Since "no" must be followed by a noun, we can first rule out any option that is not a noun phrase, then check which preposition fits the noun "desire" correctly.
Ruling out the adjective form and the wrong prepositions leaves "desire for" as the only phrase that fits both the grammar and the meaning of the sentence.
Let's summarize:
Therefore, the correct answer is desire for.
This question is really about spotting the correctly spelt word, so we can check each option purely as a spelling problem.
Checking the letters one by one, only "jewellery" has the correct double "l" and full spelling, so it is the one that fits.
Let's summarize:
Therefore, the correct answer is jewellery.
The main clause "I would have gone to see him" is the result half of a third conditional, the kind used for an unreal past situation. That means the other half of the sentence needs the matching past perfect form, not a simple present or a repeated "would have".
Only the past perfect "had known" correctly matches the past hypothetical result "would have gone to see him".
Let's summarize:
Therefore, the correct answer is I had known.