MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark.

The symmetric group $S_n$ has $n!$ elements, hence it is not true that $S_{10}$ has 10 elements. Find the characteristic of the ring 2Z.

1. A.0Correct
2. B.30
3. C.3
4. D.10
5. E.12
6. F.50
7. G.2
8. H.100
9. I.20
10. J.5

Let A be the set of all ordered pairs of integers (m, n) such that 7m + 12n = 22. What is the greatest negative number in the set B = {m + n : (m, n) ∈ A}?

1. A.-5
2. B.0
3. C.-3
4. D.-7
5. E.-4Correct
6. F.-6
7. G.-1
8. H.-2
9. I.-9
10. J.N/A

Where do most short-period comets come from and how do we know?

1. A.The Kuiper belt; short period comets tend to be in the plane of the solar system just like the Kuiper belt.Correct
2. B.The asteroid belt; short period comets tend to come from random directions indicating a spherical distribution of comets called the asteroid belt.
3. C.The asteroid belt; short period comets tend to be in the plane of the solar system just like the asteroid belt.
4. D.The Oort cloud; short period comets tend to come from random directions indicating a spherical distribution of comets called the Oort cloud.
5. E.The Oort cloud; short period comets tend to be in the plane of the solar system just like the Oort cloud.
6. F.The Oort cloud; short period comets have orbital periods similar to asteroids.
7. G.The asteroid belt; short period comets have orbital periods similar to asteroids.
8. H.The Kuiper belt; short period comets tend to come from random directions indicating a spherical distribution of comets called the Kuiper belt.
9. I.The Kuiper belt; short period comets have orbital periods similar to asteroids.
10. J.The Oort cloud; short period comets tend to be in the plane of the solar system just like the asteroid belt.