Which one of the commercial products is used to grow microbes and in the preparation of ice-creams and jellies?

The formulas of $A$ and $B$ for the following reaction sequence are:

Assertion : Treatment of $D$-glucose with dilute alkali affords an equilibrium mixture consisting of $D$-mannose,$D$-fructose and starting substance $D$-glucose.
Reason : The reaction involves an intermediate in which hybridization of $C_2$ changes from $sp^3$ to $sp^2$.

Which of the following contains a dextrorotatory sugar?

$A$ polysaccharide '$X$' on boiling with dil $H_2SO_4$ at $393 \ K$ under $2-3 \ atm$ pressure yields '$Y$'. '$Y$' on treatment with bromine water gives gluconic acid. '$X$' contains $\beta-$glycosidic linkages only. Compound '$X$' is ..... .

Which of the following on hydrolysis forms invert sugar?