What will be the final product when the above bridged compound is heated with concentrated sulfuric acid?
Protonation of both $\ce{OH}$ groups and subsequent formation of the corresponding cations is possible.


The tertiary cation will yield an exomethylene group
The "secondary" non-classical cation leads to a $\ce{C=C}$ double bond in the ring. With other words, a norbornene is formed.


The combined eliminations will give 7-methylene bicyclo[2.2.1]hept-2-ene as the product.

In J. Am. Chem. Soc., 1973, 95, 7801-7813, the same product was obtained by elimination from the tosylate of 7-hydroxy-7-methylnorborn-2-ene.