question stringlengths 326 9.6k | answer stringlengths 1 406 | taskname stringclasses 36
values | doc_id int64 0 670 | o3-mini-high_correct bool 2
classes | o4-mini-high_correct bool 2
classes |
|---|---|---|---|---|---|
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Let $S=\{1,2, \ldots, 20\}$, and l... | ["140"] | olympiadbench_OE_TO_maths_en_COMP | 397 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Circle $\omega$ is tangent to para... | ["$5 \\sqrt{10}$"] | olympiadbench_OE_TO_maths_en_COMP | 419 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: The mean, median, and unique mode ... | ["12"] | olympiadbench_OE_TO_maths_en_COMP | 436 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: In quadrilateral $A B C D, \mathrm... | ["$\\sqrt{130}$"] | olympiadbench_OE_TO_maths_en_COMP | 438 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Three non-overlapping squares of p... | ["32"] | olympiadbench_OE_TO_maths_en_COMP | 455 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: In triangle $A B C, A B=B C$. A tr... | ["146"] | olympiadbench_OE_TO_maths_en_COMP | 463 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Let $T=11$. In ARMLvania, license ... | ["256"] | olympiadbench_OE_TO_maths_en_COMP | 468 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: The graphs of $y=x^{2}-|x|-12$ and... | ["$10+2 \\sqrt{2}$"] | olympiadbench_OE_TO_maths_en_COMP | 476 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Let $k$ be the least common multip... | ["23"] | olympiadbench_OE_TO_maths_en_COMP | 499 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: If $6 \tan ^{-1} x+4 \tan ^{-1}(3 ... | ["$\\frac{15-8 \\sqrt{3}}{33}$"] | olympiadbench_OE_TO_maths_en_COMP | 503 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: For a positive integer $n$, define... | ["9046"] | olympiadbench_OE_TO_maths_en_COMP | 522 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Points $P, Q, R$, and $S$ lie in t... | ["$2-\\sqrt{3}$"] | olympiadbench_OE_TO_maths_en_COMP | 539 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Let $\mathcal{R}$ denote the circu... | ["48"] | olympiadbench_OE_TO_maths_en_COMP | 541 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Each of the six faces of a cube is... | ["$\\frac{9}{32}$"] | olympiadbench_OE_TO_maths_en_COMP | 581 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Let $T=67$. Rectangles $F A K E$ a... | ["262"] | olympiadbench_OE_TO_maths_en_COMP | 593 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: In non-right triangle $A B C$, dis... | ["$\\frac{45}{2}$"] | olympiadbench_OE_TO_maths_en_COMP | 609 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Compute the least positive integer... | ["7986"] | olympiadbench_OE_TO_maths_en_COMP | 612 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: In equilateral hexagon $A B C D E ... | ["$\\frac{9}{2}$"] | olympiadbench_OE_TO_maths_en_COMP | 654 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Two square tiles of area 9 are pla... | ["$\\frac{5}{4}$"] | olympiadbench_OE_TO_maths_en_COMP | 659 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Jerry spots a truckload of his fav... | ["10.9375"] | olympiadbench_OE_TO_physics_en_COMP | 19 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: What is the smallest number of $1 ... | ["5"] | olympiadbench_OE_TO_physics_en_COMP | 22 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: A straight ladder $A B$ of mass $m... | ["$11.5$"] | olympiadbench_OE_TO_physics_en_COMP | 28 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: For this problem, assume the Earth... | ["-2"] | olympiadbench_OE_TO_physics_en_COMP | 39 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: In quantum mechanics, when calcula... | ["$0.0254$"] | olympiadbench_OE_TO_physics_en_COMP | 52 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Suppose we have a non-ideal gas, a... | ["$\\frac{7}{4}$"] | olympiadbench_OE_TO_physics_en_COMP | 56 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: (a) What value of $\theta$ maximiz... | ["$\\frac{\\pi}{4}$"] | olympiadbench_OE_TO_physics_en_COMP | 82 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: (b) What value of $\theta$ maximiz... | ["$\\pi / 3$"] | olympiadbench_OE_TO_physics_en_COMP | 83 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: B.4 Using the information provided... | ["p=1"] | olympiadbench_OE_TO_physics_en_COMP | 166 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Assume all gases are perfect... | -1.5 | scibench | 9 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Assume all gases are perfect... | -114.40 | scibench | 22 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: To get an idea of the distan... | 0.23 | scibench | 111 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Show how to approximate the ... | 3857 | scibench | 125 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: A planning engineer for a ne... | 9.8 | scibench | 133 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Using the Bohr theory, calcu... | 54.394 | scibench | 184 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Shot towers were popular in ... | 2.26 | scibench | 238 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Find the value of the integr... | -\pi | scibench | 243 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Show that the small angular ... | 6 | scibench | 274 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Calculate the maximum height... | 0.54 | scibench | 280 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: A certain spring-mass system... | 25.6773 | scibench | 287 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Consider the initial value p... | 2.84367 | scibench | 299 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Radiation from an X-ray sour... | 2.14 | scibench | 419 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Suppose that the normalized ... | 0.020 | scibench | 429 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: The equilibrium pressure of ... | -11.2 | scibench | 440 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Find $Y_l^m(\theta, \phi)$ ... | \frac{1}{\sqrt{4\pi}} | scibench | 514 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Consider the half-cell react... | -131.1 | scibench | 609 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: The molar constant volume he... | 7.82 | scibench | 615 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: The diffusion coefficient fo... | 0.318 | scibench | 616 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: For $\mathrm{N}_2$ at $298 \... | 0.132 | scibench | 646 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Calculate $\Delta H_f^{\circ... | 91.7 | scibench | 670 | true | true |
Answer the following question.
A 60-year-old man presents with a 2-day history of increasing difficulty in breathing with a productive cough. He reports having shortness of breath over the last 6 months, but he has felt worse since he contracted a cold that has been traveling around his office. Today, he reports body ... | A | scieval_biology_knowledge_application | 186 | true | true |
Answer the following question.
During an experiment, a scientist crosses a pea plant that has purple flowers with a pea plant that has white flowers. The plants that result from this cross in the F1 generation have both purple and white flowers. What can the scientist conclude?
A. Scientist can conclude that white is... | C | scieval_biology_scientific_calculation | 25 | true | true |
Answer the following question.
How do monoclonal antibodies work to fight autoimmune disease?
A. Monoclonal antibodies replace damaged cells, promoting tissue repair in autoimmune diseases.
B. Monoclonal antibodies suppress the immune system, preventing it from attacking healthy cells in autoimmune diseases.
C. Monoc... | D | scieval_biology_scientific_calculation | 122 | true | true |
Answer the following question.
Given the rest of reaction components:
reactant 1: Clc1ccc2ncccc2c1
reactant 2: Cc1ccc2c(cnn2C2CCCCO2)c1B(O)O
base: CN(C)C=O
solvent: [OH-].[Na+]
Ligand list for selection:
c1ccc(P(c2ccccc2)c2ccccc2)cc1,CN(C)Cc1ccc(P(C(C)(C)C)C(C)(C)C)cc1,C1CCC(P(C2CCCCC2)C2CCCCC2)CC1,Cc1ccccc1P(c1cccc... | CC(C)c1cc(C(C)C)c(-c2ccccc2P(C2CCCCC2)C2CCCCC2)c(C(C)C)c1 | scieval_chemistry_knowledge_application | 26 | true | true |
Answer the following question.
Given the rest of reaction components:
reactant 1: Clc1ccc2ncccc2c1
reactant 2: Cc1ccc2c(cnn2C2CCCCO2)c1B(O)O
ligand: CC(C)(C)P(C(C)(C)C)C(C)(C)C
base: [O-]P(=O)([O-])[O-].[K+].[K+].[K+]
Solvent list for selection:
C1CCOC1,CN(C)C=O,CO
Which one is the optimal solvent?
Finish your respo... | C1CCOC1 | scieval_chemistry_knowledge_application | 159 | true | true |
Answer the following question.
Given the rest of reaction components:
reactant 1: Clc1ccc2ncccc2c1
reactant 2: Cc1ccc2c(cnn2C2CCCCO2)c1B(O)O
base: CN(C)C=O
solvent: CCN(CC)CC
Ligand list for selection:
c1ccc(P(c2ccccc2)c2ccccc2)cc1,CN(C)Cc1ccc(P(C(C)(C)C)C(C)(C)C)cc1,C1CCC(P(C2CCCCC2)C2CCCCC2)CC1,Cc1ccccc1P(c1ccccc1... | COc1cccc(OC)c1-c1ccccc1P(C1CCCCC1)C1CCCCC1 | scieval_chemistry_knowledge_application | 178 | true | true |
Answer the following question.
What are the chiral centers in sucralose?
A. 1, 2, 3, 4, 5, 2', 3', 4', and 6'
B. 1, 2, 3, 4, 5, 2', 3', 4', and 5'
C. 1, 2, 3, 4, 5, 1', 3', 4', and 5'
D. 1, 2, 3, 4, 5, 2', 3', 5', and 6'
Answer:
Finish your response with "Answer: X" where X is one of A, B, C, D, etc.
Let's think s... | B | scieval_chemistry_scientific_calculation | 35 | true | true |
Answer the following question.
What are states of hybridization in homodesmotic reactions?
A. sp³, sp², or sp¹ bonds
B. sp³, sp², or sp hybridized bonds
C. sp, sp², or sp³ orbitals
D. sp¹, sp², or sp³ hybridization
Answer:
Finish your response with "Answer: X" where X is one of A, B, C, D, etc.
Let's think step by... | B | scieval_chemistry_scientific_calculation | 129 | true | true |
Answer the following question.
How are lasers used to cut material?
A. Lasers emit sound waves to shatter material.
B. Lasers create pressure to break material.
C. Lasers focus light to cut material.
D. Lasers heat material to melt it.
Answer:
Finish your response with "Answer: X" where X is one of A, B, C, D, etc.... | C | scieval_physics_knowledge_application | 4 | false | true |
Answer the following question.
A solid disk, spinning counter-clockwise, has a mass of $4 kg$ and a radius of $3 m$. If a point on the edge of the disk is moving at $8/5 m/s$ in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?
A. 4.01 rad/s, 72.18 kgm²/s
B. 2.67 rad... | D | scieval_physics_scientific_calculation | 175 | true | false |
The following is an open-ended problem from Atomic Physics of the undergraduate-level Physics. The answer of The problem should be one option of a multiple choice question. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables an... | \boxed{C} | ugphysics_AtomicPhysics | 2 | true | true |
The following is an open-ended problem from Atomic Physics of the undergraduate-level Physics. The answer of The problem should be one option of a multiple choice question. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables an... | \boxed{B} | ugphysics_AtomicPhysics | 23 | true | true |
The following is an open-ended problem from Atomic Physics of the undergraduate-level Physics. The problem has multiple answers, each of them should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the ... | \boxed{0.0732, 574.2} | ugphysics_AtomicPhysics | 93 | true | true |
The following is an open-ended problem from Atomic Physics of the undergraduate-level Physics. The problem has multiple answers, each of them should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and form... | \boxed{-\frac{Z e^{2}}{8 \pi \varepsilon_{0} R^{3}}\left(3 R^{2}-r^{2}\right) \text{ for } r<R, -\frac{Z e^{2}}{4 \pi \varepsilon_{0} r} \text{ for } r \geqslant R} | ugphysics_AtomicPhysics | 141 | true | true |
The following is an open-ended problem from Classical Electromagnetism of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used... | \[
\boxed{-\frac{\mu_{0} n K r}{2} \boldsymbol{e}_{\theta}}
\] | ugphysics_ClassicalElectromagnetism | 55 | true | true |
The following is an open-ended problem from Classical Electromagnetism of the undergraduate-level Physics. The problem has multiple answers, each of them should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variab... | \boxed{-\frac{3 \mu_{0} a b^{2} m V}{2\left(a^{2}+b^{2}\right)^{5 / 2}}, \frac{3 \mu_{0} a b^{2} m V}{2\left(a^{2}+b^{2}\right)^{5 / 2}R}} | ugphysics_ClassicalElectromagnetism | 67 | true | true |
The following is an open-ended problem from Classical Electromagnetism of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used... | \boxed{-\frac{\mu_{0} d}{2 \pi} \ln \frac{4}{3} \cdot \frac{\mathrm{d} I}{\mathrm{d}t}} | ugphysics_ClassicalElectromagnetism | 113 | true | true |
The following is an open-ended problem from Classical Electromagnetism of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used... | \boxed{\boldsymbol{H}_{1} = \frac{4 \mu a^{2}}{a^{2}\left(\mu + \mu_{0}\right)^{2} - \left(\mu - \mu_{0}\right) b^{2}} \boldsymbol{B}_{0}} | ugphysics_ClassicalElectromagnetism | 182 | true | true |
The following is an open-ended problem from Classical Electromagnetism of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used... | \boxed{\frac{V_0 R^2}{r^2} \cos \theta} | ugphysics_ClassicalElectromagnetism | 193 | true | true |
The following is an open-ended problem from Classical Mechanics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and fo... | \boxed{\frac{n d \pi k^{2}}{4 E^{2}} \cot^{2}\left(\frac{\alpha}{2}\right)} | ugphysics_ClassicalMechanics | 2 | true | true |
The following is an open-ended problem from Classical Mechanics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the... | \boxed{-\left[\left(\frac{u}{a}+\frac{v}{a+b}\right)^{2}(a+b) \sin \alpha+\left(\frac{u}{a}+\frac{v}{b}\right)^{2} b \sin \beta\right] \boldsymbol{i} + \left[\left(\frac{u}{a}+\frac{v}{a+b}\right)^{2}(a+b) \cos \alpha+\left(\frac{u}{a}+\frac{v}{b}\right)^{2} b \cos \beta\right] \boldsymbol{j}} | ugphysics_ClassicalMechanics | 5 | true | true |
The following is an open-ended problem from Classical Mechanics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the... | \boxed{R} | ugphysics_ClassicalMechanics | 13 | true | true |
The following is an open-ended problem from Classical Mechanics of the undergraduate-level Physics. The problem has multiple answers, each of them should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and... | \boxed{\omega_{x} = \dot{\psi} \sin \varphi + \dot{\theta} \cos \psi \cos \varphi, \omega_{y} = \dot{\psi} \cos \varphi - \dot{\theta} \cos \psi \sin \varphi, \omega_{z} = \dot{\varphi} + \dot{\theta} \sin \psi} | ugphysics_ClassicalMechanics | 49 | true | true |
The following is an open-ended problem from Classical Mechanics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the... | \boxed{-\frac{m h^{2}}{2 r^{2}}} | ugphysics_ClassicalMechanics | 59 | true | true |
The following is an open-ended problem from Classical Mechanics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and fo... | \boxed{\frac{\pi}{2}} | ugphysics_ClassicalMechanics | 175 | true | true |
The following is an open-ended problem from Classical Mechanics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and fo... | \[
\boxed{3a \sqrt{\frac{3k}{m}}}
\] | ugphysics_ClassicalMechanics | 181 | true | true |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formul... | \boxed{0.13} | ugphysics_Electrodynamics | 70 | true | true |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The answer of The problem should be a range inteval. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the s... | \boxed{n_{e} < \frac{\varepsilon_{0} m_{e} \omega^{2}}{e^{2}}} | ugphysics_Electrodynamics | 73 | true | true |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the sol... | \boxed{-\frac{e \rho r}{2 \varepsilon_{0} \gamma^{2}} \boldsymbol{e}_{r}} | ugphysics_Electrodynamics | 88 | true | true |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the sol... | \[\boxed{\frac{v q^{2} r^{2}}{4 \pi^{2} \varepsilon_{0} c^{2} R^{4} l^{2}} \boldsymbol{e}_{x}, \frac{v q^{2}}{4 \pi^{2} \varepsilon_{0} c^{2} r^{2} l^{2}} \boldsymbol{e}_{x}}\] | ugphysics_Electrodynamics | 109 | true | true |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the sol... | \boxed{\frac{e E_{0}}{m\left(\omega^{2} - \omega_{0}^{2}\right)} e^{-\mathrm{i} \omega t}} | ugphysics_Electrodynamics | 118 | true | true |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The answer of The problem should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the solut... | \[
\boxed{\boldsymbol{B}(\boldsymbol{r}, t) =-\frac{\mu_{0} q^{2}}{4 \pi m r c} \mathrm{e}^{\mathrm{i}(k r-\omega t)} \boldsymbol{e}_{\mathrm{r}} \times \boldsymbol{E}_{0}, \boldsymbol{E}(\boldsymbol{r}, t) =\frac{\mu_{0} q^{2}}{4 \pi m r} \mathrm{e}^{\mathrm{i}(k r-\omega t)}\left[\left(\boldsymbol{E}_{0} \cdot \bolds... | ugphysics_Electrodynamics | 156 | true | true |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formul... | \boxed{\frac{a^{6} \omega^{4}}{c^{4}}\left(\frac{\varepsilon-\varepsilon_{0}}{\varepsilon+2 \varepsilon_{0}}\right)^{2} \sin^2 \theta} | ugphysics_Electrodynamics | 169 | true | true |
The following is an open-ended problem from Geometrical Optics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and for... | \boxed{1} | ugphysics_GeometricalOptics | 8 | true | true |
The following is an open-ended problem from Geometrical Optics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and for... | \boxed{2.08} | ugphysics_GeometricalOptics | 22 | true | true |
The following is an open-ended problem from Geometrical Optics of the undergraduate-level Physics. The problem has multiple answers, with the answers in order being either True or False, a range inteval. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX forma... | \boxed{No, (9.00, \infty)} | ugphysics_GeometricalOptics | 52 | true | true |
The following is an open-ended problem from Quantum Mechanics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and form... | \boxed{1-\frac{3}{4Z^{2}}} | ugphysics_QuantumMechanics | 45 | true | true |
The following is an open-ended problem from Quantum Mechanics of the undergraduate-level Physics. The problem has multiple answers, each of them should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and for... | \boxed{\lambda^{\prime} = \lambda + \Delta \lambda, n\left(\lambda^{\prime}\right) = n + \lambda n \frac{\mathrm{d} n}{\mathrm{~d} \lambda} \cdot \frac{v}{c}} | ugphysics_QuantumMechanics | 47 | true | true |
The following is an open-ended problem from Quantum Mechanics of the undergraduate-level Physics. The answer of The problem should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the sol... | \boxed{\alpha_{2} = \tan^{-1} \left(\frac{k_{1}}{k_{2}}\right)} | ugphysics_QuantumMechanics | 100 | true | true |
The following is an open-ended problem from Quantum Mechanics of the undergraduate-level Physics. The problem has multiple answers, each of them should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and for... | \boxed{\left[-\frac{\hbar^{2}}{2 m} \frac{\mathrm{d}^{2}}{\mathrm{d} x^{2}} + V(x, t)\right] \psi(x, t) = \mathrm{i} \hbar \frac{\partial}{\partial t} \psi(x, t), \left[-\frac{\hbar^{2}}{2 m} \frac{\mathrm{d}^{2}}{\mathrm{d} x^{\prime 2}} + V^{\prime}\left(x^{\prime}, t\right)\right] \psi\left(x^{\prime}, t\right) = \m... | ugphysics_QuantumMechanics | 105 | true | true |
The following is an open-ended problem from Relativity of the undergraduate-level Physics. The problem has multiple answers, each of them should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas u... | \boxed{v = a t^{\prime} \left[1+\left(\frac{a t^{\prime}}{c}\right)^2\right]^{-1/2}, a_x^{\prime} = \gamma a} | ugphysics_Relativity | 4 | true | true |
The following is an open-ended problem from Relativity of the undergraduate-level Physics. The answer of The problem should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the solution p... | \[
\boxed{\theta = 2 \arccos \sqrt{\frac{E_0 + m_0 c^2}{E_0 + 3 m_0 c^2}}}
\] | ugphysics_Relativity | 23 | true | true |
The following is an open-ended problem from Relativity of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas us... | \boxed{\frac{1}{\sqrt{1 - \left(\frac{500}{3 \times 10^{8}}\right)^{2}}}} | ugphysics_Relativity | 94 | true | true |
The following is an open-ended problem from Semiconductor Physics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and ... | \boxed{3.33 \times 10^{15}} | ugphysics_SemiconductorPhysics | 69 | true | true |
The following is an open-ended problem from Semiconductor Physics of the undergraduate-level Physics. The problem has multiple answers, each of them should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represe... | \boxed{10^{20}, 2.745 \times 10^{11}, \frac{1}{3} \times 10^{12}, \frac{1}{3} \times 10^{12}} | ugphysics_SemiconductorPhysics | 140 | true | true |
The following is an open-ended problem from Solid-State Physics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and fo... | \boxed{\frac{9}{16}} | ugphysics_Solid-StatePhysics | 29 | true | true |
The following is an open-ended problem from Solid-State Physics of the undergraduate-level Physics. The answer of The problem should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the s... | \boxed{\omega=\sqrt{\frac{4 c_{1}}{m}} \sin \left(\frac{q_{1} a}{2}\right)} | ugphysics_Solid-StatePhysics | 131 | true | true |
The following is an open-ended problem from Solid-State Physics of the undergraduate-level Physics. The answer of The problem should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the s... | \boxed{m_{l} = \frac{m_{2}^{*2}}{m_{1}^{*}}} | ugphysics_Solid-StatePhysics | 134 | true | true |
The following is an open-ended problem from Statistical Mechanics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and ... | \boxed{7.5} | ugphysics_StatisticalMechanics | 38 | true | true |
The following is an open-ended problem from Statistical Mechanics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in t... | \[
\boxed{\frac{1}{4} n A \bar{v} \exp \left(-\frac{e U}{k T}\right)}
\] | ugphysics_StatisticalMechanics | 66 | true | true |
The following is an open-ended problem from Statistical Mechanics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and ... | \boxed{30} | ugphysics_StatisticalMechanics | 68 | true | true |
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