When an object, say an apple, falls towards the Earth, the Earth rises up to meet it. Is this true? If so, why is the Earth's motion not noticeable?

(N/A) Yes, the statement is true. According to Newton's $Third$ $Law$ of $Motion$, the Earth exerts a gravitational force on the apple, and the apple exerts an equal and opposite force on the Earth. According to Newton's $Second$ $Law$ of $Motion$ $(F = ma)$, the acceleration produced is inversely proportional to the mass of the object $(a = F/m)$. Since the mass of the Earth is extremely large compared to the mass of the apple, the acceleration produced in the Earth is negligible and therefore not noticeable.