MikaStars39/nano-eval huggingface dataset:
Cobalt (Co) has an HCP crystal structure, an atomic radius of 0.1253 nm, and a c/a ratio of 1.623. The volume of the unit cell for Co.is().

Options:
A. $$
7. 9 4 \, \times\, 1 0^{-2} \mathrm{~ n m}^{3}
$$
B. $$
5. 8 9 \, \times\, 1 0^{-2} \mathrm{~ n m}^{3}
$$
C. $$
5. 3 2 \, \times\, 1 0^{-2} \mathrm{~ n m}^{3}
$$
D. $$
4. 5 5 \, \times\, 1 0^{-2} \mathrm{~ n m}^{3}
$$
E. $$
6. 6 4 \, \times\, 1 0^{-2} \mathrm{~ n m}^{3}
$$
F. $$
5. 7 8 \, \times\, 1 0^{-2} \mathrm{~ n m}^{3}
$$
G. $$
7. 0 7 \, \times\, 1 0^{-2} \mathrm{~ n m}^{3}
$$
H. $$
3. 9 8 \, \times\, 1 0^{-2} \mathrm{~ n m}^{3}
$$
I. $$
6. 1 1 \, \times\, 1 0^{-2} \mathrm{~ n m}^{3}
$$
J. $$
8. 2 1 \, \times\, 1 0^{-2} \mathrm{~ n m}^{3}
$$
Answer: E
Germanium (Ge) forms a substitutional solid solution with silicon (Si). The weight percent of germanium that must be added to silicon to yield an alloy that contains $2. 4 3 \times1 0^{2 1}$ Ge atoms per cubic centimeter is(). The densities of pure Ge and Si are 5.32 and 2.33 g/cm-, respectively.

Options:
A. $$ 4. 6 \, \mathrm{w t}\% $$
B. $$
1 1. 7 \, \mathrm{w t}\%
$$
C. $$ 3. 9 \, \mathrm{w t}\% $$
D. $$ 1 3. 0 \, \mathrm{w t}\% $$
E. $$ 6. 3 \, \mathrm{w t}\% $$
F. $$ 2. 1 \, \mathrm{w t}\% $$
G. $$
8. 7 \, \mathrm{w t}\%
$$
H. $$ 5. 2 \, \mathrm{w t}\% $$
I. $$ 9. 5 \, \mathrm{w t}\% $$
J. $$ 7. 4 \, \mathrm{w t}\% $$
Answer: B
A sheet of BCC iron 2-mm thick was exposed to a carburizing gas atmosphere on one side and $a$ decarburizing atmosphere on the other side at 675°C. After reaching steady state, the iron was quickly cooled to room temperature. The carbon concentrations at the two surfaces of the she et were determined to be 0.015 and 0.0068 wt%, respectively. What is the diffusion coefficient if the diffusion flux is $7. 3 6 \times1 0^{-9} kg/m^{2} \cdot s$?

Options:
A. $$
1. 8 \times1 0^{-1 2} \mathrm{~ m^{2} / s}
$$
B. $$
7. 9 \times1 0^{-1 2} \mathrm{~ m^{2} / s}
$$
C. $$
3. 5 \times1 0^{-1 0} \mathrm{~ m^{2} / s}
$$
D. $$
2. 3 \times1 0^{-1 1} \mathrm{~ m^{2} / s}
$$
E. $$
5. 2 \times1 0^{-1 1} \mathrm{~ m^{2} / s}
$$
F. $$
2. 1 \times1 0^{-1 2} \mathrm{~ m^{2} / s}
$$
G. $$
8. 4 \times1 0^{-1 0} \mathrm{~ m^{2} / s}
$$
H. $$
6. 7 \times1 0^{-1 3} \mathrm{~ m^{2} / s}
$$
I. $$
9. 6 \times1 0^{-1 1} \mathrm{~ m^{2} / s}
$$
J. $$
4. 1 \times1 0^{-1 1} \mathrm{~ m^{2} / s}
$$
Answer: D
Indium atoms are to be diffised into a silicon wafer using both predeposition and drive-in heat treatments; the background concentration of In in this silicon material is known to be $2 \times1 0^{2 0} atoms/m^{3}$. The drive-in diffusion treatment is to be carried out at $1175^\circ C$ for a period of 2.0 h, which gives a junction depth $x_{j}$ of $2.35 \mu m$. The predeposition diffusion time at 925 °C if the surface concentration is maintained at a constant level of $2. 5 \times1 0^{2 6} atoms/m^{3}$ is(). For the diffusion of In in $S_{i}$, values of $Q_{d}$ and $D_{0}$ are 3.63 eV/atom and $7. 8 5 \times1 0^{-5} m^{2}/s$, respectively.

Options:
A. $$
2. 4 8 \, \mathbf{h}
$$
B. $$
1. 5 3 \, \mathbf{h}
$$
C. $$
9. 4 6 \, \mathbf{h}
$$
D. $$
7. 9 5 \, \mathbf{h}
$$
E. $$
0. 5 9 \, \mathbf{h}
$$
F. $$
3. 7 1 \, \mathbf{h}
$$
G. $$
5. 6 4 \, \mathbf{h}
$$
H. $$
4. 2 0 \, \mathbf{h}
$$
I. $$
8. 1 7 \, \mathbf{h}
$$
J. $$
6. 8 3 \, \mathbf{h}
$$
Answer: B
For some metal alloy, a true stress of 345 MPa (50,000 psi) produces a plastic true strain of 0.02. How much does a specimen of this material elongate when a true stress of 415 MPa (60,000 psi) is applied if the original length is 500 mm (20 in.)? Assume a value of 0.22 for the strain-hardening exponent, $n$ .

Options:
A. $$2 5. 3 \ \mathrm{m m} \ ( 1. 0 0 0 \ \mathrm{i n}. )$$
B. $$1 7. 4 \ \mathrm{m m} \ ( 0. 6 8 5 \ \mathrm{i n}. )$$
C. $$2 2. 5 \ \mathrm{m m} \ ( 0. 8 8 2 \ \mathrm{i n}. )$$
D. $$2 0. 5 \ \mathrm{m m} \ ( 0. 8 0 7 \ \mathrm{i n}. )$$
E. $$
2 3. 7 \ \mathrm{m m} \ ( 0. 9 4 8 \ \mathrm{i n}. )
$$
F. $$3 0. 1 \ \mathrm{m m} \ ( 1. 1 8 5 \ \mathrm{i n}. )$$
G. $$3 5. 6 \ \mathrm{m m} \ ( 1. 4 0 0 \ \mathrm{i n}. )$$
H. $$1 9. 8 \ \mathrm{m m} \ ( 0. 7 8 0 \ \mathrm{i n}. )$$
I. $$3 2. 9 \ \mathrm{m m} \ ( 1. 2 9 5 \ \mathrm{i n}. )$$
J. $$2 7. 5 \ \mathrm{m m} \ ( 1. 0 8 3 \ \mathrm{i n}. )$$
Answer: E
The lower yield point for an iron that has an average grain diameter of $1 \times 1 0^{-2}$ mm is 230 MPa (33,000 psi), At a grain diameter of $6 \times1 0^{-3}$ mm, the yield point increases to 275 MPa (40 000 psi). At what grain diameter will the lower yield point be 310 MPa (45,000 psi)?

Options:
A. $$ 3. 6 2 \times1 0^{-3} \mathrm{~ m m} $$
B. $$ 4. 9 8 \times1 0^{-3} \mathrm{~ m m} $$
C. $$ 3. 8 9 \times1 0^{-3} \mathrm{~ m m} $$
D. $$ 5. 7 2 \times1 0^{-3} \mathrm{~ m m} $$
E. $$ 5. 3 4 \times1 0^{-3} \mathrm{~ m m} $$
F. $$ 5. 0 3 \times1 0^{-3} \mathrm{~ m m} $$
G. $$ 6. 0 1 \times1 0^{-3} \mathrm{~ m m} $$
H. $$ 7. 1 5 \times1 0^{-3} \mathrm{~ m m} $$
I. $$ 6. 5 6 \times1 0^{-3} \mathrm{~ m m} $$
J. $$
4. 3 4 \times1 0^{-3} \mathrm{~ m m}
$$
Answer: J
A specimen of a 4340 stel alloy wih a planestran fracture toughness of 54.8 MPa $\sqrt{m}$ (50 ksi $\sqrt{i n}$ is exposed to a stress of 1030 MPa (150,000 psi). Will his specimen experience fracture if the largest surface crack is 0.5 mm (0.02 in.) long? Assume that the parameter $Y$ has a value of 1.0.is().

Options:
A. $$
1 0 5 0 \mathrm{~ M P a ~} ( 1 5 2, 0 0 0 \mathrm{~ p s i} )
$$
B. $$
1 3 2 0 \mathrm{~ M P a ~} ( 1 9 2, 0 0 0 \mathrm{~ p s i} )
$$
C. $$
9 0 0 \mathrm{~ M P a ~} ( 1 3 5, 0 0 0 \mathrm{~ p s i} )
$$
D. $$
1 3 8 0 \mathrm{~ M P a ~} ( 2 0 0, 0 0 0 \mathrm{~ p s i} )
$$
E. $$
1 1 5 0 \mathrm{~ M P a ~} ( 1 6 7, 0 0 0 \mathrm{~ p s i} )
$$
F. $$
7 5 0 \mathrm{~ M P a ~} ( 1 1 0, 0 0 0 \mathrm{~ p s i} )
$$
G. $$
1 4 0 0 \mathrm{~ M P a ~} ( 2 1 0, 0 0 0 \mathrm{~ p s i} )
$$
H. $$
1 2 0 0 \mathrm{~ M P a ~} ( 1 7 4, 0 0 0 \mathrm{~ p s i} )
$$
I. $$
9 5 0 \mathrm{~ M P a ~} ( 1 4 0, 0 0 0 \mathrm{~ p s i} )
$$
J. $$
8 9 0 \mathrm{~ M P a ~} ( 1 3 0, 0 0 0 \mathrm{~ p s i} )
$$
Answer: D
It is known that the kinetics of recrystallization for some alloy obeys the Avrami equation, and that the value of $n$ in the exponential is 5.0. If, at some temperature, the fraction recrystallized is 0.30 after 100 min, determine the rate of recrystallization at this temperature.

Options:
A. $$
2. 9 0 \, \times\, 1 0^{-4} \mathrm{( m i n )}^{-1}
$$
B. $$
6. 4 4 \, \times\, 1 0^{-3} \mathrm{( m i n )}^{-1}
$$
C. $$
7. 2 2 \, \times\, 1 0^{-3} \mathrm{( m i n )}^{-1}
$$
D. $$
9. 5 2 \, \times\, 1 0^{-3} \mathrm{( m i n )}^{-1}
$$
E. $$
4. 9 8 \, \times\, 1 0^{-3} \mathrm{( m i n )}^{-1}
$$
F. $$
5. 3 8 \, \times\, 1 0^{-3} \mathrm{( m i n )}^{-1}
$$
G. $$
3. 4 6 \, \times\, 1 0^{-3} \mathrm{( m i n )}^{-1}
$$
H. $$
8. 7 6 \, \times\, 1 0^{-3} \mathrm{( m i n )}^{-1}
$$
I. $$
1. 2 0 \, \times\, 1 0^{-2} \mathrm{( m i n )}^{-1}
$$
J. $$
7. 1 8 \, \times\, 1 0^{-3} \mathrm{( m i n )}^{-1}
$$
Answer: H
Calculate the number of Frenkel defects per cubic meter in silver chloride at $350^oC$ is().The energy for defect formation is 1.1 eV, whereas the density for AgCl is 5.50 g/$cm^3$ at $350^{°}C$.

Options:
A. $$
4. 5 8 \times1 0^{2 1} \ \mathrm{b o n d s / m}^{3}
$$
B. $$
6. 3 1 \times1 0^{2 4} \ \mathrm{i o n s / m}^{3}
$$
C. $$
3. 7 2 \times1 0^{1 8} \ \mathrm{p a i r s / m}^{3}
$$
D. $$
9. 0 5 \times1 0^{1 9} \ \mathrm{a t o m s / m}^{3}
$$
E. $$
6. 1 1 \times1 0^{2 3} \ \mathrm{p a r t i c l e s / m}^{3}
$$
F. $$
2. 9 9 \times1 0^{2 0} \ \mathrm{m o l e c u l e s / m}^{3}
$$
G. $$
5. 7 0 \times1 0^{2 2} \ \mathrm{g / m}^{3}
$$
H. $$
8. 2 4 \times1 0^{2 3} \ \mathrm{d c f e c t s / m}^{3}
$$
I. $$
7. 8 9 \times1 0^{2 0} \ \mathrm{h o l e s / m}^{3}
$$
J. $$
1. 4 6 \times1 0^{2 5} \ \mathrm{v a c a n c i e s / m}^{3}
$$
Answer: H
A three-point transverse bending test is conducted on a cylindrical speciman of aluminum oxide having a reported flexural strength of 300 MPa (43,500 psi). If the specimen radius is 5.0 mm (0.20 in.) and the support point separation distance is 15.0 mm (0.61 in), would you expect the specimen to fracture when a load of 7500 $N$ (1690 $lb_f$) is applied?

Options:
A. $$
3. 1 5. 0 \ \mathrm{M P a} \ \ ( 4 5, 7 2 0 \ \mathrm{p s i} )
$$
B. $$
3. 2 0. 2 \ \mathrm{M P a} \ \ ( 4 6, 5 3 0 \ \mathrm{p s i} )
$$
C. $$
2. 9 0. 3 \ \mathrm{M P a} \ \ ( 4 2, 1 1 5 \ \mathrm{p s i} )
$$
D. $$
2. 5 0. 5 \ \mathrm{M P a} \ \ ( 3 6, 3 0 0 \ \mathrm{p s i} )
$$
E. $$
2. 9 8. 4 \ \mathrm{M P a} \ \ ( 4 3, 2 7 0 \ \mathrm{p s i} )
$$
F. $$
3. 0 0. 6 \ \mathrm{M P a} \ \ ( 4 3, 6 5 0 \ \mathrm{p s i} )
$$
G. $$
2. 8 3. 4 \ \mathrm{M P a} \ \ ( 3 9, 3 5 0 \ \mathrm{p s i} )
$$
H. $$
2. 7 0. 0 \ \mathrm{M P a} \ \ ( 3 8, 6 0 0 \ \mathrm{p s i} )
$$
I. $$
2. 6 8. 0 \ \mathrm{M P a} \ \ ( 3 8, 9 7 0 \ \mathrm{p s i} )
$$
J. $$
2. 8 6. 5 \ \mathrm{M P a} \ \ ( 4 0, 3 0 0 \ \mathrm{p s i} )
$$
Answer: J
The fracture strength of glass may be increased by etching away a thin suface layer. It is believed that the etching may alter surface crack geometry (ie., reduce the crack length and increase the tip radus). Compute the ratio of the etched and original cracktip radi for a fufol i inceasein frature strength if hlfof the crack length is removed is().

Options:
A. 9
B. 12
C. 11
D. 7
E. 10
F. 8
G. 5
H. 6
I. 13
J. 14
Answer: F
The ratio of butadiene to acrylonitrile repeat units in a copolymer having a number- average molecular weight of 250,000 g/mol and a degree of polymerization of 4640.

Options:
A. 6.0
B. 4.5
C. 5.5
D. 5.0
E. 4.0
F. 1.5
G. 2.0
H. 2.5
I. 3.5
J. 3.0
Answer: E
Carbon dioxcide diffuses through a high-density polyethylene (DPE) sheet 50 mm thick at a rate of $2.2 \times 10^{-8} \, \left( \text{cm}^3 \, \text{STP} \right) / \text{cm}^2 \cdot \text{s}$ at 325 K. The pressures of carbon dioxide at the two faces are 4000 kPa and 2500 kPa, which are maintained constant. Assuming conditions of steady state, what is the permeability coefficient at 325 K?

Options:
A. $$
4. 4 6 \, \times\, 1 0^{-1 4} \, {\frac{( \mathrm{c m}^{3} \mathrm{S T P} ) ( \mathrm{c m} )} {\mathrm{c m}^{2}-\mathrm{s-P a}}}
$$
B. $$
3. 0 8 \, \times\, 1 0^{-1 4} \, {\frac{( \mathrm{c m}^{3} \mathrm{S T P} ) ( \mathrm{c m} )} {\mathrm{c m}^{2}-\mathrm{s-P a}}}
$$
C. $$
1. 0 7 \, \times\, 1 0^{-1 2} \, {\frac{( \mathrm{c m}^{3} \mathrm{S T P} ) ( \mathrm{c m} )} {\mathrm{c m}^{2}-\mathrm{s-P a}}}
$$
D. $$
1. 6 4 \, \times\, 1 0^{-1 2} \, {\frac{( \mathrm{c m}^{3} \mathrm{S T P} ) ( \mathrm{c m} )} {\mathrm{c m}^{2}-\mathrm{s-P a}}}
$$
E. $$
2. 9 5 \, \times\, 1 0^{-1 3} \, {\frac{( \mathrm{c m}^{3} \mathrm{S T P} ) ( \mathrm{c m} )} {\mathrm{c m}^{2}-\mathrm{s-P a}}}
$$
F. $$
0. 5 8 \, \times\, 1 0^{-1 3} \, {\frac{( \mathrm{c m}^{3} \mathrm{S T P} ) ( \mathrm{c m} )} {\mathrm{c m}^{2}-\mathrm{s-P a}}}
$$
G. $$
2. 2 1 \, \times\, 1 0^{-1 3} \, {\frac{( \mathrm{c m}^{3} \mathrm{S T P} ) ( \mathrm{c m} )} {\mathrm{c m}^{2}-\mathrm{s-P a}}}
$$
H. $$
5. 1 3 \, \times\, 1 0^{-1 5} \, {\frac{( \mathrm{c m}^{3} \mathrm{S T P} ) ( \mathrm{c m} )} {\mathrm{c m}^{2}-\mathrm{s-P a}}}
$$
I. $$
3. 5 9 \, \times\, 1 0^{-1 4} \, {\frac{( \mathrm{c m}^{3} \mathrm{S T P} ) ( \mathrm{c m} )} {\mathrm{c m}^{2}-\mathrm{s-P a}}}
$$
J. $$
0. 7 3 \, \times\, 1 0^{-1 3} \, {\frac{( \mathrm{c m}^{3} \mathrm{S T P} ) ( \mathrm{c m} )} {\mathrm{c m}^{2}-\mathrm{s-P a}}}
$$
Answer: J
The longituinal strength of an aligned carbon fiber-epoxy matrix composite having a 0.20 volue fraction of fibers, assuming the following: (1) an average fiber diameter of $6 \times1 0^{-3}$ mm $(2. 4 \times1 0^{-4}$ in.), (2) an average fiber length of 8.0 mm (0.31 in), (3) a fiber fracture strength of 4.5 GPa ( $6. 5 \times1 0^{5}$ psi), (4) a fiber- matrix bond strength of 75 MPa (10,900 psi), (5) a matrix stress at composite failure of 6.0 MPa (870 psi), and (6) a matrix tensile strength of 60 MPa (8700 psi) is().

Options:
A. $$
5 6 0 \mathrm{~ M P a ~} ( 8 1, 2 5 0 \mathrm{~ p s i} )
$$
B. $$
1 2 5 0 \mathrm{~ M P a ~} ( 1 8 1, 3 0 0 \mathrm{~ p s i} )
$$
C. $$
1 4 0 0 \mathrm{~ M P a ~} ( 2 0 3, 3 0 0 \mathrm{~ p s i} )
$$
D. $$
1 1 0 0 \mathrm{~ M P a ~} ( 1 5 9, 5 0 0 \mathrm{~ p s i} )
$$
E. $$
6 9 0 \mathrm{~ M P a ~} ( 1 0 0, 0 0 0 \mathrm{~ p s i} )
$$
F. $$
7 8 0 \mathrm{~ M P a ~} ( 1 1 3, 1 0 0 \mathrm{~ p s i} )
$$
G. $$
3 2 0 \mathrm{~ M P a ~} ( 4 6, 3 5 0 \mathrm{~ p s i} )
$$
H. $$
9 0 5 \mathrm{~ M P a ~} ( 1 3 0, 7 0 0 \mathrm{~ p s i} )
$$
I. $$
4 7 0 \mathrm{~ M P a ~} ( 6 8, 2 0 0 \mathrm{~ p s i} )
$$
J. $$
8 3 5 \mathrm{~ M P a ~} ( 1 2 1, 1 0 0 \mathrm{~ p s i} )
$$
Answer: H
The drift velocity of electrons in silicon at room temperature and when the magnitude of the electric field is 500 V/m is().

Options:
A. 77.1 m/s
B. 68.9 m/s
C. 69.5 m/s
D. 76.0 m/s
E. 70.3 m/s
F. 75.4 m/s
G. 73.8 m/s
H. 74.6 m/s
I. 72.5 m/s
J. 71.2 m/s
Answer: I
At temperatures near room temperature, the temperature dependence of the conductivity for intrinsic germanium is found to be given by
$$
\sigma=C T^{-3 / 2} \operatorname{e x p} \! \left(-{\frac{E_{g}} {2 k T}} \right)
$$
where $C$ is a temperature-independent constant and $T$ is in Kelvins. Using the above equation, calculate the intrinsic
electrical conductivity of germanium at 175°C.

Options:
A. $$
9 4. 4 \ ( \Omega\mathrm{-m} )^{-1}
$$
B. $$
9 6. 7 \ ( \Omega\mathrm{-m} )^{-1}
$$
C. $$
9 1. 3 \ ( \Omega\mathrm{-m} )^{-1}
$$
D. $$
1 0 0. 5 \ ( \Omega\mathrm{-m} )^{-1}
$$
E. $$
8 8. 8 \ ( \Omega\mathrm{-m} )^{-1}
$$
F. $$
9 5. 8 \ ( \Omega\mathrm{-m} )^{-1}
$$
G. $$
9 3. 2 \ ( \Omega\mathrm{-m} )^{-1}
$$
H. $$
9 9. 1 \ ( \Omega\mathrm{-m} )^{-1}
$$
I. $$
1 0 1. 0 \ ( \Omega\mathrm{-m} )^{-1}
$$
J. $$
1 0 2. 2 \ ( \Omega\mathrm{-m} )^{-1}
$$
Answer: A
A hypothetical metal is known to have an electrical resistivity of $3. 3 \times1 0^{-8} (\Omega \cdot m)$ . curen of 25is passed through aspecimen of this metal 15 mm thick When a magnetic field of 0.95 tesla is simtaneously imposed in a direction perpendicular to that of the current, a Hall voltage of $- 2. 4 \times1 0^{-7} V$ is measured.The following:
the electron mobility for this metal is ().

Options:
A. $$
0. 0 0 9 1 1 \ \mathrm{m}^{2} / \mathrm{V-s}
$$
B. $$
0. 0 0 8 4 9 \ \mathrm{m}^{2} / \mathrm{V-s}
$$
C. $$
0. 0 0 5 6 4 \ \mathrm{m}^{2} / \mathrm{V-s}
$$
D. $$
0. 0 0 1 3 7 \ \mathrm{m}^{2} / \mathrm{V-s}
$$
E. $$
0. 0 0 2 9 5 \ \mathrm{m}^{2} / \mathrm{V-s}
$$
F. $$
0. 0 0 7 8 2 \ \mathrm{m}^{2} / \mathrm{V-s}
$$
G. $$
0. 0 0 2 5 6 \ \mathrm{m}^{2} / \mathrm{V-s}
$$
H. $$
0. 0 0 3 5 0 \ \mathrm{m}^{2} / \mathrm{V-s}
$$
I. $$
0. 0 0 6 5 9 \ \mathrm{m}^{2} / \mathrm{V-s}
$$
J. $$
0. 0 0 4 5 5 \ \mathrm{m}^{2} / \mathrm{V-s}
$$
Answer: J
A copper wire 15 m (49.2 ft) long is cooled from 40°C to -9°C (104°F to 15°F). How much change in length does it experience?

Options:
A. $$
-7 . 8 \mathrm{\ m m} \quad(-0. 3 1 \mathrm{\ i n} )
$$
B. $$
-2 1. 0 \mathrm{\ m m} \quad(-0. 8 3 \mathrm{\ i n} )
$$
C. $$
-8 . 4 \mathrm{\ m m} \quad(-0. 3 3 \mathrm{\ i n} )
$$
D. $$
-9 . 5 \mathrm{\ m m} \quad(-0. 3 7 \mathrm{\ i n} )
$$
E. $$
-1 0. 1 \mathrm{\ m m} \quad(-0. 4 0 \mathrm{\ i n} )
$$
F. $$
-5 . 9 \mathrm{\ m m} \quad(-0. 2 3 \mathrm{\ i n} )
$$
G. $$
-1 1. 0 \mathrm{\ m m} \quad(-0. 4 3 \mathrm{\ i n} )
$$
H. $$
-1 4. 3 \mathrm{\ m m} \quad(-0. 5 6 \mathrm{\ i n} )
$$
I. $$
-1 2. 5 \mathrm{\ m m} \quad(-0. 5 0 \mathrm{\ i n} )
$$
J. $$
-1 6. 2 \mathrm{\ m m} \quad(-0. 6 4 \mathrm{\ i n} )
$$
Answer: I
An iron bar magnet having a coercivity of 7000 A/m is to be demagnetized. If the bar is inserted within a cylindrical wire coil 0.25 m long and having 150 turns, what electric current is required to generate the necessary magnetic field?

Options:
A. $$
2 9. 6 A
$$
B. $$
6 4. 2 A
$$
C. $$
3 5. 4 A
$$
D. $$
7 0. 1 A
$$
E. $$
5 8. 3 A
$$
F. $$
2 2. 9 A
$$
G. $$
1 1. 7 A
$$
H. $$
3 1. 8 A
$$
I. $$
4 1. 5 A
$$
J. $$
4 5. 7 A
$$
Answer: G
It was noted that the intensity of light absorbed while passing through a 16-km length of optical fiber glass is equivalent to the light intensity absorbed through a 25-mm thickness of ordinary window glass. Calculate the absorption coefficient $\beta$ of the optical fiber glass if the value of $\beta$ for the window glass is $1 0^{-4} mm^{-1}$.

Options:
A. $$
3. 9 2 \times1 0^{-2 0} \, {\mathrm{m m}}^{-1}
$$
B. $$
5. 7 3 \times1 0^{-1 5} \, {\mathrm{m m}}^{-1}
$$
C. $$
2. 4 8 \times1 0^{-1 2} \, {\mathrm{m m}}^{-1}
$$
D. $$
8. 5 8 \times1 0^{-1 4} \, {\mathrm{m m}}^{-1}
$$
E. $$
7. 1 8 \times1 0^{-1 8} \, {\mathrm{m m}}^{-1}
$$
F. $$
0. 1 5 \times1 0^{-1 3} \, {\mathrm{m m}}^{-1}
$$
G. $$
9. 3 7 \times1 0^{-1 6} \, {\mathrm{m m}}^{-1}
$$
H. $$
1. 5 6 \times1 0^{-1 0} \, {\mathrm{m m}}^{-1}
$$
I. $$
4. 2 9 \times1 0^{-1 7} \, {\mathrm{m m}}^{-1}
$$
J. $$
6. 4 4 \times1 0^{-1 1} \, {\mathrm{m m}}^{-1}
$$
Answer: H
Let $\alpha_{1}, \ldots, \alpha_{n}$ and $b_{1}, \ldots, b_{n}$ be complex numbes such that $a_{i} \!+\! b_{j} \neq 0$ for all $i, j=1, \ldots, n$ . Define $c_{i j} :={\frac{1} {a_{i}+b_{j}}}$ for all $i, j=1, \ldots, n$ , and let $C$ be the $n\times n$ determinant with entries $c_{ij}$. So $\operatorname* {d e t} ( C )=( )$ .

Options:
A. $$\frac{\prod_{1 \leq i < j \leq n} ( a_{i}-b_{j} ) ( b_{i}+a_{j} )} {\prod_{1 \leq i, j \leq n} ( a_{i}+b_{j} )}$$
B. $$\frac{\prod_{1 \leq i < j \leq n} ( a_{i} \cdot a_{j} ) ( b_{i} \cdot b_{j} )} {\prod_{1 \leq i, j \leq n} ( a_{i}+b_{j} )}$$
C. $$\frac{\prod_{1 \leq i < j \leq n} ( a_{i}+a_{j} ) ( b_{i}-b_{j} )} {\prod_{1 \leq i, j \leq n} ( a_{i}+b_{j} )}$$
D. $$\frac{\prod_{1 \leq i < j \leq n} ( a_{i}+a_{j} ) ( b_{i}+b_{j} )} {\prod_{1 \leq i, j \leq n} ( a_{i}+b_{j} )}$$
E. $$\frac{\prod_{1 \leq i < j \leq n} ( a_{i}+b_{j} ) ( b_{i}+a_{j} )} {\prod_{1 \leq i, j \leq n} ( a_{i}+b_{j} )}$$
F. $$\frac{\prod_{1 \leq i < j \leq n} ( a_{i} \cdot b_{j} ) ( b_{i} \cdot a_{j} )} {\prod_{1 \leq i, j \leq n} ( a_{i}+b_{j} )}$$
G. $$\frac{\prod_{1 \leq i < j \leq n} ( a_{i} \cdot a_{j} ) ( b_{i}-b_{j} )} {\prod_{1 \leq i, j \leq n} ( a_{i}+b_{j} )}$$
H. $$\frac{\prod_{1 \leq i < j \leq n} ( a_{i}-a_{j} ) ( b_{i}-b_{j} )} {\prod_{1 \leq i, j \leq n} ( a_{i}+b_{j} )}$$
I. $$\frac{\prod_{1 \leq i < j \leq n} ( a_{i}+b_{j} ) ( b_{i}-a_{j} )} {\prod_{1 \leq i, j \leq n} ( a_{i}+b_{j} )}$$
J. $$\frac{\prod_{1 \leq i < j \leq n} ( a_{i}-b_{j} ) ( b_{i}-a_{j} )} {\prod_{1 \leq i, j \leq n} ( a_{i}+b_{j} )}$$
Answer: H
A polynomial $f ( x )$ with integer coficients which has roots over $\mathbb{F}_{p}$ for all prime $p$ but not over $\mathbb{O}$ .What is the smallest possible degree of $f$ ?

Options:
A. $$
(1, ( 1, 1, 1 ) )
$$
B. $$
(-2, ( 5, 8, 9 ) )
$$
C. $$
(-1, ( 1, 0, 4 ) )
$$
D. $$
(2, ( 0, 1, 2 ) )
$$
E. $$
(3, ( 5, 6, 7 ) )
$$
F. $$
(-1, ( 1, 2, 3 ) )
$$
G. $$
(2, ( 2, 4, 6 ) )
$$
H. $$
(4, ( 3, 3, 3 ) )
$$
I. $$
(5, ( 1, 4, 5 ) )
$$
J. $$
(0, ( 2, 2, 2 ) )
$$
Answer: F
Let $G$ be a non-abelian finite group. Let $c ( G )$ be the number of conjugacy classes in $G$ Define $\overline{{{c}}} ( G ) :=c ( G ) / | G |, \, ( | G |=\mathrm{C a r d} ( G ) )$ . Suppose that there exists a prime number $p$ and an element $x \in G$ such that the cardinality of the conjugacy class of $x$ is divisible by $p$ . Find a good/sharp upper bound for $\overline{{{c}}} ( G )$ .

Options:
A. $$
| S | \leq1-{\frac{( | G |+| Z |+p )} {2}}
$$
B. $$
| S | \geq1+{\frac{( | G |-| Z |/p )} {2}}
$$
C. $$
| S | \leq1+{\frac{( | G |-| Z |-p )} {2}}
$$
D. $$
| S | \geq1-{\frac{( | G |-| Z |+p )} {2}}
$$
E. $$
| S | \geq1+{\frac{( | G |+| Z |/p )} {2}}
$$
F. $$
| S | \geq1+{\frac{( | G |+| Z |-p )} {2}}
$$
G. $$
| S | = 1+{\frac{( | G |-| Z |-2p )} {2}}
$$
H. $$
| S | \leq1+{\frac{( | G |+p-| Z | )} {2}}
$$
I. $$
| S | \leq1+{\frac{( | G |+| Z |-p^2 )} {2}}
$$
J. $$
| S | \leq1+{\frac{( | G |-2| Z |-p )} {2}}
$$
Answer: C
The atmospheric pressure on the surface of Mars, where $g=3. 7 \mathrm{~ m ~ s}^{-2},$ is only 0.0060 atm. To what extent is that low pressure due to the low gravitational attraction and not to the thinness of the atmosphere? What pressure would the same atmosphere exert on Earth, where $g=9. 8 1 \mathrm{~ m ~ s^{-2}?}$

Options:
A. $$
0. 7 4 \mathrm{~ a t m}
$$
B. $$
1. 9 5 \mathrm{~ a t m}
$$
C. $$
0. 2 5 \mathrm{~ a t m}
$$
D. $$
0. 9 8 \mathrm{~ a t m}
$$
E. $$
2. 4 9 \mathrm{~ a t m}
$$
F. $$
1. 1 2 \mathrm{~ a t m}
$$
G. $$
0. 5 6 \mathrm{~ a t m}
$$
H. $$
5. 7 6 \mathrm{~ a t m}
$$
I. $$
3. 0 1 \mathrm{~ a t m}
$$
J. $$
4. 2 0 \mathrm{~ a t m}
$$
Answer: D
Atmospheric pollution is a problem that has received much attention. Not all pollution, however, is from industrial sources. Volcanic eruptions can be a significant source of air pollution. The Kilauea volcano in Hawail emits 200-300 t of $\mathrm{S O}_{2}$ per day. If this gas is emitted at 800°C and 1.0 atm, what volume of gas is emitted?

Options:
A. $$
{2. 9 \times1 0^{7} \mathrm{d m^{3}}}
$$
B. $$
{7. 3 \times1 0^{7} \mathrm{d m^{3}}}
$$
C. $$
{5. 2 \times1 0^{7} \mathrm{d m^{3}}}
$$
D. $$
{9. 0 \times1 0^{9} \mathrm{d m^{3}}}
$$
E. $$
{2. 1 \times1 0^{8} \mathrm{d m^{3}}}
$$
F. $$
{1. 5 \times1 0^{8} \mathrm{d m^{3}}}
$$
G. $$
{8. 4 \times1 0^{9} \mathrm{d m^{3}}}
$$
H. $$
{6. 8 \times1 0^{9} \mathrm{d m^{3}}}
$$
I. $$
{4. 9 \times1 0^{8} \mathrm{d m^{3}}}
$$
J. $$
{3. 4 \times1 0^{8} \mathrm{d m^{3}}}
$$
Answer: J
How reliable is the perfect gas law in comparison with the van der Waals equation? Calculate the difference in pressure of 10.00 g of carbon dioxide confined to a container of volume 100 cm$^{3}$ at 25.0°C between treating it as a perfect gas and a van der Waals gas.

Options:
A. $$
6 0. 2 \mathrm{~ a t m}
$$
$$
4 0. 1 \mathrm{~ a t m}
$$
B. $$
5 0. 7 \mathrm{~ a t m}
$$
$$
4 5. 5 \mathrm{~ a t m}
$$
C. $$
4 7. 2 \mathrm{~ a t m}
$$
$$
4 4. 6 \mathrm{~ a t m}
$$
D. $$
5 3. 9 \mathrm{~ a t m}
$$
$$
4 7. 5 \mathrm{~ a t m}
$$
E. $$
5 2. 4 \mathrm{~ a t m}
$$
$$
4 8. 3 \mathrm{~ a t m}
$$
F. $$
5 8. 6 \mathrm{~ a t m}
$$
$$
3 9. 4 \mathrm{~ a t m}
$$
G. $$
6 2. 1 \mathrm{~ a t m}
$$
$$
3 7. 2 \mathrm{~ a t m}
$$
H. $$
5 7. 0 \mathrm{~ a t m}
$$
$$
4 2. 8 \mathrm{~ a t m}
$$
I. $$
4 9. 8 \mathrm{~ a t m}
$$
$$
4 1. 3 \mathrm{~ a t m}
$$
J. $$
5 5. 6 \mathrm{~ a t m}
$$
$$
4 3. 0 \mathrm{~ a t m}
$$
Answer: J
Isopropanol (2-propanol) is commonly used as 'rubbing alcohol' to relieve sprain injuries in sport: its action is due to the cooling effect that accompanies its rapid evaporation when applied to the skin. In an experiment to determine its enthalpy of vaporization, a sample was brought to the boil. It was found that when an electric current of 0.812 $\mathsf{A}$ from a 11.5 V supply was passed for 303 s, then 4.27 g of the alcohol was vaporized. What is the (molar) enthalpy of vaporization of isopropanol at its boiling point?

Options:
A. $$
+ 3 6. 8 k J \ m o l^{-1}
$$
B. $$
+ 3 9. 1 k J \ m o l^{-1}
$$
C. $$
+ 4 1. 2 k J \ m o l^{-1}
$$
D. $$
+ 3 8. 3 k J \ m o l^{-1}
$$
E. $$
+ 4 2. 1 k J \ m o l^{-1}
$$
F. $$
+ 3 5. 9 k J \ m o l^{-1}
$$
G. $$
+ 3 9. 8 k J \ m o l^{-1}
$$
H. $$
+ 4 0. 6 k J \ m o l^{-1}
$$
I. $$
+ 3 7. 5 k J \ m o l^{-1}
$$
J. $$
+ 3 5. 0 k J \ m o l^{-1}
$$
Answer: G
$\mathsf{A}$ monatomic perfect gas at a temperature $T_{\mathrm{i}}$ is expanded isothermally to twice its initial volume. To what temperature should it be cooled to restore its entropy to its initia value? Take $C_{V, \mathrm{m}}={\frac{3} {2}} R.$

Options:
A. $$
1. 5 2 0 0 \, T_{i}
$$
B. $$
0. 5 0 0 0 \, T_{i}
$$
C. $$
0. 6 3 0 0 \, T_{i}
$$
D. $$
1. 2 5 0 0 \, T_{i}
$$
E. $$
1. 0 0 0 0 \, T_{i}
$$
F. $$
0. 9 4 0 0 \, T_{i}
$$
G. $$
0. 8 7 5 0 \, T_{i}
$$
H. $$
2. 5 0 0 0 \, T_{i}
$$
I. $$
2. 1 0 0 0 \, T_{i}
$$
J. $$
2. 5 7 5 0 \, T_{i}
$$
Answer: C
Natural gas (methane, CHA) to the various regions of the United States is on the order of $2. 7 \times1 0^{1 2} \, \mathrm{L}$ per day, measured at STP. What is the total enthalpy change for combustion of this quantity of methane?(Note: Less than this amount of methane is actually combusted daily. Some of the delivered gas is passed through to other regions.)

Options:
A. $$
- 3. 3 \times1 0^{1 5} \mathrm{~ k J}
$$
B. $$
- 6. 6 \times1 0^{1 4} \mathrm{~ k J}
$$
C. $$
- 7. 2 \times1 0^{1 5} \mathrm{~ k J}
$$
D. $$
- 4. 4 \times1 0^{1 3} \mathrm{~ k J}
$$
E. $$
- 1. 1 \times1 0^{1 4} \mathrm{~ k J}
$$
F. $$
- 5. 7 \times1 0^{1 2} \mathrm{~ k J}
$$
G. $$
- 1. 5 \times1 0^{1 3} \mathrm{~ k J}
$$
H. $$
- 8. 8 \times1 0^{1 4} \mathrm{~ k J}
$$
I. $$
- 9. 9 \times1 0^{1 4} \mathrm{~ k J}
$$
J. $$
- 2. 1 \times1 0^{1 4} \mathrm{~ k J}
$$
Answer: E
What are the two roots of the equation $x^{2} - 56 \, x + 1 = 0$? Ensure they have at least four significant figures ($\sqrt{783} \approx 27.98 2$).

Options:
A. $$
x_{1}=55.982
$$
$$
x_{2}=0.01785
$$
B. $$
x_{1}=55.984
$$
$$
x_{2}=0.01780
$$
C. $$
x_{1}=54.997
$$
$$
x_{2}=0.00218
$$
D. $$
x_{1}=57.891
$$
$$
x_{2}=0.00100
$$
E. $$
x_{1}=55.980
$$
$$
x_{2}=0.01787
$$
F. $$
x_{1}=55.983
$$
$$
x_{2}=0.01786
$$
G. $$
x_{1}=55.000
$$
$$
x_{2}=0.01675
$$
H. $$
x_{1}=53.901
$$
$$
x_{2}=0.01400
$$
I. $$
x_{1}=56.000
$$
$$
x_{2}=0.00015
$$
J. $$
x_{1}=56.018
$$
$$
x_{2}=0.00019
$$
Answer: F
To perform linear interpolation on the square root table for $10 \leqslant x \leqslant 999$, with a step size of $h=1$, try to provide the error bound for the interpolated value of $\sqrt{x}$ as ____ and the number of significant figures is____. Assume that the function values given in the table are sufficiently accurate.

Options:
A. $$10 \leqslant x \leqslant 100 \text{,} \mid R(x) \mid \approx 0.0015$$
$$100 \leqslant x \leqslant 999 \text{,} \mid R(x) \mid = 0.000032$$
$$5 \text{ digits}$$
B. $$1 \leqslant x \leqslant 100 \text{,} \mid R(x) \mid \approx 0.0011$$
$$100 \leqslant x \leqslant 999 \text{,} \mid R(x) \mid = 0.000035$$
$$7 \text{ digits}$$
C. $$10 \leqslant x \leqslant 100 \text{,} \mid R(x) \mid \approx 0.00099$$
$$100 \leqslant x \leqslant 999 \text{,} \mid R(x) \mid = 0.0000313$$
$$6 \text{ digits}$$
D. $$1 \leqslant x \leqslant 100 \text{,} \mid R(x) \mid \approx 0.00095$$
$$100 \leqslant x \leqslant 999 \text{,} \mid R(x) \mid = 0.000034$$
$$6 \text{ digits}$$
E. $$1 \leqslant x \leqslant 100 \text{,} \mid R(x) \mid \approx 0.0014$$
$$100 \leqslant x \leqslant 999 \text{,} \mid R(x) \mid = 0.000038$$
$$8 \text{ digits}$$
F. $$1 \leqslant x \leqslant 100 \text{,} \mid R(x) \mid \approx 0.0012$$
$$100 \leqslant x \leqslant 999 \text{,} \mid R(x) \mid = 0.000036$$
$$7 \text{ digits}$$
G. $$10 \leqslant x \leqslant 100 \text{,} \mid R(x) \mid \approx 0.001$$
$$100 \leqslant x \leqslant 999 \text{,} \mid R(x) \mid = 0.00003$$
$$5 \text{ digits}$$
H. $$1 \leqslant x \leqslant 100 \text{,} \mid R(x) \mid \approx 0.0016$$
$$100 \leqslant x \leqslant 999 \text{,} \mid R(x) \mid = 0.000039$$
$$8 \text{ digits}$$
I. $$10 \leqslant x \leqslant 100 \text{,} \mid R(x) \mid \approx 0.00098$$
$$100 \leqslant x \leqslant 999 \text{,} \mid R(x) \mid = 0.000033$$
$$5 \text{ digits}$$
J. $$1 \leqslant x \leqslant 100 \text{,} \mid R(x) \mid \approx 0.0013$$
$$100 \leqslant x \leqslant 999 \text{,} \mid R(x) \mid = 0.000037$$
$$7 \text{ digits}$$
Answer: C
Let $f(x) = 1 / (1 + x^{2})$. On the interval $-5 \leq x \leq 5$, with $n = 10$, estimate the error between the values of $I_{h}(x)$ at the midpoint of each node and $f(x)$ as _____.

Options:
A. $$
\mid R_{1} ( x ) \mid\leq\frac{1} {2} \, h^{3}
$$
B. $$
\mid R_{1} ( x ) \mid\leq\frac{1} {8} \, h^{3}
$$
C. $$
\mid R_{1} ( x ) \mid\geq\frac{1} {4} \, h^{3}
$$
D. $$
\mid R_{1} ( x ) \mid\leq\frac{1} {3} \, h^{2}
$$
E. $$
\mid R_{1} ( x ) \mid\geq\frac{1} {5} \, h^{2}
$$
F. $$
\mid R_{1} ( x ) \mid\geq\frac{1} {2} \, h^{2}
$$
G. $$
\mid R_{1} ( x ) \mid\leq\frac{1} {10} \, h^{2}
$$
H. $$
\mid R_{1} ( x ) \mid\leq\frac{1} {4} \, h^{2}
$$
I. $$
\mid R_{1} ( x ) \mid\leq\frac{1} {6} \, h^{4}
$$
J. $$
\mid R_{1} ( x ) \mid\geq\frac{1} {3} \, h^{5}
$$
Answer: H
Using the orthogonalization method, find the first three orthogonal polynomials $P_{0} \left( \begin{array} {c} {{x}} \\ \end{array} \right), P_{1} \left( \begin{array} {c} {{x}} \\ \end{array} \right), P_{2} \left( \begin{array} {c} {{x}} \\ \end{array} \right)$ on the interval $\left[ 0, 1 \right]$ with the weight $\rho( x )=\operatorname{l n} \frac{1} {x}$
as ______.

Options:
A. $$
P_{0} \left( x \right)=1
$$
$$
P_{1} ( x )=x-\frac{1} {3}
$$
$$
P_{2} ( x )=x^{2}-\frac{2} {5} \, x+\frac{1 6} {1 4 4}
$$
B. $$
P_{0} \left( x \right)=x
$$
$$
P_{1} ( x )=x-\frac{1} {4}
$$
$$
P_{2} ( x )=x^{2}-\frac{5} {9} \, x+\frac{1 9} {2 2 8}
$$
C. $$
P_{0} \left( x \right)=1
$$
$$
P_{1} ( x )=x-\frac{1} {5}
$$
$$
P_{2} ( x )=x^{2}-\frac{4} {9} \, x+\frac{2 1} {2 5 6}
$$
D. $$
P_{0} \left( x \right)=1
$$
$$
P_{1} ( x )=x-\frac{1} {2}
$$
$$
P_{2} ( x )=x^{2}-\frac{3} {8} \, x+\frac{1 3} {1 8 2}
$$
E. $$
P_{0} \left( x \right)=x
$$
$$
P_{1} ( x )=x-\frac{1} {5}
$$
$$
P_{2} ( x )=x^{2}-\frac{2} {7} \, x+\frac{1 8} {2 2 5}
$$
F. $$
P_{0} \left( x \right)=x
$$
$$
P_{1} ( x )=x^{2}-\frac{1} {3}
$$
$$
P_{2} ( x )=x^{3}-\frac{4} {9} \, x+\frac{1 5} {3 6}
$$
G. $$
P_{0} \left( x \right)=1
$$
$$
P_{1} ( x )=x-\frac{1} {3}
$$
$$
P_{2} ( x )=x^{2}-\frac{2} {6} \, x+\frac{2 3} {2 9 5}
$$
H. $$
P_{0} \left( x \right)=1
$$
$$
P_{1} ( x )=x-\frac{1} {4}
$$
$$
P_{2} ( x )=x^{2}-\frac{5} {7} \, x+\frac{1 7} {2 5 2}
$$
I. $$
P_{0} \left( x \right)=x
$$
$$
P_{1} ( x )=x-\frac{1} {4}
$$
$$
P_{2} ( x )=x^{2}-\frac{5} {7} \, x+\frac{1 6} {2 4 2}
$$
J. $$
P_{0} \left( x \right)=1
$$
$$
P_{1} ( x )=x-\frac{1} {6}
$$
$$
P_{2} ( x )=x^{2}-\frac{4} {7} \, x+\frac{1 5} {3 1 2}
$$
Answer: H
What is the circumference of the ellipse $\frac{x^{2}}{4} + y^{2} = 1$? Provide the result with five significant figures.

Options:
A. $$
I \approx8. 9 0 4 7
$$
B. $$
I \approx9. 5 0 7 9
$$
C. $$
I \approx9. 6 8 8 4
$$
D. $$
I \approx8. 1 5 5 3
$$
E. $$
I \approx9. 3 1 6 2
$$
F. $$
I \approx9. 2 4 7 1
$$
G. $$
I \approx7. 8 9 2 4
$$
H. $$
I \approx7. 9 3 4 2
$$
I. $$
I \approx8. 7 5 1 8
$$
J. $$
I \approx10. 0 0 0
$$
Answer: C
Using the second-order Taylor expansion method to find the approximate solution of the initial value problem
$$
\left\{\begin{array} {l} {{{y^{\prime}=x^{2}+y^{2} \,,}}} \\ {{{y ( 1 )=1}}} \\ \end{array} \right.
$$
at $x=1.5$ is ______. (With step size $h=0.25$, keep at least 5 decimal places).

Options:
A. $$
\begin{aligned} {{y ( 1. 2 5 )}} & {{} {{} {} =1. 6 9 0 8,}} \\ {{y ( 1. 5 0 )}} & {{} {{} =3. 2 6 7 7 2}} \\ \end{aligned}
$$
B. $$
\begin{aligned} {{y ( 1. 2 5 )}} & {{} {{} {} =1. 6 7 9 4,}} \\ {{y ( 1. 5 0 )}} & {{} {{} =3. 2 8 4 6 1}} \\ \end{aligned}
$$
C. $$
\begin{aligned} {{y ( 1. 2 5 )}} & {{} {{} {} =1. 6 9 3 2,}} \\ {{y ( 1. 5 0 )}} & {{} {{} =3. 2 4 5 8 1}} \\ \end{aligned}
$$
D. $$
\begin{aligned} {{y ( 1. 2 5 )}} & {{} {{} {} =1. 5 9 8 4,}} \\ {{y ( 1. 5 0 )}} & {{} {{} =3. 0 2 5 9 2}} \\ \end{aligned}
$$
E. $$
\begin{aligned} {{y ( 1. 2 5 )}} & {{} {{} {} =1. 7 1 0 3,}} \\ {{y ( 1. 5 0 )}} & {{} {{} =3. 5 0 4 7 5}} \\ \end{aligned}
$$
F. $$
\begin{aligned} {{y ( 1. 2 5 )}} & {{} {{} {} =1. 7 0 2 5,}} \\ {{y ( 1. 5 0 )}} & {{} {{} =3. 4 2 3 1 0}} \\ \end{aligned}
$$
G. $$
\begin{aligned} {{y ( 1. 2 5 )}} & {{} {{} {} =1. 6 8 7 5,}} \\ {{y ( 1. 5 0 )}} & {{} {{} =3. 3 3 3 2 9 8}} \\ \end{aligned}
$$
H. $$
\begin{aligned} {{y ( 1. 2 5 )}} & {{} {{} {} =1. 6 4 5 7,}} \\ {{y ( 1. 5 0 )}} & {{} {{} =3. 1 9 3 8 9}} \\ \end{aligned}
$$
I. $$
\begin{aligned} {{y ( 1. 2 5 )}} & {{} {{} {} =1. 6 5 3 8,}} \\ {{y ( 1. 5 0 )}} & {{} {{} =3. 2 0 9 5 3}} \\ \end{aligned}
$$
J. $$
\begin{aligned} {{y ( 1. 2 5 )}} & {{} {{} {} =1. 6 3 8 0,}} \\ {{y ( 1. 5 0 )}} & {{} {{} =3. 2 1 5 4 3}} \\ \end{aligned}
$$
Answer: G
Determine the equation by dichotomy
$$
x^{3}-3 x+1=0
$$
The interval $\left[a, b \right]$of the smallest positive root is ______, so that it is satisfied
$$
K=\frac{M_{2}} {2 m} < 1,
$$
Including $$M_ {2} = \ operatorname * {m a x} _ {\ \ leqslant leqslant x b} \ bigl | \, f ^ {\ prime \ prime} \ \, (x), | \,, m=\operatorname* {m i n}_{a \leqslant x \leqslant b} \bigl| \, f^{\prime} ( \, x ) \, \bigr| \,.$$

Options:
A. $$[2.75,\ 3.25]$$
B. $$[0.5,\ 1.5]$$
C. $$[2.5,\ 3]$$
D. $$[2,\ 2.5]$$
E. $$[1.5,\ 2]$$
F. $$[1.25,\ 1.75]$$
G. $$[3,\ 3.5]$$
H. $$[0.5,\ 1]$$
I. $$[0,\ 0.5]$$
J. $$[1,\ 1.5]$$
Answer: I
Set the system of equations
$$
\left\{\begin{array} {l} {{{5 \, {\boldsymbol{x}}_{1}+2 \, {\boldsymbol{x}}_{2}+{\boldsymbol{x}}_{3}=-1 2 \,,}}} \\ {{{-\, {\boldsymbol{x}}_{1}+4 \, {\boldsymbol{x}}_{2}+2 \, {\boldsymbol{x}}_{3}=2 0 \,,}}} \\ {{{2 \, {\boldsymbol{x}}_{1}+3 \, {\boldsymbol{x}}_{2}+1 0 \, {\boldsymbol{x}}_{3}=3 \,.}}} \\ \end{array} \right.
$$
Solve this system of equations using the Jacobi iterative method and the Gauss-Seidel (G-S) iterative method, with the iteration terminating when
$$\parallel
\boldsymbol{X}^{( k+1 )}-\boldsymbol{X}^{( k )} \parallel_{\infty} < 1 0^{-4}
$$.
The result is ____.

Options:
A. Jacobi:
$$
X^{( 1 8 )}=(-3. 9 9 8 9 9 6 4, 2. 9 9 8 9 7 3 9, 2. 0 0 9 9 9 9 9 )^{\mathsf{T}}
$$
G-S:
$$
X^{( 8 )}=(-4. 0 0 0 0 2 6 \,, 2. 9 8 9 8 5 \,, 2. 0 0 1 0 0 3 \, )^{\mathsf{T}}
$$
B. Jacobi:
$$
X^{( 1 8 )}=(-3. 9 9 9 9 9 6 4, 2. 9 9 9 9 7 3 9, 1. 9 9 9 9 9 9 9 )^{\mathsf{T}}
$$
G-S:
$$
X^{( 8 )}=(-4. 0 0 0 0 3 6 \,, 2. 9 9 9 9 8 5 \,, 2. 0 0 0 0 0 3 \, )^{\mathsf{T}}
$$
C. Jacobi:
$$
X^{( 1 8 )}=(-3. 9 9 9 9 9 5 2, 2. 9 9 9 9 8 2 0, 1. 9 9 9 9 9 8 8 )^{\mathsf{T}}
$$
G-S:
$$
X^{( 8 )}=(-4. 0 0 1 0 0 3 6 \,, 2. 9 9 9 9 7 5 \,, 1. 9 9 9 9 9 8 \, )^{\mathsf{T}}
$$
D. Jacobi:
$$
X^{( 1 8 )}=(-3. 9 9 3 9 9 6 4, 2. 9 8 9 9 9 3 9, 1. 9 9 5 9 9 9 9 )^{\mathsf{T}}
$$
G-S:
$$
X^{( 8 )}=(-4. 0 0 0 3 2 6 \,, 2. 9 9 7 9 8 5 \,, 2. 0 0 0 0 5 3 \, )^{\mathsf{T}}
$$
E. Jacobi:
$$
X^{( 1 8 )}=(-3. 9 9 9 2 9 6 4, 2. 9 8 9 9 7 3 9, 1. 9 9 9 0 9 9 9 )^{\mathsf{T}}
$$
G-S:
$$
X^{( 8 )}=(-4. 0 0 7 0 3 6 \,, 2. 9 9 9 7 8 5 \,, 2. 0 0 0 0 0 9 \, )^{\mathsf{T}}
$$
F. Jacobi:
$$
X^{( 1 8 )}=(-3. 9 9 7 9 9 6 4, 2. 9 9 7 9 7 3 9, 1. 9 9 8 9 9 9 9 )^{\mathsf{T}}
$$
G-S:
$$
X^{( 8 )}=(-4. 0 0 0 1 3 6 \,, 2. 9 9 9 9 8 9 \,, 2. 0 0 0 9 0 3 \, )^{\mathsf{T}}
$$
G. Jacobi:
$$
X^{( 1 8 )}=(-3. 9 9 9 9 1 6 4, 2. 9 9 0 9 7 3 9, 1. 9 9 2 9 9 9 9 )^{\mathsf{T}}
$$
G-S:
$$
X^{( 8 )}=(-4. 0 0 0 8 3 6 \,, 2. 9 8 9 9 8 5 \,, 2. 0 0 0 0 8 3 \, )^{\mathsf{T}}
$$
H. Jacobi:
$$
X^{( 1 8 )}=(-3. 9 2 9 9 9 6 4, 2. 9 3 9 9 7 3 9, 1. 9 1 9 9 9 9 9 )^{\mathsf{T}}
$$
G-S:
$$
X^{( 8 )}=(-4. 0 1 0 0 3 6 \,, 2. 9 9 8 9 8 5 \,, 2. 0 0 0 1 0 3 \, )^{\mathsf{T}}
$$
I. Jacobi:
$$
X^{( 1 8 )}=(-3. 9 9 9 9 9 7 4, 2. 9 9 9 9 7 8 9, 1. 9 9 8 9 9 9 1 )^{\mathsf{T}}
$$
G-S:
$$
X^{( 8 )}=(-4. 0 0 0 2 6 6 \,, 2. 9 9 7 9 8 5 \,, 2. 0 0 0 0 2 3 \, )^{\mathsf{T}}
$$
J. Jacobi:
$$
X^{( 1 8 )}=(-3. 9 9 9 6 9 6 4, 2. 9 9 9 5 7 3 9, 1. 9 9 9 8 9 9 9 )^{\mathsf{T}}
$$
G-S:
$$
X^{( 8 )}=(-4. 0 0 0 1 6 6 \,, 2. 9 9 9 9 7 5 \,, 2. 0 0 0 0 1 3 \, )^{\mathsf{T}}
$$
Answer: B
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 following for the star:\
Radiant flux at Earth's surface (compare this with the solar irradiance).

Options:
A. $$
5. 4 \times1 0^{-6} \ \mathrm{W} \ \mathrm{m}^{-2}
$$
B. $$
9. 9 \times1 0^{-8} \ \mathrm{W} \ \mathrm{m}^{-2}
$$
C. $$
3. 2 \times1 0^{-8} \ \mathrm{W} \ \mathrm{m}^{-2}
$$
D. $$
2. 1 \times1 0^{-9} \ \mathrm{W} \ \mathrm{m}^{-2}
$$
E. $$
1. 0 \times1 0^{-7} \ \mathrm{W} \ \mathrm{m}^{-2}
$$
F. $$
4. 8 \times1 0^{-9} \ \mathrm{W} \ \mathrm{m}^{-2}
$$
G. $$
6. 5 \times1 0^{-8} \ \mathrm{W} \ \mathrm{m}^{-2}
$$
H. $$
8. 3 \times1 0^{-8} \ \mathrm{W} \ \mathrm{m}^{-2}
$$
I. $$
7. 6 \times1 0^{-9} \ \mathrm{W} \ \mathrm{m}^{-2}
$$
J. $$
4. 7 \times1 0^{-7} \ \mathrm{W} \ \mathrm{m}^{-2}
$$
Answer: G
To demonstrate the relative strengths of the electrical and gravitational forces of attraction between the electron and the proton in the Bohr atom, suppose the hydrogen atom was held together solely by the force of gravity. Determine the radius of the ground-state orbit (in units of nm and AU) and the energy of the ground state (in eV).

Options:
A. $$
5. 9 8 \times1 0^{1 7} \mathrm{A U}
$$
$$
- 2. 7 3 \times1 0^{-7 8} \mathrm{~ e V}
$$
B. $$
6. 3 5 \times1 0^{1 7} \mathrm{A U}
$$
$$
- 2. 2 9 \times1 0^{-7 8} \mathrm{~ e V}
$$
C. $$
8. 0 3 \times1 0^{1 7} \mathrm{A U}
$$
$$
- 2. 6 4 \times1 0^{-7 8} \mathrm{~ e V}
$$
D. $$
6. 7 2 \times1 0^{1 7} \mathrm{A U}
$$
$$
- 1. 9 4 \times1 0^{-7 8} \mathrm{~ e V}
$$
E. $$
7. 5 4 \times1 0^{1 7} \mathrm{A U}
$$
$$
- 3. 1 7 \times1 0^{-7 8} \mathrm{~ e V}
$$
F. $$
1. 5 0 \times1 0^{1 7} \mathrm{A U}
$$
$$
- 3. 2 0 \times1 0^{-7 8} \mathrm{~ e V}
$$
G. $$
7. 2 1 \times1 0^{1 7} \mathrm{A U}
$$
$$
- 1. 8 2 \times1 0^{-7 8} \mathrm{~ e V}
$$
H. $$
8. 9 6 \times1 0^{1 7} \mathrm{A U}
$$
$$
- 3. 4 1 \times1 0^{-7 8} \mathrm{~ e V}
$$
I. $$
9. 1 5 \times1 0^{1 7} \mathrm{A U}
$$
$$
- 2. 8 3 \times1 0^{-7 8} \mathrm{~ e V}
$$
J. $$
8. 4 0 \times1 0^{1 7} \mathrm{A U}
$$
$$
- 2. 0 4 \times1 0^{-7 8} \mathrm{~ e V}
$$
Answer: C
Estimate the minimum size of a crater on the Moon that can be resolved by a 20-cm (8-in) telescope.

Options:
A. $$
1. 6 ~ \mathrm{k m}
$$
B. $$
1. 1 ~ \mathrm{k m}
$$
C. $$
1. 10 ~ \mathrm{k m}
$$
D. $$
1. 12 ~ \mathrm{k m}
$$
E. $$
1. 2 ~ \mathrm{k m}
$$
F. $$
1. 4 ~ \mathrm{k m}
$$
G. $$
1. 7 ~ \mathrm{k m}
$$
H. $$
1. 5 ~ \mathrm{k m}
$$
I. $$
1. 8 ~ \mathrm{k m}
$$
J. $$
1. 3 ~ \mathrm{k m}
$$
Answer: J
How much must the pointing angle of a two-element radio interferometer be changed in order to move from one interference maximum to the next? Assume that the two telescopes are separated by the diameter of Earth and that the observation is being made at a wavelength of 21 em. Express your answer in arcseconds.

Options:
A. $$
0. 2 9 \ \mathrm{m}
$$
$$
0. 0 0 2 2^{\prime\prime}
$$
B. $$
0. 3 0 \ \mathrm{m}
$$
$$
0. 0 0 3 0^{\prime\prime}
$$
C. $$
0. 4 2 \ \mathrm{m}
$$
$$
0. 0 0 3 8^{\prime\prime}
$$
D. $$
0. 3 5 \ \mathrm{m}
$$
$$
0. 0 0 1 8^{\prime\prime}
$$
E. $$
0. 0 8 \ \mathrm{m}
$$
$$
0. 0 0 4 0^{\prime\prime}
$$
F. $$
0. 1 5 \ \mathrm{m}
$$
$$
0. 0 0 3 6^{\prime\prime}
$$
G. $$
0. 5 5 \ \mathrm{m}
$$
$$
0. 0 0 4 5^{\prime\prime}
$$
H. $$
0. 4 0 \ \mathrm{m}
$$
$$
0. 0 0 2 0^{\prime\prime}
$$
I. $$
0. 0 1 \ \mathrm{m}
$$
$$
0. 0 0 2 5^{\prime\prime}
$$
J. $$
0. 2 1 \ \mathrm{m}
$$
$$
0. 0 0 3 4^{\prime\prime}
$$
Answer: J
Due to differences in race and geographical conditions, people's understanding of what constitutes being "tall" also varies. Let the domain of discourse $U = \{$people$\}$, and define the fuzzy set $\underset{\sim}{A}$ as "tall", with the condition that anyone taller than 1.80 meters is considered tall, while those shorter than 1.60 meters are not considered tall. Let $x$ represent height, and provide the membership function of $\underset{\sim}{A}$, $\underset{\sim}{A}(x)$, as follows:
$$
\underset{\sim}{A}(x)=
\begin{cases}
0, & x < 1.60, \\
2\left(\frac{x - 1.60}{0.2} \right)^2, & 1.60 \leq x < 1.70, \\
1 - 2 \left( \frac{x - 1.80}{0.2} \right)^2, & 1.70 \leq x < 1.80, \\
1, & x \geq 1.80.
\end{cases}
$$
What is the value of $\underset{\sim}{A}$(1.65)?

Options:
A. 0.375
B. 0.275
C. 0.150
D. 0.400
E. 0.200
F. 0.300
G. 0.250
H. 0.100
I. 0.125
J. 0.050
Answer: I
$\text{max} f = 3x_1 + 4x_2 + 4x_3$
$$
s.t.\begin{cases}
6x_1 + 3x_2 + 4x_3 \leq [1200, 100] \\
5x_1 + 4x_2 + 5x_3 \leq [1550, 200] \\
x_1, x_2, x_3 \geq 0
\end{cases}
$$
What are the fuzzy optimal solution and fuzzy optimal value?

Options:
A. The fuzzy optimal solution is $\mathbf{x}=(150, 150, 0)^{\mathsf{T}}$, with a fuzzy optimal value of 1350.00.
B. The fuzzy optimal solution is $\mathbf{x}=(0, 250, 200)^{\mathsf{T}}$, with a fuzzy optimal value of 1700.00.
C. The fuzzy optimal solution is $\mathbf{x}=(30, 380, 0)^{\mathsf{T}}$, with a fuzzy optimal value of 1620.00.
D. The fuzzy optimal solution is $\mathbf{x}=(0, 411.41, 0)^{\mathsf{T}}$, with a fuzzy optimal value of 1645.65.
E. The fuzzy optimal solution is $\mathbf{x}=(0, 300, 0)^{\mathsf{T}}$, with a fuzzy optimal value of 1200.00.
F. The fuzzy optimal solution is $\mathbf{x}=(200, 0, 100)^{\mathsf{T}}$, with a fuzzy optimal value of 1800.00.
G. The fuzzy optimal solution is $\mathbf{x}=(0, 350, 0)^{\mathsf{T}}$, with a fuzzy optimal value of 1400.00.
H. The fuzzy optimal solution is $\mathbf{x}=(0, 0, 400)^{\mathsf{T}}$, with a fuzzy optimal value of 1600.00.
I. The fuzzy optimal solution is $\mathbf{x}=(50, 50, 50)^{\mathsf{T}}$, with a fuzzy optimal value of 850.00.
J. The fuzzy optimal solution is $\mathbf{x}=(100, 0, 100)^{\mathsf{T}}$, with a fuzzy optimal value of 1600.00.
Answer: D
In the numerical integration formula
$$
\int_{-1}^{1} f ( x ) d x \approx a f (-1 )+b f ( c ),
$$
Find the constants $a, \, b, \, c$ for which the formula is exact for all polynomials of degree up to this $k$ .

Options:
A. $$
a=\frac{5} {4}, \qquad b=\frac{3} {6}, \qquad c=\frac{2} {7}
$$
B. $$
a=\frac{3} {2}, \qquad b=\frac{1} {3}, \qquad c=\frac{2} {5}
$$
C. $$
a=\frac{1} {3}, \qquad b=\frac{2} {4}, \qquad c=\frac{3} {5}
$$
D. $$
a=\frac{1} {5}, \qquad b=\frac{2} {3}, \qquad c=\frac{3} {8}
$$
E. $$
a=\frac{2} {7}, \qquad b=\frac{1} {5}, \qquad c=\frac{4} {6}
$$
F. $$
a=\frac{2} {3}, \qquad b=\frac{1} {6}, \qquad c=\frac{4} {5}
$$
G. $$
a=\frac{3} {4}, \qquad b=\frac{2} {5}, \qquad c=\frac{1} {4}
$$
H. $$
a=\frac{1} {2}, \qquad b=\frac{3} {2}, \qquad c=\frac{1} {3}
$$
I. $$
a=\frac{2} {5}, \qquad b=\frac{1} {4}, \qquad c=\frac{3} {6}
$$
J. $$
a=\frac{4} {3}, \qquad b=\frac{1} {5}, \qquad c=\frac{2} {7}
$$
Answer: H
Let $( M^{2}, d s^{2} )$ be a minimal surface in $\mathbb{R}^{3}$ , where $d s^{2}$ igtereticig of the Euclidean metric. Assume that the Gaussian curvature $K$ of $( M^{2}, d s^{2} )$ Hatin Daote v $\widetilde{K}$ the Gaussian curvature of the metric $\widetilde{d s^{2}}=-K d s^{2}$ . So $\widetilde{K}=$ _______ .

Options:
A. $$-3$$
B. $$\pi$$
C. $$\frac{1}{2}$$
D. $$\frac{-1}{2}$$
E. $$1$$
F. $$0$$
G. $$-2$$
H. $$3$$
I. $$-1$$
J. $$2$$
Answer: E
Consider the real Lie group $\mathrm{S L}_{2} ( \mathbb{R} )$ of 2 by $2$ matrices of determi- nant one. Compute the fundamental group of $\mathrm{S L}_{2} ( \mathbb{R} )$ .

Options:
A. $$\mathbb{Z}_4$$
B. $$\mathbb{Z}_{10}$$
C. $$\mathbb{Z}_2$$
D. $$\mathbb{Z}$$
E. $$\mathbb{Z}_3$$
F. $$\mathbb{Z}_5$$
G. $$\mathbb{Q}$$
H. $$\mathbb{R}$$
I. $$\mathbb{C}$$
J. $$\mathbb{N}$$
Answer: D
The works written by Tan Sitong during the Wuxu Reform period to promote the ideas of reform and innovation are as follows ().

Options:
A. Reflections on Modern Governance
B. The Study of Benevolence
C. The Path to National Renewal
D. Japanese Political Change Exam
E. Essays on Social Progress
F. The Future of Chinese Society
G. General Principles of Reform
H. Examination of New Learning and Pseudo Classics
I. The Role of Education in National Development
J. Treatise on Economic Reform
Answer: B
In the early and middle period of the Agrarian Revolutionary War, the "Left" mistakes were successively made in the CPC, and the leading organs of the central government gained the dominant position ().

Options:
A. Five times
B. Ten times
C. Four times
D. Three times
E. Once
F. Six times
G. Second time
H. Eight times
I. Nine times
J. Seven times
Answer: D
What is the first rebellion of astronomy against the theological worldview?

Options:
A. Copernicus
B. Newton
C. Kepler
D. Galileo
E. Tycho Brahe
F. Odox
G. Aristotle
H. Apolloni
I. Brahe
J. Ptolemy
Answer: A
What is the anthropological basis of deontology?

Options:
A. Happiness Theory
B. Moral Relativism
C. Ethical Egoism
D. Good Will
E. Virtue Ethics
F. Social Contract
G. Utilitarianism
H. Freedom and responsibility
I. Effect Theory
J. Consequentialism
Answer: D
From the perspective of the relationship between religion and morality, one of the basic tasks we face in the process of moral rationalization in modern society is to ____ with the power and method of reason.

Options:
A. Based on reality, advocating materialism in China
B. Integrating ancient philosophies with contemporary moral dilemmas
C. Emphasizing the importance of secular ethics in governance
D. Based on tradition, restore the sacredness of heaven in Chinese tradition
E. Based on religion, introducing Western religious beliefs in China
F. Rejecting all forms of religious influence in moral decision-making
G. Analyzing the historical impact of religion on modern legal systems
H. Seeking the sanctity of morality and faith
I. Encouraging interfaith dialogue to enhance moral understanding
J. Promoting universal moral principles independent of religious beliefs
Answer: H
The foundation of social morality is ____.

Options:
A. Vigorously promoting social moral norms such as love for work, honesty and trustworthiness, respect for the elderly and love for the young, and harmony between husband and wife in society
B. The public concept and the distinction between the public and private spheres in a certain national culture
C. Focusing on technological advancements to improve societal behavior
D. Establishing a universal code of ethics recognized by all religions
E. Promoting cultural heritage and traditions as the basis for morality
F. Implementing strict legal measures to enforce moral behavior
G. going beyond the limit and vigorously supporting the promotion of private consciousness in society
H. Prioritizing economic growth over social values and norms
I. Vigorously promoting the "Five Loves" and other moral norms in society
J. Encouraging individualism and personal gain above societal norms
Answer: B
The significance of death education is ____.

Options:
A. Explore the nature of death
B. Seeking a viable path to heaven
C. Understanding cultural perspectives on mourning
D. Discussing the environmental impact of burials
E. Promoting the importance of funeral traditions
F. To help the educated to adapt to death
G. Learning about legal matters related to wills
H. Preparing for the financial implications of death
I. Examining the psychological effects of grief
J. Establishing the criteria for brain death
Answer: A
Fairness not only refers to similarity in form, but also emphasizes the__of fairness.

Options:
A. Context
B. nature
C. Base
D. content
E. Connotation
F. Method
G. Essence
H. Objective
I. Definition
J. Appearance
Answer: D
The principle we should follow when dealing with the relationship between individuals and the collective, and between individuals and others is ___.

Options:
A. Emphasize personal gain before considering collective impact
B. Prioritize individual interests regardless of the collective
C. Treat everyone equally without considering the collective context
D. Subjective for yourself, objective for others
E. Focus solely on collective well-being, ignore individual concerns
F. Balance individual needs with collective goals
G. There is only collective interest, no individual interest
H. Put the collective first, then the individual; put others first, then yourself
I. Follow individual preferences at the expense of others
J. Self-centered, everything is based on personal interests
Answer: H
In the pairs of nature judgments, if two judgments are contradictory, then they ( ).

Options:
A. Both constant and variable terms are different
B. Neither term is related to the nature of the judgments
C. constant term is different, variable term is the same
D. The relationship between terms determines their truth value
E. Both the constant and the variable are different
F. All judgments must use opposing variables
G. The constant term is the same, variable term is irrelevant
H. One term is constant while the other is non-existent
I. Both constant and variable terms are the same
J. Constants are the same, variables are different
Answer: C
Logic is the science of ______ and ______.

Options:
A. Laws of Thought, Methods of Argumentation
B. Arguments, Fallacies
C. Conclusions, Hypotheses
D. Analysis, Synthesis
E. Interpretation, Evaluation
F. Reasoning, Decision Making
G. Theories, Practices
H. Deduction, Induction
I. Concepts, Principles
J. Inference, Assumption
Answer: A