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General· olympiad

OlympicArena

SJTU (GAIR) · 2024

11,163 olympiad-level problems across seven disciplines for multi-discipline cognitive reasoning.

Mathematics
GitHub stars
Task type
QA
Modality
multimodal
Access
open
Size
11,163 items
License
CC-BY-NC-SA-4.0
Metrics
accuracy
id
Astronomy_1007
problem
The event horizon of a non-spinning, uncharged black hole can be thought of as a sphere with a radius equal to the Schwarzschild radius, $r_{S}=2 G M / c^{2}$ where $M$ is the mass of the black hole and $c$ is the speed of light. If the black hole at the centre of the Milky Way has a mass of $4.15 \times 10^{6} M_{\odot}$, what is the approximate average density within the event horizon? A: $\sim 1 \mathrm{~kg} \mathrm{~m}^{-3}$ B: $\sim 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$ C: $\sim 10^{6} \mathrm{~kg} \mathrm{~m}^{-3}$ D: $\sim 10^{9} \mathrm{~kg} \mathrm{~m}^{-3}$
prompt
You are participating in an international Astronomy competition and need to solve the following question. This is a multiple choice question (only one correct answer). problem: The event horizon of a non-spinning, uncharged black hole can be thought of as a sphere with a radius equal to the Schwarzschild radius, $r_{S}=2 G M / c^{2}$ where $M$ is the mass of the black hole and $c$ is the speed of light. If the black hole at the centre of the Milky Way has a mass of $4.15 \times 10^{6} M_{\odot}$, what is the approximate average density within the event horizon? A: $\sim 1 \mathrm{~kg} \mathr …
answer_type
SC
subject
Astronomy
language
EN
modality
text-only
id
Astronomy_951
problem
The very first image released by the James Webb Space Telescope (JWST) was of a galaxy cluster called SMACS 0723. The image is considered to be Webb's first deep field, since a long exposure time of 12.5 hours was used to allow the light from very faint and distant galaxies to be seen. The spectrum of one such galaxy is shown in Figure 2. [figure1] Figure 2: Highly redshifted emission lines in the spectrum of a galaxy that is 13.1 billion years old, captured using the JWST's near-infrared spectrometer (NIRSpec). Credit: NASA, ESA, CSA, STScI. The spectrum shows four bright hydrogen lines, w …
prompt
You are participating in an international Astronomy competition and need to solve the following question. The answer to this question is a numerical value. problem: The very first image released by the James Webb Space Telescope (JWST) was of a galaxy cluster called SMACS 0723. The image is considered to be Webb's first deep field, since a long exposure time of 12.5 hours was used to allow the light from very faint and distant galaxies to be seen. The spectrum of one such galaxy is shown in Figure 2. [figure1] Figure 2: Highly redshifted emission lines in the spectrum of a galaxy that is 13 …
figure_urls
https://cdn.mathpix.com/cropped/2024_03_06_116c30b1e79c82f9c667g-06.jpg?height=985&width=1588&top_left_y=547&top_left_x=240 https://cdn.mathpix.com/cropped/2024_03_06_116c30b1e79c82f9c667g-07.jpg?height=997&width=1334&top_left_y=187&top_left_x=361
answer_type
NV
subject
Astronomy
language
EN
modality
multi-modal

Real rows from the Hugging Face datasets server · long values truncated