We are basically looking for ionic compounds versus covalent compounds. Compounds with ionic bonds are excellent electrolytes and conduct electricity. Compounds with covalent bonds are much weaker electrolytes and poorer conductors of electricity. Lets look at each compound individually.
C12H22O11: This is a carbohydrate and a covalent compound. Not conductive.
KNO3: An ionic compound. Conductive.
KOH: An ionic compound. Conductive.
CH3OH: This is methanol and it is covalent. Not conductive.
K2SO4: An ionic compound. Conductive.
KNO3: This is a repeat. See the above prior response.
AgNO3: An ionic compound. Conductive.
Compounds undergoing dissociation in solution (or in fluid state) into ions are conductive. These are called electrolytes. Ionic compounds generally behave so. Among the given chemicals C12H22O11, and CH3OH are covalent compounds and hence non-electrolytic, or non-conductive. Rest of the compounds is all electrolytic, hence conductive. Colour of flame, imparted by certain cations is characteristic of that ion. Among these ionic compounds only K+ exhibit violet coloration in flame test. Hence salts having K+ as cation i.e. KNO3, KOH, K2SO4, KNO3 shall exhibit violet flame. Again, compounds giving off H+ ions in aqueous solution shall be acids, turning red litmus blue while those giving off OH- ions shall be bases, turning red litmus blue. Among the given compounds, only KOH will behave as a base.