question stringlengths 326 14.9k | answer stringlengths 1 664 | 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: $\boxed{answer}$(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 composition of the atmos... | 0.0029 | scibench | 90 | false | 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 container is divided into ... | -6.9 | scibench | 108 | false | 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: Using the explicit formulas ... | 0 | scibench | 216 | true | false |
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 a damped harmonic o... | \frac{8\pi}{\sqrt{64\pi^2+1}} | scibench | 223 | true | false |
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: A string is set into motion ... | 4.4,13.3 | scibench | 253 | false | 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: An Earth satellite has a per... | 1900 | scibench | 262 | false | 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 billiard ball of intial ve... | 45 | scibench | 268 | false | 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: A tank originally contains $... | 7.42 | scibench | 312 | false | 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: In Millikan's experiment, an... | -5 | scibench | 372 | false | 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: What is the value of the ang... | 14 | scibench | 481 | false | 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 number of CSFs in a... | 1.86 | scibench | 491 | false | 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: 5.4-19. A doorman at a hotel... | 0.5768 | scibench | 530 | true | false |
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: Let the distribution of $W$ ... | 14.80 | scibench | 551 | true | false |
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: Consider the gas phase therm... | 269 | scibench | 629 | false | 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: Imagine gaseous $\mathrm{Ar}... | 3.9 | scibench | 631 | false | 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: Determine the equilibrium co... | 2.25 | scibench | 632 | false | 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 mean ionic act... | 0.0547 | scibench | 643 | false | 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: In order to get in shape for... | 1.8 | scibench | 659 | false | 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 70-year-old obese male presents to the emergency department with shortness of breath and cough of sudden onset. The patient states that his symptoms came on while he was sleeping. The patient has a past medical history of type II diabetes and is currently taking lisinopril, metformin, ... | B | scieval_biology_knowledge_application | 124 | false | true |
Answer the following question.
A 31-year-old man comes to the emergency department because of acute onset neck pain and enlargement. Specifically, he reports that he has been experiencing pain and swelling of the anterior portion of his neck near the midline. Otherwise, he says that he has been getting tired easily an... | B | scieval_biology_knowledge_application | 161 | true | false |
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: Brc1ccc2ncccc2c1
reactant 2: Cc1ccc2c(cnn2C2CCCCO2)c1B(O)O
ligand: C1=C[C@H]2[Fe][C@@H]1[C]2P(c1ccccc1)c1ccccc1
base: [OH-].[K+]
Solvent list for selection:
C1CCOC1,CN(C)C=O,CO
Which one is the optimal solvent?
Finish your response wit... | CO | scieval_chemistry_knowledge_application | 32 | true | false |
Answer the following question.
Given the rest of reaction components:
reactant: Cc1ccc2c(cnn2C2CCCCO2)c1B1OC(C)(C)C(C)(C)O1
ligand: CCCCP(C12CC3CC(CC(C3)C1)C2)C12CC3CC(CC(C3)C1)C2
solvent: CO
base: [Li+].CC(C)(C)[O-]
Reactants list for selection:
Ic1ccc2ncccc2c1,Brc1ccc2ncccc2c1,Clc1ccc2ncccc2c1
Which one is the opt... | Ic1ccc2ncccc2c1 | scieval_chemistry_knowledge_application | 37 | false | true |
Answer the following question.
Given the rest of reaction components:
reactant 1: Clc1ccc2ncccc2c1
reactant 2: Cc1ccc2c(cnn2C2CCCCO2)c1B(O)O
base: CC#N
solvent: [Li+].CC(C)(C)[O-]
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(c1c... | CC(C)c1cc(C(C)C)c(-c2ccccc2P(C2CCCCC2)C2CCCCC2)c(C(C)C)c1 | scieval_chemistry_knowledge_application | 40 | true | false |
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: [Li+].CC(C)(C)[O-]
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... | COc1cccc(OC)c1-c1ccccc1P(C1CCCCC1)C1CCCCC1 | scieval_chemistry_knowledge_application | 58 | true | false |
Answer the following question.
Given the rest of reaction components:
reactant: Cc1ccc2c(cnn2C2CCCCO2)c1B1OC(C)(C)C(C)(C)O1
ligand: CCCCP(C12CC3CC(CC(C3)C1)C2)C12CC3CC(CC(C3)C1)C2
solvent: C1CCOC1
base: [OH-].[Na+]
Reactants list for selection:
Ic1ccc2ncccc2c1,Brc1ccc2ncccc2c1,Clc1ccc2ncccc2c1
Which one is the optim... | Brc1ccc2ncccc2c1 | scieval_chemistry_knowledge_application | 76 | true | false |
Answer the following question.
Given the rest of reaction components:
reactant 1: Clc1ccc2ncccc2c1
reactant 2: Cc1ccc2c(cnn2C2CCCCO2)c1B(O)O
ligand: CC(C)c1cc(C(C)C)c(-c2ccccc2P(C2CCCCC2)C2CCCCC2)c(C(C)C)c1
base: C(=O)(O)[O-].[Na+]
Solvent list for selection:
C1CCOC1,CN(C)C=O,CO
Which one is the optimal solvent?
Fin... | C1CCOC1 | scieval_chemistry_knowledge_application | 128 | true | false |
Answer the following question.
Given the rest of reaction components:
reactant: Cc1ccc2c(cnn2C2CCCCO2)c1Br
ligand: Cc1ccccc1P(c1ccccc1C)c1ccccc1C
solvent: CO
base: [OH-].[Na+]
Reactants list for selection:
F[B-](F)(F)c1ccc2ncccc2c1,CC1(C)OB(c2ccc3ncccc3c2)OC1(C)C
Which one is the optimal reactant?
Finish your respon... | F[B-](F)(F)c1ccc2ncccc2c1 | scieval_chemistry_knowledge_application | 156 | false | 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.
Given the rest of reaction components:
reactant 1: O=S(=O)(Oc1cnc2ccccc2c1)C(F)(F)F
reactant 2: Cc1ccc2c(cnn2C2CCCCO2)c1B(O)O
base: C1CCOC1
solvent: [Li+].CC(C)(C)[O-]
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... | CC(C)c1cc(C(C)C)c(-c2ccccc2P(C2CCCCC2)C2CCCCC2)c(C(C)C)c1 | scieval_chemistry_knowledge_application | 183 | true | false |
Answer the following question.
Considering the following, which state or states is the substance after this time?
A. Solid with some gas
B. Mostly gas with some liquid
C. Mostly liquid with some gas
D. Solid and liquid
Answer:
Finish your response with "Answer: X" where X is one of A, B, C, D, etc.
Let's think ste... | C | scieval_chemistry_scientific_calculation | 34 | true | false |
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 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 so... | \boxed{(- \infty, 91.1)} | ugphysics_AtomicPhysics | 3 | false | 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 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 solu... | \boxed{\frac{r I}{2 \pi \varepsilon_{0} v R^{2}}} | ugphysics_AtomicPhysics | 64 | true | false |
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{S = 1, l^{\prime} = 1} | ugphysics_AtomicPhysics | 101 | true | false |
The following is an open-ended problem from Atomic Physics 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 solu... | \boxed{2^{+}} | ugphysics_AtomicPhysics | 103 | false | true |
The following is an open-ended problem from Atomic 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 soluti... | \boxed{-\frac{1}{2 \mu} \Psi_{0}^{\prime \prime}(r)-\frac{1}{\mu r} \Psi_{0}^{\prime}(r)+\left[V_{1}(r)+V_{2}(r)-E_{\mathrm{c}}\right] \Psi_{0}(r)=0} | ugphysics_AtomicPhysics | 119 | false | 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 Atomic 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 formula... | \boxed{4.6 \times 10^{-5}} | ugphysics_AtomicPhysics | 143 | false | 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{7 \times 10^{5}, 6.6 \times 10^{15}} | ugphysics_AtomicPhysics | 172 | false | 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{A} | ugphysics_AtomicPhysics | 184 | false | 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{7 \times 10^{9}, 6.6 \times 10^{15}} | ugphysics_AtomicPhysics | 185 | false | 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{\sqrt{\frac{R_{1} R_{2}}{\omega^{2}} + \frac{R_{1}}{R_{2}} L^{2}}, \frac{R_{2}}{\omega^{2} L \left(R_{1} + R_{2}\right)}} | ugphysics_ClassicalElectromagnetism | 34 | true | false |
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} Q R^{2} \omega_{0}}{2 \rho L t_{0}}} | ugphysics_ClassicalElectromagnetism | 52 | false | 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 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... | \boxed{0.069} | ugphysics_ClassicalElectromagnetism | 69 | false | 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{(k-1) Q^{2}}{2 \rho g \varepsilon_{0} b^{2}[(k-1) x+a]^{2}}} | ugphysics_ClassicalElectromagnetism | 72 | false | 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 equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variable... | \boxed{\sigma = -\frac{q}{4 \pi a^{2}}, \tau = -\frac{q}{4 \pi a} \boldsymbol{e}_{r}} | ugphysics_ClassicalElectromagnetism | 77 | true | false |
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{v_{z}, z} | ugphysics_ClassicalElectromagnetism | 79 | true | false |
The following is an open-ended problem from Classical Electromagnetism 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 ... | \boxed{a} | ugphysics_ClassicalElectromagnetism | 84 | false | 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{-\frac{1}{\mu_{0}} v B_{0} r \boldsymbol{e}_{\theta}} | ugphysics_ClassicalElectromagnetism | 114 | false | true |
The following is an open-ended problem from Classical Electromagnetism 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 ... | \boxed{b} | ugphysics_ClassicalElectromagnetism | 123 | true | false |
The following is an open-ended problem from Classical Electromagnetism 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 ... | \boxed{b} | ugphysics_ClassicalElectromagnetism | 126 | true | false |
The following is an open-ended problem from Classical Electromagnetism 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... | \boxed{\frac{q a^{2}(3 r+a)}{r(r+a)^{2}}} | ugphysics_ClassicalElectromagnetism | 136 | false | 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... | \[
\boxed{\frac{4\pi \mu_{0} \sigma^{2} \omega R^{5}}{9N}}
\] | ugphysics_ClassicalElectromagnetism | 137 | false | true |
The following is an open-ended problem from Classical Electromagnetism 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... | \boxed{\frac{4 \pi \varepsilon_{0} a d}{d-a}} | ugphysics_ClassicalElectromagnetism | 148 | true | false |
The following is an open-ended problem from Classical Electromagnetism of the undergraduate-level Physics. The problem has multiple answers, with the answers in order being an equation, a numerical value without units, a numerical value without units, an expression. Please calculate the answer according to the given re... | \boxed{E_{n}=\frac{Q_{F}}{A\left(\varepsilon_{1} \cos ^{2} \theta+\varepsilon_{2} \sin ^{2} \theta\right)}, D_{n}=\frac{Q_{F}}{A}, E_{t}=0, D_{t}=\frac{Q_{F}\left(\varepsilon_{1}-\varepsilon_{2}\right) \sin \theta \cos \theta}{A\left(\varepsilon_{1} \cos ^{2} \theta+\varepsilon_{2} \sin ^{2} \theta\right)}} | ugphysics_ClassicalElectromagnetism | 168 | false | 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{\Delta R = \frac{2 \rho}{\pi}\left[\frac{1}{b^{2}}\left(\frac{3 V}{4 \pi}\right)^{1 / 3}-\frac{1}{\sqrt{b^{2}-\left(\frac{3 V}{4 \pi}\right)^{2 / 3}}} \arctan \frac{\left(\frac{3 V}{4 \pi}\right)^{1 / 3}}{\sqrt{b^{2}-\left(\frac{3 V}{4 \pi}\right)^{2 / 3}}}\right]} | ugphysics_ClassicalElectromagnetism | 171 | false | 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 Electromagnetism 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... | \boxed{6.7 \times 10^{-4}} | ugphysics_ClassicalElectromagnetism | 195 | false | 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{(M+m-\lambda t) g} | ugphysics_ClassicalMechanics | 7 | false | 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 a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent... | \boxed{\dot{\varphi}(\theta)|_{\theta=30^{\circ}}=-10.0, \dot{\varphi}(\theta)|_{\theta=33.15^{\circ}}=9.2} | ugphysics_ClassicalMechanics | 11 | true | false |
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 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{m a^{2} v^{2} \left(\frac{1}{r^{3}} - \frac{2 c^{2}}{r^{5}}\right)} | ugphysics_ClassicalMechanics | 27 | true | false |
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... | \[
\boxed{2 \Omega h \cos \alpha}
\] | ugphysics_ClassicalMechanics | 38 | false | 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 |
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