Some, much, any
1. I haven’t got any rice in the house. Please go out to buy a few kilogrammes from the shop nearby.
2. How much do you know about his plans for further studies abroad? I know only a little about him.
3. Is this correct: I haven’t any coins in my pocket.
4. Are they any/much rats in your house?
5. There isn’t much/any ink in this bottle.
1. In the first sentence,
“I haven’t got any rice in the house.”,
“any” is correctly used as a determiner with the uncountable noun “rice”, in a negative sentence.
2. “Much” here is used after “how” in “how much”, which begins a wh-question and means “to what extent” in this context. What is asked about is not “his plans …” as such, but “how much you know about his plans.” So “how much” relates to “do you know” and not to the noun “plans”. We can rephrase the question as: “How much knowledge do you have about his plans for further studies abroad?” Here, “much” is used before the uncountable noun “knowledge”. “Much” is never used immediately before a countable noun like “plan(s)”. “How much”, however, is often used before the auxiliary verb in a question, e.g. in your question “How much do you know about …?” or “How much has he travelled?”
The second sentence,
“I know only a little about him.”, means
“I only have a small amount of information about him.” It would be better to use the negative sentence “I don’t know much about him.”
3. Yes, “any” is correctly used there, with a plural noun in a negative sentence.
4. “Much” should not be used with countable nouns like “rats”. The correct sentence is:
“Are there any rats in your house?”
“Any” is the correct word to use with a plural noun in a question.
5. You can use either “much” or “any” before the uncountable noun “ink” in a negative sentence. But the meaning of the sentence would depend on the word you use.
“There isn’t much ink in this bottle.”
Means there is a small amount of ink in the bottle.
BUT “There isn’t any ink in this bottle.”
Means there is no ink at all in the bottle.
For more details, you can consult the following free online dictionaries at:
Learning English by Uncle Teng 
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