(CH₃)₂SiCl₂ undergoes hydrolysis but (CH₃)₂CCl₂ does not. This is because

Due to the presence of empty d-orbitals in the valence shell of 'Si'

(CH₃)₂SiCl₂ can accept the electron pair from water and undergoes hydrolysis

Excited state configuration of 'Si'  is  [Ne] 3S¹ 3P³ 3d⁰

Where as in case of  (CH₃)₂CCl₂ , the central atom carbon donot have empty d-orbitals in its valence shell

and it is unable to accept the electron pair from water

   Hence it can not undergo hydrolysis