Правильно ли There is no pen in the box.

There is no pen in the box. (Правильно).

Yes, the sentence is correct. We can use no in negative sentences.

 В коробке нет ручки.

We can also make the sentence with not.

There is not a pen in the box.

There are no pens in the boxes. (Plural).

There are not pens in the boxes. (Plural).