If R owns two handsets, which of the following combinations cannot be owned by R?

Let's tabulate the conditions one by one.  

Since we have ten handsets, we have two cases

1: T owns 2 headsets
2: T owns 1 headset
Case 1 :
If T owns 2 handsets, then S owns 4 handsets
But Q owns handsets of three different brands.
So we are left with only 1 handset to be given between P and R.
This case will not serve the purpose
Case 2: T owns 1 handset.
If T owns 1 handset, then S owns 2 handsets
Since the person who owns Nokia does not own any other handsets 
It cannot be T as T and R have at least one headset brand in common
It cannot be Q as it owns three different brands. 
It cannot be S as it has 2 handsets and the person who owns Nokia doesn't own any other handsets.
So it has to be P : P owns a Nokia handset.

Let's consider the options one by one,

Option A: If R owns handsets of Samsung and One Plus then T can own Samsung ,Q can own Motorola ,Iphone ,One Plus , S can own Iphone brand handsets. So this combination is possible.

Option B: If R owns handsets of Samsung and Iphone then T can own Samsung ,Q can own Motorola ,Iphone ,One Plus , S can own One Plus brand handsets. So this combination is possible.

Option C: If R owns handsets of One Plus and Motorola then T can own One Plus.We are left with only two brands but Q has handsets of 3 different brands. So this combination is not possible.

Hence C is the correct answer.