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The dataset generation failed
Error code: DatasetGenerationError
Exception: ArrowInvalid
Message: JSON parse error: Invalid value. in row 0
Traceback: Traceback (most recent call last):
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 324, in _generate_tables
df = pandas_read_json(f)
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 38, in pandas_read_json
return pd.read_json(path_or_buf, **kwargs)
~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/pandas/io/json/_json.py", line 791, in read_json
json_reader = JsonReader(
path_or_buf,
...<16 lines>...
engine=engine,
)
File "/usr/local/lib/python3.14/site-packages/pandas/io/json/_json.py", line 905, in __init__
self.data = self._preprocess_data(data)
~~~~~~~~~~~~~~~~~~~~~^^^^^^
File "/usr/local/lib/python3.14/site-packages/pandas/io/json/_json.py", line 917, in _preprocess_data
data = data.read()
File "/usr/local/lib/python3.14/site-packages/datasets/utils/file_utils.py", line 844, in read_with_retries
out = read(*args, **kwargs)
File "<frozen codecs>", line 325, in decode
UnicodeDecodeError: 'utf-8' codec can't decode byte 0xff in position 0: invalid start byte
During handling of the above exception, another exception occurred:
Traceback (most recent call last):
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1816, in _prepare_split_single
for key, table in generator:
^^^^^^^^^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 613, in wrapped
for item in generator(*args, **kwargs):
~~~~~~~~~^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 327, in _generate_tables
raise e
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 290, in _generate_tables
pa_table = paj.read_json(
io.BytesIO(batch), read_options=paj.ReadOptions(block_size=block_size)
)
File "pyarrow/_json.pyx", line 342, in pyarrow._json.read_json
File "pyarrow/error.pxi", line 155, in pyarrow.lib.pyarrow_internal_check_status
File "pyarrow/error.pxi", line 92, in pyarrow.lib.check_status
raise convert_status(status)
pyarrow.lib.ArrowInvalid: JSON parse error: Invalid value. in row 0
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1369, in compute_config_parquet_and_info_response
parquet_operations, partial, estimated_dataset_info = stream_convert_to_parquet(
~~~~~~~~~~~~~~~~~~~~~~~~~^
builder, max_dataset_size_bytes=max_dataset_size_bytes
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
)
^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 948, in stream_convert_to_parquet
builder._prepare_split(split_generator=splits_generators[split], file_format="parquet")
~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1683, in _prepare_split
for job_id, done, content in self._prepare_split_single(
~~~~~~~~~~~~~~~~~~~~~~~~~~^
gen_kwargs=gen_kwargs, job_id=job_id, **_prepare_split_args
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
):
^
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1869, in _prepare_split_single
raise DatasetGenerationError("An error occurred while generating the dataset") from e
datasets.exceptions.DatasetGenerationError: An error occurred while generating the datasetNeed help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
id string | ques_image_paths string | question string | choices string | answer string | category string | grade null | dataset string | task string | text_score float64 | visual_score null | composite_score null | M1 float64 | M2 float64 | M3 float64 | M4 float64 | pass bool | fail_reason string | error null | ques_image_path_lst string | sub category string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
cac967c9-422a-42b8-b57d-9ef61d278f84 | cac967c9-422a-42b8-b57d-9ef61d278f84_1.jpg | How many points are there in the three unseen sides of dice?
<image1> | [] | 11 | Discrete Mathematics & Formal Logic | null | MathVision | Arithmetic | 26 | null | null | 2 | 3 | 4 | 4 | true | pass | null | ['cac967c9-422a-42b8-b57d-9ef61d278f84_1.jpg'] | Arithmetic & Concrete Number Theory |
bbe07578-d02f-4428-985d-7c0a1225de2b | bbe07578-d02f-4428-985d-7c0a1225de2b_1.jpg | Six different numbers, chosen from integers 1 to 9 , are written on the faces of a cube, one number per face. The sum of the numbers on each pair of opposite faces is always the same. Which of the following numbers could have been written on the opposite side with the number 8 ?
<image1> | [] | 3 | Discrete Mathematics & Formal Logic | null | MathVision | Logic | 56 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['bbe07578-d02f-4428-985d-7c0a1225de2b_1.jpg'] | Abstract Logic & Procedural Puzzles |
0cd379fa-0ae3-4f23-bce4-7dfbfffd946e | 0cd379fa-0ae3-4f23-bce4-7dfbfffd946e_1.jpg | Three of the cards shown will be dealt to Nadia, the rest to Riny. Nadia multiplies the three values of her cards and Riny multiplies the two values of his cards. It turns out that the sum of those two products is a prime number. Determine the sum of the values of Nadia's cards.
<image1> | [] | 13 | Continuous Mathematics & Analysis | null | MathVision | Algebra | 110 | null | null | 2 | 3 | 4 | 4 | true | pass | null | ['0cd379fa-0ae3-4f23-bce4-7dfbfffd946e_1.jpg'] | Foundations of Algebra |
1eb3ceb1-a773-4985-96a5-a479eb7a75a3 | 1eb3ceb1-a773-4985-96a5-a479eb7a75a3_1.jpg | Frank laid out his dominoes as shown in the picture. (Dominoes which touch must always have the same number of points). Before his brother George removed two dominoes there were 33 points altogether. How many points is the questionmark worth?
<image1> | [] | 4 | Continuous Mathematics & Analysis | null | MathVision | Algebra | 41 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['1eb3ceb1-a773-4985-96a5-a479eb7a75a3_1.jpg'] | Foundations of Algebra |
bfcd8e97-37a5-4e81-a210-7fbee1e97fed | bfcd8e97-37a5-4e81-a210-7fbee1e97fed_1.jpg | Baris has a few dominoes as shown in the picture. He wants to lay them in a line according to the rules of dominoes, that is that two dominoes can only be laid together if the neighbouring squares have the same number of dots in them. What is the biggest number of these dominoes that he can lay in a single line?
<image... | [] | 5 | Discrete Mathematics & Formal Logic | null | MathVision | Graph Theory | 63 | null | null | 2 | 3 | 4 | 4 | true | pass | null | ['bfcd8e97-37a5-4e81-a210-7fbee1e97fed_1.jpg'] | Combinatorics & Graph Structures |
1cf3d4a0-2216-4666-b3df-3a2ab13b92d3 | 1cf3d4a0-2216-4666-b3df-3a2ab13b92d3_1.jpg | Amy, Bert, Carl, Doris and Ernst each throw two dice. Who has got the biggest total altogether?
<image1> | ['Amy', 'Bert', 'Carl', 'Doris', 'Ernst'] | E | Discrete Mathematics & Formal Logic | null | MathVision | Arithmetic | 18 | null | null | 2 | 3 | 4 | 4 | true | pass | null | ['1cf3d4a0-2216-4666-b3df-3a2ab13b92d3_1.jpg'] | Arithmetic & Concrete Number Theory |
dbbfa00d-f717-476b-9939-27fba44134ff | dbbfa00d-f717-476b-9939-27fba44134ff_1.jpg | The sum of the dots on opposite sides of an ordinary die is 7. Which of the following dice could be an ordinary die?
<image1> | ['A', 'B', 'C', 'D', 'E'] | E | Geometry Reasoning | null | MathVision | Solid Geometry | 25 | null | null | 2 | 3 | 4 | 4 | true | pass | null | ['dbbfa00d-f717-476b-9939-27fba44134ff_1.jpg'] | Solid Geometry & Volumetrics |
0c2740e4-5aa4-47c8-b407-b47ac8873347 | 0c2740e4-5aa4-47c8-b407-b47ac8873347_1.jpg | In a game of dominoes the tiles always have to be placed so that the touching halves of two adjacent domino tiles show the same number of dots. Paul has six domino tiles in front of him (see diagram).
<image1>
In several steps Paul tries to arrange them in a correct order. In each step he is either allowed to swap any ... | [] | 3 | Discrete Mathematics & Formal Logic | null | MathVision | Graph Theory | 93 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['0c2740e4-5aa4-47c8-b407-b47ac8873347_1.jpg'] | Combinatorics & Graph Structures |
a7276d84-c4bc-4cc9-8782-e336efa98a09 | a7276d84-c4bc-4cc9-8782-e336efa98a09_1.jpg | Four identical dice are arranged in a row as shown in the diagram. Although each die does have 1, 2, 3, 4, 5, 6 dots, the sum of the numbers of dots on each pair of opposite faces is not necessarily 7 . What is the total number of dots on the six touching faces of the dice?
<image1> | [] | 20 | Discrete Mathematics & Formal Logic | null | MathVision | Arithmetic | 118 | null | null | 2 | 3 | 4 | 4 | true | pass | null | ['a7276d84-c4bc-4cc9-8782-e336efa98a09_1.jpg'] | Arithmetic & Concrete Number Theory |
bae0c03b-7d37-4a2e-9b82-7ebe0f9f1297 | bae0c03b-7d37-4a2e-9b82-7ebe0f9f1297_1.jpg | Dominoes are said to be arranged correctly if, for each pair of adjacent dominoes, the numbers of spots on the adjacent ends are equal. Paul laid six dominoes in a line as shown in the diagram.
<image1>
He can make a move either by swapping the position of any two dominoes (without rotating either domino) or by rotatin... | [] | 3 | Discrete Mathematics & Formal Logic | null | MathVision | Combinatorics | 77 | null | null | 2 | 3 | 4 | 3 | true | pass | null | ['bae0c03b-7d37-4a2e-9b82-7ebe0f9f1297_1.jpg'] | Combinatorics & Graph Structures |
48786c87-48cd-4275-9420-630075f6a2bf | 48786c87-48cd-4275-9420-630075f6a2bf_1.jpg | The numbers on each pair of opposite faces on a die add up to 7 . A die is rolled without slipping around the circuit shown. At the start the top face is 3 . What number will be displayed on the top face at the end point? <image1> | [] | 6 | Geometry Reasoning | null | MathVision | Solid Geometry | 49 | null | null | 2 | 3 | 4 | 4 | true | pass | null | ['48786c87-48cd-4275-9420-630075f6a2bf_1.jpg'] | Solid Geometry & Volumetrics |
1173374b-7f00-4b60-8bf1-28ef0aeba3b3 | 1173374b-7f00-4b60-8bf1-28ef0aeba3b3_1.jpg | The diagram shows two ordinary dice. What is the total number of spots on all the faces that cannot be seen in the diagram? <image1> | [] | 27 | Geometry Reasoning | null | MathVision | Solid Geometry | 50 | null | null | 3 | 3 | 4 | 4 | true | pass | null | ['1173374b-7f00-4b60-8bf1-28ef0aeba3b3_1.jpg'] | Solid Geometry & Volumetrics |
7a08e6cc-85a0-4a73-b1ba-9201c6a99cb3 | 7a08e6cc-85a0-4a73-b1ba-9201c6a99cb3_1.jpg | Three dice with faces numbered 1 through 6 are stacked as shown. Seven of the eighteen faces are visible, leaving eleven faces hidden (back, bottom, between). The total number of dots NOT visible in this view is
<image1> | [] | 41 | Geometry Reasoning | null | MathVision | Solid Geometry | 76 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['7a08e6cc-85a0-4a73-b1ba-9201c6a99cb3_1.jpg'] | Solid Geometry & Volumetrics |
19b50313-a3b8-420f-8e4b-a3c8ae02bc81 | 19b50313-a3b8-420f-8e4b-a3c8ae02bc81_1.jpg | (1) First, consider just the 5 3D dice. Assume that all dice in the image are standard dice with the numbers on opposite sides adding up to 7. For the following question ignore the dice in the front and in the back and focus just on the three dice in the middle. Additionally, some splodges of paint have been split on t... | null | 1638 | Discrete Mathematics & Formal Logic | null | zerobench | Puzzle | 764 | null | null | 2 | 3 | 4 | 4 | true | pass | null | ['19b50313-a3b8-420f-8e4b-a3c8ae02bc81_1.jpg'] | Abstract Logic & Procedural Puzzles |
6ecf41ce-e874-49c4-bdfd-cc542cc600f4 | 6ecf41ce-e874-49c4-bdfd-cc542cc600f4_1.jpg | Frank laid out his dominoes as shown in the picture. (Dominoes which touch must always have the same number of points). Before his brother George removed two dominoes there were 33 points altogether. How many points is the questionmark worth?
<image1> | [] | 4 | Continuous Mathematics & Analysis | null | STELAR-topo_vision_reasoning_preference_50k | Algebra | 41 | null | null | 2 | 3 | 4 | 4 | true | pass | null | ['6ecf41ce-e874-49c4-bdfd-cc542cc600f4_1.jpg'] | Foundations of Algebra |
6e9a970b-51ec-43fd-962e-49c4cbe644b5 | 6e9a970b-51ec-43fd-962e-49c4cbe644b5_1.jpg | Dominoes are said to be arranged correctly if, for each pair of adjacent dominoes, the numbers of spots on the adjacent ends are equal. Paul laid six dominoes in a line as shown in the diagram.
<image1>
He can make a move either by swapping the position of any two dominoes (without rotating either domino) or by rotatin... | [] | 3 | Discrete Mathematics & Formal Logic | null | STELAR-topo_vision_reasoning_preference_50k | Combinatorics | 77 | null | null | 2 | 3 | 4 | 4 | true | pass | null | ['6e9a970b-51ec-43fd-962e-49c4cbe644b5_1.jpg'] | Combinatorics & Graph Structures |
9cab2582-6fce-4786-b477-bad72fda417a | 9cab2582-6fce-4786-b477-bad72fda417a_1.jpg | Dominoes are said to be arranged correctly if, for each pair of adjacent dominoes, the numbers of spots on the adjacent ends are equal. Paul laid six dominoes in a line as shown in the diagram.
<image1>
He can make a move either by swapping the position of any two dominoes (without rotating either domino) or by rotatin... | [] | 3 | Discrete Mathematics & Formal Logic | null | STELAR-topo_vision_reasoning_preference_50k | Combinatorics | 77 | null | null | 2 | 3 | 4 | 4 | true | pass | null | ['9cab2582-6fce-4786-b477-bad72fda417a_1.jpg'] | Combinatorics & Graph Structures |
7981518b-a124-4e17-9ef1-4d3c747a9092 | 7981518b-a124-4e17-9ef1-4d3c747a9092_1.jpg | Dominoes are said to be arranged correctly if, for each pair of adjacent dominoes, the numbers of spots on the adjacent ends are equal. Paul laid six dominoes in a line as shown in the diagram.
<image1>
He can make a move either by swapping the position of any two dominoes (without rotating either domino) or by rotatin... | [] | 3 | Discrete Mathematics & Formal Logic | null | STELAR-topo_vision_reasoning_preference_50k | Combinatorics | 77 | null | null | 2 | 3 | 4 | 4 | true | pass | null | ['7981518b-a124-4e17-9ef1-4d3c747a9092_1.jpg'] | Combinatorics & Graph Structures |
197c0210-016d-4d5e-9f14-e02ca30a0df7 | 197c0210-016d-4d5e-9f14-e02ca30a0df7_1.jpg | Dominoes are said to be arranged correctly if, for each pair of adjacent dominoes, the numbers of spots on the adjacent ends are equal. Paul laid six dominoes in a line as shown in the diagram.
<image1>
He can make a move either by swapping the position of any two dominoes (without rotating either domino) or by rotatin... | [] | 3 | Discrete Mathematics & Formal Logic | null | STELAR-topo_vision_reasoning_preference_50k | Combinatorics | 77 | null | null | 2 | 3 | 4 | 4 | true | pass | null | ['197c0210-016d-4d5e-9f14-e02ca30a0df7_1.jpg'] | Combinatorics & Graph Structures |
0c184ffe-d083-43c8-95ec-c8a50dc4f27f | 0c184ffe-d083-43c8-95ec-c8a50dc4f27f_1.jpg | Dominoes are said to be arranged correctly if, for each pair of adjacent dominoes, the numbers of spots on the adjacent ends are equal. Paul laid six dominoes in a line as shown in the diagram.
<image1>
He can make a move either by swapping the position of any two dominoes (without rotating either domino) or by rotatin... | [] | 3 | Discrete Mathematics & Formal Logic | null | STELAR-topo_vision_reasoning_preference_50k | Combinatorics | 77 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['0c184ffe-d083-43c8-95ec-c8a50dc4f27f_1.jpg'] | Combinatorics & Graph Structures |
5fd06605-5d24-4aea-ade3-08fc729f93cf | 5fd06605-5d24-4aea-ade3-08fc729f93cf_1.jpg | Dominoes are said to be arranged correctly if, for each pair of adjacent dominoes, the numbers of spots on the adjacent ends are equal. Paul laid six dominoes in a line as shown in the diagram.
<image1>
He can make a move either by swapping the position of any two dominoes (without rotating either domino) or by rotatin... | [] | 3 | Discrete Mathematics & Formal Logic | null | STELAR-topo_vision_reasoning_preference_50k | Combinatorics | 77 | null | null | 2 | 3 | 4 | 4 | true | pass | null | ['5fd06605-5d24-4aea-ade3-08fc729f93cf_1.jpg'] | Combinatorics & Graph Structures |
f24c60ea-22d7-49f6-950f-90fd6f6964e7 | f24c60ea-22d7-49f6-950f-90fd6f6964e7_1.jpg | Dominoes are said to be arranged correctly if, for each pair of adjacent dominoes, the numbers of spots on the adjacent ends are equal. Paul laid six dominoes in a line as shown in the diagram.
<image1>
He can make a move either by swapping the position of any two dominoes (without rotating either domino) or by rotatin... | [] | 3 | Discrete Mathematics & Formal Logic | null | STELAR-topo_vision_reasoning_preference_50k | Combinatorics | 77 | null | null | 2 | 2 | 4 | 4 | true | pass | null | ['f24c60ea-22d7-49f6-950f-90fd6f6964e7_1.jpg'] | Combinatorics & Graph Structures |
5701f970-ad9a-49c4-8495-f9e0b1c218f1 | 5701f970-ad9a-49c4-8495-f9e0b1c218f1_1.jpg | Dominoes are said to be arranged correctly if, for each pair of adjacent dominoes, the numbers of spots on the adjacent ends are equal. Paul laid six dominoes in a line as shown in the diagram.
<image1>
He can make a move either by swapping the position of any two dominoes (without rotating either domino) or by rotatin... | [] | 3 | Discrete Mathematics & Formal Logic | null | STELAR-topo_vision_reasoning_preference_50k | Combinatorics | 77 | null | null | 2 | 3 | 4 | 4 | true | pass | null | ['5701f970-ad9a-49c4-8495-f9e0b1c218f1_1.jpg'] | Combinatorics & Graph Structures |
7bcdb4ea-b501-4175-b41a-05129dec8c42 | 7bcdb4ea-b501-4175-b41a-05129dec8c42_1.jpg | Dominoes are said to be arranged correctly if, for each pair of adjacent dominoes, the numbers of spots on the adjacent ends are equal. Paul laid six dominoes in a line as shown in the diagram.
<image1>
He can make a move either by swapping the position of any two dominoes (without rotating either domino) or by rotatin... | [] | 3 | Discrete Mathematics & Formal Logic | null | STELAR-topo_vision_reasoning_preference_50k | Combinatorics | 77 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['7bcdb4ea-b501-4175-b41a-05129dec8c42_1.jpg'] | Combinatorics & Graph Structures |
344c6514-cd1d-41bb-814d-fd5bdc6805b9 | 344c6514-cd1d-41bb-814d-fd5bdc6805b9_1.jpg | Dominoes are said to be arranged correctly if, for each pair of adjacent dominoes, the numbers of spots on the adjacent ends are equal. Paul laid six dominoes in a line as shown in the diagram.
<image1>
He can make a move either by swapping the position of any two dominoes (without rotating either domino) or by rotatin... | [] | 3 | Discrete Mathematics & Formal Logic | null | STELAR-topo_vision_reasoning_preference_50k | Combinatorics | 77 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['344c6514-cd1d-41bb-814d-fd5bdc6805b9_1.jpg'] | Combinatorics & Graph Structures |
05819ef6-132c-4a7e-944b-3be40b4cef0d | 05819ef6-132c-4a7e-944b-3be40b4cef0d_1.jpg | The sum of the dots on opposite sides of an ordinary die is 7. Which of the following dice could be an ordinary die?
<image1> | ['A', 'B', 'C', 'D', 'E'] | E | Geometry Reasoning | null | STELAR-topo_vision_reasoning_preference_50k | Solid Geometry | 25 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['05819ef6-132c-4a7e-944b-3be40b4cef0d_1.jpg'] | Solid Geometry & Volumetrics |
96fc26c3-6717-4d62-b55a-61f6fcf6528d | 96fc26c3-6717-4d62-b55a-61f6fcf6528d_1.jpg | Tom writes down two five-digit number. He places different shapes on different digits. He places the same shape on the same digits. Find the value of first five-digit number. | null | 46444 | Discrete Mathematics & Formal Logic | null | DynaMath_Sample | Arithmetic | 145 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['96fc26c3-6717-4d62-b55a-61f6fcf6528d_1.jpg'] | Arithmetic & Concrete Number Theory |
d5375371-378c-4980-9b85-921008f67fd2 | d5375371-378c-4980-9b85-921008f67fd2_1.jpg | Tom writes down two five-digit number. He places different shapes on different digits. He places the same shape on the same digits. Find the value of first five-digit number. | null | 99274 | Discrete Mathematics & Formal Logic | null | DynaMath_Sample | Arithmetic | 145 | null | null | 3 | 3 | 4 | 4 | true | pass | null | ['d5375371-378c-4980-9b85-921008f67fd2_1.jpg'] | Arithmetic & Concrete Number Theory |
2b629a93-0a96-4b70-a33f-d7f8d613a6fd | 2b629a93-0a96-4b70-a33f-d7f8d613a6fd_1.jpg | Given the outer surface of a paper box on the left, which option on the right can be folded into it? | null | A | Geometry Reasoning | null | MM-IQ | 3D-Geometry | 21 | null | null | 2 | 2 | 3 | 4 | true | pass | null | ['2b629a93-0a96-4b70-a33f-d7f8d613a6fd_1.jpg'] | Solid Geometry & Volumetrics |
39c3d5ce-d9ca-4e9c-a82e-56f28eb30cca | 39c3d5ce-d9ca-4e9c-a82e-56f28eb30cca_1.jpg | Pick out the one that is different from the four figures: | null | D | Geometry Reasoning | null | MM-IQ | 3D-Geometry | 11 | null | null | 4 | 2 | 3 | 4 | true | pass | null | ['39c3d5ce-d9ca-4e9c-a82e-56f28eb30cca_1.jpg'] | Solid Geometry & Volumetrics |
292c6d44-badd-49b4-a94a-809939c846a9 | 292c6d44-badd-49b4-a94a-809939c846a9_1.jpg | The sum of the points on the opposite faces of the cube in the figure below is 7. First, rotate the cube 3 times in the direction of B, then 1 time in the direction of A, and then 2 times in the direction of D. The number of points on the upward face at this time is ().
A: 5
B: 4
C: 3
D: 2 | null | D | Geometry Reasoning | null | MM-IQ | 3D-Geometry | 67 | null | null | 3 | 3 | 4 | 4 | true | pass | null | ['292c6d44-badd-49b4-a94a-809939c846a9_1.jpg'] | Solid Geometry & Volumetrics |
bd8c3859-e72b-4f0d-82da-c9a74fa4a6b6 | bd8c3859-e72b-4f0d-82da-c9a74fa4a6b6_1.jpg | Here are data on two companies. The T-bill rate is 4% and the market risk premium is 6%. <image 1> What would be the fair return for each company, according to the capital asset pricing model(CAPM) | ['13%', '11%', '10%'] | C | Socio-Economic & Contextual Mathematics | null | MMMU | Investment | 36 | null | null | 2 | 3 | 4 | 4 | true | pass | null | ['bd8c3859-e72b-4f0d-82da-c9a74fa4a6b6_1.jpg'] | Operational & Financial Analytics |
6c378338-84c5-4ff7-b758-cc01f8ab1c13 | 6c378338-84c5-4ff7-b758-cc01f8ab1c13_1.jpg | Match the concept on the left to its correct description. <image 1> | ['V. III. VI. I. IV. II. VII.', 'VI. I. II. V. III. VII. IV.', 'IV. II. I. V. III. VI. VII.', 'IV. VII. II. I. III. V. VI.'] | A | Socio-Economic & Contextual Mathematics | null | MMMU | Managerial Accounting | 12 | null | null | 2 | 2 | 4 | 3 | true | pass | null | ['6c378338-84c5-4ff7-b758-cc01f8ab1c13_1.jpg'] | Operational & Financial Analytics |
c8ed7fea-cd00-4530-ba3b-24781d6cca1e | c8ed7fea-cd00-4530-ba3b-24781d6cca1e_1.jpg | On the basis of the utility formula above, which investment would you select if you were risk averse with A= 4? <image 1> | ['1', '2', '3', '4'] | C | Socio-Economic & Contextual Mathematics | null | MMMU | Investment | 23 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['c8ed7fea-cd00-4530-ba3b-24781d6cca1e_1.jpg'] | Operational & Financial Analytics |
b991f48d-ff20-43ce-b0b1-d3206830d77a | b991f48d-ff20-43ce-b0b1-d3206830d77a_1.jpg | An excursion company is considering adding small boats to their fleet. The company has $200,000 to invest in this venture. At present there is an estimated maximum demand of 6,000 customers per season for these tours. The company does not wish to provide capacity in excess of the estimated maximum demand. The basic dat... | ['4 boats of Type 1 and 1 boat of Type 2', '5 boats of Type 1 and 0 boats of Type 2', '3 boats of Type 1 and 2 boats of Type 2', '6 boats of Type 1 and 0 boats of Type 2'] | B | Socio-Economic & Contextual Mathematics | null | MMMU | Operations Research | 132 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['b991f48d-ff20-43ce-b0b1-d3206830d77a_1.jpg'] | Operational & Financial Analytics |
4cdb9e5b-0636-4ba0-8628-94f53d0f8958 | 4cdb9e5b-0636-4ba0-8628-94f53d0f8958_1.jpg | Consider the following problem: Minimize (x1 - 3)^2 + (x2 - 2)^2 subject to x1^2 - x2 - 3 $\le $ 0 x2 - 1 $\le $ 0 - x1 $\le $ 0 Give the solution.
<image 1> | ['(0, 0)', '(2, 2)', '(3, 3)', '(2, 1)'] | D | Socio-Economic & Contextual Mathematics | null | MMMU | Operations Research | 38 | null | null | 2 | 3 | 3 | 3 | true | pass | null | ['4cdb9e5b-0636-4ba0-8628-94f53d0f8958_1.jpg'] | Operational & Financial Analytics |
af08241c-fb06-4e3d-a079-744ba36934e8 | af08241c-fb06-4e3d-a079-744ba36934e8_1.jpg | Consider the optimal allocation of a scarce resource between two processes where the total amount of resource available is b (see Fig. 1). It is required to maximize the return from both processes. Thus, one has max(x)1, (x)2 f(x1) + f(x2) such that x1 + x2 = b. Use the Lagrangian Multipliers to solve.
<image 1> | ['x1* = x2* = (b/2), $\\lambda $* = b - 4, and for b = 4, $\\lambda $* = 0', 'x1* = 2x2*, $\\lambda $* = b + 4, and for b = 4, $\\lambda $* = 2', 'x1* = x2* = (b/4), $\\lambda $* = b - 2, and for b = 4, $\\lambda $* = 1', 'x1* = x2* = (b/3), $\\lambda $* = b - 3, and for b = 4, $\\lambda $* = 1'] | A | Socio-Economic & Contextual Mathematics | null | MMMU | Operations Research | 56 | null | null | 2 | 3 | 3 | 3 | true | pass | null | ['af08241c-fb06-4e3d-a079-744ba36934e8_1.jpg'] | Operational & Financial Analytics |
e459ce8b-15b9-4a24-bfb5-d3e168619e65 | e459ce8b-15b9-4a24-bfb5-d3e168619e65_1.jpg | A company produces two types of mopeds. The low speed moped is produced at their New Jersey plant which can only handle 1,000 mopeds per month. The high speed moped is produced at their Maryland plant which can only handle 850 mopeds per month. The company has a sufficient supply of parts to build 1,175 low speed moped... | ['(0, 0)', '(850, 0)', '(850, 384 1/3)', '(600, 800)'] | D | Socio-Economic & Contextual Mathematics | null | MMMU | Operations Research | 118 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['e459ce8b-15b9-4a24-bfb5-d3e168619e65_1.jpg'] | Operational & Financial Analytics |
87925bda-bd05-45b3-9ebf-c00df8c5f5fa | 87925bda-bd05-45b3-9ebf-c00df8c5f5fa_1.jpg | An airplane's Mach number M is the ratio of its speed to the speed of sound. When a plane is flying at a constant altitude, then its Mach angle is given by $\mu =2\sin^{-1}\left(\frac{1}{M}\right)$. <image 1> If $\mu $ = 1.4, Find the Mach angle (to the nearest degree) | ['92°', '42°', '27°', '82°'] | A | Continuous Mathematics & Analysis | null | MMMU | Calculus | 49 | null | null | 3 | 3 | 4 | 4 | true | pass | null | ['87925bda-bd05-45b3-9ebf-c00df8c5f5fa_1.jpg'] | Calculus & Advanced Analysis |
502b78c7-8a50-4fe5-ad2f-046c498c8434 | 502b78c7-8a50-4fe5-ad2f-046c498c8434_1.jpg | Consider: Minimize 2x1 - x2 Subject to: - x1 + x2 ≦ 2 2x1 + x2 ≦ 6 x1, x2 ≦ 0. Determine an improved basic feasible solution starting from the b. f. s. with basis B➙ = [a1➙, a2➙]. Identify the blocking variable?
<image 1> | ['x1 is the blocking variable and the new basic feasible solution is (x1, x2, x3, x4) = (0, 2, 0, 4).', 'x2 is the blocking variable and the new basic feasible solution is (x1, x2, x3, x4) = (2, 0, 4, 0).', 'x3 is the blocking variable and the new basic feasible solution is (x1, x2, x3, x4) = (2, 4, 0, 0).', 'x4 is the... | A | Socio-Economic & Contextual Mathematics | null | MMMU | Operations Research | 46 | null | null | 2 | 2 | 4 | 3 | true | pass | null | ['502b78c7-8a50-4fe5-ad2f-046c498c8434_1.jpg'] | Operational & Financial Analytics |
2dc9e6e5-c37c-4367-a689-8857aede5c9f | 2dc9e6e5-c37c-4367-a689-8857aede5c9f_1.jpg | Determine the value of $i_0$, $i_1$, $i_2$, $i_3$, $i_4$, $i_5$ in <image 1>. | ['17A, 17A, 6A, 4A, 7A, 10A', '17A, 15A, 5A, 4A, 7A, 10A', '17A, 17A, 6A, 5A, 7A, 10A', '17A, 17A, 6A, 4A, 4A, 10A', '17A, 17A, 6A, 4A, 7A, 15A'] | A | Discrete Mathematics & Formal Logic | null | MMMU | Graph Theory | 13 | null | null | 3 | 3 | 3 | 4 | true | pass | null | ['2dc9e6e5-c37c-4367-a689-8857aede5c9f_1.jpg'] | Combinatorics & Graph Structures |
1029697f-e931-48b8-b247-81d6d32d36f3 | 1029697f-e931-48b8-b247-81d6d32d36f3_1.jpg | Which is the graph of the function $y=\sqrt{|(1+x)(1-|x|)|}$?
<image1> | ['A', 'B', 'C', 'D', 'E'] | D | null | null | MathVision | Analytic Geometry | 9 | null | null | 3 | 3 | 4 | 4 | true | pass | null | ['1029697f-e931-48b8-b247-81d6d32d36f3_1.jpg'] | null |
833381a3-1ff4-46de-aa50-756d377a11cd | 833381a3-1ff4-46de-aa50-756d377a11cd_1.jpg | Which of the following graphs represents the solution set of $(x-|x|)^{2}+(y-|y|)^{2}=4$?
<image1> | ['A', 'B', 'C', 'D', 'E'] | A | null | null | MathVision | Analytic Geometry | 12 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['833381a3-1ff4-46de-aa50-756d377a11cd_1.jpg'] | null |
10cb6941-95f3-48b1-aafb-89e92de2a90f | 10cb6941-95f3-48b1-aafb-89e92de2a90f_1.jpg | The rectangles $S_{1}$ and $S_{2}$ shown in the picture have the same area. Determine the ratio $x: y$.
<image1> | ['$1: 1$', '$3: 2$', '$4: 3$', '$7: 4$', '$8: 5$'] | E | null | null | MathVision | Analytic Geometry | 19 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['10cb6941-95f3-48b1-aafb-89e92de2a90f_1.jpg'] | null |
f03a32f2-4ca9-4bd9-a3cc-92d2e3cacdf0 | f03a32f2-4ca9-4bd9-a3cc-92d2e3cacdf0_1.jpg | An ant walked $6 \mathrm{~m}$ every day to go from point $A$ to point $B$ in a straight line. One day Johnny put a straight cylinder of one meter high in that way. Now the ant walks on the same straight line or above it, having to go up and down the cylinder, as shown in the picture. How much does she have to walk now ... | ['$8 \\mathrm{~m}$', '$9 \\mathrm{~m}$', '$6+\\pi \\mathrm{~m}$', '$12-\\pi \\mathrm{~m}$', '$10 \\mathrm{~m}$'] | A | Geometry Reasoning | null | MathVision | Solid Geometry | 73 | null | null | 3 | 2 | 4 | 3 | true | pass | null | ['f03a32f2-4ca9-4bd9-a3cc-92d2e3cacdf0_1.jpg'] | Solid Geometry & Volumetrics |
e70f4c36-d6d5-408f-b840-2b38599440ae | e70f4c36-d6d5-408f-b840-2b38599440ae_1.jpg | If a laser beam hits a mirror it changes its direction (see left diagram). Each mirror has mirrored sides on both sides. At which letter does the laser beam end?
<image1> | ['A', 'B', 'C', 'D', 'E'] | B | Geometry Reasoning | null | MathVision | Transformation Geometry | 31 | null | null | 3 | 3 | 4 | 4 | true | pass | null | ['e70f4c36-d6d5-408f-b840-2b38599440ae_1.jpg'] | Kinematics, Transformations & Projections |
26f4d5d7-4731-41f5-b59d-824b2ddc4aff | 26f4d5d7-4731-41f5-b59d-824b2ddc4aff_1.jpg | Five students carry out a run. Their results are recorded in the graph opposite, according to the time taken (Zeit) and the distance covered (Strecke). Who had the greatest average speed?
<image1> | ['Anja', 'Bernd', 'Chris', 'Doris', 'Ernst'] | D | null | null | MathVision | Analytic Geometry | 32 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['26f4d5d7-4731-41f5-b59d-824b2ddc4aff_1.jpg'] | null |
7bcb2897-ba0c-4e4a-8d8b-feab31f80716 | 7bcb2897-ba0c-4e4a-8d8b-feab31f80716_1.jpg | In a drawing we can see a three quarter circle with centre M and an indicated orientation arrow. This three-quarter circle is first turned $90^{\circ}$ anti-clockwise about M and then reflected in the x - axis. Which is the resulting picture?
<image1>
<image2> | ['A', 'B', 'C', 'D', 'E'] | D | null | null | MathVision | Analytic Geometry | 43 | null | null | 4 | 3 | 3 | 4 | true | pass | null | ['7bcb2897-ba0c-4e4a-8d8b-feab31f80716_1.jpg'] | null |
6632f688-52b7-4a94-a99d-ec98829b6ed4 | 6632f688-52b7-4a94-a99d-ec98829b6ed4_1.jpg | The trapezium shown in the diagram is rotated anti-clockwise by $90^{\circ}$ around the origin $O$, and then reflected in the $x$-axis. Which of the following shows the end result of these transformations? <image1>
<image2> | ['A', 'B', 'C', 'D', 'E'] | A | null | null | MathVision | Analytic Geometry | 34 | null | null | 4 | 2 | 3 | 4 | true | pass | null | ['6632f688-52b7-4a94-a99d-ec98829b6ed4_1.jpg'] | null |
87f4dd10-49d1-490d-8a2c-d430a5966dcc | 87f4dd10-49d1-490d-8a2c-d430a5966dcc_1.jpg | A unit cube is cut twice to form three triangular prisms, two of which are congruent, as shown in Figure 1. The cube is then cut in the same manner along the dashed lines shown in Figure 2. This creates nine pieces. What is the volume of the piece that contains vertex $ W$?
<image1> | ['$\\frac{1}{12}$', '$\\frac{1}{9}$', '$\\frac{1}{8}$', '$\\frac{1}{6}$', '$\\frac{1}{4}$'] | A | Geometry Reasoning | null | MathVision | Solid Geometry | 55 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['87f4dd10-49d1-490d-8a2c-d430a5966dcc_1.jpg'] | Solid Geometry & Volumetrics |
42dcb542-3f89-47e1-a22c-addd29721740 | 42dcb542-3f89-47e1-a22c-addd29721740_1.jpg | The vertical axis indicates the number of employees, but the scale was accidentally omitted from this graph. What percent of the employees at the Gauss company have worked there for $5$ years or more?
<image1> | ['$9\\%$', '$23\\frac{1}{3}\\%$', '$30\\%$', '$42\\frac{6}{7}\\%$', '$50\\%$'] | C | Applied Sciences & Grounded Reasoning | null | MathVision | Statistics | 35 | null | null | 3 | 2 | 3 | 4 | true | pass | null | ['42dcb542-3f89-47e1-a22c-addd29721740_1.jpg'] | Probability, Statistics & Analytics |
8181c1de-f0df-4f89-add1-e3a8a00f1810 | 8181c1de-f0df-4f89-add1-e3a8a00f1810_1.jpg | Mike leaves home and drives slowly east through city traffic. When he reaches the highway he drives east more rapidly until he reaches the shopping mall where he stops. He shops at the mall for an hour. Mike returns home by the same route as he came, driving west rapidly along the highway and then slowly through cit... | ['A', 'B', 'C', 'D', 'E'] | B | Applied Sciences & Grounded Reasoning | null | MathVision | Statistics | 91 | null | null | 3 | 3 | 4 | 4 | true | pass | null | ['8181c1de-f0df-4f89-add1-e3a8a00f1810_1.jpg'] | Probability, Statistics & Analytics |
5ad41385-861b-4f0a-8493-d1a0cb583ed3 | 5ad41385-861b-4f0a-8493-d1a0cb583ed3_1.jpg | Car M traveled at a constant speed for a given time. This is shown by the dashed line. Car N traveled at twice the speed for the same distance. If Car N's speed and time are shown as solid line, which graph illustrates this?
<image1> | ['A', 'B', 'C', 'D', 'E'] | D | Applied Sciences & Grounded Reasoning | null | MathVision | Statistics | 45 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['5ad41385-861b-4f0a-8493-d1a0cb583ed3_1.jpg'] | Probability, Statistics & Analytics |
858bee9c-550b-49ee-a05b-aef3f3436ff4 | 858bee9c-550b-49ee-a05b-aef3f3436ff4_1.jpg | A birdbath is designed to overflow so that it will be self-cleaning. Water flows in at the rate of 20 milliliters per minute and drains at the rate of 18 milliliters per minute. One of these graphs shows the volume of water in the birdbath during the filling time and continuing into the overflow time. Which one is it?
... | ['$\\text{A}$', '$\\text{B}$', '$\\text{C}$', '$\\text{D}$', '$\\text{E}$'] | A | Applied Sciences & Grounded Reasoning | null | MathVision | Statistics | 60 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['858bee9c-550b-49ee-a05b-aef3f3436ff4_1.jpg'] | Probability, Statistics & Analytics |
447e38a7-e40d-4545-8d3b-a4f83e2751c6 | 447e38a7-e40d-4545-8d3b-a4f83e2751c6_1.jpg | Amanda Reckonwith draws five circles with radii 1, 2, 3, 4 and 5. Then for each circle she plots the point (C; A), where C is its circumference and A is its area. Which of the following could be her graph? | ['<image1>', '<image2>', '<image3>', '<image4>', '<image5>'] | A | Applied Sciences & Grounded Reasoning | null | MathVision | Statistics | 41 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['447e38a7-e40d-4545-8d3b-a4f83e2751c6_1.jpg'] | Probability, Statistics & Analytics |
85ced6f8-0b8a-4339-9883-deb2180760a7 | 85ced6f8-0b8a-4339-9883-deb2180760a7_1.jpg | A tortoise challenges a hare to a race. The hare eagerly agrees and quickly runs ahead, leaving the slow-moving tortoise behind. Confident that he will win, the hare stops to take a nap. Meanwhile, the tortoise walks at a slow steady pace for the entire race. The hare awakes and runs to the finish line, only to find th... | ['A', 'B', 'C', 'D', 'E'] | B | Applied Sciences & Grounded Reasoning | null | MathVision | Statistics | 90 | null | null | 2 | 3 | 4 | 4 | true | pass | null | ['85ced6f8-0b8a-4339-9883-deb2180760a7_1.jpg'] | Probability, Statistics & Analytics |
2d5190fb-587d-42a2-a3ee-f796f82f1792 | 2d5190fb-587d-42a2-a3ee-f796f82f1792_1.jpg | When a spring does work on an object, we cannot find the work by simply multiplying the spring force by the object's displacement. The reason is that there is no one value for the force-it changes. However, we can split the displacement up into an infinite number of tiny parts and then approximate the force in each as ... | null | 1.2 | Applied Sciences & Grounded Reasoning | null | MathVista | Scientific Reasoning | 393 | null | null | 4 | 2 | 4 | 4 | true | pass | null | ['2d5190fb-587d-42a2-a3ee-f796f82f1792_1.jpg'] | Probability, Statistics & Analytics |
9fa7d654-782c-4aaf-a7c8-4c52b2f7b383 | 9fa7d654-782c-4aaf-a7c8-4c52b2f7b383_1.jpg | The diagrams below show two pure samples of gas in identical closed, rigid containers. Each colored ball represents one gas particle. Both samples have the same number of particles. Compare the average kinetic energies of the particles in each sample. Which sample has the higher temperature? | ['neither; the samples have the same temperature', 'sample A', 'sample B'] | sample A | Applied Sciences & Grounded Reasoning | null | MathVista | Scientific Reasoning | 368 | null | null | 4 | 2 | 4 | 3 | true | pass | null | ['9fa7d654-782c-4aaf-a7c8-4c52b2f7b383_1.jpg'] | Probability, Statistics & Analytics |
71c8b46b-53df-48b1-80c2-cfef0a428831 | 71c8b46b-53df-48b1-80c2-cfef0a428831_1.jpg | What is the sum of accuracies of the algorithm liver for all the datasets? | null | 24 | Applied Sciences & Grounded Reasoning | null | MathVista | Arithmetic and Statistical Reasoning | 28 | null | null | 4 | 2 | 4 | 4 | true | pass | null | ['71c8b46b-53df-48b1-80c2-cfef0a428831_1.jpg'] | Probability, Statistics & Analytics |
98c833a5-477b-4dd8-9d59-ba62743c84f2 | 98c833a5-477b-4dd8-9d59-ba62743c84f2_1.jpg | An image has the gray level PDF $p_r(r)$ shown in Fig. Q1a. One wants to do histogram specification SO that the processed image will have the specified $p_z(z)$ shown in Fig. Q1b. Can we use intensity mapping function $T: z=1-r$ to achieve the goal? | ['True', 'False'] | False | Continuous Mathematics & Analysis | null | MathVista | Geometry and Algebraic Reasoning | 220 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['98c833a5-477b-4dd8-9d59-ba62743c84f2_1.jpg'] | Foundations of Algebra |
6e9af27c-5cc9-4def-a3f4-1f82a6c69b2f | 6e9af27c-5cc9-4def-a3f4-1f82a6c69b2f_1.jpg | What is the lowest accuracy reported in the whole chart? | null | 1 | Applied Sciences & Grounded Reasoning | null | MathVista | Statistical Reasoning | 10 | null | null | 3 | 2 | 4 | 4 | true | pass | null | ['6e9af27c-5cc9-4def-a3f4-1f82a6c69b2f_1.jpg'] | Probability, Statistics & Analytics |
a479ed9a-9a12-4fd0-851c-62b4f4798383 | a479ed9a-9a12-4fd0-851c-62b4f4798383_1.jpg | The diagram below is a model of two solutions. Each pink ball represents one particle of solute. Which solution has a higher concentration of pink particles? | ['neither; their concentrations are the same', 'Solution B', 'Solution A'] | Solution B | Applied Sciences & Grounded Reasoning | null | MathVista | Scientific Reasoning | 260 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['a479ed9a-9a12-4fd0-851c-62b4f4798383_1.jpg'] | Probability, Statistics & Analytics |
20da8d80-4700-47bd-b53b-03ad98179014 | 20da8d80-4700-47bd-b53b-03ad98179014_1.jpg | Consider the infinitely long chain of resistors shown below. What is the resistance between terminals a and b if R=1? | null | 0.73 | Applied Sciences & Grounded Reasoning | null | MathVista | Scientific Reasoning | 80 | null | null | 4 | 3 | 4 | 4 | true | pass | null | ['20da8d80-4700-47bd-b53b-03ad98179014_1.jpg'] | Probability, Statistics & Analytics |
f830f2aa-d5cf-4a72-acad-d505a5f8c938 | f830f2aa-d5cf-4a72-acad-d505a5f8c938_1.jpg | How many algorithms have accuracy lower than 8 in at least one dataset? | null | 3 | Applied Sciences & Grounded Reasoning | null | MathVista | Statistical Reasoning | 13 | null | null | 2 | 2 | 3 | 4 | true | pass | null | ['f830f2aa-d5cf-4a72-acad-d505a5f8c938_1.jpg'] | Probability, Statistics & Analytics |
5bad6b29-b5cc-47ee-8739-3acad2a77c91 | 5bad6b29-b5cc-47ee-8739-3acad2a77c91_1.jpg | A perceptual audio codec is used to compress an audio signal. The codec groups every 4 barks into a subband and then allocates bits to different subbands according to the result of a spectrum analysis based on a psychoacoustic model. All samples in the same subband are quantized with the same quantizer, and the bit res... | null | 7 | Applied Sciences & Grounded Reasoning | null | MathVista | Scientific Reasoning | 118 | null | null | 4 | 2 | 3 | 4 | true | pass | null | ['5bad6b29-b5cc-47ee-8739-3acad2a77c91_1.jpg'] | Probability, Statistics & Analytics |
511d725d-69b4-43ae-bd1e-0f4e7a9c5335 | 511d725d-69b4-43ae-bd1e-0f4e7a9c5335_1.jpg | In Figure, suppose that Barbara's velocity relative to Alex is a constant $v_{B A}=52 \mathrm{~km} / \mathrm{h}$ and car $P$ is moving in the negative direction of the $x$ axis.
(a) If Alex measures a constant $v_{P A}=-78 \mathrm{~km} / \mathrm{h}$ for car $P$, what velocity $v_{P B}$ will Barbara measure? | null | -130 | Applied Sciences & Grounded Reasoning | null | MathVista | Scientific Reasoning | 204 | null | null | 4 | 2 | 4 | 4 | true | pass | null | ['511d725d-69b4-43ae-bd1e-0f4e7a9c5335_1.jpg'] | Probability, Statistics & Analytics |
8bc1cfec-5eaf-482b-a0e6-a7c9d75cf419 | 8bc1cfec-5eaf-482b-a0e6-a7c9d75cf419_1.jpg | What is the lowest accuracy reported in the whole chart? | null | 1 | Applied Sciences & Grounded Reasoning | null | MathVista | Statistical Reasoning | 10 | null | null | 4 | 3 | 3 | 4 | true | pass | null | ['8bc1cfec-5eaf-482b-a0e6-a7c9d75cf419_1.jpg'] | Probability, Statistics & Analytics |
397438bb-46b0-4a0f-afae-51cf97187391 | 397438bb-46b0-4a0f-afae-51cf97187391_1.jpg | You can see how organisms are interconnected from the diagram given. What will be the effect if all the Killer whales are removed? | ['The population of tuna will increase', 'Mouse will decrease in number', 'The phytoplankton will decrease', 'The grasshopper will die'] | The population of tuna will increase | Applied Sciences & Grounded Reasoning | null | MathVista | Scientific Reasoning | 828 | null | null | 4 | 2 | 4 | 4 | true | pass | null | ['397438bb-46b0-4a0f-afae-51cf97187391_1.jpg'] | Probability, Statistics & Analytics |
f2132369-b63a-4980-bdb7-f0d9563de15a | f2132369-b63a-4980-bdb7-f0d9563de15a_1.jpg | Part of an ecosystem is shown in this diagram. Imagine the algae and floating plants are prevented from growing. How will that most likely affect this ecosystem? | ['The number of ducks will increase', 'The number of minnows will increase', 'There will be no effect on this ecosystem', 'The number of aquatic crustaceans will decrease'] | The number of aquatic crustaceans will decrease | Applied Sciences & Grounded Reasoning | null | MathVista | Scientific Reasoning | 1,269 | null | null | 3 | 2 | 3 | 4 | true | pass | null | ['f2132369-b63a-4980-bdb7-f0d9563de15a_1.jpg'] | Probability, Statistics & Analytics |
7d6443d6-78fc-49a5-a426-24ee4a42f468 | 7d6443d6-78fc-49a5-a426-24ee4a42f468_1.jpg | What is the highest accuracy reported in the whole chart? | null | 8 | Applied Sciences & Grounded Reasoning | null | MathVista | Statistical Reasoning | 10 | null | null | 3 | 3 | 3 | 4 | true | pass | null | ['7d6443d6-78fc-49a5-a426-24ee4a42f468_1.jpg'] | Probability, Statistics & Analytics |
eecc3e62-9765-4a47-8a75-690ebf0364c1 | eecc3e62-9765-4a47-8a75-690ebf0364c1_1.jpg | <image>In the figure, $m ∠ 12 = 64$. Find the measure of $ \angle 9$. | null | 116 | null | null | geometry3k | Geometry | 45 | null | null | 3 | 3 | 4 | 4 | true | pass | null | ['eecc3e62-9765-4a47-8a75-690ebf0364c1_1.jpg'] | null |
7a62c31a-a663-4379-a7cb-8a2d71b95655 | 7a62c31a-a663-4379-a7cb-8a2d71b95655_1.jpg | <image>In the figure, line $l$ is parallel to line $m$. Line $n$ intersects both $l$ and $m$. Which of the following lists includes all of the angles that are supplementary to $ ∠1 $? | null | angles 2,3, 6, and 7 | null | null | geometry3k | Geometry | 680 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['7a62c31a-a663-4379-a7cb-8a2d71b95655_1.jpg'] | null |
6f0c2be4-dba3-457c-bfee-509478fa89ff | 6f0c2be4-dba3-457c-bfee-509478fa89ff_1.jpg | <image>For the pair of similar figures, use the given areas to find the scale factor from the blue to the green figure. | null | \frac { 1 } { 2 } | null | null | geometry3k | Geometry | 374 | null | null | 3 | 2 | 3 | 4 | true | pass | null | ['6f0c2be4-dba3-457c-bfee-509478fa89ff_1.jpg'] | null |
2eaa354e-e3df-4fe9-8f87-6baa03f7e61d | 2eaa354e-e3df-4fe9-8f87-6baa03f7e61d_1.jpg | Let $Z$ be the set of integers. $f: Z \rightarrow Z$ is defined by $f(n) = n - 10$ for $n > 100$ and $f(n) = f(f(n+11))$ for $n = 100$. Find the set of possible values of $f$. | null | ['We show that $f(n) = 91$ for $n \\le 100$. For $n = 100, 99, \\dots, 90$, we have $f(n) = f(f(n+11)) = f(n+11-10) = f(n+1)$. But $f(101) = 91$, so $f(n) = 91$ for $n = 100, 99, \\dots, 90$. Now for $n = 89, 88, \\dots, 1, 0, -1, \\dots$ we use induction. We have $f(n) = f(f(n+11)) = f(91)$ which, by induction, is 91.... | Continuous Mathematics & Analysis | null | MathNet | Algebraic Expressions | 15,249 | null | null | 2 | 2 | 4 | 4 | true | pass | null | ['2eaa354e-e3df-4fe9-8f87-6baa03f7e61d_1.jpg'] | Foundations of Algebra |
be44ee16-7991-4d26-823c-64fba0a40da6 | be44ee16-7991-4d26-823c-64fba0a40da6_1.jpg | Xiaoming's home (point A) and the school (point B) are on a straight street. Xiaoming wants to find a place P near the street to set up a relay station, such that the distances from P to Xiaoming's home and to the school satisfy the relationship shown in the figure. Please find the equation of the locus of P. | null | $(x-\frac{5}{2})^{2}+y^{2}=4$ | Geometry Reasoning | null | We-Math2.0-Pro | Solid Geometry | 1,711 | null | null | 3 | 2 | 3 | 4 | true | pass | null | ['be44ee16-7991-4d26-823c-64fba0a40da6_1.jpg'] | Solid Geometry & Volumetrics |
1f1b37bc-a114-48d8-91df-60b757e0bbe2 | 1f1b37bc-a114-48d8-91df-60b757e0bbe2_1.jpg | Xiaoming is studying differential calculus. Help Xiaoming calculate the approximate value of expression B shown in the figure (rounded to four decimal places). | null | 1.0067 | Geometry Reasoning | null | We-Math2.0-Pro | Solid Geometry | 138 | null | null | 2 | 2 | 4 | 3 | true | pass | null | ['1f1b37bc-a114-48d8-91df-60b757e0bbe2_1.jpg'] | Solid Geometry & Volumetrics |
65d9ccad-69d5-496a-a1b5-a4a9fc87c69b | 65d9ccad-69d5-496a-a1b5-a4a9fc87c69b_1.jpg | In a scientific experiment, researcher Xiao Ming needs to use an automatic computer to analyze experimental data. The computer performs a post-order traversal of the input expression tree (structure as shown in the figure) and outputs the maximum value of the corresponding expression within a specified interval. It is ... | null | 6 | Geometry Reasoning | null | We-Math2.0-Pro | Solid Geometry | 100 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['65d9ccad-69d5-496a-a1b5-a4a9fc87c69b_1.jpg'] | Solid Geometry & Volumetrics |
3235882b-6408-42ae-8bec-9e47a55d036b | 3235882b-6408-42ae-8bec-9e47a55d036b_1.jpg | As shown in the picture, When foot D touches the ground, the head point E rises () | ['0.5m', '0.6m', '0.3m', '0.9m'] | A | Geometry Reasoning | null | MathVerse | Plane Geometry - Applied | 17 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['3235882b-6408-42ae-8bec-9e47a55d036b_1.jpg'] | Plane Geometry & Metric Analysis |
ba543e3e-051b-4d77-913f-522ecb52457f | ba543e3e-051b-4d77-913f-522ecb52457f_1.jpg | In the figure below, point B is due East of point A. We want to find the position of point A relative to point C. Triangle ABC formed by the dashed line, angle A is 49° and angle B is 39°.
Find the true bearing of point A from point C. | [] | 319 ^\circ T | Geometry Reasoning | null | MathVerse | Plane Geometry - Angle | 612 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['ba543e3e-051b-4d77-913f-522ecb52457f_1.jpg'] | Plane Geometry & Metric Analysis |
6a5971fe-4f48-4397-9c03-f0f744e4e988 | 6a5971fe-4f48-4397-9c03-f0f744e4e988_1.jpg | Let us find the surface area of the solid given (constructed by removing a hemisphere from a cylinder). The radius is 15 cm. The height of cylinder is 22 cm.
Hence, find the total surface area of the shape.
Give our answer to two decimal places. | [] | Total surface area $=4194.03 \mathrm{~cm}^{2}$ | Geometry Reasoning | null | MathVerse | Solid Geometry - Area | 2,116 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['6a5971fe-4f48-4397-9c03-f0f744e4e988_1.jpg'] | Solid Geometry & Volumetrics |
d6ec7950-d1ab-4b21-a305-c9d6d69e9aac | d6ec7950-d1ab-4b21-a305-c9d6d69e9aac_1.jpg | While exploring outer space, Darth Vader comes upon a purely reflective spherical planet with radius $R_{p}=$ $40,000 \mathrm{~m}$ and mass $M_{p}=8.128 \times 10^{24} \mathrm{~kg}$. Around the planet is a strange moon of orbital radius $R_{s}=$ $6,400,000 \mathrm{~m}\left(R_{s} \gg R_{p}\right)$ and mass $M_{s}=9.346 ... | null | ['$1.33 \\cdot 10^{35}$'] | Applied Sciences & Grounded Reasoning | null | OlympiadBench | Physics - Modern Physics | 4,950 | null | null | 3 | 2 | 3 | 4 | true | pass | null | ['d6ec7950-d1ab-4b21-a305-c9d6d69e9aac_1.jpg'] | Physical Systems Reasoning |
078cc9c0-a64d-4675-8706-2924caf60dec | 078cc9c0-a64d-4675-8706-2924caf60dec_1.jpg | A bicycle wheel of mass $M=2.8 \mathrm{~kg}$ and radius $R=0.3 \mathrm{~m}$ is spinning with angular velocity $\omega=5 \mathrm{rad} / \mathrm{s}$ around its axis in outer space, and its center is motionless. Assume that it has all of its mass uniformly concentrated on the rim. A long, massless axle is attached to its ... | null | ['0.568'] | Applied Sciences & Grounded Reasoning | null | OlympiadBench | Physics - Mechanics | 1,260 | null | null | 2 | 3 | 4 | 4 | true | pass | null | ['078cc9c0-a64d-4675-8706-2924caf60dec_1.jpg'] | Physical Systems Reasoning |
8b505e07-fb37-4ac7-b24a-9ccd0151f71b | 8b505e07-fb37-4ac7-b24a-9ccd0151f71b_1.jpg | In the circuit shown below, a capacitor $C=4 \mathrm{~F}$, inductor $L=5 \mathrm{H}$, and resistors $R_{1}=3 \Omega$ and $R_{2}=2 \Omega$ are placed in a diamond shape and are then fed an alternating current with peak voltage $V_{0}=1 \mathrm{~V}$ of unknown frequency. Determine the magnitude of the maximum instantaneo... | null | ['0.65'] | Applied Sciences & Grounded Reasoning | null | OlympiadBench | Physics - Electromagnetism | 432 | null | null | 2 | 2 | 4 | 3 | true | pass | null | ['8b505e07-fb37-4ac7-b24a-9ccd0151f71b_1.jpg'] | Physical Systems Reasoning |
e980a9a4-d35d-4ebd-bc06-46f8c5f93d24 | e980a9a4-d35d-4ebd-bc06-46f8c5f93d24_1.jpg | Colliding Conducting Slab A thin conducting square slab with side length $s=5 \mathrm{~cm}$, initial charge $q=0.1 \mu \mathrm{C}$, and mass $m=100 \mathrm{~g}$ is given a kick and sent bouncing between two infinite conducting plates separated by a distance $d=0.5 \mathrm{~cm} \ll s$ and with surface charge density $\p... | null | ['25273'] | Applied Sciences & Grounded Reasoning | null | OlympiadBench | Physics - Electromagnetism | 1,251 | null | null | 2 | 3 | 3 | 3 | true | pass | null | ['e980a9a4-d35d-4ebd-bc06-46f8c5f93d24_1.jpg'] | Physical Systems Reasoning |
1074df75-b4b7-4102-ba24-f4ec2a8a2da9 | 1074df75-b4b7-4102-ba24-f4ec2a8a2da9_1.jpg | A truck (denoted by $S$ ) is driving at a speed $v=2 \mathrm{~m} / \mathrm{s}$ in the opposite direction of a car driving at a speed $u=3 \mathrm{~m} / \mathrm{s}$, which is equipped with a rear-view mirror. Both $v$ and $u$ are measured from an observer on the ground. Relative to this observer, what is the speed (in $... | null | ['$8$'] | Applied Sciences & Grounded Reasoning | null | OlympiadBench | Physics - Mechanics | 546 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['1074df75-b4b7-4102-ba24-f4ec2a8a2da9_1.jpg'] | Physical Systems Reasoning |
f8b6161b-91d2-46e9-95ab-5600ca29088b | f8b6161b-91d2-46e9-95ab-5600ca29088b_1.jpg | At Hanoi-Amsterdam High School in Vietnam, every subject has its own flag (see Figure A, taken by Tung X. Tran). While the flags differ in color, they share the same central figure. Consider a planar conducting frame of that figure rotating at a constant angular velocity in a uniform magnetic field (see Figure B). The ... | null | ['$0.864$'] | Applied Sciences & Grounded Reasoning | null | OlympiadBench | Physics - Electromagnetism | 935 | null | null | 2 | 3 | 4 | 4 | true | pass | null | ['f8b6161b-91d2-46e9-95ab-5600ca29088b_1.jpg'] | Physical Systems Reasoning |
41deb27b-538b-43d5-81fd-b27bcca20e53 | 41deb27b-538b-43d5-81fd-b27bcca20e53_1.jpg | D.1 Using Eqs. 2 and 3 obtain the expression for the potential energy $V(\vec{r})$ as a function of $\vec{r}=(x, y)$ in the plane of the beams.
Hint: the result can be neatly expressed as a constant term plus a sum of three cosine functions of arguments $\vec{b}_{i} \cdot \vec{r}$. Please write your result in this for... | null | ['$V(\\vec{r})=-\\alpha E_{0}^{2}\\left(\\frac{3}{2}+\\sum_{j=1}^{3} \\cos \\vec{b}_{j} \\cdot \\vec{r}\\right)$,$\\vec{b}_{1}=\\vec{k}_{2}-\\vec{k}_{3}, \\quad \\vec{b}_{2}=\\vec{k}_{3}-\\vec{k}_{1}, \\quad \\vec{b}_{3}=\\vec{k}_{1}-\\vec{k}_{2}$'] | Applied Sciences & Grounded Reasoning | null | OlympiadBench | Physics - Modern Physics | 15,189 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['41deb27b-538b-43d5-81fd-b27bcca20e53_1.jpg'] | Physical Systems Reasoning |
dfd51501-6768-4c21-89ed-31a7b6ce5988 | dfd51501-6768-4c21-89ed-31a7b6ce5988_1.jpg | B.1 The principle states that between two fixed points, a light ray moves along a path such that time taken between the two points is an extremum. Derive the relation between $\sin i_{1}$ and $\sin i_{2}$ on the basis of Fermat's principle. | null | ['$n_{1} \\sin i_{1}=n_{2} \\sin i_{2}$'] | Applied Sciences & Grounded Reasoning | null | OlympiadBench | Physics - Mechanics | 1,722 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['dfd51501-6768-4c21-89ed-31a7b6ce5988_1.jpg'] | Physical Systems Reasoning |
6282c23a-7500-4d05-b4b7-38e41fb65500 | 6282c23a-7500-4d05-b4b7-38e41fb65500_1.jpg | C.2 The fuel channels are in a square arrangement (Fig-III) with nearest neighbour distance $0.286 \mathrm{~m}$. The effective radius of a fuel channel (if it were solid) is $3.617 \times 10^{-2} \mathrm{~m}$. Estimate the number of fuel channels $F_{n}$ in the reactor and the mass $M$ of $\mathrm{UO}_{2}$ required to ... | null | ['$F_{n}=387$ , $M=9.892 \\times 10^{4}$'] | Applied Sciences & Grounded Reasoning | null | OlympiadBench | Physics - Modern Physics | 2,352 | null | null | 2 | 2 | 3 | 4 | true | pass | null | ['6282c23a-7500-4d05-b4b7-38e41fb65500_1.jpg'] | Physical Systems Reasoning |
31d29d99-493c-45fd-8f88-7fc976b2e873 | 31d29d99-493c-45fd-8f88-7fc976b2e873_1.jpg | B5 Find the total current $I$ and express it in terms of $Z_{\mathrm{ext}}, \alpha, \gamma, e, L, S$. Assume that it remains finite | null | ['$I=\\frac{e Z_{e x t} S}{\\alpha}(\\frac{1}{e^{-\\alpha L}(1+\\gamma)-\\gamma}-1)$'] | Applied Sciences & Grounded Reasoning | null | OlympiadBench | Physics - Electromagnetism | 1,978 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['31d29d99-493c-45fd-8f88-7fc976b2e873_1.jpg'] | Physical Systems Reasoning |
10aad735-c060-48a7-8da3-743ccc334342 | 10aad735-c060-48a7-8da3-743ccc334342_1.jpg | b) Express $q^{\prime}$ and the distance $d^{\prime}$ of the charge $q^{\prime}$ from the center of the sphere, in terms of $q, d$, and $R$. | null | ['$d^{\\prime}=\\frac{R^{2}}{d}$ , $q^{\\prime}=-q \\frac{R}{d}$'] | Applied Sciences & Grounded Reasoning | null | OlympiadBench | Physics - Electromagnetism | 1,584 | null | null | 4 | 2 | 4 | 3 | true | pass | null | ['10aad735-c060-48a7-8da3-743ccc334342_1.jpg'] | Physical Systems Reasoning |
ce25eb38-6179-4c21-b958-4a22cbb39e03 | ce25eb38-6179-4c21-b958-4a22cbb39e03_1.jpg | a) What is the minimal height of the chimney needed in order that the chimney functions efficiently, so that it can release all of the produced gas into the atmosphere? Express your result in terms of $B, A, T_{\text {Air, }} g=9.81 \mathrm{~m} / \mathrm{s}^{2}, \Delta T=T_{\text {Smoke }}-T_{\text {Air }}$. Important:... | null | ['$\\frac{B^{2}}{A^{2}} \\frac{1}{2 g} \\frac{T_{\\text {Air }}}{\\Delta T}$'] | Applied Sciences & Grounded Reasoning | null | OlympiadBench | Physics - Thermodynamics | 5,226 | null | null | 2 | 3 | 3 | 4 | true | pass | null | ['ce25eb38-6179-4c21-b958-4a22cbb39e03_1.jpg'] | Physical Systems Reasoning |
0ecb318c-bfe2-4ce8-a347-76fc7ae832b8 | 0ecb318c-bfe2-4ce8-a347-76fc7ae832b8_1.jpg | a) What is the efficiency of the solar chimney power plant? | null | ['$\\eta=\\frac{g h}{c T_{A t m}}$'] | Applied Sciences & Grounded Reasoning | null | OlympiadBench | Physics - Thermodynamics | 396 | null | null | 2 | 2 | 3 | 3 | true | pass | null | ['0ecb318c-bfe2-4ce8-a347-76fc7ae832b8_1.jpg'] | Physical Systems Reasoning |
64298643-de8c-45b9-bb1b-2a6695f1bb83 | 64298643-de8c-45b9-bb1b-2a6695f1bb83_1.jpg | a) In modern physics, the energetics of nuclei and their reactions is described in terms of masses. For example, if a nucleus (with zero velocity) is in an excited state with energy $E_{\text {exc }}$ above the ground state, its mass is $m=m_{0}+E_{e x c} / c^{2}$, where $m_{0}$ is its mass in the ground state at rest.... | null | ['10.8636'] | Applied Sciences & Grounded Reasoning | null | OlympiadBench | Physics - Modern Physics | 3,058 | null | null | 2 | 2 | 3 | 3 | true | pass | null | ['64298643-de8c-45b9-bb1b-2a6695f1bb83_1.jpg'] | Physical Systems Reasoning |
7923710c-72ef-4407-bfc7-1c1aea43a173 | 7923710c-72ef-4407-bfc7-1c1aea43a173_1.jpg | iii. Consider another tube, identical and parallel to the first one.
<image_3>
The second tube has the same magnetic field but in the opposite direction and its centre is placed at $y=l, x=z=0$ (so that the tubes form opposite sides of a square). Determine the magnetic interaction force $F$ between the two tubes. | null | ['$F=\\frac{4-\\sqrt{2}}{8 \\pi \\mu_{0}} \\frac{\\Phi^{2}}{l^{2}}$'] | Applied Sciences & Grounded Reasoning | null | OlympiadBench | Physics - Electromagnetism | 3,657 | null | null | 2 | 3 | 3 | 3 | true | pass | null | ['7923710c-72ef-4407-bfc7-1c1aea43a173_1.jpg'] | Physical Systems Reasoning |
4847868b-68a6-4640-8019-ef7b5fc97dfc | 4847868b-68a6-4640-8019-ef7b5fc97dfc_1.jpg | iii. The dropper's functioning can be hindered by the effect shown in Part A-iii. In addition, a limit $U_{\max }$ to the achievable potential between the electrodes is set by the electrostatic push between a droplet and the bowl beneath it. Find $U_{\text {max }}$. | null | ['$U_{\\max }=\\sqrt[6]{\\frac{H^{3} g \\sigma^{2} \\rho d^{2}}{6 \\varepsilon_{0}^{3}}}$'] | Applied Sciences & Grounded Reasoning | null | OlympiadBench | Physics - Thermodynamics | 4,095 | null | null | 2 | 2 | 3 | 3 | true | pass | null | ['4847868b-68a6-4640-8019-ef7b5fc97dfc_1.jpg'] | Physical Systems Reasoning |
f5aa3b17-ba2c-4e8f-9df3-c9cb64ab488c | f5aa3b17-ba2c-4e8f-9df3-c9cb64ab488c_1.jpg | B.3 Estimate the average power $P$ dissipated by the non-linear element over the course of one oscillation. An order of magnitude is sufficient. | null | ['19.3'] | Applied Sciences & Grounded Reasoning | null | OlympiadBench | Physics - Electromagnetism | 184 | null | null | 2 | 2 | 3 | 3 | true | pass | null | ['f5aa3b17-ba2c-4e8f-9df3-c9cb64ab488c_1.jpg'] | Physical Systems Reasoning |
65ae65d9-700f-42d9-8ad1-75021695e3af | 65ae65d9-700f-42d9-8ad1-75021695e3af_1.jpg | C.2 Find the expression and the numerical value of the critical time $\tau_{\text {crit }}$ for which the scenario switches. | null | ['$\\tau_{\\text {crit }}=9.36 \\cdot 10^{-7}$'] | Applied Sciences & Grounded Reasoning | null | OlympiadBench | Physics - Electromagnetism | 960 | null | null | 2 | 2 | 3 | 3 | true | pass | null | ['65ae65d9-700f-42d9-8ad1-75021695e3af_1.jpg'] | Physical Systems Reasoning |
8b1fc2f7-86d6-45cc-aef5-901deb41fffb | 8b1fc2f7-86d6-45cc-aef5-901deb41fffb_1.jpg | B.1 Express the particle mass $m$ in terms of of the momentum $p$, the flight length $l$ and the flight time $t$, assuming that particles have elementary charge $e$ and travel with velocity close to $c$ on straight tracks in the ToF detector and that they travel perpendicular to the two detection planes (see figure 2). | null | ['$m=\\frac{p}{l \\cdot c} \\cdot \\sqrt{t^{2} \\cdot c^{2}-l^{2}}$'] | Applied Sciences & Grounded Reasoning | null | OlympiadBench | Physics - Modern Physics | 3,864 | null | null | 2 | 2 | 3 | 3 | true | pass | null | ['8b1fc2f7-86d6-45cc-aef5-901deb41fffb_1.jpg'] | Physical Systems Reasoning |
04a483d2-1806-4536-bc2b-a41d3cc339a0 | 04a483d2-1806-4536-bc2b-a41d3cc339a0_1.jpg | 3b Write down the momentum of the emitted photon $p_{p h}$, after the emission process in the $+x$ direction, as seen in the laboratory. | null | ['$\\frac{\\hbar \\omega_{L}}{c}\\left(1+2 \\frac{v}{c}\\right)$'] | Applied Sciences & Grounded Reasoning | null | OlympiadBench | Physics - Modern Physics | 1,584 | null | null | 2 | 2 | 3 | 4 | true | pass | null | ['04a483d2-1806-4536-bc2b-a41d3cc339a0_1.jpg'] | Physical Systems Reasoning |
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