prompt_text stringclasses 328 values | prompt_ids listlengths 12 530 | decode_ids listlengths 64 64 | prompt_pattern listlengths 27 27 | decode_pattern listlengths 27 27 |
|---|---|---|---|---|
Two quantum states with energies E1 and E2 have a lifetime of 10^-9 sec and 10^-8 sec, respectively. We want to clearly distinguish these two energy levels. Which one of the following options could be their energy difference so that they can be clearly resolved?
| [
100000,
12201,
8633,
4605,
366,
18511,
427,
16,
285,
427,
17,
463,
245,
17476,
280,
207,
16,
15,
13502,
24,
4746,
285,
207,
16,
15,
13502,
23,
4746,
11,
6357,
13,
1003,
1121,
276,
7765,
18688,
1069,
984,
3164,
6125,
13,
11692,
634,
... | [
64,
8,
207,
17,
13,
17,
20,
9,
16,
15,
13502,
24,
4746,
185,
65,
8,
16,
13,
19,
13,
20,
9,
16,
15,
13502,
24,
4746,
185,
66,
8,
207,
24,
13,
15,
13,
16,
15,
13502,
16,
4746,
185,
67,
8,
207,
16,
13,
17,
13,
16,
15,
1... | [
[
[
14,
34,
2,
42,
47,
1,
46,
40
],
[
14,
42,
34,
5,
60,
57,
26,
20
],
[
34,
14,
42,
57,
43,
60,
33,
20
],
[
35,
50,
4,
... | [
[
[
34,
40,
5,
24,
4,
51,
21,
37
],
[
1,
48,
46,
34,
17,
7,
42,
53
],
[
40,
33,
37,
52,
34,
12,
2,
43
],
[
26,
0,
44,
5,... |
trans-cinnamaldehyde was treated with methylmagnesium bromide, forming product 1.
1 was treated with pyridinium chlorochromate, forming product 2.
3 was treated with (dimethyl(oxo)-l6-sulfaneylidene)methane in DMSO at elevated temperature, forming product 3.
how many carbon atoms are there in product 3? | [
100000,
1839,
12,
66,
5962,
303,
266,
96861,
438,
10433,
366,
99238,
12045,
4893,
2605,
75387,
546,
11,
19742,
1943,
207,
16,
13,
185,
185,
16,
438,
10433,
366,
15445,
3736,
246,
2605,
36472,
8988,
421,
387,
11,
19742,
1943,
207,
17,
... | [
185,
185,
185,
3673,
4313,
327,
437,
1012,
418,
207,
16,
13,
16199,
245,
6133,
338,
11,
1275,
338,
9,
32,
13,
207,
17,
13,
16199,
6133,
338,
11,
1275,
254,
5856,
280,
254,
6225,
280,
338,
13,
207,
18,
13,
11424,
254,
5856,
280,
... | [
[
[
14,
34,
2,
42,
47,
1,
46,
40
],
[
34,
24,
4,
20,
51,
10,
55,
42
],
[
28,
6,
54,
46,
14,
7,
2,
16
],
[
43,
5,
24,
34,... | [
[
[
47,
2,
13,
14,
18,
3,
22,
44
],
[
47,
2,
14,
13,
3,
18,
44,
22
],
[
47,
2,
61,
15,
3,
34,
54,
44
],
[
6,
42,
48,
22,... |
"A spin-half particle is in a linear superposition 0.5|\\uparrow\\rangle+sqrt(3)/2|\\downarrow\\rang(...TRUNCATED) | [100000,32,7319,12,15209,11874,317,279,245,6312,59843,207,15,13,20,3318,26123,59,4825,10,4221,7,18,9(...TRUNCATED) | [13,100001,100000,549,3299,285,2408,280,245,2696,9597,317,245,2131,6088,24703,36396,3791,13,429,9597(...TRUNCATED) | [[[14,34,2,42,47,1,46,40],[37,34,14,5,42,24,57,40],[33,60,37,41,50,55,23,34],[28,6,46,33,7,14,44,2],(...TRUNCATED) | [[[7,2,6,47,49,46,25,54],[43,50,6,16,2,0,29,46],[14,34,2,47,6,53,40,18],[8,6,14,20,12,34,22,37],[63,(...TRUNCATED) |
"In a parallel universe where a magnet can have an isolated North or South pole, Maxwell’s equatio(...TRUNCATED) | [100000,774,245,9304,14188,1066,245,15771,481,463,274,18202,5226,410,5178,18601,11,37741,487,82,8935(...TRUNCATED) | [185,185,185,31,44,13,2353,74,49442,37741,487,82,8935,3780,254,12900,478,2172,59,6021,59,3560,90,37,(...TRUNCATED) | [[[14,34,2,42,47,1,46,40],[15,22,20,42,8,34,10,9],[40,21,14,12,33,37,5,24],[33,60,19,37,20,23,45,10](...TRUNCATED) | [[[2,47,14,13,44,37,40,18],[2,47,14,13,44,40,37,18],[47,2,34,14,1,44,15,61],[49,7,1,46,16,14,45,15],(...TRUNCATED) |
"Calculate the eigenvector of a quantum mechanical operator $\\vec{P}$ for a muon along an arbitrary(...TRUNCATED) | [100000,72001,254,74529,280,245,8633,16666,7086,628,5016,90,47,759,327,245,53963,2726,274,12954,5489(...TRUNCATED) | [40,1006,946,276,1275,254,24790,280,274,7086,11,548,304,536,441,1006,946,276,1275,254,61171,13,185,1(...TRUNCATED) | [[[14,34,2,42,47,1,46,40],[4,34,42,20,1,41,50,45],[12,14,52,22,8,27,57,18],[63,23,59,35,33,32,60,26](...TRUNCATED) | [[[42,48,24,34,1,5,8,61],[38,39,36,42,34,29,51,1],[53,56,8,30,36,33,57,18],[17,9,53,32,22,13,57,15],(...TRUNCATED) |
"A quantum mechanical particle of mass m moves in two dimensions in the following potential, as a fu(...TRUNCATED) | [100000,32,8633,16666,11874,280,2929,273,13412,279,984,11698,279,254,1893,3968,11,372,245,1157,280,3(...TRUNCATED) | [185,185,12971,254,3164,6125,13,185,12971,254,3164,9656,13,185,12971,254,3164,6125,13,185,26074,9154(...TRUNCATED) | [[[14,34,2,42,47,1,46,40],[14,37,34,5,42,24,57,40],[34,57,14,42,33,43,60,20],[55,33,19,20,37,23,8,14(...TRUNCATED) | [[[47,2,14,34,58,44,15,18],[47,2,14,34,15,58,44,18],[42,41,50,20,1,62,54,29],[12,57,63,52,14,8,13,25(...TRUNCATED) |
"The universe is filled with the Cosmic Microwave Background. Consider the annihilation of high ener(...TRUNCATED) | [100000,549,14188,317,8148,366,254,96248,79170,39371,13,14326,254,48318,280,1461,3164,357,2705,12,19(...TRUNCATED) | [185,185,1862,2705,3,29304,543,441,55922,387,881,7177,12,60519,2114,12016,13,12393,879,418,254,3903,(...TRUNCATED) | [[[14,34,2,42,47,1,46,40],[14,34,8,6,20,49,57,12],[59,63,58,23,61,35,37,34],[4,36,14,30,32,27,24,45](...TRUNCATED) | [[[2,47,14,44,40,15,18,39],[2,47,14,40,44,34,15,18],[16,1,53,34,7,14,49,46],[5,4,0,34,55,31,43,2],[1(...TRUNCATED) |
"You perform a high-throughput experiment on white lupine to find genes contributing to resistance t(...TRUNCATED) | [100000,2054,2111,245,1461,12,10416,921,6101,331,3682,93548,479,276,1275,29556,28563,276,8545,276,25(...TRUNCATED) | [40,6,313,2571,2215,344,254,29556,6591,279,254,8545,418,38962,280,452,16,11,558,657,6,647,1230,279,3(...TRUNCATED) | [[[14,34,2,42,47,1,46,40],[34,42,14,48,61,8,1,57],[29,36,41,50,17,11,14,12],[40,21,12,14,5,24,2,57],(...TRUNCATED) | [[[48,42,34,5,24,8,1,57],[53,6,14,1,34,49,46,40],[30,36,34,11,39,44,42,13],[58,30,17,22,36,38,57,62](...TRUNCATED) |
"which of the following molecules has c3h symmetry?\ntriisopropyl borate\nquinuclidine\nbenzo[1,2-c:(...TRUNCATED) | [100000,3262,280,254,1893,27788,643,258,18,71,12754,30,185,13857,262,425,1718,3987,26294,387,185,328(...TRUNCATED) | [185,11137,280,1069,185,185,17237,344,254,39731,3707,643,258,18,71,12754,11,588,280,254,1893,317,192(...TRUNCATED) | [[[14,34,2,42,47,1,46,40],[34,56,14,45,53,20,8,48],[56,9,21,14,50,42,15,20],[12,14,22,27,40,8,20,49](...TRUNCATED) | [[[47,2,14,37,22,15,39,54],[42,45,1,33,60,32,34,8],[56,21,9,20,33,45,42,57],[6,48,21,14,63,57,62,12](...TRUNCATED) |
"Among the following exoplanets, which one has the highest density?\n\na) An Earth-mass and Earth-ra(...TRUNCATED) | [100000,26892,254,1893,411,88009,1550,11,588,634,643,254,7492,6422,30,185,185,64,8,1640,11687,12,154(...TRUNCATED) | [185,185,68,8,338,12438,366,254,1246,14939,372,11687,548,207,16,15,15,2602,691,11542,853,11687,13,18(...TRUNCATED) | [[[14,34,2,42,47,1,46,40],[56,42,15,34,14,9,20,57],[12,14,40,49,22,8,18,21],[63,14,56,50,59,29,53,21(...TRUNCATED) | [[[47,2,14,44,18,15,58,37],[47,2,14,18,37,44,54,15],[5,34,13,24,51,31,57,4],[48,1,46,7,6,32,17,28],[(...TRUNCATED) |
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