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  1. I have picked top 10 out from these students.
  2. I have picked top 10 up from these students.

What's the subtle differences between "pick up" and "pick out"?

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    Neither one is idiomatic US English. – Hot Licks Mar 24 '17 at 2:23
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    "I have picked out the top ten from these students." "Pick out" means "select" or "remove". "Pick up" means "lift from the table" or "hook up with at the bar". – Hot Licks Mar 24 '17 at 2:24
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There are no subtle differences because the difference is quite conspicuous.

To Pick (something/someone) out means according to Cambridge - Pick Out

To choose, find, or recognize something or someone in a group

From all the puppies, we picked out the smallest one to take home. We could pick our parents out easily in the old photos.

That is to select or recognize someone/something from a group.

To Pick (something) Up means according to Merriam-Webster Pick Up

to take hold of and lift up. picked up all the pieces

Pick up can mean a lot of things depending on usage. Another particular usage is

to acquire by study or experience. Picking up a great deal of knowledge in the process

Your second sentence doesn't express the same meaning as the first. I have picked the top 10 up from these students. In fact this sentence sounds a bit strange. As @DJClayworth pointed out in his answer this might mean to physically life them up. You can also pick people up in vehicles. But pick up doesn't mean selecting from a group.

In fact, I wouldn't use Pick Out in your example sentence as well.

I would rather write it as:

I have identified the (best performers, athletes etc) from these students.

Single Out is also a good choice, but it has a slightly negative connotation.

I have singled out 10 students for punishment

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To "pick something up" means to physically or metaphorically lift it. It can also be used to mean collecting for transportation or similar, or to hook up romantically.

To "pick something out" means to select it from a group of things, or to detect or identify it.

The two are not interchangeable.

The normal version of your sentence would be

I have picked out the top ten from these students.

The definite article is normal. "I have picked the top ten out from these students" would also be acceptable. If you said "I have picked up the top ten students" it would mean you were lifting them or taking them on a date.

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