How does TF-IDF classify a document based on "Score" alloted to each word
It's not a single TFIDF score on its own which makes classification possible, the TFIDF scores are used inside a vector to represent a full document: for every single word $w_i$ in the vocabulary, the $i$th value in the vector contains the corresponding TFIDF score. By using this representation for every document in a collection (the same index always corresponds to the same word), one obtains a big set of vectors (instances), each containing $N$ TFIDF scores (features).
Assuming we have some training data (labelled documents), we can use any supervised method to learn a model, for instance Naive Bayes, Decision Trees, SVM, etc. These algorithms differ from each other but they are all able to take into account all the features for a document in order to predict a label. So in the example you give maybe the word &quot;mobile&quot; only helps the algorithm eliminate the categories &quot;sports&quot; and &quot;literature&quot;, but maybe some other words (or absence of other words) is going to help the algorithm decide between categories &quot;Business&quot; and &quot;Tech&quot;.