\ {{0. 5}} & {{1. 0}} & {{0. 6}} & {{0. 5}} \\ {{0. 5}} & {{0. 6}} & {{1. 0}} & {{0. 5}} \\ {{0. 9}} & {{0. 5}} & {{0. 5}} & {{1. 0}} \\ \end{matrix} \right]
$$
D. $$ t(R)=\left[ \begin{matrix} {{1. 0}} & {{0. 5}} & {{0. 5}} & {{0. 7}} \\ {{0. 5}} & {{1. 0}} & {{0. 6}} & {{0. 3}} \\ {{0. 5}} & {{0. 6}} & {{1. 0}} & {{0. 6}} \\ {{0. 7}} & {{0. 3}} & {{0. 6}} & {{1. 0}} \\ \end{matrix} \right] $$
E. $$ t(R)=\left[ \begin{matrix} {{1. 0}} & {{0. 5}} & {{0. 5}} & {{0. 6}} \\ {{0. 5}} & {{1. 0}} & {{0. 5}} & {{0. 5}} \\ {{0. 5}} & {{0. 5}} & {{1. 0}} & {{0. 5}} \\ {{0. 6}} & {{0. 5}} & {{0. 5}} & {{1. 0}} \\ \end{matrix} \right] $$
F. $$ t(R)=\left[ \begin{matrix} {{1. 0}} & {{0. 5}} & {{0. 4}} & {{0. 9}} \\ {{0. 4}} & {{1. 0}} & {{0. 6}} & {{0. 5}} \\ {{0. 4}} & {{0. 6}} & {{1. 0}} & {{0. 4}} \\ {{0. 9}} & {{0. 5}} & {{0. 4}} & {{1. 0}} \\ \end{matrix} \right] $$
G. $$ t(R)=\left[ \begin{matrix} {{1. 0}} & {{0. 6}} & {{0. 5}} & {{0. 6}} \\ {{0. 6}} & {{1. 0}} & {{0. 7}} & {{0. 5}} \\ {{0. 5}} & {{0. 7}} & {{1. 0}} & {{0. 8}} \\ {{0. 6}} & {{0. 5}} & {{0. 8}} & {{1. 0}} \\ \end{matrix} \right] $$
H. $$ t(R)=\left[ \begin{matrix} {{1. 0}} & {{0. 6}} & {{0. 5}} & {{0. 9}} \\ {{0. 6}} & {{1. 0}} & {{0. 7}} & {{0. 5}} \\ {{0. 5}} & {{0. 7}} & {{1. 0}} & {{0. 6}} \\ {{0. 9}} & {{0. 5}} & {{0. 6}} & {{1. 0}} \\ \end{matrix} \right] $$
I. $$ t(R)=\left[ \begin{matrix} {{1. 0}} & {{0. 5}} & {{0. 6}} & {{0. 9}} \\ {{0. 5}} & {{1. 0}} & {{0. 5}} & {{0. 6}} \\ {{0. 6}} & {{0. 5}} & {{1. 0}} & {{0. 7}} \\ {{0. 9}} & {{0. 6}} & {{0. 7}} & {{1. 0}} \\ \end{matrix} \right] $$
J. $$ t(R)=\left[ \begin{matrix} {{1. 0}} & {{0. 4}} & {{0. 5}} & {{0. 8}} \\ {{0. 4}} & {{1. 0}} & {{0. 5}} & {{0. 4}} \\ {{0. 5}} & {{0. 5}} & {{1. 0}} & {{0. 5}} \\ {{0. 8}} & {{0. 4}} & {{0. 5}} & {{1. 0}} \\ \end{matrix} \right] $$
Answer: C
In the comprehensive evaluation of the teaching process, let $U = \{ \text{clear and easy to understand}, \text{proficient with the teaching materials}, \text{lively and interesting}, \text{neat and clear blackboard writing} \}$, and $V = \{ \text{very good}, \text{good}, \text{average}, \text{poor} \}$. Suppose the evaluation matrix of a class of students for the teacher's teaching is:
$$
R = \begin{pmatrix}
0.4 & 0.5 & 0.1 & 0 \\
0.6 & 0.3 & 0.1 & 0 \\
0.1 & 0.2 & 0.6 & 0.1 \\
0.1 & 0.2 & 0.5 & 0.2
\end{pmatrix}
$$
If considering the weight $A = (0.5, 0.2, 0.2, 0.1)$, what is the comprehensive evaluation $\underset{\sim}{B}$ by the students for this teacher?

Options:
A. $$\underset{\sim}{B}=( 0. 2 8, 0. 4 0, 0. 2 2, 0. 1 0 )$$
B. $$\underset{\sim}{B}=( 0. 3 5, 0. 3 8, 0. 2 0, 0. 0 7 )$$
C. $$\underset{\sim}{B}=( 0. 2 0, 0. 5 0, 0. 1 5, 0. 1 5 )$$
D. $$\underset{\sim}{B}=( 0. 3 8, 0. 3 9, 0. 2 0, 0. 0 3 )$$
E. $$\underset{\sim}{B}=( 0. 2 5, 0. 4 5, 0. 2 0, 0. 1 0 )$$
F. $$\underset{\sim}{B}=( 0. 2 9, 0. 4 1, 0. 2 0, 0. 1 0 )$$
G. $$\underset{\sim}{B}=( 0. 2 7, 0. 4 3, 0. 2 1, 0. 0 9 )$$
H. $$\underset{\sim}{B}=( 0. 3 3, 0. 4 2, 0. 1 7, 0. 0 8 )$$
I. $$\underset{\sim}{B}=( 0. 4 0, 0. 3 0, 0. 2 0, 0. 1 0 )$$
J. $$\underset{\sim}{B}=( 0. 3 0, 0. 3 5, 0. 2 5, 0. 1 0 )$$
Answer: H
Suppose we have two independent random samples $\{Y_{1}, \: i=1, \ldots, n \}$ from Poisson with (unknown) mean $\lambda_{1}$ and $\{Y_{i}, \ i=n+1, \ldots, 2 n \}$ from Poisson with (unknown) mean $\lambda_{2}$ . Let $\theta=\lambda_{1} / ( \lambda_{1}+\lambda_{2} )$ . Find an unbiased estimator of $\theta$ .

Options:
A. $$
\hat{\theta}=\frac{Y+Y^{\prime}} {2Y}
$$
B. $$
\hat{\theta}=\frac{Y-Y^{\prime}} {Y+Y^{\prime}}
$$
C. $$
\hat{\theta}=\frac{2Y} {Y+Y^{\prime}}
$$
D. $$
\hat{\theta}=\frac{Y} {Y+Y^{\prime}}
$$
E. $$
\hat{\theta}=\frac{Y^{\prime}} {Y+Y^{\prime}}
$$
F. $$
\hat{\theta}=\frac{\sum Y} {\sum Y^{\prime}}
$$
G. $$
\hat{\theta}=\frac{\bar{Y}} {\bar{Y}+\bar{Y}^{\prime}}
$$
H. $$
\hat{\theta}=\frac{\sqrt{Y}} {Y+Y^{\prime}}
$$
I. $$
\hat{\theta}=\frac{Y+1} {Y+Y^{\prime}+2}
$$
J. $$
\hat{\theta}=\frac{Y^{2}} {Y+Y^{\prime}}
$$
Answer: D
Any $C^{\infty}$ function $f$ on a compact smooth manifold $M$ (without boundary) must have at least two critical points. When $M$ is the 2-torus, $f$ must have more than ______ critical points.

Options:
A. $$0$$
B. $$5$$
C. $$8$$
D. $$1$$
E. $$2$$
F. $$3$$
G. $$4$$
H. $$6$$
I. $$9$$
J. $$7$$
Answer: E
Let $x \, : \, M \to\mathbb{R}^{3}$ be a closed surface in 3-dimensional Euclidean space. Its Gaussian curvature and mean curvature are denoted by $K$ and $H$ re- spectively. And $\iint_{M} H d A+\iint_{M} p K d A=$ ______ , $\quad\iint_{M} p H d A+\iint_{M} d A=$ ________ .

Options:
A. $$0,0$$
B. $$2,-2$$
C. $$\pi,2\pi$$
D. $$-2,2$$
E. $$0,\pi$$
F. $$1,1$$
G. $$0.5,0.5$$
H. $$2,1$$
I. $$-1,-1$$
J. $$\frac{\pi}{2},0$$
Answer: A
How many point does every closed hypersurface in $\mathbb{R}^{n}$ have at which the second fundamental form is positive definite?

Options:
A. $$6$$
B. $$n-1$$
C. $$0$$
D. $$2$$
E. $$1$$
F. $$-1$$
G. $$4$$
H. $$5$$
I. $$3$$
J. $$n$$
Answer: E
The New Democratic Society belongs to ().

Options:
A. Colonial system
B. Feudal system
C. Theocratic system
D. Oligarchic system
E. Socialist system
F. Semi colonial and semi feudal system
G. Monarchical system
H. Federal system
I. Capitalist system
J. Mixed economy system
Answer: E
What kind of social relationship is the true guarantee of morality?

Options:
A. Religion
B. Interpersonal relationships
C. Culture
D. Law
E. Society
F. Economy
G. Tradition
H. Education
I. Politics
J. Internal
Answer: B
Utilitarianism believes that the premise for the effective operation of representative government is ( ).

Options:
A. universal suffrage without restrictions
B. limited governmental intervention
C. a single-party system
D. frequent public referendums
E. a strong central authority
F. reasonable division of government functions and allocation of power
G. direct democracy without representatives
H. each citizen may actually exercise sovereignty
I. sovereignty belongs to the people
J. citizens can enjoy equal political rights
Answer: F
Administrative ethics refers to the sum of ethical concepts, ethical norms and ( ) that administrative entities (including state administrative organs and their service personnel) should establish and abide by when performing official activities.

Options:
A. Administrative Responsibilities
B. Moral Standards
C. Ethical Responsibility
D. Operational Guidelines
E. Ethical Conduct
F. Legal Obligations
G. Ideological norms
H. Ethical Thought
I. Professional Conduct
J. Social Duties
Answer: C
Confucius proposed the idea of ​​the unity of "benevolence" and "propriety", which, in the final analysis, was to shape an ideal personality that could shoulder the historical mission, which is ____.

Options:
A. king
B. philosopher
C. gentleman
D. warrior
E. leader
F. saint
G. Sage
H. scholar
I. hero
J. mentor
Answer: C
"Human nature is like a turbulent stream. If it is diverted from the east, it will flow east; if it is diverted from the west, it will flow west. Human nature is neither good nor bad, just as water is neither east nor west." Whose point of view does this sentence represent?

Options:
A. Han Feizi
B. Xunzi
C. Confucius
D. Zhuangzi
E. Yang Xiong
F. Mozi
G. Laozi
H. Mencius
I. Gaozi
J. Dong Zhongshu
Answer: I
The basic question of morality should be ___.

Options:
A. Interest issues
B. Ethical dilemmas
C. Relationship Problems
D. Historical context
E. Political issues
F. Interests and their relationship issues
G. Cultural traditions
H. Legal considerations
I. Personal beliefs
J. Social norms
Answer: F
Marx said: "As a definite person, a real person, you have a definition, a mission, and a task. Whether you are aware of this or not is irrelevant." Here, the "definition", "mission" and "task" of a definite real person refer to ___.

Options:
A. Life Duty
B. Life Faith
C. Life Purpose
D. Life Goal
E. Life Challenge
F. Life Responsibility
G. Life Ambition
H. Life Journey
I. Life Existence
J. Life realm
Answer: F
According to the law of contradiction in the basic law of adaptive logic, when "Team A can win only if Xiao Wang plays" is true, which conjunctive judgment is false?

Options:
A. Xiao Wang doesn't play if Team A loses
B. Xiao Wang plays or Team A doesn't win
C. Xiao Wang doesn't play and Team A loses
D. Xiao Wang and Team A both do not play
E. Xiao Wang plays if and only if Team A wins
F. Xiao Wang plays and Team A loses
G. Xiao Wang plays and Team A wins
H. Team A wins only if Xiao Wang doesn't play
I. Xiao Wang doesn't play and Team A wins
J. Team A loses and Xiao Wang does not play
Answer: I
SOP can be introduced from not-SAP on the basis of the ( ) relation in the logical square.

Options:
A. Biconditional
B. Lower Opposition
C. Distribution
D. Contraposition
E. Contradiction
F. Inversion
G. Subalternation
H. Opposition
I. Difference and Equality
J. Conversion
Answer: E