Well, fruit jam would have one primary ketohexose. Before we think about what the answer is, let's think about what a ketohexose is. the -ose ending gives away that it is a sugar (carbohydrate). We know immediately, then, that it will be of the form CnH(2n)On.
Based on the "hex" portion of ketohexose, we know it will be a six-carbon sugar, giving our chemical formula: C6H12O6.
Finally, the "keto" part tells us what kind of the two types of sugars that are common. Sugars (in linear form, not when in cyclic form) will have either an aldehyde group or a ketone group. Because it is a "keto" sugar, we know it will have a ketone group. This is actually very important in terms of eliminating possibilities, because many sugars you've heard of are definitely aldoses (glucose, galactose, etc.).
The only common sugar that you likely know of that has all of these properties (is a sugar with 6 carbons and a ketone group) is fructose. The idea that this is our sugar is bolstered by the fact that it would have been derived from a fruit based product!
Now, let's talk about properties. We already discussed the chemical formula and a few other properties of the molecule. We did not discuss, though, that often sugars cyclize. In the fructose case, it can cyclyze in two ways, as fructopyranose and fructofuranose. These names are derived from the fact that their central cyclic structure looks like pyran and furan, respectively.
The most important property, though, is likely its sweetness! Fructose is a relatively sweet sugar, and that's why fruits are so sweet! It's also why sweet foods are flavored with high-fructose corn syrup. Only problem is that in terms of sugar metabolism regulation, fructose skips a very important regulatory step in glycolysis! So, if you want to put on some weight, go ahead and eat a ton of fructose!
Hope that helps!