MikaStars39/nano-eval huggingface dataset:
There are n boys and m girls (m ≤ n+1) randomly lined up. What is the probability that any two girls are not adjacent to each other?

Options:
A. $$
P_{n,m}={\frac{\left( \begin{matrix} {{{n+1}}} \\ {{{m+1}}} \\ \end{matrix} \right)} {\left( \begin{matrix} {{{n+m}}} \\ {{{m}}} \\ \end{matrix} \right)}}
$$
B. $$P_{n,m}={\frac{\left( \begin{matrix} {{{n+2}}} \\ {{{m}}} \\ \end{matrix} \right)} {\left( \begin{matrix} {{{n+m+4}}} \\ {{{m}}} \\ \end{matrix} \right)}}$$
C. $$P_{n,m}={\frac{\left( \begin{matrix} {{{n+3}}} \\ {{{m}}} \\ \end{matrix} \right)} {\left( \begin{matrix} {{{n+m+1}}} \\ {{{m}}} \\ \end{matrix} \right)}}$$
D. $$
P_{n,m}={\frac{\left( \begin{matrix} {{{n}}} \\ {{{m+1}}} \\ \end{matrix} \right)} {\left( \begin{matrix} {{{n+m-1}}} \\ {{{m}}} \\ \end{matrix} \right)}}
$$
E. $$P_{n,m}={\frac{\left( \begin{matrix} {{{n+2}}} \\ {{{m}}} \\ \end{matrix} \right)} {\left( \begin{matrix} {{{n+m+1}}} \\ {{{m}}} \\ \end{matrix} \right)}}$$
F. $$P_{n,m}={\frac{\left( \begin{matrix} {{{n+2}}} \\ {{{m}}} \\ \end{matrix} \right)} {\left( \begin{matrix} {{{n-m+1}}} \\ {{{m}}} \\ \end{matrix} \right)}}$$
G. $$
P_{n,m}={\frac{\left( \begin{matrix} {{{n+1}}} \\ {{{m+1}}} \\ \end{matrix} \right)} {\left( \begin{matrix} {{{n+m+1}}} \\ {{{m}}} \\ \end{matrix} \right)}}
$$
H. $$
P_{n,m}={\frac{\left( \begin{matrix} {{{n+1}}} \\ {{{m-1}}} \\ \end{matrix} \right)} {\left( \begin{matrix} {{{n+m}}} \\ {{{m}}} \\ \end{matrix} \right)}}
$$
I. $$P_{n,m}={\frac{\left( \begin{matrix} {{{n+2}}} \\ {{{m}}} \\ \end{matrix} \right)} {\left( \begin{matrix} {{{n+m+3}}} \\ {{{m}}} \\ \end{matrix} \right)}}$$
J. $$P_{n,m}={\frac{\left( \begin{matrix} {{{n+1}}} \\ {{{m}}} \\ \end{matrix} \right)} {\left( \begin{matrix} {{{n+m}}} \\ {{{m}}} \\ \end{matrix} \right)}}$$
Answer: J
There are 5 balls in the pocket, numbered 1, 2, 3, 4, 5. Take any 3 balls from them, and let X represent the highest number among the three balls taken.
(1) What is the distribution table of $X$?
(2) What is the distribution function of $X$?

Options:
A. (1)$$P(X=3)={\frac{5} {10}},P(X=4)={\frac{1} {10}},P(X=5)={\frac{4} {10}}, $$
(2)
$$
F(x)=P ( X \leq x )=\begin{cases} {{{1,}}} & {{{x < 3}}} \\ {{{0. 1,}}} & {{{3 \leq x < 4}}} \\ {{{0. 4,}}} & {{{4 \leq x < 5}}} \\ {{{1,}}} & {{{x \geq5}}} \\ \end{cases}
$$
B. (1)$$P(X=3)={\frac{3} {10}},P(X=4)={\frac{3} {10}},P(X=5)={\frac{6} {10}}, $$
(2)
$$
F(x)=P ( X \leq x )=\begin{cases} {{{2,}}} & {{{x < 3}}} \\ {{{0. 1,}}} & {{{3 \leq x < 4}}} \\ {{{0. 4,}}} & {{{4 \leq x < 5}}} \\ {{{1,}}} & {{{x \geq5}}} \\ \end{cases}
$$
C. (1)$$P(X=3)={\frac{1} {10}},P(X=4)={\frac{3} {10}},P(X=5)={\frac{6} {10}}, $$
(2)
$$
F(x)=P ( X \leq x )=\begin{cases} {{{1,}}} & {{{x < 3}}} \\ {{{0. 1,}}} & {{{3 \leq x < 4}}} \\ {{{0. 4,}}} & {{{4 \leq x < 5}}} \\ {{{5,}}} & {{{x \geq5}}} \\ \end{cases}
$$
D. (1)$$P(X=3)={\frac{8} {10}},P(X=4)={\frac{1} {10}},P(X=5)={\frac{1} {10}}, $$
(2)
$$
F(x)=P ( X \leq x )=\begin{cases} {{{1,}}} & {{{x < 3}}} \\ {{{0. 1,}}} & {{{3 \leq x < 4}}} \\ {{{0. 4,}}} & {{{4 \leq x < 5}}} \\ {{{1,}}} & {{{x \geq5}}} \\ \end{cases}
$$
E. (1)$$P(X=3)={\frac{6} {10}},P(X=4)={\frac{1} {10}},P(X=5)={\frac{3} {10}}, $$
(2)
$$
F(x)=P ( X \leq x )=\begin{cases} {{{1,}}} & {{{x < 3}}} \\ {{{0. 1,}}} & {{{3 \leq x < 4}}} \\ {{{0. 4,}}} & {{{4 \leq x < 5}}} \\ {{{1,}}} & {{{x \geq5}}} \\ \end{cases}
$$
F. (1)$$P(X=3)={\frac{3} {10}},P(X=4)={\frac{1} {10}},P(X=5)={\frac{6} {10}}, $$
(2)
$$
F(x)=P ( X \leq x )=\begin{cases} {{{1,}}} & {{{x < 3}}} \\ {{{0. 1,}}} & {{{3 \leq x < 4}}} \\ {{{0. 4,}}} & {{{4 \leq x < 5}}} \\ {{{1,}}} & {{{x \geq5}}} \\ \end{cases}
$$
G. (1)$$P(X=3)={\frac{1} {10}},P(X=4)={\frac{3} {10}},P(X=5)={\frac{6} {10}}, $$
(2)
$$
F(x)=P ( X \leq x )=\begin{cases} {{{0,}}} & {{{x < 3}}} \\ {{{0. 1,}}} & {{{3 \leq x < 4}}} \\ {{{0. 4,}}} & {{{4 \leq x < 5}}} \\ {{{1,}}} & {{{x \geq5}}} \\ \end{cases}
$$
H. (1)$$P(X=3)={\frac{1} {10}},P(X=4)={\frac{3} {10}},P(X=5)={\frac{6} {10}}, $$
(2)
$$
F(x)=P ( X \leq x )=\begin{cases} {{{3,}}} & {{{x < 3}}} \\ {{{0. 1,}}} & {{{3 \leq x < 4}}} \\ {{{0. 4,}}} & {{{4 \leq x < 5}}} \\ {{{1,}}} & {{{x \geq5}}} \\ \end{cases}
$$
I. (1)$$P(X=3)={\frac{7} {10}},P(X=4)={\frac{1} {10}},P(X=5)={\frac{2} {10}}, $$
(2)
$$
F(x)=P ( X \leq x )=\begin{cases} {{{1,}}} & {{{x < 3}}} \\ {{{0. 1,}}} & {{{3 \leq x < 4}}} \\ {{{0. 4,}}} & {{{4 \leq x < 5}}} \\ {{{1,}}} & {{{x \geq5}}} \\ \end{cases}
$$
J. (1)$$P(X=3)={\frac{1} {10}},P(X=4)={\frac{3} {10}},P(X=5)={\frac{6} {10}}, $$
(2)
$$
F(x)=P ( X \leq x )=\begin{cases} {{{1,}}} & {{{x < 3}}} \\ {{{0. 1,}}} & {{{3 \leq x < 4}}} \\ {{{0. 4,}}} & {{{4 \leq x < 5}}} \\ {{{1,}}} & {{{x \geq5}}} \\ \end{cases}
$$
Answer: G
The provisions of a certain type of insurance policy from an insurance company state: If a specific event A occurs within a year, the insurance company shall pay the policyholder an amount of "a" yuan, the probability of event A occurring within a year is p. If the insurance company charges the policyholder a premium of ka, what should k be in order to achieve a 10% expected return on a for the insurance company?

Options:
A. $$
\mathrm{k} \geq\ ( 0. 6+p ) \ \mathrm{/} \ \ ( 1-p )
$$
B. $$
\mathrm{k} \geq\ ( 0. 9+p ) \ \mathrm{/} \ \ ( 1-p )
$$
C. $$
\mathrm{k} \geq\ ( 0. 4+p ) \ \mathrm{/} \ \ ( 2-p )
$$
D. $$
\mathrm{k} \geq\ ( 0. 1+p ) \ \mathrm{/} \ \ ( 1-p )
$$
E. $$
\mathrm{k} \geq\ ( 0. 5+p ) \ \mathrm{/} \ \ ( 1-p )
$$
F. $$
\mathrm{k} \geq\ ( 0. 1+p ) \ \mathrm{/} \ \ ( 2-p )
$$
G. $$
\mathrm{k} \geq\ ( 0. 8+p ) \ \mathrm{/} \ \ ( 1-p )
$$
H. $$
\mathrm{k} \geq\ ( 0. 7+p ) \ \mathrm{/} \ \ ( 1-p )
$$
I. $$
\mathrm{k} \geq\ ( 0. 3+p ) \ \mathrm{/} \ \ ( 1-p )
$$
J. $$
\mathrm{k} \geq\ ( 0. 2+p ) \ \mathrm{/} \ \ ( 1-p )
$$
Answer: D
Let the random variable X follow a Poisson distribution with parameter A. Prove that: $\operatorname{E} \ \left( \mathbf{X}^{n} \right)=\lambda\operatorname{E} [ \left( \mathbf{X}+1 \right)^{n-1} ]$. Using this result, $\mathrm{E} \ ( \mathbf{X}^{3} )$ is ____.

Options:
A. $\lambda^{3}+3 \lambda^{2}+\lambda^{2}$
B. $\lambda^{2}+2 \lambda+1$
C. $\lambda^{3}+3 \lambda^{2}+4 \lambda$
D. $\lambda^{3}-3 \lambda^{2}+\lambda$
E. $\lambda^{3}+3 \lambda+\lambda$
F. $\lambda^{3}+3 \lambda^{2}-\lambda$
G. $\lambda^{3}+2 \lambda+\lambda$
H. $\lambda^{3}+3 \lambda^{2}+\lambda$
I. $\lambda^{3}+3 \lambda^{2}+\lambda+1$
J. $\lambda^{3}+3 \lambda^{2}+2 \lambda$
Answer: H
What is the solution to the following indefinite integral?$$
\int\frac{3 x+6} {( x-1 )^{2} ( x^{2}+x+1 )} \mathrm{d} x
$$

Options:
A. $$ - 2 \operatorname{l n} | x+1 |-{\frac{3} {x-1}}+\operatorname{l n} ( x^{2}+x+1 )+C $$
B. $$ 2 \operatorname{l n} | x-1 |-{\frac{3} {x-3}}+\operatorname{l n} ( x^{2}+x+1 )+C $$
C. $$ - 2 \operatorname{l n} | x-1 |-{\frac{2} {x-1}}+\operatorname{l n} ( x^{2}+x+1 )+C $$
D. $$ - \operatorname{l n} | x-1 |-{\frac{3} {x-1}}+\operatorname{l n} ( x^{2}+x+1 )+C $$
E. $$ 2 \operatorname{l n} | x+1 |-{\frac{3} {x-1}}+\operatorname{l n} ( x^{2}+x+1 )+C $$
F. $$ 2 \operatorname{l n} | x-3 |-{\frac{3} {x-1}}+\operatorname{l n} ( x^{2}+x+1 )+C $$
G. $$ - 2 \operatorname{l n} | x-1 |-{\frac{3} {x-1}}+\operatorname{l n} ( x^{2}+x-1 )+C $$
H. $$ 2 \operatorname{l n} | x-1 |-{\frac{3} {x-1}}+\operatorname{l n} ( x^{2}+x+1 )+C $$
I. $$ - 2 \operatorname{l n} | x-1 |-{\frac{3} {x-1}}+\operatorname{l n} ( x^{2}+x+1 )+C $$
J. $$ 2 \operatorname{l n} | x-1 |-{\frac{3} {x-1}}+\operatorname{l n} ( x^{2}+x+2 )+C $$
Answer: I
Arrange the infinitesimal quantities $\alpha=\sqrt{1+x^{2}}-\cos x \, \quad\beta=\int_{0}^{1 n ( 1-x^{2} )} \sin t \mathrm{d} t \, \quad\gamma=\mathrm{a r c s i n x}-\mathrm{x}$ at $x \to0$ so that after them is the infinitesimal of the previous order,What is the correct order of $\alpha, \beta, \gamma$ ?

Options:
A. $$
\ \gamma, \ \beta, \ \alpha
$$
B. $$
\ \beta, \ \gamma, \ \alpha
$$
C. $$
\ \alpha, \ \beta, \ \gamma
$$
D. $$
\ \gamma, \ \alpha, \ \beta
$$
E. $$
\ \alpha, \ \gamma, \ \beta
$$
F. $$
\ \beta, \ \alpha, \ \gamma
$$
Answer: E
Given the plane region $\mathbf{D}=\{\ \ ( \mathbf{x}, \ \ \mathbf{y} ) |\ \ \ x^{2}+\mathbf{y}^{2} \leq2 \mathbf{y} \}$, what is the value of the double integral $\iint_{D} ( x+1 )^{2} \mathrm{d} x \mathrm{d} y$ ?

Options:
A. $$
{\frac{3} {2}} \pi
$$
B. $$
{\frac{5} {4}} \pi
$$
C. $$
{\frac{5} {8}} \pi
$$
D. $$
{\frac{1} {8}} \pi
$$
E. $$
{\frac{3} {8}} \pi
$$
F. $$
\pi
$$
G. $$
{\frac{1} {2}} \pi
$$
H. $$
{\frac{7} {4}} \pi
$$
I. $$
2 \pi
$$
J. $$
{\frac{1} {4}} \pi
$$
Answer: B
What are the solutions to the following matrix equations? $\left( \begin{matrix} {{{-1}}} & {{{2}}} \\ {{{3}}} & {{{-2}}} \\ \end{matrix} \right) X=\left( \begin{matrix} {{{2}}} & {{{-3}}} & {{{-1}}} \\ {{{0}}} & {{{2}}} & {{{1}}} \\ \end{matrix} \right)$

Options:
A. $$
\left[ \begin{matrix} {{1}} & {{-\frac{3} {2}}} & {{0}} \\ {{\frac{3} {2}}} & {{\frac{7} {4}}} & {{-\frac{1} {2}}} \\ \end{matrix} \right]
$$
B. $$
\left[ \begin{matrix} {{1}} & {{\frac{3} {2}}} & {{0}} \\ {{\frac{3} {2}}} & {{\frac{7} {4}}} & {{-\frac{1} {2}}} \\ \end{matrix} \right]
$$
C. $$
\left[ \begin{matrix} {{1}} & {{-\frac{1} {2}}} & {{0}} \\ {{\frac{3} {2}}} & {{-\frac{7} {4}}} & {{-\frac{1} {2}}} \\ \end{matrix} \right]
$$
D. $$
\left[ \begin{matrix} {{-3}} & {{-\frac{3} {2}}} & {{0}} \\ {{-\frac{5} {2}}} & {{\frac{5} {4}}} & {{-\frac{1} {2}}} \\ \end{matrix} \right]
$$
E. $$
\left[ \begin{matrix} {{1}} & {{-\frac{3} {2}}} & {{0}} \\ {{\frac{3} {2}}} & {{\frac{5} {4}}} & {{-\frac{1} {2}}} \\ \end{matrix} \right]
$$
F. $$
\left[ \begin{matrix} {{-1}} & {{-\frac{3} {2}}} & {{0}} \\ {{\frac{3} {2}}} & {{\frac{5} {4}}} & {{-\frac{1} {2}}} \\ \end{matrix} \right]
$$
G. $$
\left[ \begin{matrix} {{1}} & {{\frac{1} {2}}} & {{0}} \\ {{\frac{3} {2}}} & {{\frac{7} {4}}} & {{-\frac{1} {2}}} \\ \end{matrix} \right]
$$
H. $$
\left[ \begin{matrix} {{-1}} & {{-\frac{3} {2}}} & {{0}} \\ {{-\frac{3} {2}}} & {{\frac{5} {4}}} & {{-\frac{1} {2}}} \\ \end{matrix} \right]
$$
I. $$
\left[ \begin{matrix} {{-1}} & {{-\frac{3} {2}}} & {{0}} \\ {{-\frac{5} {2}}} & {{\frac{5} {4}}} & {{-\frac{1} {2}}} \\ \end{matrix} \right]
$$
J. $$
\left[ \begin{matrix} {{4}} & {{-\frac{3} {2}}} & {{0}} \\ {{-\frac{5} {2}}} & {{\frac{5} {4}}} & {{-\frac{1} {2}}} \\ \end{matrix} \right]
$$
Answer: C
What is the value of $\lambda, \mu$ when the homogeneous linear system $\left\{\begin{matrix} {{\lambda x_{1}+x_{2}+x_{3}=0}} \\ {{x_{1}+\mu x_{2}+x_{3}=0}} \\ {{x_{1}+2 \mu x_{2}+x_{3}=0}} \\ \end{matrix} \right.$ has a nonzero solution?

Options:
A. $\mu=1$ or $\lambda=2$
B. $\mu=1$ or $\lambda=0$
C. $\mu=1$ & $\lambda=1$
D. $\mu=2$ & $\lambda=1$
E. $\mu=0$ or $\lambda=1$
F. $\mu=2$ & $\lambda=2$
G. $\mu=2$ or $\lambda=1$
H. $\mu=0$ & $\lambda=1$
I. $\mu=1$ or $\lambda=1$
J. $\mu=1$ & $\lambda=0$
Answer: E
What is the equation for the surface of revolution resulting from the rotation of line
${\frac{x} {2}}={\frac{y} {1}}={\frac{z-1} {0}}$ around line $x=y=z$ ?

Options:
A. $$
3 ( x^{2}+y^{2}+z^{2} )-5 ( x y+x z+y z )+5 ( x+y+z )-7=0
$$
B. $$
( x^{2}+y^{2}+z^{2} )-4 ( x y+x z+y z )+5 ( x+y+z )-7=0
$$
C. $$
2 ( x^{2}+y^{2}+z^{2} )-5 ( x y+x z+y z )+5 ( x+y+z )-7=0
$$
D. $$
( x^{2}+y^{2}+z^{2} )- ( x y+x z+y z )+5 ( x+y+z )-7=0
$$
E. $$
2 ( x^{2}+y^{2}+z^{2} )-5 ( x y+x z+y z )+5 ( x+y+z )-5=0
$$
F. $$
5 ( x^{2}+y^{2}+z^{2} )-5 ( x y+x z+y z )+5 ( x+y+z )-7=0
$$
G. $$
4 ( x^{2}+y^{2}+z^{2} )-5 ( x y+x z+y z )+5 ( x+y+z )-7=0
$$
H. $$
( x^{2}+y^{2}+z^{2} )-5 ( x y+x z+y z )+5 ( x+y+z )-7=0
$$
I. $$
( x^{2}+y^{2}+z^{2} )-2 ( x y+x z+y z )+5 ( x+y+z )-7=0
$$
J. $$
( x^{2}+y^{2}+z^{2} )-3 ( x y+x z+y z )+5 ( x+y+z )-7=0
$$
Answer: C
$\left\{\begin{matrix} {{2 x_{1}-5 x_{2}+x_{3}-3 x_{4}=0}} \\ {{-3 x_{1}+4 x_{2}-2 x_{3}+x_{4}=0}} \\ {{x_{1}+2 x_{2}-x_{3}+3 x_{4}=0}} \\ {{-2 x_{1}+1 5 x_{2}-6 x_{3}+1 3 x_{4}=0}} \\ \end{matrix} \right.$
What are the solutions to these equations?

Options:
A. $$
\left(-1,0, 0, 1 \right)^{T}
$$
B. $$
\left(0,-1, 0, 1 \right)^{T}
$$
C. $$
\left(-1,1, -1, 1 \right)^{T}
$$
D. $$
\left(-1,-1, 0, -1 \right)^{T}
$$
E. $$
\left(-1,-1, 1, 1 \right)^{T}
$$
F. $$
\left(-1,-1, 0, 1 \right)^{T}
$$
G. $$
\left(-1,-1, 0, 0 \right)^{T}
$$
H. $$
\left(-1,1, 0, 1 \right)^{T}
$$
I. $$
\left(1,1, -1, -1 \right)^{T}
$$
J. $$
\left(1,-1, 0, 1 \right)^{T}
$$
Answer: F
Let $R^{4}$ basis of subspace $W$ of a be $\alpha_{1} \!=\! ( 1, \ -1, 1, \ -1 ), \ \ \alpha_{2} \!=\! ( 0, 1, 1, 0 )$ .
What is the interior projection of the vector $\alpha{=} ( 1, \,-3, \, 1, \,-3 )$ on $W$ ?

Options:
A. $$
2 \alpha_{1}-5\alpha_{2}
$$
B. $$
2 \alpha_{1}-\alpha_{2}
$$
C. $$
3 \alpha_{1}-\alpha_{2}
$$
D. $$
\alpha_{1}-\alpha_{2}
$$
E. $$
2 \alpha_{1}-2\alpha_{2}
$$
F. $$
\alpha_{1}+\alpha_{2}
$$
G. $$
2 \alpha_{1}+\alpha_{2}
$$
H. $$
2 \alpha_{1}+3\alpha_{2}
$$
I. $$
2 \alpha_{1}-3\alpha_{2}
$$
J. $$
3 \alpha_{1}-4\alpha_{2}
$$
Answer: B
What is the solution to the system $\left\{\begin{matrix} {{x_{1}+2 x_{2}-x_{3}+3 x_{4}=2}} \\ {{2 x_{1}-x_{2}+3 x_{3}-2 x_{4}=7}} \\ {{3 x_{2}-x_{3}+x_{4}=6}} \\ {{x_{1}-x_{2}+x_{3}+4 x_{4}=-4}} \\ \end{matrix} \right.$ using Cramer's law?

Options:
A. $$
x_{1}=1 \,, x_{2}=4 \,, x_{3}=2 \,, x_{4}=1
$$
B. $$
x_{1}=-1 \,, x_{2}=3 \,, x_{3}=-2 \,, x_{4}=-1
$$
C. $$
x_{1}=-1 \,, x_{2}=3 \,, x_{3}=2 \,, x_{4}=1
$$
D. $$
x_{1}=1 \,, x_{2}=3 \,, x_{3}=2 \,, x_{4}=-5
$$
E. $$
x_{1}=1 \,, x_{2}=3 \,, x_{3}=2 \,, x_{4}=-1
$$
F. $$
x_{1}=-1 \,, x_{2}=4 \,, x_{3}=2 \,, x_{4}=-1
$$
G. $$
x_{1}=1 \,, x_{2}=3 \,, x_{3}=-2 \,, x_{4}=-1
$$
H. $$
x_{1}=-1 \,, x_{2}=3 \,, x_{3}=5 \,, x_{4}=-1
$$
I. $$
x_{1}=1 \,, x_{2}=-3 \,, x_{3}=2\,, x_{4}=-1
$$
J. $$
x_{1}=-1 \,, x_{2}=-3 \,, x_{3}=2 \,, x_{4}=-1
$$
Answer: E
We know that the matrix $A {=} \left( \begin{matrix} {{{{1}}}} & {{{{0}}}} & {{{{-1}}}} \\ {{{{1}}}} & {{{{1}}}} & {{{{-1}}}} \\ {{{{0}}}} & {{{{1}}}} & {{{{0}}}} \\ \end{matrix} \right)$ has rank 2, If a non-zero matrix $C$ is such that $AC=0$ , what is this matrix?

Options:
A. $$
\left( \begin{matrix} {{0}} & {{0}} & {{1}} \\ {{0}} & {{0}} & {{0}} \\ {{0}} & {{1}} & {{1}} \\ \end{matrix} \right)
$$
B. $$
\left( \begin{matrix} {{0}} & {{0}} & {{1}} \\ {{1}} & {{0}} & {{0}} \\ {{0}} & {{0}} & {{1}} \\ \end{matrix} \right)
$$
C. $$
\left( \begin{matrix} {{0}} & {{0}} & {{1}} \\ {{0}} & {{0}} & {{0}} \\ {{0}} & {{0}} & {{2}} \\ \end{matrix} \right)
$$
D. $$
\left( \begin{matrix} {{0}} & {{0}} & {{1}} \\ {{0}} & {{1}} & {{0}} \\ {{0}} & {{0}} & {{1}} \\ \end{matrix} \right)
$$
E. $$
\left( \begin{matrix} {{0}} & {{0}} & {{1}} \\ {{0}} & {{0}} & {{1}} \\ {{0}} & {{0}} & {{1}} \\ \end{matrix} \right)
$$
F. $$
\left( \begin{matrix} {{1}} & {{0}} & {{1}} \\ {{0}} & {{0}} & {{0}} \\ {{0}} & {{0}} & {{1}} \\ \end{matrix} \right)
$$
G. $$
\left( \begin{matrix} {{2}} & {{0}} & {{1}} \\ {{0}} & {{0}} & {{0}} \\ {{0}} & {{0}} & {{1}} \\ \end{matrix} \right)
$$
H. $$
\left( \begin{matrix} {{0}} & {{1}} & {{1}} \\ {{0}} & {{0}} & {{0}} \\ {{0}} & {{0}} & {{1}} \\ \end{matrix} \right)
$$
I. $$
\left( \begin{matrix} {{0}} & {{0}} & {{1}} \\ {{0}} & {{0}} & {{0}} \\ {{1}} & {{0}} & {{1}} \\ \end{matrix} \right)
$$
J. $$
\left( \begin{matrix} {{0}} & {{0}} & {{1}} \\ {{0}} & {{0}} & {{0}} \\ {{0}} & {{0}} & {{1}} \\ \end{matrix} \right)
$$
Answer: J
What is the result of replacing the following quadratic form with the standard form $- 4 x_{1} x_{2}+2 x_{1} x_{3}+2 x_{2} x_{3}$ by a non-degenerate linear substitution?

Options:
A. $$
2 {y_{1}}^{2}-{\frac{1} {2}} {y_{2}}^{2}+5 {y_{3}}^{2}
$$
B. $$
2 {y_{1}}^{2}-{\frac{3} {2}} {y_{2}}^{2}+4 {y_{3}}^{2}
$$
C. $$-2 {y_{1}}^{2}-{\frac{1} {2}} {y_{2}}^{2}+4 {y_{3}}^{2}
$$
D. $$
{y_{1}}^{2}- {y_{2}}^{2}+ {y_{3}}^{2}
$$
E. $$
- {y_{1}}^{2}-{\frac{1} {2}} {y_{2}}^{2}+4 {y_{3}}^{2}
$$
F. $$
{y_{1}}^{2}+ {y_{2}}^{2}- {y_{3}}^{2}
$$
G. $$
2 {y_{1}}^{2}-{\frac{1} {2}} {y_{2}}^{2}+4 {y_{3}}^{2}
$$
H. $$
{y_{1}}^{2}-{\frac{1} {2}} {y_{2}}^{2}+4 {y_{3}}^{2}
$$
I. $$
{y_{1}}^{2}+ {y_{2}}^{2}+ {y_{3}}^{2}
$$
J. $$
{y_{1}}^{2}- {y_{2}}^{2}- {y_{3}}^{2}
$$
Answer: G
If we set $f ( x ) \! \in\! F [ x ], a, b \! \in\! F, \ \operatorname{H} a \neq\! b$ , What is the remainder of $(x-a) (x-b)$ by dividing $f (x)$ ?

Options:
A. $$
\frac{f ( a )-f ( b )} {a-b} x+\frac{b f ( a )-a f ( b )} {b+a}
$$
B. $$
\frac{f ( a )-f ( b )} {a-b} x-\frac{b f ( a )-a f ( b )} {b+a}
$$
C. $$
\frac{f ( a )-f ( b )} {a+b} x+\frac{b f ( a )-a f ( b )} {b-a}
$$
D. $$
\frac{f ( a )-f ( b )} {a-b} x+\frac{b f ( a )-a f ( b )} {b-a}
$$
E. $$
\frac{f ( a )+f ( b )} {a-b} x+\frac{b f ( a )-a f ( b )} {b-a}
$$
F. $$
\frac{f ( a )-f ( b )} {a-b} x+\frac{b f ( a )+a f ( b )} {b-a}
$$
G. $$
\frac{f ( a )-f ( b )} {a-b} x-\frac{b f ( a )-a f ( b )} {b-a}
$$
H. $$
\frac{f ( a )-f ( b )} {a+b} x-\frac{b f ( a )-a f ( b )} {b-a}
$$
I. $$
\frac{f ( a )-f ( b )} {a-b} x-\frac{b f ( a )+a f ( b )} {b-a}
$$
J. $$
\frac{f ( a )+f ( b )} {a-b} x-\frac{b f ( a )-a f ( b )} {b-a}
$$
Answer: D
Let $\alpha_{1} \!=\! (-1, 0, \ -2 ), \alpha_{2} \!=\! ( 0, 1, 2 ), \quad\alpha_{3} \!=\! ( 1, 2, 5 ), \ \beta_{1} \!=\! (-1,$ 1, 0), $\beta_{2} {=} ( 1, \, 0, \, 1 ), \, \beta_{3} {=} ( 0, \, 1, \, 2 ), \, \, \, \xi{=} ( 0, \, 3, \, 5 )$ be a vector in ${\bf R}^{3}$ , $\sigma$ be a linear transformation of ${\bf R}^{3}$ , and $\sigma( \alpha_{1} ) {=} ( 2, 0, \ -1 ), \sigma( \alpha_{2} ) {=} ( 0, 0, 1 ), \sigma( \alpha_{3} ) {=} ( 0, 1, 2 )$ . So what is the matrix of F with respect to $\{\beta_{1}, \beta_{2}, \beta_{3} \}$?

Options:
A. $$
\left( \begin{matrix} {{2}}\\{{4}} \\ {{-1}} \\ \end{matrix} \right)
$$
B. $$
\left( \begin{matrix} {{2}}\\{{2}} \\ {{-1}} \\ \end{matrix} \right)
$$
C. $$
\left( \begin{matrix} {{2}}\\{{4}} \\ {{1}} \\ \end{matrix} \right)
$$
D. $$
\left( \begin{matrix} {{2}}\\{{3}} \\ {{-1}} \\ \end{matrix} \right)
$$
E. $$
\left( \begin{matrix} {{2}}\\{{4}} \\ {{2}} \\ \end{matrix} \right)
$$
F. $$
\left( \begin{matrix} {{2}}\\{{4}} \\ {{-2}} \\ \end{matrix} \right)
$$
G. $$
\left( \begin{matrix} {{2}}\\{{1}} \\ {{-1}} \\ \end{matrix} \right)
$$
H. $$
\left( \begin{matrix} {{3}}\\{{4}} \\ {{-1}} \\ \end{matrix} \right)
$$
I. $$
\left( \begin{matrix} {{4}}\\{{4}} \\ {{-1}} \\ \end{matrix} \right)
$$
J. $$
\left( \begin{matrix} {{1}}\\{{4}} \\ {{-1}} \\ \end{matrix} \right)
$$
Answer: A
Using the orthogonal transformation method to transform the quadratic form into canonical form, what is the result?
$$
f ( x_{1}, x_{2}, x_{3} )=( x_{1}-x_{2} )^{2}+( x_{2}-x_{3} )^{2}+( x_{3}-x_{1} )^{2} \,.
$$

Options:
A. $$
f=-2 y_{2}^{2}+3 y_{3}^{2}
$$
B. $$
f=- y_{2}^{2}+3 y_{3}^{2}
$$
C. $$
f=3 y_{2}^{2}+ y_{3}^{2}
$$
D. $$
f=3 y_{2}^{2}-2 y_{3}^{2}
$$
E. $$
f=3 y_{2}^{2}+3 y_{3}^{2}
$$
F. $$
f= y_{2}^{2}+3 y_{3}^{2}
$$
G. $$
f=-3 y_{2}^{2}+3 y_{3}^{2}
$$
H. $$
f=3 y_{2}^{2}+2 y_{3}^{2}
$$
I. $$
f=2 y_{2}^{2}+3 y_{3}^{2}
$$
J. $$
f=3 y_{2}^{2}-3 y_{3}^{2}
$$
Answer: E
Let $A$be a third-order matrix, $\alpha_{1}, \alpha_{2}$ be the eigenvectors of $A$ belonging to the eigenvalues $- 1, 1$ , and vector $\alpha_{3}$ satisfy $A \alpha_{\frac{1} {3}}=\alpha_{\frac{1} {2}}+\alpha_{\frac{1} {3}}$ . Let $P=( \alpha_{1}, \alpha_{2}, \alpha_{3} )$, then what is the value of $P^{-1} A P$ ?

Options:
A. $$
P^{-1} A P=\left( \begin{matrix} {{{-1}}} & {{{-1}}} & {{{0}}} \\ {{{0}}} & {{{1}}} & {{{1}}} \\ {{{0}}} & {{{0}}} & {{{1}}} \\ \end{matrix} \right)
$$
B. $$
P^{-1} A P=\left( \begin{matrix} {{{-1}}} & {{{0}}} & {{{0}}} \\ {{{0}}} & {{{1}}} & {{{1}}} \\ {{{0}}} & {{{0}}} & {{{1}}} \\ \end{matrix} \right)
$$
C. $$
P^{-1} A P=\left( \begin{matrix} {{{-1}}} & {{{0}}} & {{{0}}} \\ {{{1}}} & {{{1}}} & {{{1}}} \\ {{{0}}} & {{{0}}} & {{{1}}} \\ \end{matrix} \right)
$$
D. $$
P^{-1} A P=\left( \begin{matrix} {{{-1}}} & {{{0}}} & {{{0}}} \\ {{{0}}} & {{{1}}} & {{{1}}} \\ {{{0}}} & {{{1}}} & {{{1}}} \\ \end{matrix} \right)
$$
E. $$
P^{-1} A P=\left( \begin{matrix} {{{-1}}} & {{{0}}} & {{{0}}} \\ {{{-1}}} & {{{1}}} & {{{1}}} \\ {{{0}}} & {{{0}}} & {{{1}}} \\ \end{matrix} \right)
$$
F. $$
P^{-1} A P=\left( \begin{matrix} {{{-1}}} & {{{0}}} & {{{0}}} \\ {{{0}}} & {{{1}}} & {{{2}}} \\ {{{0}}} & {{{0}}} & {{{1}}} \\ \end{matrix} \right)
$$
G. $$
P^{-1} A P=\left( \begin{matrix} {{{-1}}} & {{{0}}} & {{{0}}} \\ {{{0}}} & {{{1}}} & {{{1}}} \\ {{{1}}} & {{{0}}} & {{{1}}} \\ \end{matrix} \right)
$$
H. $$
P^{-1} A P=\left( \begin{matrix} {{{1}}} & {{{0}}} & {{{0}}} \\ {{{0}}} & {{{1}}} & {{{1}}} \\ {{{0}}} & {{{0}}} & {{{1}}} \\ \end{matrix} \right)
$$
I. $$
P^{-1} A P=\left( \begin{matrix} {{{-1}}} & {{{0}}} & {{{0}}} \\ {{{0}}} & {{{2}}} & {{{1}}} \\ {{{0}}} & {{{0}}} & {{{1}}} \\ \end{matrix} \right)
$$
J. $$
P^{-1} A P=\left( \begin{matrix} {{{-1}}} & {{{0}}} & {{{0}}} \\ {{{2}}} & {{{1}}} & {{{1}}} \\ {{{0}}} & {{{0}}} & {{{1}}} \\ \end{matrix} \right)
$$
Answer: B
Let the matrix $A=\left( \begin{matrix} {{{1}}} & {{{-1}}} & {{{1}}} \\ {{{2}}} & {{{4}}} & {{{-2}}} \\ {{{-3}}} & {{{-3}}} & {{{c}}} \\ \end{matrix} \right)$ be similar to $\left( \begin{matrix} {{{2}}} & {{{0}}} & {{{0}}} \\ {{{0}}} & {{{2}}} & {{{0}}} \\ {{{0}}} & {{{0}}} & {{{d}}} \\ \end{matrix} \right)$, what are the values of $c$ and $d$ respectively?

Options:
A. $$
c=5 \,, d=6
$$
B. $$
c=5 \,, d=5
$$
C. $$
c=2 \,, d=6
$$
D. $$
c=5 \,, d=4
$$
E. $$
c=1 \,, d=6
$$
F. $$
c=4 \,, d=6
$$
G. $$
c=5 \,, d=3
$$
H. $$
c=0 \,, d=6
$$
I. $$
c=6 \,, d=6
$$
J. $$
c=3 \,, d=6
$$
Answer: A
Let $A=\left( \begin{matrix} {{{1}}} & {{{2}}} & {{{3}}} \\ {{{x}}} & {{{y}}} & {{{z}}} \\ {{{0}}} & {{{0}}} & {{{1}}} \\ \end{matrix} \right)$ , and the eigenvalues of $A$ are 1,2,3, then what are the values of $x$, $y$, and $z$ ?

Options:
A. $$
x=-6, y=2, z \in R
$$
B. $$
x=-1, y=4, z=3
$$
C. $$
x=-1, y=0, z \in R
$$
D. $$
x=-2, y=2, z \in R
$$
E. $$
x=-4, y=2, z \in R
$$
F. $$
x=0, y=4, z \in R
$$
G. $$
x=-1, y=4, z \in R
$$
H. $$
x=-1, y=-4, z \in R
$$
I. $$
x=-1, y=8, z \in R
$$
J. $$
x=2, y=4, z=8
$$
Answer: G
Given a 3x3 real symmetric matrix $A$ with eigenvalues 6, 3, 3, and the eigenvector corresponding to the eigenvalue 6 is $\xi_{1}=(1, 1, 1) r$, what is the eigenvector corresponding to the eigenvalue 3 ?

Options:
A. $$
k_{2} \xi_{2}-k_{3} \xi_{3}
$$
B. $$
k_{1} \xi_{1}-k_{3} \xi_{3}
$$
C. $$
k_{1} \xi_{1}+k_{2} \xi_{2}
$$
D. $$
k_{1} \xi_{1}
$$
E. $$
k_{1} \xi_{1}-k_{2} \xi_{2}
$$
F. $$
k_{2} \xi_{2}+k_{3} \xi_{3}
$$
G. $$
k_{2} \xi_{2}
$$
H. $$
k_{3} \xi_{3}
$$
I. $$
k_{1} \xi_{1}+k_{3} \xi_{3}
$$
J. $$
k_{1} \xi_{1}+k_{2} \xi_{2}+k_{3} \xi_{3}
$$
Answer: F
Let $A=\left( \begin{matrix} {{{-4}}} & {{{-1 0}}} & {{{0}}} \\ {{{1}}} & {{{3}}} & {{{0}}} \\ {{{3}}} & {{{6}}} & {{{1}}} \\ \end{matrix} \right)$ , then what is the eigenvalue of $2 E-3 A_{-1}$?

Options:
A. $$\varphi ( 1 ) \!=\!1, \varphi (-2 ) \!=\! \frac{7} {2}$$
B. $$\varphi ( 1 ) \!=\!-1, \varphi (-2 ) \!=\! \frac{5} {2}$$
C. $$\varphi ( 1 ) \!=\!-1, \varphi (-2 ) \!=\! \frac{7} {3}$$
D. $$\varphi ( 1 ) \!=\!-1, \varphi (-2 ) \!=\! \frac{7} {4}$$
E. $$\varphi ( 1 ) \!=\!-1, \varphi (-2 ) \!=\! 1$$
F. $$\varphi ( 1 ) \!=\!-1, \varphi (-2 ) \!=\! \frac{3} {2}$$
G. $$\varphi ( 1 ) \!=\!-1, \varphi (-2 ) \!=\! -\frac{7} {2}$$
H. $$\varphi ( 1 ) \!=\!-1, \varphi (-2 ) \!=\! \frac{1} {2}$$
I. $$\varphi ( 1 ) \!=\!-1, \varphi (-2 ) \!=\! -1$$
J. $$\varphi ( 1 ) \!=\!-1, \varphi (-2 ) \!=\! \frac{7} {2}$$
Answer: J
Known third-order phalanx three characteristic value $A$ are $1, -1, 2$, matrix $B = A_ {3} - 5 A_ {2}$. So what is the eigenvalue of the matrix $B$ and the value of the determinant of $\left| B \right|$ ?

Options:
A. $$\varphi( 1 ) \!=\!-\! 4, \varphi(-1 ) \!=\!\! 6, \varphi( 2 ) \!=\!-\! 1 2$$
$$\left| B \right|=\varphi( 1 ) \varphi(-1 ) \varphi( 2 )=2 8 8
$$
B. $$\varphi( 1 ) \!=\!-\! 2, \varphi(-1 ) \!=\!-\! 3, \varphi( 2 ) \!=\!-\! 1 2$$
$$\left| B \right|=\varphi( 1 ) \varphi(-1 ) \varphi( 2 )=-7 2
$$
C. $$\varphi( 1 ) \!=\!-\! 2, \varphi(-1 ) \!=\!-\! 6, \varphi( 2 ) \!=\!-\! 1 2$$
$$\left| B \right|=\varphi( 1 ) \varphi(-1 ) \varphi( 2 )=-14 4
$$
D. $$\varphi( 1 ) \!=\!-\! 16, \varphi(-1 ) \!=\!-\! 3, \varphi( 2 ) \!=\!-\! 1 2$$
$$\left| B \right|=\varphi( 1 ) \varphi(-1 ) \varphi( 2 )=-5 7 6
$$
E. $$\varphi( 1 ) \!=\!-\! 4, \varphi(-1 ) \!=\!-\! 6, \varphi( 2 ) \!=\!-\! 1 2$$
$$\left| B \right|=\varphi( 1 ) \varphi(-1 ) \varphi( 2 )=-2 8 8
$$
F. $$\varphi( 1 ) \!=\!\! 4, \varphi(-1 ) \!=\!-\! 6, \varphi( 2 ) \!=\!-\! 1 2$$
$$\left| B \right|=\varphi( 1 ) \varphi(-1 ) \varphi( 2 )=2 8 8
$$
G. $$\varphi( 1 ) \!=\!-\! 4, \varphi(-1 ) \!=\!-\! 6, \varphi( 2 ) \!=\!\! 1 2$$
$$\left| B \right|=\varphi( 1 ) \varphi(-1 ) \varphi( 2 )=2 8 8
$$
H. $$\varphi( 1 ) \!=\!-\! 8, \varphi(-1 ) \!=\!-\! 6, \varphi( 2 ) \!=\!-\! 1 2$$
$$\left| B \right|=\varphi( 1 ) \varphi(-1 ) \varphi( 2 )=-5 7 6
$$
I. $$\varphi( 1 ) \!=\!-\! 4, \varphi(-1 ) \!=\!-\! 6, \varphi( 2 ) \!=\!-\! 2 4$$
$$\left| B \right|=\varphi( 1 ) \varphi(-1 ) \varphi( 2 )=-5 7 6
$$
J. $$\varphi( 1 ) \!=\!-\! 4, \varphi(-1 ) \!=\!-\! 1 2, \varphi( 2 ) \!=\!-\! 1 2$$
$$\left| B \right|=\varphi( 1 ) \varphi(-1 ) \varphi( 2 )=-5 7 6
$$
Answer: E
What is the expression for $\beta$ being linearly represented by $\alpha_{1}, \alpha_{2}, \alpha_{3}, \alpha_{4}$?
$$
\beta={\left( \begin{matrix} {{0}} \\ {2} \\ {0} \\ {-1} \\ \end{matrix} \right)} ; \alpha_{1}={\left( \begin{matrix} {1} \\ {1} \\ {1} \\ {1} \\ \end{matrix} \right)}, \alpha_{2}={\left( \begin{matrix} {1} \\ {1} \\ {1} \\ {0} \\ \end{matrix} \right)}, \alpha_{3}={\left( \begin{matrix} {1} \\ {1} \\ {0}\\ {0} \\ \end{matrix} \right)}, \alpha_{4}={\left( \begin{matrix} {1} \\ {0} \\ {0} \\ {0} \\ \end{matrix} \right)}
$$

Options:
A. $$ \beta=-\alpha_{1}+\alpha_{2}+ \alpha_{3}-2 \alpha_{4}
$$
B. $$ \beta=\alpha_{1}+\alpha_{2}+2 \alpha_{3}-2 \alpha_{4}
$$
C. $$ \beta=-2\alpha_{1}+2\alpha_{2}+2 \alpha_{3}-2 \alpha_{4}
$$
D. $$ \beta=-\alpha_{1}+\alpha_{2}+2 \alpha_{3}- \alpha_{4}
$$
E. $$ \beta=-\alpha_{1}-\alpha_{2}+2 \alpha_{3}-2 \alpha_{4}
$$
F. $$ \beta=-\alpha_{1}+\alpha_{2}-2 \alpha_{3}-2 \alpha_{4}
$$
G. $$ \beta=-2\alpha_{1}+\alpha_{2}+2 \alpha_{3}-2 \alpha_{4}
$$
H. $$ \beta=-\alpha_{1}+\alpha_{2}+2 \alpha_{3}+2 \alpha_{4}
$$
I. $$ \beta=-\alpha_{1}+\alpha_{2}+2 \alpha_{3}-2 \alpha_{4}
$$
J. $$ \beta=-\alpha_{1}+2\alpha_{2}+2 \alpha_{3}-2 \alpha_{4}
$$
Answer: I
Let the matrix $A=\left( \begin{matrix} {{{{1}}}} & {{{{\frac{1} {2}}}}} & {{{{0}}}} \\ {{{{2}}}} & {{{{1}}}} & {{{{0}}}} \\ {{{{1}}}} & {{{{\frac{1} {2}}}}} & {{{{0}}}} \\ \end{matrix} \right), \beta=\left( \begin{matrix} {{{{0}}}} \\ {{{{0}}}} \\ {{{{1}}}} \\ \end{matrix} \right)$ , and the matrix $X$satisfies $A X=2 X+\beta$, so what is the expression for the matrix $X$?

Options:
A. $$X={\left( \begin{matrix} {{c-{\frac{1} {2}}}} \\ {{2 c+1}} \\ {{c}} \\ \end{matrix} \right)}, c\in R
$$
B. $$X={\left( \begin{matrix} {{-c+{\frac{1} {2}}}} \\ {{2 c+1}} \\ {{c}} \\ \end{matrix} \right)}, c\in R
$$
C. $$X={\left( \begin{matrix} {{c+{\frac{1} {2}}}} \\ {{2 c+1}} \\ {{-c}} \\ \end{matrix} \right)}, c\in R
$$
D. $$X={\left( \begin{matrix} {{c+{\frac{1} {2}}}} \\ {{2 c+1}} \\ {{c}} \\ \end{matrix} \right)}, c\in R
$$
E. $$X={\left( \begin{matrix} {{c+{\frac{1} {2}}}} \\ {{2 c+1}} \\ {{2c-2}} \\ \end{matrix} \right)}, c\in R
$$
F. $$X={\left( \begin{matrix} {{c+{\frac{1} {2}}}} \\ {{2 c+1}} \\ {{c-1}} \\ \end{matrix} \right)}, c\in R
$$
G. $$X={\left( \begin{matrix} {{c+{\frac{1} {2}}}} \\ {{2 c+1}} \\ {{c+1}} \\ \end{matrix} \right)}, c\in R
$$
H. $$X={\left( \begin{matrix} {{c+{\frac{1} {2}}}} \\ {{2 c-1}} \\ {{c}} \\ \end{matrix} \right)}, c\in R
$$
I. $$X={\left( \begin{matrix} {{c+{\frac{1} {2}}}} \\ {{-2 c+1}} \\ {{c}} \\ \end{matrix} \right)}, c\in R
$$
J. $$X={\left( \begin{matrix} {{c+{\frac{1} {2}}}} \\ {{2 c+1}} \\ {{3c}} \\ \end{matrix} \right)}, c\in R
$$
Answer: D
Let $A =diag(1, -2, 1)$ and the matrix $B$ satisfies $A^* B A = 2 B A - 8 E$. Therefore, what is the value of matrix $B$?

Options:
A. $$B=A +E
$$
B. $$B=2 E
$$
C. $$B=2 A ^2-E
$$
D. $$B=E
$$
E. $$B=2 A +E
$$
F. $$B=2 A
$$
G. $$B= A ^2-E
$$
H. $$B=A
$$
I. $$B=2 A ^2
$$
J. $$B=2 A -E
$$
Answer: F
Given a 3x3 matrix $A=\left( \begin{matrix} {{{a_{1}}}} & {{{c_{1}}}} & {{{d_{1}}}} \\ {{{a_{2}}}} & {{{c_{2}}}} & {{{d_{2}}}} \\ {{{a_{3}}}} & {{{c_{3}}}} & {{{d_{3}}}} \\ \end{matrix} \right), \ B=\left( \begin{matrix} {{{b_{1}}}} & {{{c_{1}}}} & {{{d_{1}}}} \\ {{{b_{2}}}} & {{{c_{2}}}} & {{{d_{2}}}} \\ {{{b_{3}}}} & {{{c_{3}}}} & {{{d_{3}}}} \\ \end{matrix} \right)$, and $\left| A \right| = 1$, $\left| B \right| = 2$, what is the value of $\left| A + 2B \right|$?

Options:
A. $$40
$$
B. $$20
$$
C. $$35
$$
D. $$15
$$
E. $$10
$$
F. $$30
$$
G. $$50
$$
H. $$45
$$
I. $$5
$$
J. $$25
$$
Answer: H
When executing the query statement, the DBMS retrieves the corresponding internal schema description from the data dictionary and maps the schema to the internal schema to determine which should be read in?

Options:
A. Physical data
B. Syntax tree
C. Sequence of operations
D. Virtual tables
E. Optimize the strategy
F. Logical data
G. Network schema
H. Execution logs
I. Cache metadata
J. External schema
Answer: A
What is the meaning of enum in the following line of the ODL definition?

Options:
A. Attribute method
B. Attribute parameter
C. Attribute object
D. Attribute value
E. Attribute constant
F. Attribute type
G. Attribute field
H. Attribute name
I. Attribute class
J. Attribute element
Answer: F
Of the following characteristics of tuples and objects, it is correct that ( ).

Options:
A. The tuple is identified, but the object is not
B. tuples have identity, objects do not
C. Objects have invariance, tuples do not
D. Objects are inheritable, tuples are not
E. Both tuples and objects have identity
F. Tuples have dynamic bindings, objects do not
G. Neither tuple nor object has identity
H. Objects are encapsulated, tuples are not
I. Tuples are polymorphic, objects are not polymorphic
J. Objects have identity, tuples do not
Answer: J
To find the name of the professor (p) associated only with the course (c) of "xx University", use the following OQL statement:
SEIECT p.name
FROM Professors p
WHERE ( ) c IN p. professorRelated:
c. ownedBy. name ='xx University';

Options:
A. NOT
B. ANY
C. EACH
D. EXIST
E. FOR ALL
F. EXISTS
G. IS
H. UNIQUE
I. ALL
J. SOME
Answer: E
If there are author table (author number, city) and publisher table (publication name, city) in a database, please complete the following query statement, so that the query statement can query all the non-duplicate cities where the author and publisher are located.
SELECT city FROM author table ____
SELECT city FROM publisher table;

Options:
A. JOIN
B. HAVING
C. DISTINCT
D. GROUP BY
E. ORDER BY
F. INTERSECT
G. WHERE
H. UNION ALL
I. AND
J. EXCEPT
Answer: J
The "between 15 and 30 years old" constraint is a ( ) function of the DBMS.

Options:
A. Recovery
B. Query optimization
C. Integrity constraint
D. Access control
E. Completeness
F. Security
G. Data redundancy
H. Storage limitation
I. User permission
J. Concurrency control
Answer: E
Locking data objects can cause problems with live locks and deadlocks. A simple way to avoid live locks is to adopt the policy of ( ).

Options:
A. Sequential locking method
B. Sequential blocking method
C. Priority inversion handling
D. Minimal resource allocation
E. Round-robin scheduling
F. Randomized locking mechanism
G. Mutual exclusion protocol
H. Last in, first out strategy
I. High priority service
J. First come, first served
Answer: J
If there is A waiting transaction set {T1, T2, T3, T4, T5} in a database system, T1 is waiting for data item A2 to be locked by T2, T2 is waiting for data item A4 to be locked by T4, T3 is waiting for data item A4 to be locked by T4, and T5 is waiting for data item A to be locked by T1. Of the following statements about the state of this system and what needs to be done, the correct is ( ).

Options:
A. The system is in the deadlock state. Restart all transactions to escape the deadlock state
B. The system is in the deadlock state. You need to unlock data item A4 to exit the deadlock state
C. The system is in the deadlock state. You can cancel T4 to exit the deadlock state
D. The system is not in a deadlock state but requires a restart of transaction T5
E. The system is in the deadlock state and needs manual cancellation of transaction T1
F. The system is not in a deadlock state and does not need to undo any transactions in it
G. The system is not in a deadlock state but requires undoing data item A2 locks
H. The system is not in deadlock state, but needs to reschedule transactions T2 and T4
I. The system is in A deadlock state, and you need to cancel any of the transactions to exit the deadlock state
J. The system is in the deadlock state. Undo T5 to exit the deadlock state
Answer: F
The file structure that stores the newly inserted record at the end of the file and distributes the records randomly in the physical storage space of the files are ( ).

Options:
A. Hash files
B. Queue files
C. Linked files
D. Aggregate files
E. Batch files
F. Index files
G. Segment files
H. Tree files
I. Cluster files
J. Stack files
Answer: J
The task of logical structure design using the relational model is to convert the E-R diagram into a set of ( ), and carry out ( ) processing.

Options:
A. Data Chart; Normalization
B. Relationship Analysis; Simplification
C. Entity-Relationship Diagram; Normalization
D. Data Model; Normalization
E. Object relationship; Optimization
F. Relationship Model; Normalization
G. Object Pattern; Regularization
H. Instance method; Standardization
I. Relational Database; Serialization
J. Relationship Diagram; Standardization
Answer: F
In the database system blocking protocol, level 1 protocol: "transaction must add X lock to data A before modifying it, and do not release X lock until the end of the transaction", the protocol can prevent (); The second-level protocol is based on the first-level protocol to add "transaction T must add S lock before reading data R, and then release S lock after reading", which can prevent (); The three-level protocol is based on the first-level protocol, adding "transaction T must add S lock before reading data R, and will not release S lock until the end of the transaction", which can prevent ().

Options:
A. read dirty data and non-repeatable reads; non-repeatable reads; loss of changes, read dirty data, and non-repeatable reads
B. loss of changes; loss of changes and read dirty data; loss of changes, read dirty data, and non-repeatable reads
C. non-repeatable reads; non-repeatable reads; loss of changes, read dirty data, and non-repeatable reads
D. loss of changes; non-repeatable reads; loss of changes, read dirty data, and non-repeatable reads
E. read dirty data; non-repeatable reads; loss of changes, read dirty data, and non-repeatable reads
F. non-repeatable reads; loss of changes and read dirty data; loss of changes, read dirty data, and non-repeatable reads
G. loss of changes; non-repeatable reads and read dirty data; loss of changes, read dirty data, and non-repeatable reads
H. loss of changes; loss of changes, read dirty data, and non-repeatable reads; loss of changes and read dirty data
I. loss of changes; loss of changes and non-repeatable reads; loss of changes, read dirty data, and non-repeatable reads
J. read dirty data; loss of changes and read dirty data; loss of changes, read dirty data, and non-repeatable reads
Answer: B
If there is an expression a/b in the transaction program, if the expression is evaluated when b is 0, the fault that will occur belongs to ().

Options:
A. The media is faulty
B. Operating system error
C. Clock error
D. User input error
E. The machine stops
F. Application error
G. Cache overflow
H. Transaction failure
I. System fault
J. Network failure
Answer: H
Suppose there are relations R and S, in the following relational operation, the ( ) operation is not required: "R and S have the same number of elements, and their corresponding properties have the same data type".

Options:
A. projection operation on R
B. R and S's right outer join
C. union of R and S
D. left outer join of R and S
E. R divided by S
F. selection operation on R
G. R and S's natural join
H. difference set of R and S
I. the Cartesian product of R and S
J. intersection of R and S
Answer: I
If the actual realized value of the goal planning is not to exceed the target value, the corresponding deviation variable should satisfy ().

Options:
A. d+>0 and d=>0
B. d+>0
C. d->=0
D. d-<0
E. d->0
F. d<=0
G. d<0
H. d==0
I. d+=0
J. d+<0
Answer: I
The initial point taken by the 0.618 method on the interval [2,6] is___.

Options:
A. 4.236
B. 3.382
C. 2.618
D. 5.472
E. 3.902
F. 3.764
G. 3.528
H. 2.764
I. 5.000
J. 4.618
Answer: G
If there are two infinitely long straight current-carrying wires and the magnetic field distribution in space does not have simple symmetry, this magnetic field distribution ( ).

Options:
A. Can be calculated using both Ampere's circuital theorem and the principle of superposition of magnetic field intensities
B. Can be predicted using Ampere's circuital theorem alone and basic principles of electromagnetism
C. Can only be calculated using the Biot-Savart law
D. Cannot be calculated using Ampere's circuital theorem
E. Can be measured using a standard magnetic flux density meter
F. Should be described using Gauss's law for magnetism only
G. Can be evaluated with Ampere's circuital theorem alone and basic principles of electromagnetism
H. Might be simplified using the principles of electromagnetic induction
I. Can be directly calculated using Ampere's circuital theorem
J. May be verified through Ampere's circuital theorem together with basic electromagnetic theory principles
Answer: A
The stretching vibration of the polyethylene chain $\cdots-C H=C H-C H=C H-\cdots$ can be described by a one-dimensional diatomic chain model. The mass of both atoms in the original cell is $M$, but each atom The force constants on the left and right are $\beta_{1}$ and $\beta_{2}$ respectively, and the period of the atomic chain is $a$ . Find the vibration frequency $\omega^{2}$=______.

Options:
A. $$
\frac{\beta_{1}+\beta_{2}} {M} \left[ 1 \pm\left( 1-\frac{4 \beta_{1} \beta_{2} \operatorname{s i n}^{2} \frac{q a} {2}} {\left( \beta_{1}+\beta_{2} \right)^{2}} \right)^{\frac{1} {2}} \right]
$$
B. $$
\frac{\beta_{1}-\beta_{2}} {M} \left[ 1 \pm\left( 1-\frac{4 \beta_{1} \beta_{2} \operatorname{s i n}^{2} \frac{q a} {2}} {\left( \beta_{1}+\beta_{2} \right)^{2}} \right)^{\frac{1} {2}} \right]
$$
C. $$
\frac{\beta_{1}+\beta_{2}} {M} \left[ 1 \pm\left( 1+\frac{4 \beta_{1} \beta_{2} \operatorname{s i n}^{2} \frac{q a} {2}} {\left( \beta_{1}-\beta_{2} \right)^{2}} \right)^{\frac{1} {2}} \right]
$$
D. $$
\frac{\beta_{1}+\beta_{2}} {2M} \left[ 1 \pm\left( 1-\frac{4 \beta_{1} \beta_{2} \operatorname{s i n}^{2} \frac{q a} {2}} {\left( \beta_{1}+\beta_{2} \right)^{2}} \right)^{\frac{1} {2}} \right]
$$
E. $$
2\frac{\beta_{1}+\beta_{2}} {M} \left[ 1 \pm\left( 1-\frac{4 \beta_{1} \beta_{2} \operatorname{s i n}^{2} \frac{q a} {2}} {\left( \beta_{1}+\beta_{2} \right)^{2}} \right)^{\frac{1} {2}} \right]
$$
F. $$
\frac{\beta_{1}+\beta_{2}} {4M} \left[ 1 \pm\left( 1-\frac{4 \beta_{1} \beta_{2} \operatorname{s i n}^{2} \frac{q a} {2}} {\left( \beta_{1}+\beta_{2} \right)^{2}} \right)^{\frac{1} {2}} \right]
$$
G. $$
\frac{\beta_{1}-\beta_{2}} {M} \left[ 1 \pm\left( 1-\frac{4 \beta_{1} \beta_{2} \operatorname{s i n}^{2} \frac{q a} {2}} {\left( \beta_{1}-\beta_{2} \right)^{2}} \right)^{\frac{1} {2}} \right]
$$
H. $$
\frac{\beta_{1}+\beta_{2}} {3M} \left[ 1 \pm\left( 1-\frac{4 \beta_{1} \beta_{2} \operatorname{s i n}^{2} \frac{q a} {2}} {\left( \beta_{1}+\beta_{2} \right)^{2}} \right)^{\frac{1} {2}} \right]
$$
I. $$
\frac{\beta_{1}+\beta_{2}} {M} \left[ 1 \pm\left( 1-\frac{4 \beta_{1} \beta_{2} \operatorname{s i n}^{2} \frac{q a} {2}} {\left( \beta_{1}-\beta_{2} \right)^{2}} \right)^{\frac{1} {2}} \right]
$$
J. $$
\frac{\beta_{1}+\beta_{2}} {M} \left[ 1 \pm\left( 1+\frac{4 \beta_{1} \beta_{2} \operatorname{s i n}^{2} \frac{q a} {2}} {\left( \beta_{1}+\beta_{2} \right)^{2}} \right)^{\frac{1} {2}} \right]
$$
Answer: A
The potential energy of electrons in the periodic field $$ \mathrm{V} \ \mathrm{( X )}=\left\{\begin{array} {l} {{{\frac{1} {2} m \omega^{2} \bigg[ b^{2}-\big( x-n a \big)^{2} \bigg], \frac{\mathrm{s t r}} {\to} m a-b \leq x \leq n a+b}}} \\ {{{0, \frac{\mathrm{s t r}} {\to} \big( n-1 \big) a+b \leq x \leq n a-b}}} \\ \end{array} \right. $$ and $\mathrm{a=4 b,} \omega$ are constants. Try and find the average of this potential energy =_____.

Options:
A. $$\frac{m\omega^2a^2}{52}$$
B. $$\frac{m\omega^2a^2}{76}$$
C. $$\frac{m\omega^2a^2}{64}$$
D. $$\frac{m\omega^2a^2}{58}$$
E. $$\frac{m\omega^2a^2}{46}$$
F. $$\frac{m\omega^2a^2}{67}$$
G. $$\frac{m\omega^2a^2}{32}$$
H. $$\frac{m\omega^2a^2}{96}$$
I. $$\frac{m\omega^2a^2}{84}$$
J. $$\frac{m\omega^2a^2}{72}$$
Answer: H
The atomic weights of $N a$ and $C l$ are 23 and 37 respectively. The side length of the sodium chloride cubic unit cell is 0. 5 6 nm and can be set as a set of parallel ion chains in the [100] direction. Ion concentration $d=0. 28nm$. The Young's modulus of $N a C l$ crystal is $5 \times1 0^{1 0} \, N \cdot m^{-2}$ , if the light frequency of total radiation is the same as the light frequency of $q= 0$ The mode frequency is fixed, and the corresponding light wave wavelength ( ) is found (the experimental value is $6 1 \mu m )$ .

Options:
A. $52.8 \mu m$
B. $58.3 \mu m$
C. $59.1 \mu m$
D. $53.5 \mu m$
E. $61.0 \mu m$
F. $56.4 \mu m$
G. $55.7 \mu m$
H. $54.6 \mu m$
I. $50.2 \mu m$
J. $57.4 \mu m$
Answer: H
Aluminum is known to be a trivalent metal with an atomic mass of 27 and a density of 2.7 g/cm³. The Fermi wave vector______ of aluminum metal at T=0 K.

Options:
A. $$ 1. 8 0 \times 1 0^{1 0} ( m^{-1} ) $$;
B. $$ 1. 2 5 \times 1 0^{1 0} ( m^{-1} ) $$;
C. $$ 1. 7 5 \times 1 0^{9} ( m^{-1} ) $$;
D. $$ 1. 9 0 \times 1 0^{1 0} ( m^{-1} ) $$;
E. $$ 1. 4 8 \times 1 0^{9} ( m^{-1} ) $$;
F. $$ 2. 4 0 \times 1 0^{9} ( m^{-1} ) $$;
G. $$ 2. 0 8 \times 1 0^{9} ( m^{-1} ) $$;
H. $$ 2. 4 8 \times 1 0^{9} ( m^{-1} ) $$;
I. $$ 1. 7 5 \times1 0^{1 0} ( m^{-1} ) $$;
J. $$ 1. 6 0 \times 1 0^{1 0} ( m^{-1} ) $$;
Answer: I
The atomic surface density of the (110) planes of the face-centered cubic structure, given the lattice constant a, is?

Options:
A. $$\frac{1} {a^{2}} $$
B. $$\frac{\sqrt{3}} {a^{2}} $$
C. $$\frac{\sqrt{5}} {a^{2}} $$
D. $$\frac{\sqrt{2}} {a^{2}} $$
E. $$\frac{\sqrt{2}} {3a^{2}} $$
F. $$\frac{2} {a^{2}} $$
G. $$\frac{3\sqrt{2}} {a^{2}} $$
H. $$\frac{\sqrt{2}} {2a^{2}} $$
I. $$\frac{5\sqrt{2}} {a^{2}} $$
J. $$\frac{2\sqrt{2}} {a^{2}} $$
Answer: D
It is known that $E \! \left( k \right) \!=\! {\frac{\hbar^{2}} {ma^{2}}} \! \left( {\frac{7} {8}} \!-\! \operatorname{cos} ka \!+\! {\frac{1} {8}} \! \operatorname{cos} 2 ka \right )$ where a is the lattice constant, m is the mass of the electron, and the average speed of the electron is?

Options:
A. $$ \frac{\hbar} {ma} \biggl( \operatorname{cos} k a-\frac{1} {4} \operatorname{cos} 2 ka \biggr) $$
B. $$ \frac{\hbar} {ma} \biggl( \operatorname{cos} ka + \frac{2} {3} \operatorname{sin} ka \biggr) $$
C. $$ \frac{\hbar} {ma} \biggl( \operatorname{sin} ka - \frac{1} {3} \operatorname{sin} 2 ka \biggr) $$
D. $$ \frac{\hbar} {ma} \biggl( \operatorname{sin} k a + \frac{1} {4} \operatorname{cos} 2 ka \biggr) $$
E. $$ \frac{\hbar} {ma} \biggl( \operatorname{cos} k a-\frac{1} {4} \operatorname{sin} 2 ka \biggr) $$
F. $$ \frac{\hbar} {ma} \biggl( \operatorname{sin} k a-\frac{1} {4} \operatorname{sin} 2 ka \biggr) $$
G. $$ \frac{\hbar} {ma} \biggl( \operatorname{sin} ka - \frac{5} {8} \operatorname{sin} 2 ka \biggr) $$
H. $$ \frac{\hbar} {ma} \biggl( \operatorname{sin} ka + \frac{1} {3} \operatorname{sin} 2 ka \biggr) $$
I. $$ \frac{\hbar} {ma} \biggl( \operatorname{cos} ka - \frac{5} {8} \operatorname{cos} 2 ka \biggr) $$
J. $$ \frac{\hbar}{ma} \biggl( \operatorname{sin} ka + \frac{1}{4} \operatorname{sin} 2 ka \biggr) $$
Answer: F
In a single-phase bridge rectifier circuit, if one of the diodes is connected in reverse, then _______.

Options:
A. It will enhance the output efficiency greatly
B. The entire circuit will stop conducting
C. The output voltage will drop to zero
D. The output voltage will be approximately 2VD
E. The diode will burn out due to excessive current
F. The diode will conduct current normally always
G. The voltage output will double effectively
H. It will become a half-wave rectifier
I. The diode will increase output current slightly
J. It forms a completely non-functional circuit
Answer: E
An infinitely long cylindrical conductor with a radius of $\mathbf{R}$ has a current of size $\mathbf{I}$ uniformly flowing through its cross-section. The magnetic energy per unit length within the cylindrical conductor is ___.

Options:
A. $\frac{\mu_{0} I^{2}} {1 4 \pi}$
B. $\frac{\mu_{0} I^{2}} {3 2 \pi}$
C. $\frac{\mu_{0} I^{2}} {1 0 \pi}$
D. $\frac{\mu_{0} I^{2}} {2 4 \pi}$
E. $\frac{\mu_{0} I^{2}} {4 \pi}$
F. $\frac{\mu_{0} I^{2}} {1 2 \pi}$
G. $\frac{\mu_{0} I^{2}} {1 6 \pi}$
H. $\frac{\mu_{0} I^{2}} {1 8 \pi}$
I. $\frac{\mu_{0} I^{2}} {8 \pi}$
J. $\frac{\mu_{0} I^{2}} {2 0 \pi}$
Answer: G
The non-electrostatic force that produces motional electromotive force is ___ , and the non-electrostatic force that induces electromotive force is ___.

Options:
A. Thermal pressure, magnetic resistance
B. Centripetal force, electric charge
C. Magnetic force, induced current
D. Frictional force, electric potential
E. Electric field, electrical resistance
F. Gravitational pull, magnetic flux
G. Magnetic field, electric current
H. Lorentz force, electromotive force
I. Normal force, magnetic field
J. Kinetic force, electric current
Answer: H
Water vapor decomposes into hydrogen and oxygen at the same temperature, i.e., $\mathrm{H}_{2} \mathrm{O} \to\mathrm{H}_{2} + \frac{1} {2} \mathrm{O}_{2}$ , that is, 1 mol of water vapor decomposes into 1 mol of hydrogen and $\frac{1} {2}$ mol at the same temperature. Oxygen the increment of internal energy during this process ____.

Options:
A. ${\frac{2} {3}} R T$
B. ${\frac{5} {7}} R T$
C. ${\frac{7} {9}} R T$
D. ${\frac{3} {4}} R T$
E. ${\frac{7} {10}} R T$
F. ${\frac{3} {5}} R T$
G. ${\frac{1} {2}} R T$
H. ${\frac{4} {5}} R T$
I. ${\frac{1} {4}} R T$
J. ${\frac{2} {5}} R T$
Answer: D
A train is traveling at 90 km/h and its whistle has a frequency of $5 0 0 \mathrm{H z}$ , how much does the frequency change of the whistle a person hears when the train passes him as he stands by the tracks ___.

Options:
A. $5 5 0 \ \mathrm{H z}$
B. $6 0 0 \ \mathrm{H z}$
C. $4 6 6 \ \mathrm{H z}$
D. $5 7 0 \ \mathrm{H z}$
E. $4 9 0 \ \mathrm{H z}$
F. $5 0 0 \ \mathrm{H z}$
G. $5 2 0 \ \mathrm{H z}$
H. $4 0 0 \ \mathrm{H z}$
I. $4 5 0 \ \mathrm{H z}$
J. $5 3 0 \ \mathrm{H z}$
Answer: C
Ferrous oxide can form non-stoichiometric compounds. A sample of ferrous oxide is present in which the mass fraction of iron is 77.45% and the mass fraction of oxygen is 22.55%. The ferrous oxide is known to have a NaCl-type structure with intercontacting $\mathrm{F e}^{2}$ * and $\mathrm{O}^{2}$ nuclei spaced at 0.215 nm. The density of the compound is ____.

Options:
A. $6. 5 0 \ \mathrm{g \cdot c m}^{-3}$
B. $6. 4 0 \ \mathrm{g \cdot c m}^{-3}$
C. $5. 4 5 \ \mathrm{g \cdot c m}^{-3}$
D. $5. 8 4 \ \mathrm{g \cdot c m}^{-3}$
E. $6. 2 3 \ \mathrm{g \cdot c m}^{-3}$
F. $6. 3 0 \ \mathrm{g \cdot c m}^{-3}$
G. $5. 9 3 \ \mathrm{g \cdot c m}^{-3}$
H. $5. 7 8 \ \mathrm{g \cdot c m}^{-3}$
I. $5. 6 7 \ \mathrm{g \cdot c m}^{-3}$
J. $6. 1 0 \ \mathrm{g \cdot c m}^{-3}$
Answer: G
An aqueous solution containing a non-volatile solute $\mathbf{B}$ begins to crystallize ice at 270.15K under a pressure of 101325Pa. Given the cryoscopic constant of water $K_{1} \!=\! 1.86 \mathrm{~K} \! \cdot\! \mathrm{kg} \! \cdot\! \mathrm{mol}^{-1}$ and the ebullioscopic constant $K_{b} = 0.52 \mathrm{~K \cdot~ kg \cdot mol^{-1}}$, the normal boiling point of the solution is______.

Options:
A. 372.95K
B. 375.01K
C. 373.77K
D. 374.58K
E. 374.40K
F. 374.90K
G. 374.33K
H. 375.25K
I. 373.82K
J. 373.99K
Answer: J
What is the optimal range for the migration value of leaves? What is the usable range?

Options:
A. 0.2~0.4, 0.1~0.6
B. 0.3~0.5, 0.1~0.8
C. 0.5~0.7, 0.3~0.9
D. 0.4~0.5, 0.3~0.8
E. 0.4~0.6, 0.3~0.7
F. 0.3~0.5, 0.2~0.8
G. 0.2~0.6, 0.1~0.7
H. 0.3~0.5, 0.3~0.8
I. 0.1~0.4, 0.2~0.5
J. 0.7~0.9, 0.5~1.0
Answer: F
Sirius is known to have a visual magnitude of -1.45, and at a distance of 2.7pc, its absolute apparent magnitude is ___.

Options:
A. +1.8
B. +2.3
C. +0.5
D. +1.2
E. +3.1
F. +1.5
G. +2.0
H. -0.2
I. +1.0
J. +0.8
Answer: F
Any object orbiting the Earth at a speed of ( ) km/s and less than 11.2 km/s must be able to orbit the Earth in an elliptical orbit.

Options:
A. 9.7
B. 7.2
C. 10.7
D. 9.2
E. 7.9
F. 8.9
G. 10.3
H. 8.2
I. 6.5
J. 9.5
Answer: E
The true distance of the Andromeda Galaxy from Earth is () million light-years.

Options:
A. 350
B. 290
C. 310
D. 240
E. 400
F. 220
G. 150
H. 180
I. 300
J. 260
Answer: B